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\section{Introduction}
Inflow motion is a fundamental phenomenon during stellar formation.
Although the search for inflow is usually more difficult than that
for outflow, studies of inflow have made great progress since the
1990s. In low-mass star forming regions, inflow motions were
detected at different evolutionary stages, including Class --I,
Class 0 and Class I cores \citep{zho93, mmt97, lee99, gre00,
evans03}. Recently, a number of inflow candidates were found in high
mass star formation regions. Among a sample of 28 massive cores, 12
were found to show line profiles that peak at blue-shifted
velocities (hereafter "blue profiles"; see Sect.\,3.1), the expected
signature of inflow \citep{we03}. \citet{fws05} (hereafter FWS05)
detected such asymmetric profiles in 22 cores within a sample of 77
high-mass proto-stellar objects (HMPOs). Most recently,
\citet{wyr06} detected 9 sources with a blue profile in a sample of
12 ultracompact (UC)~H{\sc ii} regions.
Variation of inflow motion with time is critical for high mass star
formation. It has been indicated that when a protostar reaches $>$10
M$_{\odot}$ it can generate enough radiation pressure to halt
spherical infall and inhibit its mass increasing\citep{wc87}.
Observationally, however, it is not yet clear how inflow is related
to the evolution of massive (proto)stars. To study this problem, we
have carried out a survey for a sample including both cores of
UC~H{\sc ii} regions and precursors of UC~H{\sc ii} regions.
While previous surveys using single point observations provided some
statistical evidence for the occurrence of infall within massive
cores, blue profiles can also be caused by rotation. Therefore maps
of the molecular environment are indispensable. Mapping also allows
us to locate the center of the inflow and to identify cores that are
simultaneously showing evidence for in- and outflow.
Therefore, we conducted a mapping survey including 46 high mass
star-forming regions which were selected applying three criteria:
(1) The sources must have been mapped in the submillimeter or
millimeter wavelengths with continuum or spectroscopy; (2)
signal-to-noise ratios should be $>$5 at 350\,$\mu$m (Mueller et al.
2002) and higher at other wavelengths; (3) there should be no other
core within one arcmin \citep{zhs97, hnb98, tie98, hat00, mbc00,
bsp02, mse02}. With respect to their stellar content, we can divide
the sample into two different groups of targets: (1) Thirty three
sources lack 6 cm continuum emission and are precursors of UC~H{\sc
ii} regions or HMPOs \citep{mbc00, bsp02}. Among these, thirty are
hosting a luminous IRAS source. The remaining three are associated
with IRAC (the InfraRed Array Camera on the Spitzer Space Telescope)
point sources (W3-W and W3-SE) or are not hosting an IRAC source
(18454--3). All 33 cores comprise `group~I'. (2) Thirteen UC~H{\sc
ii} regions are assigned to `group~II'. This letter presents a list
of the identified collapse candidates and provides the statistics of
blue excesses. Detailed properties of individual cores will be
analyzed in a future paper.
\section{Observations}
The observations were performed with the IRAM 30\,m telescope at
Pico Veleta, Spain, from July 28 to Aug. 1, 2005. Four receivers
were used simultaneously, usually two at $\lambda$$\sim$3\,mm and
two at $\lambda$$\sim$1.3\,mm (A/B configuration). For some sources,
none of the four 3 and 1.3\,mm lines were optically thin. In these
cases the tracer lines were changed employing two receivers at
$\lambda$$\sim$2\,mm and the other two to cover the upper part of
the 1.3\,mm window (C/D configuration). The lines and corresponding
beam sizes, efficiencies, and channel widths
are given in Table 1. The channel spacing and the bandwidth are
78.125 kHz and 105 MHz respectively. The weather was extremely good
for summer conditions, allowing us to observe the HCO$^+$ $J$=3--2
transition at 268\,GHz and leading to 3 and 1.3\,mm (2 and 1.2\,mm)
system temperatures of order 150 and 400\,K (200 and 550\,K) on a
$T_{\rm A}^*$ scale. Pointing and calibration were checked by
continuum measurements of the standard sources W3(OH), G34.24, and
NGC 7027 and were found to be better than 4\arcsec\ and $\pm$20\%,
respectively. All observations were carried out in a position
switching mode. For each source we observed a nine point map in a
cross pattern with a spacing of 15\arcsec. If inflow signature was
detected, the map was enlarged in most cases to cover the entire
region showing this signature. The on-source integration time per
position was 1 minute, yielding a $T_{\rm A}$* 1$\sigma$ noise level
of 0.07\,K for the 3\,mm N$_2$H$^+$ (1--0) line. For the data
analysis, the GILDAS software package (CLASS/GREG) was used
\citep{gl00}.
\section{Results and discussion}
\subsection{Blue profile identification}
For self-absorbed optically thick lines, the classical signature of
inflow is a double peaked profile with the blue-shifted peak being
stronger, or a line asymmetry with the peak skewed to the blue side.
While optically thin lines should show a single velocity component
peaking at the line center.
Among the 46 cores observed, five (05490+2658, G31.41+0.31, 18454-3,
18454-4, 19266+1745) will be ignored because they show either too
complex spectral profiles, inhibiting a detailed analysis, or a lack
of optically thin lines. Estimates of optical depths were obtained
from line ratios between different isotopomers of CO and CS and from
the relative intensities of individual hyperfine components in the
case of C$^{17}$O and N$_2$H$^+$. C$^{18}$O, C$^{17}$O, C$^{34}$S
and N$_2$H$^+$ tend to be optically thin, while CS is optically
thick. HCO$^+$ opacities could not be estimated. However, the
similarity of HCO$^+$ and CS line shapes (see Sect.\,3.2) as well as
the results of \cite{gre00} and FWS05 clearly indicate that HCO$^+$
is also optically thick.
The 41 remaining sources were detected in at least one optically
thick and one optically thin line. A blue profile caused by inflow
motion with velocity $v \propto r^{-1/2}$ in a region with higher
excitation temperature ($T_{ex}$) inside requires $T_{\rm
A}$*(B)/$T_{\rm A}$*(R) $>$ 1. Here $r$ is the radius of the
collapsing core \citep{zho93}. $T_{\rm A}$*(B) and $T_{\rm A}$*(R)
are the blue and red peak intensities of the optically thick line.
We also define a dimensionless asymmetry parameter following
\cite{mmt97}, $\delta V$ = ($V_{\rm thick}$-$V_{\rm
thin}$)/$\Delta$$V_{\rm thin}$. $V_{\rm thick}$ is the peak velocity
of the opaque line, $V_{\rm thin}$ and $\Delta$$V_{\rm thin}$ denote
the peak velocity and width of the optically thin line. Only for
$\delta V < -0.25$ or $> 0.25$ the line profile is rated blue or
red, respectively.
Our sources (Table~2) discriminate among five main types of line
shapes: (1) cores with lines showing a ``blue profile'' (in the
following denoted with B); (2) cores with lines showing a "red
profile" (R); (3) cores exhibiting blue and red profiles at
different spatial positions (BRS); (4) cores where some lines show a
blue profile, while others display a red profile (BRL); (5) cores
without obvious asymmetric lines (S). Only cores showing at least
one line of type B, but no lines of type R are identified as targets
potentially undergoing inflow motion.
\subsection{Collapse candidates and their profile ``excess''} \label{bozomath}
With the criteria outlined in Sect.\,3.1, seventeen inflow
candidates are identified (see Table~2). Ten belong to group~I and
seven are part of group~II. To provide a typical example, Fig.\,1
shows the infall signature of the group~I core W3-SE. Fig. 1a
displays the HCO$^+$\,(1--0) spectra, showing the angular size of
the core. Fig. 1b shows a number of profiles towards the central
position. The HCO$^+$\,(1--0) and (3--2) lines as well as the
CS\,(3--2) transition show the blue asymmetry. For the
HCO$^+$\,(1--0) line this is also demonstrated in the
position-velocity (P-V) diagram of Fig.\,1c. For comparison,
Fig.\,1d shows a P-V diagram of the optically thin C$^{18}$O\,(1--0)
emission.
The quantity ``excess'' as defined by \cite{mmt97} is $E$ = ($N_{\rm
B} - N_{\rm R}$)/$N_{\rm T}$, where $N_{\rm B}$ and $N_{\rm R}$ mark
the numbers of sources with blue and red profiles. $N_{\rm T}$ is
the total number of sources. For our survey the excess was
calculated for the two HCO$^+$ transitions and the CS\,(3--2) line.
Fig. 2 shows the log[$T_{\rm A}$*(B)/$T_{\rm A}$*(R)] and $\delta$V
(see Sect.\,3.1) distributions of the three individual lines.
Statistical results are given in Table~3. The observed excess
derived from the HCO$^+$\,(1--0) and (3--2) lines is 0.29 and 0.11,
respectively. Both are larger than those obtained by FWS05 for the
same lines (0.15 and 0.04). For the CS transition we obtain 0.29. To
evaluate the statistical significance of the determined values, we
conducted the binomial test (see FWS05 and references therein).
Probabilities that the excesses are a product of a random
distribution are given in the last column of Table~3. These are
0.006 and 0.01 for HCO$^+$\,(1--0) and CS (3--2) respectively.
Apparently, both lines are sensitive tracers of potential inflow
motion in massive cores.
To evaluate differences between the two classes of cores (I and II;
see Sect.\,1) with respect to the excess, we used the HCO$^+$\,(1--0)
line, which was mapped in the largest number of sources. The results
listed in the lower part of Table~3 include 16 sources with profiles
of type B. The excesses observed for group~I and II are 0.17 and 0.58,
respectively.
Twenty of our 46 sources overlap with those of FWS05. Among them are
19 group~I sources (out of 33), but only one source is from group~II
(out of 13). Our study includes various CO and CS lines. We also
made maps. Thus we can view the common objects from a different
perspective and can check, how far the choice of different molecular
transitions and the presence of maps is leading to contradictions
with previously published results. Differences are indeed
significant. For eight of the 19 overlapping type I cores we obtain
different line asymmetry classification, emphasizing the need for
detailed maps. Nevertheless, the overall difference in the
HCO$^+$\,(1--0) excess is negligible (0.17 versus 0.15).
To summarize, both data sets indicate that the HCO$^+$\,(1--0)
excess is low for UC~H{\sc ii} precursors. For UC~H{\sc ii}
regions, our results and those of \cite{wyr06} suggest that the
excess is larger and more significant. From the binomial test for
group~I and II, the probability that the blue excesses (0.17 and
0.58 respectively) are arising by chance is 0.13 and 0.008,
respectively.
\subsection{A comparison with low mass star-forming surveys}
While low mass star-forming regions show infall from the Class --I
to the Class I stages of evolution, high mass star-forming regions
also exhibit infall signatures from their earliest stages till a UC
H{\sc ii} region has formed \citep{wzx05,bkl06,qzm06}. In low mass
cores the profile excess was found to be 0.30, 0.31 and 0.31 for
Class --I, 0 and I core samples in the HCO$^+$\,(3--2) line
(\cite{evans03} and references therein). There seem to be no
significant differences among the cores in different evolutionary
phases. However, our samples show the excess of UC~H{\sc ii} regions
far surpassing that of the UC~H{\sc ii} precursors. This may point
to fundamental differences between low and high mass star-forming
conditions. Possible causes to the higher blue excess in Group II
sources may be: (1) The molecular gas surrounding UC H{\sc ii}
regions may be more adequately thermalized to show the blue excess,
i.e. the excitation temperature of specific lines may increase more
monotonically towards the center. Thus all lines may produce blue
profiles indicating infall motion, while in younger cores still some
lines may show red profiles. (2) The amount of dense cool gas is
larger towards younger objects. Outflows of dense molecular gas may
be more active around Group I objects, shaping more red profiles.
(3) Low mass cores are relatively isolated and their gas supply is
limited. Simulations showed that this may halt the increase of
inflow \citep{vor05}. However, high mass stars form in giant
molecular clouds and their inflow motions are not easily halted by
the exhaustion of molecular gas before most of it is dispelled. (4)
In low mass cores, star formation may be spontaneous. In high mass
cores, collapse may be trigged by extrinsic disturbances and the
collapse may take more time to develop.
With respect to potential selection effects, we used the same
criteria to identify the targets of the two separate groups of
sources. Since this study is based on a limited number of sources,
more data quantifying the blue excess as a function of evolutionary
stage would be highly desirable.
\section{Outlook}
We have carried out a mapping survey towards 46 molecular cores
associated with massive star formation. Seventeen collapse
candidates were identified. Among them are 10 UC H{\sc ii}
precursors and 7 UC~H{\sc ii} regions. Overall, statistical results
indicate a predominance of blue over red profiles which is
surprisingly similar to that obtained towards cores forming low mass
stars. Among high mass star-forming sites, the probability to detect
blue profiles seems to depend on evolutionary stage and increases
from UC~H{\sc ii} precursors to UC~H{\sc ii} regions. Toward low
mass star-forming sites, however, this effect is not observed,
suggesting a more fundamental difference in the way stellar masses
are assembled. Larger line surveys and more detailed maps in various
molecular transitions are needed to improve statistical evidence in
order to confirm or to reject this potentially important finding.
\acknowledgments
We are grateful to the IRAM staff for their assistance and F.
Wyrowski for useful discussions. This research is supported by the
Grant 10128306 and 10733030 of NSFC.
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\section{INTRODUCTION}
Neoplastic diseases are the cause of 7 million deaths annually or 12%
of deaths worldwide \cite{Who}. Mathematical and computer modelling
may lead to greater understanding of the dynamics of cancer
progression in the patient \cite{Preszosi} \cite{MMC}. These
techniques may also be useful in selecting better therapeutic
strategies by subjecting available options to computer testing ({\it
in silico}). Continuous models have been proposed to describe the
stages of tumor growth since the middle of the 20th century
\cite{Wheldon}. Initially, a tumor grows exponentially (linear
rate). After this transient stage, the growth rate decreases and a
steady state is attained, due to several factors including a lack of
nutrients and hypoxia. This nonlinear behavior characterizes
avascular tumor growth when neovascularization has not yet been
triggered. The decelerating avascular growth may be guided by
different rules such as, for example, Gompertzian and logistic
functions. Gompertzian growth has been one of the most studied
decelerating tumor growth over the past 60 years \cite{Laird},
\cite{Demicheli} \cite
{Brunton}. It is found, for example, in some solid tumors such as
breast carcinomas \cite{Clare} \cite{Spratt}. It is also observed in
tumors {\it in vitro} \cite{Bellomo}
\cite{Guiot}.
Although continuous models are capable of describing the behavior of
tumor growth, it would appear more reasonable to adopt a discrete
approach when describing the prevascular stage. Due to the fact that
the angiogenic process has not triggered early tumor growth, few
cancer cells are present and growth depends predominantly on the
interactions of these cells with adjacent cells and with the
environment \cite{Patel}. In addition, in the discrete approach, it
is easier to capture the time-spatial pattern generated by the model
in order to compare it with actual patterns \cite{Castro}. Some
cellular automata models \cite{Galam} \cite{Shen} and hybrid
cellular automata \cite{Patel} \cite{Dormann} \cite{Gerlee} have
been proposed to study tumor growth.
Another important topic that is analyzed in mathematical models is
the response to therapy, including how tumor growth changes under
the effect of a drug \cite{Rygaard}. The focus is directed towards
identifying the optimal therapy to maximize the effect on cancer
cells and minimize the effect on normal cells \cite{Martin}
\cite{Swan}. Although various continuous chemotherapy models exist
\cite{Murray}, \cite{Costa}, \cite{Matveev}, to the best of our
knowledge the majority of the discrete models cited in the
literature have not yet been used to investigate this topic.
The objective of this work is to propose a two-dimensional cellular
automata model consisting of 4 states (empty site, normal cell,
cancer cell or necrotic tumor cell) to describe avascular tumor
growth. It should be emphasized that in this study the term tumor
growth is used to refer to the number of cancer cells rather than
the volume of the tumor; in other words, it is assumed that the
tumor volume is proportional to the number of cancer cells
\cite{Wheldon}. Assuming that the angiogenic process has not yet
been triggered, there is no increase in nutrients, which are
uniformly distributed over the lattice. In this simple model, some
relevant processes involved in the prevascular phase of tumor growth
are assessed: a dynamic proliferation of cancer cells and the
competition between normal cells and cancer cells for nutrients
and/or space. Since necrosis is often present in the prevascular
stage of tumor growth \cite{Bellomo} \cite{Adam}, the possibility of
necrosis in the model must also be taken into consideration.
Finally, the effect of therapy is included in order to investigate
whether the system evolves to a state of cure.
This paper is organized as follows. In section \ref{sec2}, the model
is presented, together with its local rules, parameters and the
scope of the algorithm. Section \ref{sec3} describes the simulated
time series of cell density in the presence or absence of treatment,
and shows the features of the time-spatial pattern of simulated
solid tumors. In section \ref{sec4}, the parameter related to the
process of necrosis and the effect of therapy is analyzed. Finally,
in section \ref{sec5}, our results are discussed from the point of
view of the phenomenon and some concluding remarks are made.
\section{THE MODEL}
\label{sec2}
We propose a two-dimensional ($L \times L$) cellular automata model
\cite{Wolfram} under periodic boundary conditions, using a Moore
neighborhood with a radius of 1. At the initial condition ($t=0$),
there is only one cancer cell (to ensure better visualization, this
was taken from the center of the lattice). Since the intention it to
model a non-viral tumor, normal cells would not be transformed into
cancer cells with the exception of the cancer cell that triggers
tumor growth at $t = 0$ \cite{Thecell}. The lattice represents a
tissue sample; there is a cell in each site that may be in one of
four states: normal cell (NoC), cancer cell (CC), necrotic cell
(NeC) or empty site (ES). We assume that the nutrients are uniformly
available over the lattice. In this respect, lack of space is
identified with lack of nutrients in our model.
There is a growth potential $P_c$ value associated with each normal
or cancer cell. Although the two-dimensional character of the model
mimics the {\it in vitro} situation, the growth potential of cancer
cells simulates the three-dimensional tumor {\it in vivo} in the
sense that it represents the total number of cancer cells, i.e., in
addition to the cancer cells on the lattice, the cancer cells
generated by these cells.
The local rules are such that:
\begin{itemize}
\item [] (i) The initial value of the mitotic probability of cancer cells is
represented by a parameter $p_0$ that measures the available resources at
the beginning of the tumor. After that, it decreases by a factor $\Delta
p_{mitot}$ until reaching the null value:
\begin{equation}
\label{pmitot}
\Delta p_{mitot} = \exp \left[-
\left(\frac{n_{noc}(t)}{n_{cc}(t)}\right)^2 \right ]
\end{equation}
\noindent in which $n_{noc}$ and $n_{cc}$ are the number of normal
and cancer cells at time $t$, respectively. As shown, $\Delta
p_{mitot}(t)$ depends only on the dynamics, setting up a feedback
inhibition mechanism \cite{Castro}: as the tumor grows, $\Delta
p_{mitot}(t)$ decreases because of the combined effect of the
decrease in the number of normal cells and the increase in the
number of cancer cells. In order to intensify the effect of this
mechanism (see \cite{Lobato}), an exponent 2 in equation
(\ref{pmitot}) is considered. Since there is no new available source
of nutrients and/or space, it decreases as the density of cancer
cells increases because the available nutrients and/or space are
reduced. The effect of the proliferation of cancer cells is that
their growth potential increases by a unit at each time step.
\vspace{0.3cm}
\item [] (ii) The cancer cells compete with normal cells for the empty
sites, depending on the potential growth of neighboring cells.
According to the majority rule, a normal cell is displaced by a
cancer cell following local battles occurring between healthy and
cancerous cells [15].
\vspace{0.3cm}
\item [] (iii) If the growth potential of a cancer cell reaches a
threshold value that is a fraction $f$ of the lattice size $L$, it
becomes necrotic and its growth potential falls to zero.
\vspace{0.3cm}
\item [] (iv) Both normal and cancer cells may die, with probabilities
$p_{drugn}$ and $p_{drugc}$, respectively, due to the continuous
infusion of a drug that is applied after tap time steps; in this
case, the site becomes empty.
\vspace{0.3cm}
\item [] (v) if there are no cancer cells in the neighborhood of a dead
cell (empty site), regeneration of normal cells occurs; if the
cancer cells in the neighborhood of a necrotic cell die as a result
of the therapy, the necrotic cell is eliminated.
\end{itemize}
The algorithm was computationally implemented in FORTRAN 77 in
accordance with the following steps: input data; calculate $\Delta
p_{mitot}(t)$; identify the state of the cell (choose one of the
subroutines: normal cell (NoC), cancer cell(CC), necrotic cell(NeC),
empty site (ES); update the cells of the lattice; after N
iterations, output data.
The input data are the
following cellular automata (CA) parameters:
\begin{itemize}
\item [] 1) The spatial parameters: lattice size L; necrosis threshold
fraction $f$ of lattice size;
\vspace{0.3cm}
\item [] 2) The temporal parameters: the length of the time series t
final and the initial time of therapy infusion $t_{ap}$;
\vspace{0.3cm}
\item [] 3) The probabilities of: the initial proliferation of cancer
cells $p_0$; the effect of therapy on normal cells and cancer cells
($p_{drugn}$ and $p_{drugc}$).
\end{itemize}
The output data are the time series of the density of each type of
cell and the final configuration of the lattice at any time step. In
addition, the time-spatial configurations, controlled by a package
denominated g2 \cite{g2_manual} whose commands are inserted into the
computer program in FORTRAN, are generated in "real time". This
package may be used in C, PYTHON and PERL.
The following is a description of each subroutine based on the local
rules:
\begin{itemize}
\item [] a) {\bf Normal Cell (NoC)} - a random number $y$ is compared
to $p_{drugn}$. If $y < p_{drugn}$, the growth potential $P_{noc}$
is confirmed: if $P_{noc} = 0$, the cell dies and the site becomes
empty; otherwise, it remains occupied by a normal cell but $P_{noc}
= 0$. If $y \ge p_{drugn}$ and if there is at least one neighboring
cancer cell, then the normal cell is 'dislocated', $P_{noc} = 0$ and
the site becomes empty; otherwise it remains a normal cell.
\vspace{0.3cm}
\item [] b) {\bf Cancer Cell (CC)} - if all of its neighbors are cancer cells and
its growth potential reaches a fraction $f$ of lattice size $L$, the
cancer cell becomes necrotic. Otherwise, a number $y$ is randomly
chosen. If $y < p_{drugc}$ and $t > t_{ap}$, the potential $P_{cc}$
is confirmed: if $P_{cc} > 0$, it is reduced by a unit and the cell
remains a cancer cell; otherwise the cell dies and the site becomes
empty. Finally, if $y \ge p_{drugc}$, the cell remains a cancer
cell; however, its growth potential $P_{cc}$ increases by a unit.
\vspace{0.3cm}
\item [] c) {\bf Necrotic Cell (NeC)} - if at least one of its neighbors is neither
a cancer cell nor a necrotic cell, it is eliminated and the site
becomes empty; otherwise, it continues necrotic.
\vspace{0.3cm}
\item [] d) {\bf Empty Site (ES)} - if there are cancer and normal cells in its
neighborhood, the local battle between cancer cells and normal cells
is such that if the sum of the potential growth of its neighboring
cancer cells is greater or equal to the sum of the potential growth
of its normal cell neighbors, then the empty site is occupied by a
cancer cell that diffuses from one of the randomly chosen neighbors;
otherwise, it is occupied by one of the randomly chosen normal cells
that were previously dislocated. If there are only normal cells in
its neighborhood, it becomes a normal cell through a process of
regeneration. Finally, if none of its neighbors are cancer cells or
normal cells, it remains empty.
\end{itemize}
\section{RESULTS: SIMULATED TIME SERIES AND TIME-SPATIAL PATTERNS}
\label{sec3}
Computational simulations of the model were performed in order to
analyze two classes of behavior: cases in which no treatment was
given and treatment cases. In each subsection, the time series of
the simulated tumor as well as time-spatial patterns are shown.
\vspace{1cm}
\subsection{NO TREATMENT CASE}
\label{subsec31}
In the case of no treatment, the following parameters are
considered: $p_{drugn} = p_{drugc} = t_{ap} = 0$. For fixed values
of $L$, $t_{final}$ and $p_0$, but different values of $f$, in
Figures \ref{Figure1} and \ref{Figure3}, the time series of the
density of cells for nonnecrotic and necrotic tumors, respectively,
are shown. In both cases, the cell densities reach saturated values
due to the effects of the competition between normal cells and
cancer cells, and the time-dependent mitotic probability. Comparing
Figures \ref{Figure1}b and \ref{Figure3}b, the stationary value of
cancer cell density is clearly greater in necrotic tumors than in
nonnecrotic ones. This is a consequence of the fact that $\Delta
p_{mitot}(t)$ assumes smaller values in necrotic tumors compared to
nonnecrotic ones because it does not depend on the density of
necrotic cells. In both cases, the average of the different samples
is considered, corresponding to different seeds of random numbers.
\begin{figure}
\begin{center}
\includegraphics*[width=6.0cm]{ReisFig1a.jpg}
\includegraphics*[width=6.0cm]{ReisFig1b.jpg}
\end{center}
\caption{\label{Figure1} Nonnecrotic tumor: the average of simulated
time series of the density of: a) normal cells, b) cancer cells. We
consider $M_{samples} = 200$ and the following parameter values: $L
= 251$, $p_{0} = 0.95$, $f = 0.6$, $p_{drugn} = p_{drugc} =
0.0$.}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width=6.0cm]{ReisFig2a.jpg}
\includegraphics[width=6.0cm]{ReisFig2b.jpg}
\end{center}
\caption{\label{Figure2} Non-necrotic case: assuming
$M_{samples}=200$ and the same parameters values of Figure
\ref{Figure1}, the average of simulated time series of: a) the
number of cancer cells (grey color); b) the growth potential of
cancer cells (black color). The Gompertzian fitting is applied to
(a) (black color) those in which parameters of time series are
$\alpha_0=(6.58 \pm 0.09) \times 10^{-2}$, $\beta=(1.631 \pm 0.008)
\times 10^{-2}$ and $n_0=(1.6 \pm 0.06) \times 10^{2}$.}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics*[width=6.0cm]{ReisFig3a.jpg}
\includegraphics*[width=6.0cm]{ReisFig3b.jpg}
\end{center}
\caption{\label{Figure3} Necrotic case: the average of simulated
time series of density of a) normal cells, b) cancer cells. We
consider $M_{samples}=200$ and the following parameter values:
$L=251$, $p_0=0.95$, $f=0.2$, $p_{drugn}=0.0$, $p_{drugc}=0.0$.}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics*[width=6.0cm]{ReisFig4a.jpg}
\includegraphics*[width=6.0cm]{ReisFig4b.jpg}
\end{center}
\caption{\label{Figure4} Assuming $M_{samples}=200$ and the same
parameters values of Figure \ref{Figure3}, the average of simulated
time series of: a) the number of cancer cells (grey color); b) the
growth potential of cancer cells (black color). The Gompertzian
fitting is applied on (a) (black color) those in which parameters of
time series are $\alpha_0=(5.86 \pm 0.06) \times 10^{-2}$,
$\beta=(1.450 \pm 0.006) \times 10^{-2}$ and $n_0=(1.926 \pm 0.005)
\times 10^{2}$.}
\end{figure}
Figures \ref{Figure2}a and \ref{Figure4}a show that the tumor
growth obeys the Gompertzian function both in nonnecrotic and
necrotic cases. This behavior is observed with respect to the number
of cancer cells for a range of values of $p_0$. In Gompertzian
growth, the specific growth rate of the number of cancer cells
decreases logarithmically:
\begin{equation}
\label{gompertzrate}
\frac{1}{n_{cc}}\frac{dn_{cc}}{dt} = \alpha_0
- \beta \log \left(\frac{n_{cc}}{n_0}\right)
\end{equation}
\noindent where
\begin{itemize}
\item [] a) $n_0$ is the initial population of cancer cells;
\item [] b) $\alpha_0$ is the specific growth rate of $n_0$ cells
at $t=0$;
\item [] c) $\beta$ measures how rapidly the curve departs from a
singular exponential and curves over, assuming its characteristic
shape.
\end{itemize}
The solution of (\ref{gompertzrate}) is
\begin{equation}
\label{gompertzsolution}
n_{cc}(t)=n_0 \exp \left\{\frac{\alpha_0}{\beta}[1-\exp(-\beta t)]\right\}.
\end{equation}
It is evident that the stationary value of $n_{cc}$ is
$n_{{cc}_{\infty}}=n_0 \exp(\alpha_0/\beta)$. According to the
Gompertzian fitting represented by equation \ref{gompertzsolution},
the results of the simulations shown in Figures
\ref{Figure2} and \ref{Figure4} correspond respectively to the following parameters:
\begin{itemize}
\item [] I) The nonnecrotic tumor: $\alpha_0=(6.58 \pm 0.09) \times 10^{-2}$, $\beta=(1.631 \pm
0.008) \times 10^{-2}$ and $n_0=(1.60 \pm 0.06) \times 10^{2}$
\item [] II) The necrotic tumor: $\alpha_0=(5.86 \pm 0.06) \times
10^{-2}$, $\beta=(1.450 \pm 0.006) \times 10^{-2}$ and $n_0=(1.926
\pm 0.005) \times 10^{2}$
\end{itemize}
Comparing the above parameters of (I) and (II), the behavior of
nonnecrotic and necrotic tumors was found to be very similar. It was
also found that the number of cancer cells obeys the Gompertzian
fitting.
An important confirmation of our model is shown by comparing the
Gompertzian fitting parameters of simulated tumors with the
corresponding parameters of actual tumors \cite{Demicheli}
\cite{Brunton}. For instance, in the case of the testicular tumors
shown in Table 3 of reference \cite{Demicheli}, the $\beta$ values
are in the range of $[0.005; 0.016]$ $day^{-1}$. Our simulated
$\beta$ values are within the above range if we consider the time
step of our simulations to be one day.
In relation to the parameters $\alpha_{0}$ and $n_0$, the simulated
values are not comparable to the actual values, since no information
on the initial size of the tumor was included in our model. Both
$\alpha_0$ and $n_0$ are strongly dependent on that information.
\begin{figure}
\begin{center}
\includegraphics[width=0.4\textwidth,angle=0]{S1.jpg}
\includegraphics[width=0.4\textwidth,angle=0]{S2.jpg}
\vspace{1cm}
\includegraphics[width=0.4\textwidth,angle=0]{S3.jpg}
\includegraphics[width=0.4\textwidth,angle=0]{S4.jpg}
\end{center}
\caption{\label{Figure5} The spatial distribution of states at
consequent time steps (see the time step bar) using the same
parameters values of Figure \ref{Figure3} except $L=81$ and
$p_0=0.8$. The final time step is $t_{final}=600$. Dark colors
(light grey, grey, and dark grey) correspond, respectively,
to normal, cancer, and necrotic cells.}
\end{figure}
Finally, it would be very interesting to discover whether it is
possible to relate the cellular automata no-therapy parameters $L$,
$f$ and $p_0$ with the Gompertzian parameters for the range of
values of $p_0$ and to assess whether the number of cancer cells
obeys a Gompertzian growth pattern. In this case, some preliminary
conclusions may be drawn with respect to $n_\infty$: it decreases in
accordance with the necrotic parameter $f$ but it increases linearly
as a function of lattice size $L$ and, exponentially with $p_0$.
Concerning the other Gompertzian parameters, the answer to this
question is not so simple. Following these conclusions leads us to a
much more interesting quandary if we want to make the model more
realistic: to estimate realistic ranges of the CA no-therapy
parameters $L$, $f$ and $p_0$ based on the Gompertzian parameters of
actual solid tumors.
With respect to the time-spatial patterns of the simulated tumors,
Figure \ref{Figure5} shows the lattice configuration at some time
during the steady state in the necrotic (Figure \ref{Figure5}b)
cases. Using the g2 package, it was found that, although tumor
growth leads to the compact shape that is characteristic of solid
tumors, the growth process is such that its boundary is irregular
for any time $t$, as, for example, for the time steps represented in
Figure \ref{Figure5}. A similar type of behavior is observed for the
time-spatial patterns in the nonnecrotic tumor. In relation to the
process of necrosis, the necrotic region was found to be inside the
tumor at any time $t$ \cite{Kansal} \cite{Bellomo}, as shown in
Figure \ref{Figure5}.
\subsection{TREATMENT CASE}
\label{subsec32}
Figures \ref{Figure6}a and \ref{Figure6}b show the simulated time
series of the number of cancer cells and normal cells for the
different values of $p_{drugc} > p_0$ and $p_{drugc} < p_0$
corresponding to successful treatment (cure) and unsuccessful
treatment (non-cure), respectively. In each figure, two values of
$p_{drugn}$ are considered. It can be clearly seen that, for both
values of $p_{drugn}$, the success of the treatment does not change.
It is also clear that the tumor size increases until tap (see
figures \ref{Figure6}a and \ref{Figure6}b). However when $p_{drugc}
> p_0$, the reduction in tumor size starts, as expected, after $t_{ap}$ time steps.
When treatment is successful ($p_{drugc} > p_0$), it was found that,
for an upper value of $p_{drugn}$ ($p_{drugn} = 10^{-2}$; light
grey), more normal cells are eliminated compared with a lower value
of $p_{drugn}$ - $p_{drugn} = 10^{-4}$ as shown in Figure
\ref{Figure6}a (dark grey). Therefore, we may conclude that very
small values of $p_{drugn}$ correspond to optimal therapy. However,
in the case of unsuccessful treatment ($p_{drugc} < p_0$), when
$p_{drugn}$ is increased, both a decrease in the number of normal
cells and a slower rate of increase of cancer cells is found (see
fig \ref{Figure6}b).
A systematic analysis of the parameter space presented in the next
section will provide a more precise conclusion about the role of
$p_{drugn}$ parameter.
\begin{figure}
\begin{center}
\includegraphics[width=6.0cm]{ReisFig6a.jpg}
\includegraphics[width=6.0cm]{ReisFig6b.jpg}
\end{center}
\caption{\label{Figure6}a) Successful treatment: the average of
simulated time series of the number of normal cells (-) and cancer cells (circle) assuming
$M_{samples}=200$ and the following parameters values: $L=251$,
$p_0=0.8$, $f=0.2$, $p_{drugc}= 0.9$, $t_{ap}= 500$, and two values
for $p_{drugn}$: $10^{-4}$ (dark grey), and $10^{-2}$ (light grey);
b) Unsuccessful treatment: the time series of the number of normal
cells (-) and cancer cells (circle) assuming $M_{samples}=200$ and the following
parameters values: $L=251$, $p_0=0.8$, $f=0.2$, $p_{drugc}= 0.7$,
$t_{ap}= 500$, and two values for $p_{drugn}$: $10^{-4}$ (dark
grey), and $10^{-2}$ (light grey).}
\end{figure}
In order to analyze the effect of therapy on cancer cells, the
time-spatial distribution of the simulated tumors was followed using
the g2 package. Figure \ref{Figure7} shows the configuration of the
lattice at different time steps from the beginning of therapy until
the tumor is eliminated.
\begin{figure}
\begin{center}
\includegraphics[width=0.4\textwidth,angle=0]{C1.jpg}
\includegraphics[width=0.4\textwidth,angle=0]{C2.jpg}
\vspace{1cm}
\includegraphics[width=0.4\textwidth,angle=0]{C3.jpg}
\includegraphics[width=0.4\textwidth,angle=0]{C4.jpg}
\vspace{1cm}
\end{center}
\caption{\label{Figure7} The spatial distribution of states at
consequent time steps (see the time step bar) using the same
parameters values of Figure \ref{Figure6}a except $L=81$. The final
time step is $t_{final}=1400$. Dark colors (light grey, grey, dark
grey, and black) correspond, respectively, to normal, cancer,
necrotic cells, and empty sites.}
\end{figure}
\section{RESULTS: PARAMETER SPACE}
\label{sec4}
Analysis of the parameter space is important in order to confirm the
robustness of the model and to identify the most relevant parameters
for the dynamics of the model.
According to the relevance of some CA parameters to the features of
the phenomenon, this analysis of parameter space was divided into
two parts: the occurrence of necrosis (no treatment cases) and
reaching a state of cure (treatment cases).
\subsection{THE OCCURRENCE OF NECROSIS}
\label{subsec41}
In the first part, the parameters are again established as:
$p_{drugn} = p_{drugc} = t_{ap} = 0$ with the aim of evaluating the
effect of necrosis, and the minimum value of f is obtained for each
pair of values $(L; p_0)$. The values of $L$ are presumed to range
from 101 to 251, increasing the interval by $\Delta L = 25$. With
respect to $p_0$, the whole interval from 0.1 to 0.9 is taken into
account, increasing $\Delta p_{mitot}(t) = 0.1$. Figure
\ref{Figure8} shows that a transition exists between the nonnecrotic
(lower) and necrotic (upper) regions of parameter space.
It was found that:
\begin{equation}
\label{fmin} f_{min}=a(L) p_0 + b(L)
\end{equation}
where the linear and the angular coefficients, $b(L)$ and $a(L)$ are
different for distinct values of the lattice size.
\begin{figure}[!h]
\begin{center}
\includegraphics[width=6.0cm]{ReisFig8a.jpg}
\includegraphics[width=6.0cm]{ReisFig8b.jpg}
\end{center}
\caption{\label{Figure8} a) Parameter space in the case of no
treatment: $f^{min} \times p_0 \times L$; the following parameters
values are fixed: $p_{drugn}=0$, $p_{drugc}=0$; $t_{final}=5000$. b) the dependence of
the angular coefficient of $f_{min}$, $a(L)$, with $L$.}
\end{figure}
The angular coefficient $a(L)= a_0 L^\gamma$ where $a_0=1.12$ and
$\gamma=0.29$ (see figure \ref{Figure8}b).
Since the lattice size is an intrinsic parameter of the model, that
transition is such that the the maximal growth probability $p_0$ is
the control parameter, while the necrotic parameter $f$ is the order
parameter.
\subsection{REACHING THE CURE STATE}
\label{subsec42}
If the tumor is submitted to systemic treatment represented by a
probability $p_{drugc} \ne 0$ starting at $t_{ap} \ne 0$ that
affects normal cells with a probability $p_{drugn} < p_{drugc}$, our
aim is to establish the minimum value of $p_{drugc}$ in order to
achieve a state of cure, i.e., no cancer cells.
The analysis is now more complex than the one performed in
subsection \ref{subsec41} in the sense that there are 4 important
parameters that control the behavior of the therapeutic effect:
$p_{drugc}$, $p_{drugn}$, $t_{ap}$, and $p_{0}$. The relevance of
$p_0$ is evident in subsection \ref{subsec32}. This analysis is
divided into two parts.
In the first part, motivated by the behavior observed in figure
\ref{Figure6}a, the parameter is defined as $p_{drugn}$, assuming
very small values ($p_{drugn} = 10^{-4})$ to simulate optimal
therapy. Lattice size is also established as $L = 251$ and the
necrotic parameter $f = 0.6$. Analogously to the method applied in
subsection \ref{subsec41}, the minimum value of $p_{drugc}$ was obtained
for each pair of values $(p_0; t_{ap})$. The range of values for
$p_0$ and tap are, respectively, $[0.1; 0.9]$ and $[0; t_{final}]$.
Figure \ref{Figure9} shows the relevant role of $p_0$ dividing the
parameter subspace into two regions: the lower is the non-cure state
while the upper corresponds to the state of cure. In this case $p_0$
is again the control parameter but $p_{drugc}$ is the order
parameter.
\begin{figure}
\begin{center}
\includegraphics[width=6.0cm]{ReisFig9.jpg}
\end{center}
\caption{\label{Figure9} Parameter subspace of treatment case:
$p_{drugc}^{min} \times p_0 \times t_{ap}$; the following parameters
values are fixed: $L=251$, $f=0.6$, $p_{drugn}=10^{-4}$;
$t_{final}=5000$.}
\end{figure}
In the second part, a value of $p_0 = 0.8$ remains fixed, while the
pair varies $(p_{drugn}; t_{ap})$, again in order to obtain the
minimum value of $p_{drugc}$ that would be sufficient to effectively
eliminate the tumor, now related to the effect of the drug on the
normal cells. The whole interval of $p_{drugn}$ was taken into
account from very small values $10^{-4}$ until $0.9$. It would be
necessary to extend $t_{final}$ in order to maintain the duration of
application, since in this analysis the parameter $t_{ap}$ varied.
Since this behavior is similar for any value of $p_{drugn}$, in
figure \ref{Figure10} the minimum value of $p_{drugc}$ is shown to
increase as a function of $t_{ap}$ in accordance with a Lorentzian
function:
$$p_{drugc}^{min} = A_0 + \frac{2A_1}{\pi}\,\frac{A_3}{4(t_{ap}-A_2)^2 + A_3^2}$$
This result means that the minimal rate of infusion of the drug to
eliminate the tumor has to be greater if the treatment begins later.
It emphasizes how important it is to initiate treatment as early as
possible in order to reduce the infusion rate of the drug.
\begin{figure}
\begin{center}
\includegraphics[width=6.0cm]{ReisFig10.jpg}
\end{center}
\caption{\label{Figure10} Parameter subspace of treatment case:
$p_{drugc}^{min} \times t_{ap}$; the following parameters values are
fixed: $L=251$, $f=0.6$, $p_0=0.6$; $p_{drugn}=10^{-4}$;
$\delta_t=t_{final}-t_{ap}=500$. The Lorentzian fitting (grey color) parameters
are $A_0=0.60$, $A_1=186.61$, $A_2=4829.92$, $A_3=776.29$.}
\end{figure}
Finally in the cases in which the tumor is eliminated ($p_{drugc} >
p_0$), for fixed values of $L$, $f$, $p_0$ and $p_{drugn}$, the cure
time ($t_{cure}$) is estimated in relation to the initial time
application $t_{ap}$, and $p_{drugc}$ (see Figure \ref{Figure11}).
Note that $t_{cure}$ is not a parameter but a consequence of the
time evolution of the system. Figure ref{Figure11} shows that
$t_{cure}$ increases linearly with $t_{ap}$ with an angular
coefficient equal to 1. Figure \ref{Figure11} also shows that, for a
fixed $t_{ap}$, $t_{cure}$ decreases with $p_{drugc}$. This result
also shows how important it is to start treatment as early as
possible to reduce the amount of time required to reach the state of
cure.
\begin{figure}
\begin{center}
\includegraphics[width=6.0cm]{ReisFig11.jpg}
\end{center}
\caption{\label{Figure11} Analysis of cure time in the treatment
case: $t_{cure} \times p_{drugc}^{min} \times t_{ap}$; the following parameters values
are fixed: $L=251$, $f=0.6$, $p_0=0.6$, $p_{drugn}=10^{-4}$, $t_{final}=500$.}
\end{figure}
\section{DISCUSSION AND CONCLUDING REMARKS}
\label{sec5}
The model proposed in this study is capable of capturing the
Gompertzian behavior of avascular tumor growth. The competition
between normal and cancer cells and the dynamic character of the
mitotic probability are the relevant components of the success of
this model.
The number of cancer cells simulates tumors {\it in vitro} due to
the two-dimensional character of the model, and their potential
growth simulates a tumor in vivo due to its three-dimensional
nature. Figures \ref{Figure2} and \ref{Figure4} show that the model
is able to capture the dynamics of both {\it in vivo} and {\it in
vitro} avascular tumor growth. The simulated values for the most
important Gompertzian parameter $\beta$, which characterizes the
Gompertzian shape, are compatible with the parameter values of some
tumors \cite{Demicheli} \cite{Brunton}.
The model is also able to capture necrotic and nonnecrotic tumors
depending on the values of the parameter $f$. It is well-known that
necrosis, unlike apoptosis, is a typical phenomenon found in a group
of cells that is simulated in our model by the changing of the
potential growth of the cells.
The time-spatial patterns reveal a tumor with a compact shape and
irregular boundaries, as occurs in some solid tumors \cite{Patel},
\cite{Ferreira}. Evidence was also found to confirm the three stages
of avascular tumor growth \cite{Adam}:
\begin{itemize}
\item [] a) Stage I - when the tumor grows exponentially due to available
resources (nutrients and oxygen) - see first stage in Figure \ref{Figure5};
\item [] b) Stage II - when the stabilization of $\Delta p_{mitot}$ starts but there are
still enough resources to ensure that necrosis does not occur - see second stage in Figure \ref{Figure5}b;
\item [] c) Stage III - when necrosis
may occur depending on the value of the parameter $f$ because the resources are
insufficient to provide for tumor growth - see third stage in Figure \ref{Figure5}c in the case of necrosis.
\end{itemize}
The next stage, the angiogenic phase of the tumor \cite{Folkman},
which has not yet been dealt with in our model, corresponds to
vascular growth. To be able to evaluate this stage, the process of
angiogenesis would have to be taken into account \cite {Adam}.
In the case of no treatment ($p_{drugc} = p_{drugn} = 0$), the
minimum value of $f$ for necrosis to occur is governed by the
equation (\ref{fmin}) that was obtained from the investigation of
the parameter space. This means that, for a simulated tissue of
dimension $L$, the occurrence of necrosis depends linearly on the
maximum value of mitotic probability of the specific tumor.
In relation to the case in which therapy was implemented, a
continuous strategy of systemic therapy, i.e. chemotherapy, was
selected. Although the schedule of chemotherapy is usually periodic,
in this case it was decided to simulate this less realistic
situation so that the effect of the parameters $p_0$ and $p_{drugc}$
could be compared in a simple fashion. It was thus found that, with
respect to avascular tumor growth, when the values of the parameter
$p_{drugn}$ are very small and when $p_{drugc}$ is slightly greater
than $p_0$, the tumor is completely eliminated (see Figure
\ref{Figure7}). Since neovascularization has not yet been
triggered, a state of cure may be expected to occur with a periodic
schedule.
The time-spatial patterns of the cases in which therapy was
implemented (see Figure \ref{Figure8}) show that the drug acts from
the borders of the simulated solid tumor inwards, as would be
expected in the case of solid tumors.
With respect to the effect of parameters on the state of cure, for
fixed values of lattice size $L$ and necrotic parameter $f$, and for
a range of values of $t_{ap}$ and $p_{drugn}$, the minimum value of
$p_{drugc}$ again coincides with $p_0$ (see Figure \ref{Figure9}).
This reinforces the importance of the higher value of $p_0$ in the
response of the tumor to therapy. It retains the memory of cancer
cells with respect to the onset of mitosis.
Finally, Figures \ref{Figure10} and \ref{Figure11} illustrate a very
relevant finding from the phenomenological point of view: the
importance of initiating therapy as early as possible in order to
reach the state of cure. The cure time was found to be proportional
to $t_{ap}$ that measures the instant when the infusion starts (see
Figure \ref{Figure11}) and the minimum value of the therapeutic
infusion to eliminate the tumor increases nonlinearly as a function
of the starting point of therapy.
Future studies should be carried out to generalize the model with
the objective of including the angiogenic process and the periodic
schedule of systemic therapy. However, the most important
perspective of this line of investigation is to compare the model
with the in vitro tumor growth of cells from specific tissue samples
and to compare parameter values. It would then be possible to relate
the Gompertzian fitting parameters with the parameters of the model.
\vspace{1cm}
{\bf Acknowledgements:} The authors would like to thank Ramon
El-Bach\'a for his very useful discussions on the process of tumor
growth and Nelson Alves Jr. for his valuable collaboration at the
beginning of this study and his help in manipulating the time
spatial patterns. This work is partially supported by CNPq --
Conselho Nacional de Desenvolvimento Cient\'{\i}fico e Tecnol\'ogico
(Brazilian Agency).
|
{
"redpajama_set_name": "RedPajamaArXiv"
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| 3,921
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Based on their work with public broadcasting CEOs, LRI's expertise is a must for any organization that wants and needs to resolve tough issues.
We had a difficult challenge facing us in articulating a clear vision for PHH. LRI did a great job in getting input from all the participants while at the same time keeping us on track. We accomplished the goal of agreeing on a future direction. I don't think we would have gotten there without LRI's help. Thanks again for your facilitation and leadership.
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|
{
"redpajama_set_name": "RedPajamaC4"
}
| 5,635
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\section{Introduction}
Recently, there has been an increase in popularity in using camera sensors and cloud services to capture and process large amounts of data. The benefits are clear, cameras are cheap, and cloud computing allows for easy maintainability. However, this comes at the cost of additional security and privacy risks. As the footage these cameras capture is rich in information, there is a considerable risk of function creep~\cite{marxMissionCreepSmart2020,WhatWrongPublic2002}(i.e., using the data for other purposes than originally intended). A camera used to monitor street activity can be misused for racial profiling as the footage captured is rich enough to do both. Another key concern is possible malicious use by the third-party cloud provider. To alleviate this, we propose an edge-based filtering stage that removes privacy-sensitive attributes before the sensor data is transmitted to the cloud. As such, the cloud server should only have access to the strictly required properties for the utility task. For optimal usability, we identify three key requirements. Firstly, it should provide a clear view of what features of the data are removed or kept. In other words, the filtering should be semantically interpretable. Additionally, there should be some flexibility as to what data is allowed or prohibited. This flexibility would allow the camera footage to be used for multiple purposes, where each task only gets the strictly necessary features. Lastly, a solution where no modifications of the data processing systems are required is appealing as well, as this allows the use of pre-existing and well-maintained API's and resources for the utility task.
\begin{figure}
\centering
\includegraphics[width=\linewidth]{figures/opt-in-opt-out.pdf}
\caption{Illustration of opt-in and opt-out filtering for the gender attribute for face data. A striped pattern indicates the removal or change of data.}
\label{fig:optin-optout}
\end{figure}
We propose to use the state-of-the-art image manipulation technique ZeroDIM~\cite{gabbayImageWorthMore2021a}, which is based on disentangled representation learning, to implement privacy filters. ZeroDIM can make high-quality edits of images by disentangling them into certain semantic factors. As such it should allow the necessary flexibility and interpretability of privacy protection. We can use this model to either explicitly state what data should be removed or alternatively state what data should be kept. Explicitly stating what features should be hidden is commonly referred to as opt-out. The more secure alternative, where the allowed features are explicitly stated, is called opt-in. A simple clarification of these operations can be seen in Figure \ref{fig:optin-optout}. Here we show how an image of a human face captures a combination of underlying attributes, such as age, gender and ethnicity. Some of these attributes partially overlap (e.g., facial hair and gender). Our goal is to transform this image into another image that either hides one attribute (opt-out) or retains a single attribute while hiding all others (opt-in).
In this paper, we experimentally verify the use of the ZeroDIM image manipulation algorithm to implement privacy filters. We focus on facial imagery since the processing of face images is a use case highly relevant to privacy-preserving machine learning due to the sensitive nature of human faces. Additionally, facial imagery is one of the domains in which image manipulation is most successful because of the relative ease of disentanglement.
This paper is organized as follows: Section \ref{sec:rel_works} describes related works in image manipulation and privacy-preserving machine learning. In Section \ref{sec:zerodim} we describe the ZeroDIM model and propose how to use it as a means of filtering. We then evaluate opt-in and opt-out settings for this purpose in Section \ref{sec:filtering}. Section \ref{sec:investigations} investigates some of the inherent difficulties of filtering face attributes, such as correlations between attributes and residual information. Finally, we conclude our work and look at future research in Section \ref{sec:conclusion} and \ref{sec:future}.
\section{Related Works}
\label{sec:rel_works}
\subsection{Image manipulation}
A growing body of literature has investigated the powers of pre-trained unconditional generators such as StyleGAN~\cite{karrasStyleBasedGeneratorArchitecture2019,karrasAnalyzingImprovingImage2020a,karrasAliasFreeGenerativeAdversarial2021} for semantic image manipulation/editing. A partition of these methods leverages the naturally disentangled latent space of pre-trained GAN models to develop latent manipulations that allow for specific semantic operations~\cite{harkonenGANSpaceDiscoveringInterpretable2020,shenInterpretingLatentSpace2020a}. When coupled with a GAN inversion technique ~\cite{roichPivotalTuningLatentbased2021,abdalImage2StyleGANHowEmbed2019,alalufReStyleResidualBasedStyleGAN2021,tovDesigningEncoderStyleGAN2021}, which embeds images into the latent space of these GAN models, this allows for powerful image manipulation, especially in the domain of facial imagery.
While these methods allow high-quality image editing, finding the wanted edit requires manual human examination or a set of annotated data for each edit. Because of this, others turn to natural language for text-guided image manipulation~\cite{xiaTediGANTextGuidedDiverse2021}. Research includes StyleCLIP~\cite{patashnikStyleclipTextdrivenManipulation2021}, which uses CLIP~\cite{radfordLearningTransferableVisual2021a} for guiding the latent manipulation, as well as ZeroDIM~\cite{gabbayImageWorthMore2021a}, which uses disentangled representation learning and leverages CLIP as a form of weak supervision.
Although the field of image manipulation is already well established, only a few works have investigated their use for privacy insurance of face images. Most notable is PrivacyNet~\cite{mirjaliliPrivacyNetSemiadversarialNetworks2020}, a model that tries to hide face attributes while retaining identity information. Wang et al~\cite{wangFacePrivacyProtection2021} has a similar goal. Both works explicitly feed the new values for the face attributes to the generator to create filtered images. As such, they are limited by knowing the attribute values before filtering. Cao et al.~\cite{caoPersonalizedInvertibleFace2021} achieve the opposite goal. They remove identity information while keeping soft biometrics such as age and gender. This paper focuses on the different face attributes and how these can be changed in relation to each other. Additionally, we employ disentangled representations for all attributes (Cao et al. also use disentanglement; however it is limited to disentangling identity from attributes). An important distinction is that we do not need ground truth labels to filter attributes and provide privacy by randomising instead of explicitly changing.
\subsection{Privacy-preserving machine learning}
Privacy-preserving machine learning is an area that has evoked a significant amount of interest over the years. In this section, we will highlight some of the most popular techniques that can be used for privacy-preserving machine learning applications. For a complete overview, we refer to~\cite{mireshghallahPrivacyDeepLearning2020}.
Homomorphic encryption (HE) is a technique that allows computation over encrypted data without requiring decryption by the data processor. This allows leveraging of the benefits of cloud-based computation while mitigating privacy risks as only the data owner holds the decryption key. Examples of HE include CryptoNets~\cite{gilad-bachrachCryptoNetsApplyingNeural2016} and GAZELLE~\cite{juvekarGazelleLowLatency2018}. The main downfall of HE is its heavy computational footprint. Although significant improvements have been made over the years, real-time processing remains infeasible~\cite{mireshghallahPrivacyDeepLearning2020}.
Secure multi-party computation (SMC) ensures privacy by splitting computations over several computing parties. Services can only be completed if all parties participate, thus ensuring privacy if one party is trusted. This technique suffers from the same problem as HE in that the additional computation and communication needed infers a heavy inference time cost. Some examples of using SMC for machine learning are MiniONN~\cite{liuObliviousNeuralNetwork2017}, Crypten~\cite{knottCrypTenSecureMultiParty2021}, and XONN~\cite{riaziXONNXNORbasedOblivious2019a}.
Differential privacy~\cite{dworkDifferentialPrivacySurvey2008} is arguably the most well-known technique for privacy insurance. Privacy is guaranteed by adding noise to individual data items to prevent attackers from being able to infer the presence of a particular item in a dataset. However, most work in differential privacy focuses on dataset anonymisation and tabular data instead of inference on high dimensional image data~\cite{mireshghallahPrivacyDeepLearning2020}.
Lastly, a group of information-theoretic techniques degrade all information not necessary for a specified non-sensitive task~\cite{mireshghallahPrivacyDeepLearning2020,malekzadehMobileSensorData2019,malekzadehPrivacyUtilityPreserving2020,malekzadehProtectingSensoryData2018,ravalOlympusSensorPrivacy2019}. The focus of most of these works is sensory data, however recently works for computer vision have been published~\cite{mireshghallahShredderLearningNoise2020a,osiaDeepPrivateFeatureExtraction2018} as well. Some earlier research focuses on providing an opt-in approach, however they lack semantic interpretability~\cite{lerouxPrivacyAwareOffloading2018a,deconinckPrivacyAwarePerson2021a} making it difficult to verify privacy claims.
\section{Image manipulation for privacy}
\label{sec:zerodim}
\begin{figure}[h]
\centering
\includegraphics[width=\linewidth]{arch.pdf}
\caption{Architecture of ZeroDIM model, adapted from \cite{gabbayImageWorthMore2021a}. Disentangled factor codes are obtained through classifiers $C$, coupled with a residual code from the residual encoder $R$ and fed through the generator $G$ to reconstruct an image.}
\label{fig:zerodim-arch}
\end{figure}
To investigate image manipulation as a means of filtering data, we utilize ZeroDIM (Zero-shot Disentangled Image Manipulation)~\cite{gabbayImageWorthMore2021a} as our manipulation model. We chose this model primarily due to its state-of-the-art results on facial data, a domain which lends itself well to privacy-preserving research. Additionally, due to its use of disentangled representations, the architecture forms an excellent basis for allowing both opt-in and opt-out settings.
ZeroDIM uses a weakly supervised disentanglement technique to create latent codes for a few predefined factors. The architecture of ZeroDIM can be seen in Figure \ref{fig:zerodim-arch}. It uses a set of classifiers $C$ for each attribute or factor and translates their predictions into distinct factor codes. Moreover, a residual encoder $R$ is used to obtain a residual code which contains all additional information (such as background or non-disentangled attributes) needed for accurate recreation. Both the factor codes and the residual code are used by a StyleGAN generator $G$ to reconstruct the image. The factor and residual codes are explicitly trained to have as little informational overlap as possible.
During training, distinct factor codes are learned for every factor value in the form of vector representations. At inference, the classifier of an attribute (e.g. gender), predicts a class (e.g. male). Subsequently, the factor code of that class is chosen and used in the generation process. This makes it so manipulating an attribute can be done by switching the factor code of that attribute with the factor code of another class. Due to the disentangled nature of these codes, switching a factor code should effectively remove all information of that attribute, making it a suitable operation for filtering.
\subsection{Filtering with ZeroDIM}
We propose to make use of the disentangled nature of ZeroDIM representations to implement a privacy filter. At runtime, we replace the extracted feature vector of a privacy-sensitive attribute with a randomly selected factor code. For example, if we wish to filter gender, we replace the gender representation by choosing at random between those of male or female. Some example results can be seen in Figure \ref{fig:ex-manip}. We show the original face image on the left and subsequently the filtered images for different combinations of allowed attributes. For example, the first filtered image still allows detection of gender, beard and glasses, while hiding age, ethnicity and hair color. Note that the quality of the reconstructed images remains high even when multiple attributes are changed.
\begin{figure}[h]
\centering
\includegraphics[width=0.8\linewidth]{example_manip.pdf}
\caption{Example of filtering using the ZeroDIM model. The leftmost image shows the original version. Subsequent images show the results of filtering different combinations of allowed/disallowed attributes}
\label{fig:ex-manip}
\end{figure}
\iffalse
\begin{figure}[h]
\centering
\makebox[\textwidth][c]{\includesvg[width=1.2\textwidth]{acc.svg}}
\caption{Relative accuracy of filtering to base accuracy when using an opt-out or opt-in configuration on a specified attribute. Columns indicate the attribute that was filtered, rows the attribute that was classified. The top rows show majority class accuracy, random accuracy and accuracy of the classifier when no filtering is performed.}
\label{fig:acc_initial}
\end{figure}
\fi
\section{Experiments}
\label{sec:filtering}
\begin{figure}[h]
\centering
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[scale=0.27]{acc1.pdf}
\caption{Opt-out}
\label{fig:acc-oo}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[scale=0.27]{acc2.pdf}
\caption{Opt-in}
\label{fig:acc-oi}
\end{subfigure}
\caption{Relative accuracy of filtering when using an opt-out or opt-in configuration on a specified attribute. Columns indicate the attribute that was filtered, rows the attribute that was classified.}
\label{fig:acc_initial}
\end{figure}
In this section, we evaluate the effect of filtering on the classification accuracy of face attributes. Our method aims to transform a face image into a new face where some attributes have been replaced with random values. We use the pre-trained image classification models from ZeroDIM to obtain ground-truth values for all attributes. We then compare the accuracy of these models when recreating the faces with and without filtering. The optimal result is obtained when accuracy remains unchanged for an allowed attribute while degrading severely for disallowed attributes. For ease of interpretation, we limit ourselves to filtering single attributes. However, this is not a limitation of our approach. As shown in Figure \ref{fig:ex-manip}, we can use an arbitrary combination of allowed/disallowed attributes for filtering. For these experiments, we used the FFHQ~\cite{karrasStyleBasedGeneratorArchitecture2019} dataset, the same that was used for training ZeroDIM.
Figure \ref{fig:acc-oo} shows the result of the opt-out filtering. Here we aim to hide one attribute while still allowing accurate detection of the others. Each entry shows the relative accuracy of the column attribute when filtering the row attribute. Ideally, non-diagonal elements should have a relative accuracy of 1 (i.e., unchanged compared to unfiltered images), while elements of the diagonal should have significantly lower accuracy. The lower bound of these accuracies depends on the number of categories for each attribute. For example, gender has two categories (male and female), while age has four (child, teen, adult and elderly). Figure \ref{fig:acc-oo} confirms that our model is indeed able to hide the protected attribute while other information can still be accurately extracted. However, the accuracy of the filtered attribute is still not completely random, indicating that some information remains present in the residual code or other attributes. The only exception is the glasses attribute, we assume this to be because of the ease of disentanglement of this attribute as glasses are highly localized and easy to distinguish from other attributes. Another interesting observation is that filtering glasses causes a large drop in accuracy for the age attribute, while filtering any of the other factors does not. This is logical as glasses might be a good indicator of age. However, it raises the question of how related attributes influence filter operations.
Figure \ref{fig:acc-oi} shows the results of the opt-in filter. Here we only allow one attribute to be extracted while removing all others. Ideally, the relative accuracy on the diagonal should be close to 1, while the others should be much lower. The results indicate that opt-in filtering results in lower accuracy for all attributes, those that were filtered out but also those that were not. Additionally, filtered accuracy still does not reach random values. We hypothesize that this could be due to two reasons. The first is that some information is still captured in the residual code, as such leaving this residual unchanged results in some data leakage. The second is that there is some information overlap in the different factors due to naturally occurring correlations. As a result, filtering out one correlated attribute but not the other allows some data leakage. We will extensively investigate these two causes in Section \ref{sec:investigations}.
\section{Investigating the causes of imperfect filtering}
\label{sec:investigations}
\subsection{Correlations between facial attributes}
\label{sec:corr}
In the previous sections, we assumed that ZeroDIM could disentangle the various face attributes perfectly. However, this is not realistic as there will always be some entanglement between attributes that are related in nature. For example, men are more likely to have facial hair than women and older people are more likely to have glasses than children. As stated in the last section, we assume this affects filtering as filtering out one attribute might still leave it deducible by using others.
To identify the effect of these natural relations on filtering, we start by mapping the correlation between the different facial attributes. As these are categorical variables, we utilize Cramér's V~\cite{cramer2016mathematical} and the uncertainty coefficient~\cite{theilEstimationRelationshipsInvolving1970}. Both of these give insights into the correlation of discrete values.
\subsubsection{Cramér's V}
Cramér's V~\cite{cramer2016mathematical} is a metric for the correlation of categorical values based on Pearson's chi-squared statistic. It is symmetric and varies from 0 to 1. Cramér's V is defined as follows, with $\chi^2$ being Pearson's chi-squared test on the contingency table of $X$ and $Y$, $n$ the amount of samples, and $k$ and $r$ the number of categories of $X$ and $Y$ respectively:
\begin{equation}
V(X,Y) = \sqrt{\frac{\frac{\chi^2}{n}}{min(k-1, r-1)}}
\end{equation}
Interpretation of the values is dependent on the number of degrees of freedom. A Cramer's V score of $0.15$ signifies a medium correlation when there are four degrees of freedom and only a small to medium correlation when fewer. A categorization can be found in Table \ref{tab:cramerv_cat}.
\begin{table}[h]
\centering
\caption{Categorisation of Cramér's V correlations based on the degrees of freedom}
\begin{tabular}{*4c}
\toprule
Degrees of freedom & Small & Medium & Large\\ \midrule
1 & 0.10 & 0.30 & 0.50 \\
2 & 0.07 & 0.21 & 0.35 \\
3 & 0.06 & 0.17 & 0.29 \\
4 & 0.05 & 0.15 & 0.25 \\
5 & 0.04 & 0.13 & 0.22 \\ \bottomrule
\end{tabular}
\label{tab:cramerv_cat}
\end{table}
\subsubsection{Uncertainty coefficient}
The second metric we use is the Uncertainty Coefficient or Theil's $U$~\cite{theilEstimationRelationshipsInvolving1970}, which is based on information theory. With $H$ as entropy and $I$ mutual information, we can define the uncertainty coefficient $U$ for $X$ given $Y$ as follows:
\begin{equation}
U(X|Y) = \frac{H(X) - H(X|Y)}{H(X)} = \frac{I(X;Y)}{H(X)}
\end{equation}The uncertainty coefficient is asymmetric and returns values between 0 and 1. Its information theoretical nature allows for intuitive interpretation. $U(X|Y)$ is the relative amount of information of $X$ we can infer from $Y$. Alternatively, knowing $Y$ results in a $U(X|Y)$ per cent reduction of uncertainty for $X$.
\begin{figure}[h]
\centering
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[scale=0.27]{ffhq-cramer.pdf}
\caption{Cramér's V}
\label{fig:cramer}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[scale=0.27]{ffhq-theil.pdf}
\caption{Uncertainty coefficient}
\label{fig:uncertainty}
\end{subfigure}
\caption{Correlation matrices of the different facial factors using the Cramér's V and uncertainty coefficient metrics. Both have a range of 0 to 1 where higher values indicate more correlation between both factors. In the case of the uncertainty coefficient, one should read it as $U(row|column)$. For Cramér's V the number between parentheses indicates the degrees of freedom.}
\label{fig:correlations}
\end{figure}
Using these metrics, we calculated the correlations between all different facial attributes of images in the FFHQ dataset using the predictions of the pre-trained classifiers included in ZeroDIM. The results can be seen in Figure \ref{fig:correlations}. The figure on the left shows the result of Cramér's V score. For each different attribute, we show the degrees of freedom (number of classes - $1$ ). These can be used in conjunction with Table \ref{tab:cramerv_cat} to classify the strength of the correlation. Note that, for a given combination of two attributes, we should use the minimum of the degrees of freedom. For example, the minimum degrees of freedom of glasses and gender is $1$, while their correlation is $0.12$. Indicating that the relation between these two attributes is small according to Table \ref{tab:cramerv_cat}. Based on this categorisation, we can identify four medium strength relations of the non-diagonal elements in Figure \ref{fig:cramer}: age and gender, ethnicity and hair color, hair color and gender, and hair color and age. The first relation seems less intuitive than the latter three since gender and age have no direct correlation regarding appearance. However, this might be attributed to inherent biases or imbalances in the dataset.
For the uncertainty coefficient results in Figure \ref{fig:uncertainty} similar conclusions arise, although the asymmetrical nature shows some interesting results. For example, knowing one's age gives less information about one wearing glasses as vice versa.
\subsection{The effects of correlation on filtering}
\label{sec:corr_and_filter}
To assess whether the correlation between attributes affects filtering quality we related the results of Section \ref{sec:filtering} to those of Section \ref{sec:corr}. This was done by testing the linear correlation between the accuracy difference (i.e., the accuracy of Y without filtering - the accuracy of Y when filtering X) and the correlation between X and Y. For an opt-out operation, we expect the relationship to be positive: when two attributes are related and we filter one, the other should drop in accuracy. The inverse hypothesis holds for opt-in. If we keep an attribute that is heavily related to the other, the drop in accuracy should be lower.
\begin{table}
\centering
\caption{Regression plots indicating the relation between the drop in accuracy of Y when filtering X and the correlation of X and Y. A plot is shown for each combination of the correlation metric and filtering mode}
\begin{tabular}{l C C}
\toprule
& Opt-out & Opt-in \\
\midrule
Cramér's V & \includegraphics[width=0.4\textwidth]{corr_relation_1.pdf} & \includegraphics[width=0.4\textwidth]{corr_relation_2.pdf} \\
\shortstack{Uncertainty \\ coefficient} & \includegraphics[width=0.4\textwidth]{corr_relation_3.pdf} & \includegraphics[width=0.4\textwidth]{corr_relation_4.pdf} \\
\bottomrule
\end{tabular}
\label{tbl:cor_rel}
\end{table}
Table \ref{tbl:cor_rel} shows the result of our experiment for the Cramér's V and uncertainty coefficient metrics in both opt-out and opt-in. Each point of the figures corresponds to the combination of two attributes (e.g., age and glasses). The x-axis shows the correlation between the two attributes and the y-axis shows the drop in accuracy. We also show the Pearson's correlation coefficient $r$, to measure the nature of the correlation. A value of $0$ would indicate perfectly uncorrelated values, while $-1$ and $1$ indicate perfect negative or positive correlations. Additionally, we calculate the two-tailed $p$-value, which is defined as the probability of an uncorrelated dataset producing this Pearson correlation coefficient. A p-value lower than $0.05$ is generally accepted as statistically significant. These results show that we indeed observe the expected relation between correlation and accuracy drop. Although, the results are not statistically significant enough to make any strong conclusions.
\iffalse
\begin{figure}[h]
\centering
\includesvg[width=0.8\textwidth]{corr_relation_normal}
\caption{Regression plot indicating the relation between the drop in accuracy of Y when filtering X and the correlation of X and Y. In these cases the residual code \textbf{was not} filtered.}
\label{fig:corr_rel_norm}
\end{figure}
\begin{figure}[h]
\centering
\includesvg[width=0.8\textwidth]{corr_relation_residual}
\caption{Scatterplot indicating the relation between the drop in accuracy of Y when filtering X and the correlation of X and Y. In these cases the residual code \textbf{was} filtered.}
\label{fig:corr_rel_norm_res}
\end{figure}
\fi
\subsection{Residual code}
\label{sec:res}
In Section \ref{sec:filtering} we noticed that the accuracy of filtered attributes remained better than random. A likely cause is that some attribute information is still entangled in the residual code. To determine whether this holds true we repeat the experiment of Section \ref{sec:filtering} with filtered residuals. We chose to filter residual codes by swapping them with those of other images in the dataset to ensure good generation quality by keeping the code in the correct domain. This is in essence true opt-in filtering as no other information than the factor is passed through unchanged. The results of this experiment are visible in Figure \ref{fig:acc_residual}.
\iffalse
\begin{figure}[h]
\centering
\makebox[\textwidth][c]{\includesvg[width=1.2\textwidth]{acc_res.svg}}
\caption{}
\label{fig:acc_residual}
\end{figure}
\fi
\begin{figure}[h]
\centering
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.0\textwidth]{acc_res1.pdf}
\caption{Opt-out}
\label{fig:acc-res-oo}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width=1.0\textwidth]{acc_res2.pdf}
\caption{Opt-in}
\label{fig:acc-res-oi}
\end{subfigure}
\caption{Relative accuracy of filtering when using an opt-out or opt-in configuration on a specified attribute with filtering of the residual codes. Rows indicate the attribute that was filtered, and columns the attribute that was classified.}
\label{fig:acc_residual}
\end{figure}
Figure \ref{fig:acc_residual} indicates that the residual code affects filtering. Unsurprisingly, removal results in large reductions of accuracy for both the allowed and disallowed attributes. The accuracy of disallowed attributes is now closer to random accuracy. However, those of allowed attributes deteriorated significantly as well, especially when working in an opt-in configuration. These results indicate a clear privacy-utility trade-off.
\section{Generalisation of filtering to unseen attributes}
\label{sec:non_factorized}
As a final study, we report on the effects of filtering on non-disentangled attributes. Say, for example, you want to filter out a person's age in an opt-out manner. In principle, this should still allow you to infer that person's gender or hair color, but it also should pass through facial expressions and other non-age attributes that the filter was not explicitly trained to remove/retain. To highlight the effects of the inclusion of an attribute to filtering, we trained an additional ZeroDIM model, where emotion is included as one of the disentangled attributes. We then evaluated emotion recognition accuracy for every filtering configuration and compared the model's results with and without emotion. We use DAN~\cite{wenDistractYourAttention2021} as our emotion recognition model, which was pre-trained on the AffectNet~\cite{mollahosseiniAffectNetDatabaseFacial2019} dataset. For evaluation, we use the RAVDESS dataset~\cite{livingstoneRyersonAudioVisualDatabase2018}. On unaltered frames, DAN can achieve an accuracy of $72.45\%$. The results on filtered frames can be seen in Figure \ref{fig:emotions}.
\begin{figure}[h]
\centering
\begin{subfigure}[b]{.5\textwidth}
\centering
\includegraphics[width=1.0\textwidth]{emotion1.pdf}
\caption{Opt-out}
\label{fig:emotion-oo}
\end{subfigure}%
\begin{subfigure}[b]{.5\textwidth}
\centering
\includegraphics[width=1.0\textwidth]{emotion2.pdf}
\caption{Opt-in}
\label{fig:emotion-oi}
\end{subfigure}
\caption{Emotion accuracy when filtering other attributes using a ZeroDIM model that included emotion as an attribute and one that did not.}
\label{fig:emotions}
\end{figure}
\iffalse
\begin{figure}[h]
\centering
\makebox[\textwidth][c]{\includesvg[width=1.2\textwidth]{emotion.svg}}
\caption{Emotion accuracy when filtering other attributes using a ZeroDIM model that included emotion as an attribute and one that did not.}
\label{fig:emotion}
\end{figure}
\fi
The opt-out results indicate only a slight difference between the model with and without emotion. This leads us to believe that emotion is captured well in the residual code when not specified as a disentangled attribute. In the opt-in setting, we see clearly that we can retain the emotion better when emotion is included as a classifier. When removing emotion, results are again very similar between the two models. However, if an opt-in configuration is needed the model with the attribute included performs significantly better.
\section{Discussion and conclusion}
\label{sec:conclusion}
This paper proposed the use of the state-of-the-art image manipulation model ZeroDIM for filtering face images and studied the implications of natural correlations and residual information on filtering. The findings of this study suggest that image editing is a promising option for both opt-in and opt-out configurations. While the results were positive, we noticed accuracy of filtered attributes was not yet perfectly random. We hypothesized that this was due to two main causes.
The first is that some attributes are naturally correlated, making it so you cannot filter out one while keeping the other. While we were able to verify correlations between the facial attributes, the results of our experiment were not concise enough to draw any conclusions as to what effects these have on filtering. Further research is thus necessary to confirm or deny our hypothesis.
The second cause we identified is in the use of the residual code. We confirmed that removing this code led to better filtering. However, it also resulted in lower classification accuracy for all other attributes indicating a privacy-utility trade-off. We could attribute this to the strength of disentanglement as some attribute information clearly remains entangled in the residual code. Though another possibility is that the generator has some implicit dependencies between residual codes and factor codes making modification of the residual incompatible. A possible solution for this would be to create a general residual that allows good generation when swapping codes. This problem of excess information in the residual code becomes highlighted as we found it can capture non-disentangled elements such as emotion quite well.
\section{Future work}
\label{sec:future}
Future work will focus on tackling the investigated limitations of filtering: correlations between the attributes, and residual information. Firstly, we will further investigate the limits correlated attributes put on filtering and how this information can be incorporated to improve filtering. Secondly, we aim to improve the disentanglement of the residual code from the predefined attributes. By doing so, we can decrease information leakage. Furthermore, we aim to investigate the use of a general residual code for filtering.
To better integrate our application in real-world scenarios, we would further focus on three key aspects: compatibility with third-party API's, eligibility for edge-based cameras, and extension to video data. We would verify if the filtered images can be compatible with existing API's and models such as the Microsoft Face API and FairFace~\cite{karkkainenFairfaceFaceAttribute2021} model. Suitability for resource-constrained devices would be ensured by reducing the computational cost of our filter and investigating its usage in trusted execution environments. Lastly, we plan to expand our technique to video footage and analyze the implications on privacy when a filter operation is performed over multiple frames.
\section*{Acknowledgments}
This research received funding from the Flemish Government under the ``Onderzoeksprogramma Artifici\"ele Intelligentie (AI) Vlaanderen'' programme.
\bibliographystyle{splncs04}
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public class Main {
interface Account {}
public static void main(String[] args) {
java.util.List list;
for (int i = 0; i < list.size(); i++) {
Object o = (Account<caret>list.get(i);
System.out.println(o);
}
}
}
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\section{Introduction}
The diffusion of Brownian particles can be used to access microscopic properties of the medium in which their propagation takes place. Historically, the diffusion of small grains in water was used by Perrin to prove the atomic structure of matter and to provide a first estimate of the Avogadro number, finding ${\cal N}_A\approx 5.5-7.2\cdot 10^{23}$~\cite{Perrin:1926}. Nowadays, one of the goals of heavy-ion collisions is to exploit the \emph{relativistic} Brownian motion of heavy quarks to get an estimate of comparable accuracy of medium properties like the \emph{momentum broadening coefficient} $\kappa$. An important difference in this case is that the nature of the Brownian particle changes during its propagation, since after a few fm/c it undergoes hadronization. This introduces a source of systematic uncertainty in the extraction of transport coefficients; on the other hand it can be considered an issue of interest in itself, in particular to study how hadronization changes in the presence of a medium acting as a color reservoir. This, in the case of charm quarks, will be the subject of our study, carried out to provide an interpretation of non-trivial results concerning heavy-flavor hadrochemistry in heavy-ion collisions, but with the potential to shed light also on analogous puzzling findings obtained in smaller systems~\cite{ALICE:2020wfu}.
\section{The model}\label{Sec:model}
\begin{figure*}
\centering
\includegraphics[clip,width=0.48\textwidth]{mass-distribution.pdf}
\includegraphics[clip,width=0.48\textwidth]{mass-distribution_mixev.pdf}
\caption{Left panel: the invariant-mass distribution of the $Q\overline q$ and $Q(qq)$ clusters on the hadronization hypersurface in the different isospin, strangeness and spin channels. Right panel: cluster invariant-mass distributions with recombination occurring locally (continuous curves, default implementation), with strong correlation between the parton momenta and position, or non-locally (dashed curves), with no space-momentum correlation. All results refer to central Pb-Pb collisions at $\sqrt{s_{\rm NN}}\!=\!5.02$ TeV, with charm quark propagation before hadronization simulated using weak-coupling (HTL) transport coefficients.}
\label{fig:Mdistr}
\end{figure*}
Any hadronization model must start clustering colored partons into color-singlet structures which will give rise to the final hadrons. In proton-proton collisions partons are taken from the hard process, from the shower stage, from the underlying event and from the beam remnants. In heavy-ion collisions recombining partons are taken from the hot deconfined plasma produced in the collision and they are \emph{close in space} (the Debye radius sets the maximum distance at which two colored partons are correlated): since the fireball undergoes a collective expansion, this last detail has deep phenomenological consequences.
We now briefly describe our model for in-medium charm hadronization. For more details we refer the reader to our original publication~\cite{Beraudo:2022dpz}.
Once a $c$ quark, during its stochastic propagation through the fireball, reaches a fluid cell at $T_H=155$ MeV it recombines with a
light antiquark or diquark from the same fluid element. Both the species and the momentum of the medium particle are sampled assuming they obey a thermal distribution in the local rest frame (LRF) of the fluid. The thermal particle is then boosted to the laboratory frame and recombined with the charm quark, leading to the formation of the cluster ${\cal C}$. Since the $c$ quark and the thermal particle are taken from the same fluid cell undergoing a collective flow, typically their momenta are quite collinear and correlated to the position they occupy (Space-Momentum Correlation). This leads to the production of quite low invariant-mass clusters, as one can see from the left panel of Fig.~(\ref{fig:Mdistr}). We also check that, suppressing this SMC by randomly redistributing the HQ's on the decoupling hypersurface (see right panel of Fig.~\ref{fig:Mdistr}), the production of heavier clusters is favored.
As in Herwig~\cite{Webber:1983if}, one treats differently light and heavy clusters. Clusters with $M_{\cal C}<M_{\rm max}\approx 4$ GeV undergo an isotropic two-body decay in their LRF, giving rise to a charmed hadron and a second soft particle; the very rare heavier clusters are fragmented into multiple hadrons as Lund strings~\cite{Andersson:1983ia}.
\section{Results}\label{Sec:results}
\begin{figure*}
\centering
\includegraphics[clip,width=0.98\textwidth]{CharmHadrons-RatiosVsPt_HTLvsLat_3050-VsData.pdf}
\caption{Predictions for the relative yields of charmed hadrons (relative to $D^0$ mesons) in semi-central Pb-Pb collisions at $\sqrt{s_{\rm NN}}\!=\!5.02$ TeV for different transport coefficients compared to recent ALICE data~\cite{ALICE:2021bib,ALICE:2021kfc,ALICE:2021rxa}.}\label{Fig:D-Ds-Lc}
\end{figure*}
Interfacing our new hadronization model to numerical simulations of heavy-quark transport in the deconfined fireball one can obtain a satisfactory description of important and partially unexpected experimental findings, in particular the strong enhancement of charmed-baryon production recently observed in heavy-ion~\cite{ALICE:2021bib} and also in proton-proton collisions~\cite{ALICE:2020wfu}, which cannot be explained by any hadronization model tuned to reproduce $e^+e^-$ data.
An example of our results is given in Fig.~\ref{Fig:D-Ds-Lc}, where we plot as a function of $p_T$ the $D^+/D^0$, $D_s^+/D^0$ and $\Lambda_c^+/D^0$ ratios in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV, comparing our predictions to recent ALICE data~\cite{ALICE:2021bib,ALICE:2021kfc,ALICE:2021rxa}. Notice that if hadronization occurred as in $e^+e^-$ collisions one would get $\Lambda_c^+/D^0\approx 0.1$. As one can see the strong enhancement of the $\Lambda_c^+/D^0$ ratio for intermediate values of $p_T$ is correctly reproduced. Analogous results are obtained when our model is compared to STAR data for Au-Au collisions at $\sqrt{s_{\rm NN}}=200$ GeV~\cite{STAR:2019ank}.
\begin{figure*}
\centering
\includegraphics[clip,height=6cm]{CharmHadrons-RatiosVsPt_CentBins.pdf}
\includegraphics[clip,height=6cm]{CharmHadrons-v2_lQCD.pdf}
\caption{Charmed hadron ratios (left panel, with weak-coupling transport coefficients) and elliptic flow (right panel, with l-QCD transport coefficients) as a function of $p_T$ in Pb-Pb collisions at $\sqrt{s_{\rm NN}}\!=\!5.02$ TeV.}\label{Fig:hc-vs-pt}
\end{figure*}
In Fig.~\ref{Fig:hc-vs-pt} we extend our analysis to the yields and kinematic distributions of all ground-state charmed hadrons obtained with our new hadronization procedure. As one can see from the left panel, as a result of the larger radial flow of the thermal diquarks, going from more peripheral to more central collisions the peak in the charmed baryon/meson ratio moves to higher values of $p_T$. On the other hand, integrating the respective momentum distributions, one would find that the fragmentation fractions of charm quarks into the different hadrons is independent both of the collision centrality and of the transport coefficients affecting their propagation in the deconfined fireball: hence, in the left panel of Fig.~\ref{Fig:hc-vs-pt} one simply observes a reshuffling of the charmed hadron momenta. In the right panel of Fig.~\ref{Fig:hc-vs-pt} we study the effect of hadronization on the charmed-hadron elliptic flow. Up to $p_T\approx 3$ GeV one clearly observes a mass-ordering of the $v_2$, with two distinct bands for the charmed mesons and baryons, and an inverted hierarchy at higher momenta. This behavior in our model has to be attributed to the different masses of the thermal quarks and diquarks with which recombination takes place.
\begin{figure*}
\centering
\includegraphics[clip,height=6cm]{Lambdac-D0_SMC.png}
\includegraphics[clip,height=6cm]{CharmHadronsQuarks-v2-HTL-mixev.pdf}
\caption{Charmed-hadron ratios (left panel) and elliptic flow (right panel) with (dashed blue curves) and without (dotted brown curves) space-momentum correlation. The last case is obtained mixing momentum and position of heavy quarks from different events on the hadronization hypersurface.}\label{Fig:yields-noSMC}
\end{figure*}
We already discussed the relevance of SMC to reproduce the correct yields and kinematic distributions of charmed hadrons. The importance of SMC can be accessed by artificially breaking the connection between the position and the momentum of the hadronizing particles. This can be implemented by randomly redistributing the quarks undergoing recombination over the hadronization hypersurface. The effect on the final charmed hadrons is shown in Fig.~\ref{Fig:yields-noSMC}: the $\Lambda_c^+/D^0$ ratio is no longer enhanced, but one finds a value around 0.1, as in $e^+e^-$ collisions; furthermore the charmed hadron $v_2$ is lower, very similar to the one of the parent heavy quarks. Recombining partons are no longer collinear: this suppresses the collective flow of the clusters and increases their invariant mass, leading them to hadronize via string fragmentation, with no enhanced baryon production.
\begin{figure*}
\centering
\includegraphics[clip,width=0.46\textwidth]{pp-MPI.pdf}
\hspace{0.3cm}
\includegraphics[clip,width=0.46\textwidth]{pp-MPI-CR.pdf}
\caption{Strings stretched between outgoing partons in a schematic hadronic collision before (left panel) and after (right panel) Color-Reconnection.}\label{Fig:CR}
\end{figure*}
Finally, we wish to discuss the common features of our hadronization mechanism with other models implemented, both recently and in the far past, in QCD event generators to reproduce experimental data. First of all, notice that the formation of low invariant-mass strings which can only decay into two particles or even collapse into a single charmed hadron was the crucial ingredient to explain, within the PYTHIA framework~\cite{Norrbin:1998bw}, asymmetries in $D^-/D^+$-meson production in $\pi^-$-proton collisions as a function of rapidity~\cite{E769:1993hmj}. Analogous studies were performed for other particle ratios and colliding systems. The only difference with our model is that charm quarks are recombined with light partons belonging to the beam remnant, while in our case they are taken from the hot medium produced in the nuclear collision.
More recently, changes in the heavy-flavor hadrochemistry in proton-proton collisions, with for example an enhanced production of charmed baryons~\cite{ALICE:2020wfu}, were interpreted as due to Color Reconnection~\cite{Christiansen:2015yqa}. The mechanism of CR is schematically illustrated in Fig.~\ref{Fig:CR}, where in the left panel we draw the strings constructed following the color-flow of the event in the large-$N_c$ approximation. However this is not necessarily the energetically most convenient configuration. Strings are extended objects and, when they are stretched in the same small region, they can overlap and interact rearranging their endpoints as shown in the right panel, if this leads to a decrease of their invariant mass. In particular, this occurs if the final strings connect more collinear partons than in the initial configuration. But this is exactly what happens in our model, which can be seen as an extreme example of CR, in which the interaction with the medium leads partons to break the color connections arising from the initial production and to recombine with nearby companions from the same fluid cell, with quite collinear momenta due to the previously discussed SMC's. Hence, the next natural step is to extend our model to describe hadronization also in proton-proton collisions, assuming that also in this case a small fireball is formed. From the latter one can extract the thermal light partons with which the charm quarks are recombined at hadronization. This is currently work in progress.
\bibliographystyle{JHEP}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 7,981
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'use strict';
var grunt = require('grunt');
/*
======== A Handy Little Nodeunit Reference ========
https://github.com/caolan/nodeunit
Test methods:
test.expect(numAssertions)
test.done()
Test assertions:
test.ok(value, [message])
test.equal(actual, expected, [message])
test.notEqual(actual, expected, [message])
test.deepEqual(actual, expected, [message])
test.notDeepEqual(actual, expected, [message])
test.strictEqual(actual, expected, [message])
test.notStrictEqual(actual, expected, [message])
test.throws(block, [error], [message])
test.doesNotThrow(block, [error], [message])
test.ifError(value)
*/
var request = require('request');
exports.couchdb = {
setUp: function(done) { done(); },
document: function(test) {
test.expect(1);
request.get('http://localhost:5984/cars/d4',function( err, response, body){
var attachments = JSON.parse(body)._attachments;
test.equal("text/javascript", attachments["js/app.js"] .content_type,'js file in correct path with content type');
test.done();
});
},
app_js: function(test) {
test.expect(1);
request.get('http://localhost:5984/cars/d4/js/app.js',function( err, response, body){
test.equal('text/javascript', response.headers['content-type'] , 'js file in correct path with content type');
test.done();
});
},
};
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 7,459
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\section{#1}}
\renewcommand{\theequation}{\arabic{section}.\arabic{equation}}
\section{Introduction}
\setcounter{equation}{0}
The spacetime dimensions $D=3,4,6$ have the special property that there is an extension of the conformal group, available for all $D$, to a superconformal group \cite{Nahm:1977tg}. This is relevant to massless supersymmetric field theories, and free field theories of this type arise from quantization of the massless superparticle \cite{Brink:1981nb,Siegel:1983hh}, which is superconformal invariant precisely in dimensions $D=3,4,6$. The superconformal invariance of the massless superparticle action can be made manifest by a formulation \cite{Shirafuji:1983zd,Bengtsson:1987si}
in which the phase space is parametrized by a supertwistor \cite{Ferber:1977qx}. Spin-shell constraints then replace the usual mass-shell constraint, ensuring that the physical phase space dimension is unchanged, and also that the superparticle describes (upon quantization) a supermultiplet of zero super-helicity.
Although the action for a {\it massive} particle cannot be conformal invariant, the massive superparticle \cite{Casalbuoni:1976tz} still has a supertwistor formulation in dimensions $D=3,4,6$ (which we abbreviate to 3D etc.) but now the phase superspace is parametrized by {\it two} supertwistors. The necessity of doubling the twistor phase space was initially discovered in the context of the twistor approach to solutions of massive wave equations \cite{Hughston:1981zc}. One expects to recover such results by covariant quantization of the twistor formulation of corresponding massive particle mechanics models, which is our focus here.
The twistor formulation of at least some massive particle mechanics models may be found indirectly by ``dimensional reduction'' of known twistor formulations of massless particle mechanics models in a higher dimension; in this context, ``dimensional reduction'' amounts to the incorporation of a constraint on the particle's momentum in the extra dimensions. This naturally leads to a doubled twistor phase space in the lower dimension because (i) a twistor is a spinor of the conformal group \cite{Penrose:1986ca}, which decomposes into a pair of spinors of the lower-dimensional conformal group, and (ii) the conformal invariance in the lower dimension is broken only by the additional momentum constraint, which has no influence on the nature of the phase space.
This construction was first used in \cite{deAzcarraga:2008ik}: the supertwistor formulation of the massive 4D superparticle was found by reduction of the known supertwistor formulation of the massless 6D superparticle. In an earlier article, we reviewed and extended the known results on this topic \cite{Mezincescu:2013nta}, and two of us have recently found (by a direct method) a supertwistor formulation of the massive 6D superparticle \cite{Routh:2015ifa}. As explained in that work, the combined results for the $D=3,4,6$ massive superparticle fit nicely with the idea \cite{Kugo:1982bn,Sudbery:1983} that properties of supersymmetric theories in spacetime dimensions $D=3,4,6,10$ are related to the division algebras $\bb{R},\bb{C},\bb{H},\bb{O}$.
It has been known for a long time \cite{Townsend:1991sj} that there is also a supertwistor formulation of the 4D massless ``spinning particle'' \cite{Brink:1976sz,Brink:1976uf}, which has local worldline supersymmetry rather than global spacetime supersymmetry. The spinning particle action in supertwistor variables is remarkably similar to that of the superparticle but the spin-shell constraints are slightly different, breaking superconformal invariance to conformal invariance and leading to a quantum theory with states of a spin-1/2 particle rather than a spacetime supermultiplet. This result was generalized in \cite{Mezincescu:2013nta} to the ${\cal N}$-extended massless 4D spinning particle \cite{Gershun:1979fb,Howe:1988ft}, which describes a particle of spin $\frac{1}{2}{\cal N}$, and the results were then used to find analogous results for the {\it massive} 3D spinning particle. However, the constructions underlying these results do not appear to apply more generally.
In this paper we present a twistor formulation of the massive spinning particle in $D=3,4,6$, for any ${\cal N}$. Our 3D results duplicate those of \cite{Mezincescu:2013nta} but our improved construction generalizes to both 4D and 6D. We say ``twistor'' rather than supertwistor because the anticommuting phase-space variables turn out to be different (for $D=4,6$) from those of the superparticle. Implicit in our results is a twistor formulation of the {\it massless} spinning particle for $D=3,4,6$. We present the details for $D=3$, showing how conformal invariance is recovered in the massless limit. For $D=4$
the analogous final result differs slightly from \cite{Townsend:1991sj} because the starting point there was the standard form of the massless spinning particle, which differs from what one gets by taking the zero-mass limit of the standard massive spinning particle action.
The main point of our twistor reformulation of massive ``spinning particle'' mechanics is that {\it the twistor variables are gauge invariant with respect to local worldline supersymmetry}. New gauge invariances are introduced, but not ``fermionic'' ones, which means that all twistorial anticommuting variables are physical; they appear in the action in exactly the same way that they would in the analogous {\it non-relativistic} action! This feature simplifies the determination of some properties of the quantum theory, in particular for the ${\cal N}$-extended spinning particle.
For ${\cal N}>2$ it is known (and we confirm) that the massive spinning particle model is inconsistent for even $D$ because of a global anomaly. This follows, as pointed out in \cite{Howe:1989vn}, from a global anomaly exhibited there for the massless ${\cal N}>2$ superparticle in odd $D$. This problem can be evaded for ${\cal N}=2$ because in this case it is possible to cancel the anomaly by adding a worldline Chern-Simons (WCS) term with half-integral coefficient \cite{Howe:1989vn}. We use our results to confirm that the ${\cal N}=2$ massive 4D superparticle describes either a spin-zero or a spin-one particle depending on the choice of WCS coefficient.
We should mention here that our initial motivation for considering twistor formulations of massive particle mechanics models was a similarity to twistor formulations of the Nambu-Goto
string \cite{Shaw:1986dq,Cederwall:1989su}. In both cases a doubling of the twistor phase space is needed (compared to a massless particle). The constructions described here for the
massive spinning particle may therefore be useful in any future attempt to find a twistor formulation of the spinning string.
We begin with a summary of the ${\cal N}$-extended spinning particle action in arbitrary spacetime dimension $D$. We then proceed to its twistor formulation
for $D=3,4,6$, dealing sequentially with these dimensions. For 3D we discuss only the ${\cal N}=1$ case; this suffices to introduce the new construction
and some generic features of our spinor conventions. For 4D we first discuss the ${\cal N}=1$ case and then generalize to ${\cal N}>1$, using the results to discuss the quantum theory. For 6D we take over some results of \cite{Routh:2015ifa} for the bosonic particle, making explicit some conventions implicit in that work, and then present the twistor form of the massive spinning particle. We conclude with a discussion of some general features of our results.
Finally, we include an appendix in which the supertwistor form of the 4D superparticle action is found in the conventions of this paper. This is essentially a more elegant version of previous results but we also keep track of the sign of the energy in the solution to the mass-shell constraint in order to illustrate an important difference between spinning particles and superparticles.
\section{Spinning particle preliminaries}
\setcounter{equation}{0}
For any spacetime dimension, the phase-space action for the minimal massive spinning particle, with ${\cal N}=1$ worldline supersymmetry, is
\begin{equation}
\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! S= \int \! dt\left\{ \dot X^m P_m + \frac{i}{2}\lambda^m\dot\lambda_m + \frac{i}{2}\xi\dot \xi - \frac{1}{2} e\left(P^2+m^2\right) + i\zeta \left(\lambda^m P_m +m\xi\right)\right\}\, .
\end{equation}
We use here, and throughout the paper, the Minkowski metric with ``mostly plus'' signature.
The canonical variables $(\lambda^m,\xi)$ are anticommuting, as is the Lagrange multiplier $\zeta$. The Hamiltonian constraints are both first class, and they generate the gauge transformations
\begin{equation}
\delta X^m = a P^m -i\epsilon\lambda^m \, , \qquad
\delta \lambda^m = P^m \epsilon \, , \qquad
\delta\xi= m\epsilon\, ,
\end{equation}
for commuting parameter $a(t)$ and anticommuting parameter $\epsilon(t)$. The action is invariant if the Lagrange multipliers are assigned the transformations
\begin{equation}
\delta e= \dot a -2i\epsilon\zeta\, , \qquad \delta\zeta = \dot\epsilon\, .
\end{equation}
This model describes, upon quantization, a massive spin-1/2 particle \cite{Brink:1976uf}, the fermionic constraint becoming the Dirac equation when imposed as a physical state condition.
Notice that the bosonic phase space is spanned by two $D$-vectors subject to one first-class constraint, to which we must add one anticommuting $D$-vector and one anticommuting scalar that are also subject to one first-class constraint. This leads to a physical phase superspace with graded dimension $(2D-2|D-1)$.
If one takes the $m=0$ limit of the above results then one arrives at the action
\begin{equation}\label{masslessact}
\!\!\!\!\!\!\! S= \int \! dt\left\{ \dot X^m P_m + \frac{i}{2}\lambda^m\dot\lambda_m + \frac{i}{2}\xi\dot \xi - \frac{1}{2} e\, P^2 + i\zeta \, \lambda^m P_m \right\}\, .
\end{equation}
We could omit the $\xi\dot\xi$ term because $\xi$ is now inert under the local worldline supersymmetry, and it has dropped out of the constraints. Indeed, this term {\it is} omitted from the standard ``massless spinning particle'' action, but omitting it introduces a discontinuity into the massless limit of the massive spinning particle.
The ${\cal N}$-extended massive spinning particle is constructed by incorporating more anticommuting variables. Specifically, we make the replacement
\begin{equation}
\lambda^m \to \lambda^m_a\, , \quad \xi \to \xi_a\, , \quad \zeta\to \zeta_a \, \qquad \left(a=1,\dots,{\cal N}\right)\, ,
\end{equation}
and then gauge the resulting $SO({\cal N})$ symmetry by including additional Hamiltonian constraints, imposed by means of a new commuting antisymmetric $SO({\cal N})$-tensor Lagrange multiplier $f_{ab}$. The resulting action is \cite{Gershun:1979fb,Howe:1988ft}
\begin{eqnarray}
S &=& \int \! dt\Big\{ \dot X^m P_m + \frac{i}{2}\lambda_a \cdot \dot\lambda_a + \frac{i}{2}\xi_a\dot \xi_a - \frac{1}{2} e\left(P^2+m^2\right) + i\zeta_a \left(\lambda_a\cdot P +m\xi_a\right) \nonumber \\
&& \qquad \qquad \qquad -\, i f_{ab} \left(\lambda_a \cdot \lambda_b + \xi_a\xi_b\right)\Big\}\, ,
\end{eqnarray}
where summation over the $SO({\cal N})$ indices is implicit. This action has a local $SO({\cal N})$ gauge invariance in addition to its ${\cal N}$ local
worldline supersymmetries.
The ${\cal N}=2$ case is special because then $f_{ab}\propto \epsilon_{ab}f$ with an $SO(2)$ transformation of $f$ that is a total derivative,
allowing us to add to the action a term linear in $f$; this is the worldline Chern-Simons term. We now have the action
\begin{eqnarray}
S &=& \int \! dt \Big\{ \dot X^m P_m + \frac{i}{2}\lambda_a \cdot \dot\lambda_a + \frac{i}{2}\xi_a\dot \xi_a - \frac{1}{2} e\left(P^2+m^2\right) + i\zeta_a \left(\lambda_a\cdot P + m\xi_a\right) \nonumber \\
&& \qquad\qquad\qquad - f\left[ \epsilon^{ab} \left(\lambda_a \cdot \lambda_b + \xi_a\xi_b\right) -c\right] \Big\}\, ,
\end{eqnarray}
where the constant $c$ is the coefficient of the WCS term; it is quantized in the quantum theory with choices that lead to a particle mechanics description of massive $p$-form fields for some integer $p$ \cite{Howe:1989vn}.
\section{Massive 3D spinning particle}
\setcounter{equation}{0}
We shall use a notation in which spacetime vectors are bi-spinors of $Sl(2;\bb{R})$. We spell out our conventions here because some important features
that carry over to 4D and 6D are simpler to discuss for 3D. We start from the real $2\times2$ Dirac matrices\footnote{This differs slightly from the choice made in \cite{Mezincescu:2013nta}.}
\begin{equation}\label{gamma}
\left(\gamma^0\right)^\alpha{}_\beta = i\sigma_2 \, , \qquad \left(\gamma^1\right)^\alpha{}_\beta = \sigma_3\, , \qquad \left(\gamma^2\right)^\alpha{}_\beta =-\sigma_1\, .
\end{equation}
These matrices satisfy the identities
\begin{equation}
\left(\gamma^m\right)^\alpha{}_\beta \left(\gamma_m\right)^\gamma{}_\delta \equiv 2\delta^\alpha_\delta\delta^\gamma_\beta - \delta^\alpha_\beta\delta^\gamma_\delta \, , \qquad \left(\gamma^m\right)^\alpha{}_\beta\left(\gamma^n\right)^\beta{}_\alpha \equiv 2\eta^{mn}\, ,
\end{equation}
where $\eta$ is the (mostly plus) Minkowski metric. Spinor indices will be raised or lowered by means of the alternating invariant tensor $\varepsilon$ of $Sl(2;\bb{R})$,
using the conventions
\begin{equation}
\psi^\alpha = \varepsilon^{\alpha\beta} \psi_\beta \, , \qquad \psi^\beta\varepsilon_{\beta\alpha} = \psi_\alpha\, ,
\end{equation}
for any spinor $\psi$. We define $\varepsilon$ such that
\begin{equation}
\varepsilon^{\alpha\beta}\varepsilon_{\alpha\gamma}= \delta_\gamma^\beta \qquad \left(\varepsilon^{12}=\varepsilon_{12} =1\right).
\end{equation}
As observed by Howe in the context of $Sl(2;\bb{C})$ spinor index conventions \cite{Howe:1981gz}, these definitions have the advantage that $\varepsilon_{\alpha\beta}$ and $\varepsilon^{\alpha\beta}$ are related by raising/lowering both indices, so that $\varepsilon$ can be consistently interpreted as an $Sl(2;R)$ tensor.
Lowering the indices of the Dirac matrices amounts to a multiplication from the left by $-i\sigma_2$, so that
\begin{equation}
\gamma^m_{\alpha\beta} = \left(1,\sigma_1,\sigma_3\right)\, .
\end{equation}
Notice that these are symmetric. Now, for any Lorentz 3-vector $V$, we define
\begin{equation}
V_{\alpha\beta} = \gamma^m_{\alpha\beta} V_m \quad \Leftrightarrow \quad
V^m = -\frac{1}{2}\gamma^m_{\alpha\beta}V^{\alpha\beta} \, .
\end{equation}
It follows that
\begin{equation}
V^2 = - \frac{1}{2} V^{\alpha\beta}V_{\alpha\beta} = - \det V_{\alpha\beta}\, .
\end{equation}
Using these conventions, we find that the ${\cal N}=1$ 3D massive spinning particle action is
\begin{eqnarray}\label{act3}
S&=& \int \! dt \left\{- \frac{1}{2} \dot X^{\alpha\beta}P_{\alpha\beta} - \frac{i}{4} \lambda^{\alpha\beta}\dot\lambda_{\alpha\beta} + \frac{i}{2}\xi\dot\xi
- \frac{1}{2}e\left(P^2+m^2\right) \right. \nonumber \\
&& \qquad \qquad \qquad \qquad \left.
- \, \frac{i}{2}\zeta \left(P^{\alpha\beta}\lambda_{\alpha\beta} -2m \xi\right)\right\}\, .
\end{eqnarray}
The Poisson brackets that follow from this action are
\begin{equation}
\!\!\!\!\!\!\!\!\!\!\!\! \left\{X^{\gamma\delta}, P_{\alpha\beta}\right\}_{PB}= -2\delta^{(\gamma}_\alpha\delta^{\delta)}_\beta \, , \quad
\left\{\lambda^{\gamma\delta}, \lambda_{\alpha\beta}\right\}_{PB} = 2i \delta^{(\gamma}_\alpha\delta^{\delta)}_\beta \, ,
\quad \left\{\xi,\xi\right\}_{PB}=-i\, .
\end{equation}
It should be remembered that the Poisson bracket of two anticommuting variables is {\it symmetric} under their interchange.
Using these Poisson bracket relations, it may be verified that the constraints are first-class and that they generate the gauge transformations
\begin{equation}
\delta X^{\alpha\beta} = aP^{\alpha\beta} -i\epsilon\lambda^{\alpha\beta} \, ,\qquad \delta\lambda_{\alpha\beta} = P_{\alpha\beta}\epsilon\, ,
\qquad \delta\xi=m\epsilon\, .
\end{equation}
In addition to its gauge invariances, the action is manifestly Poincar\'e invariant. The Noether charges for translations and Lorentz rotations are, respectively,
\begin{equation}
{\cal P}_{\alpha\beta} = P_{\alpha\beta}\, , \qquad
{\cal J}_\alpha{}^\beta = X^{\beta\gamma}P_{\alpha\gamma} - \frac{1}{2} \delta_\alpha^\beta X^{\gamma\delta}P_{\gamma\delta}
-\frac{i}{2} \lambda^{\beta\gamma}\lambda_{\alpha\gamma}\, .
\end{equation}
One may construct from these Poincar\'e charges the Pauli-Lubanski pseudoscalar; in spinor notation this is
\begin{equation}
{\cal W} = \frac{1}{2}{\cal P}^{\alpha\beta}{\cal J}_{\alpha\beta}\, .
\end{equation}
To pass to the twistor form of the action we first solve the mass-shell constraint by expressing the momentum in terms of a pair of commuting spinors
$U_\alpha^I$ ($I=1,2)$:
\begin{equation}
P_{\alpha\beta} = \mp U_\alpha^IU_\beta^J\delta_{IJ}\, , \qquad \det U =m \, .
\end{equation}
The choice of top sign leads to $P^0>0$, i.e. positive energy; we allow for either sign of the energy since, ultimately, both positive and negative energies are needed in relativistic field theory. The constraint on the determinant of the $2\times 2$ matrix with entries $U_\alpha{}^I$ is essentially another version of the mass-shell constraint since $P^2=-\det P = -( \det U)^2$.
Next, we solve the fermionic constraint by writing $\lambda$ in terms of $\xi$ and two new anticommuting variables in the form of a symmetric and traceless
$SO(2)$ tensor $\psi_{IJ}$:
\begin{equation}
\lambda_{\alpha\beta} = \frac{1}{m}U_\alpha^I U_\beta^J \psi_{IJ} +
\frac{1}{m}P_{\alpha\beta}\, \xi \, , \qquad \psi_{IJ}=\psi_{JI}\, , \quad \delta^{IJ} \psi_{IJ}=0\, .
\end{equation}
Notice that the supersymmetry transformation of $\xi$ now implies that of $\lambda$, so that the new anticommuting variables $\psi_{IJ}$ are
(like $U$) inert under the local worldline supersymmetry.
Substitution for $P$ and $\lambda$ yields the Lagrangian
\begin{equation}\label{Lag}
L= \dot U_\alpha ^I W^\alpha_I + \frac{i}{4} \psi^{IJ}\dot\psi_{IJ} + \frac{d}{dt}\left(\dots\right)\, ,
\end{equation}
where
\begin{equation}\label{Wexpress}
W^{\alpha\, I} = \mp X^{\alpha\beta} U_\beta^I \mp \frac{i}{m} U^\alpha_K
\left[ \varepsilon^{JK}\psi_{IJ}\xi \mp \frac{1}{2}\varepsilon^{JL}\psi_{KL}\psi_{IJ}\right] \, .
\end{equation}
From this expression we may derive the identity
\begin{equation}
0 \equiv \Lambda := \epsilon_{IJ} \left[U_\alpha ^I W^{\alpha\, J} + \frac{i}{2} \psi_{IK}\psi_{KJ}\right]\, .
\end{equation}
It should be appreciated here that (in contrast to the 4D case to follow) there is no significance to the position (up or down) of the $I,J,K,L$ indices since they are raised or lowered using the Kronecker delta.
We see from (\ref{Lag}) that $W$ is canonically conjugate to $U$ but, as things stand, it is not an independent variable. In order to be able to consider it as an independent variable we must impose $\Lambda=0$ as a constraint by means of a Lagrange multiplier. We must also impose the new mass-shell constraint
\begin{equation}
0= \varphi := \det U -m \, .
\end{equation}
In this way we arrive at the action
\begin{equation}\label{3Dspinact}
S= \int\! dt \left\{ \dot U_\alpha ^I W^\alpha_I + \frac{i}{4} \psi^{IJ}\dot\psi_{IJ} - s\Lambda - \rho\varphi\right\}\, ,
\end{equation}
where $s$ and $\rho$ are the Lagrange multipliers. This action is manifestly $SO(2)$ invariant, and this is a gauge invariance because of the
constraint $\Lambda=0$. The new mass-shell constraint function $\varphi$ is the generator for the gauge transformations
\begin{equation}\label{atrans}
\delta W^{\alpha\, I} = b\, \epsilon^{IJ} U^\alpha_J\, , \qquad \delta\rho= \dot b\, ,
\end{equation}
for parameter $b(t)$. This transformation is equivalent to a time reparametrization. We do not present the proof, which involves consideration of ``trivial'' gauge invariances, because it is very similar to the proof in \cite{Routh:2015ifa} for an analogous gauge invariance of the twistorial 6D superparticle.
In the absence of the constraints, the action (\ref{3Dspinact}) would be invariant under the infinite-dimensional group of canonical transformations of the coordinates of a phase superspace of graded dimension $(8|3)$, but this is broken by the $\Lambda=0$ constraint to $Sp(4;\bb{R})\times SO(2)$. Each of the two spinor pairs $Z^I=(U^I,W_I)$ forms an irreducible 4-plet of $Sp(4;\bb{R})$ and together they form a doublet of $SO(2)$. As $Sp(4;\bb{R})$ is a cover of the 3D conformal group such that the $4$-plet of $Sp(4;\bb{R})$ is its spinor representation, this makes $Z^I$ a pair of 3D twistors, so the bosonic phase space is parametrized by a pair of 3D twistors, as claimed. However, the mass-shell constraint $\varphi=0$ breaks $Sp(4;\bb{R})$ to $Sl(2;\bb{R})$, i.e. to the Lorentz group, as expected for a massive particle.
What we wish to emphasize about the action (\ref{3Dspinact}) is that {\it there is no trace of the local worldline supersymmetry of the action (\ref{act3}) from which we started}. The new variables $U$ and
$\psi$ are manifestly inert under the local supersymmetry but it is not obvious that $W$ is too. Initially, $W$ was given by the expression (\ref{Wexpress}); from this expression we may compute the local supersymmetry transformation of $W$ from the known transformations of $X$ and $\xi$. Using the identity
\begin{equation}
\varepsilon^{IK}\psi_{KJ} \equiv \varepsilon^{JK}\psi_{KI}\, ,
\end{equation}
one finds that
\begin{equation}
\delta_\epsilon W^{\alpha\, I} =-i\epsilon\xi \, \varepsilon^{IJ} U^\alpha_J\, .
\end{equation}
Although this is non-zero, it has the form of (\ref{atrans}) with a parameter $b= -i\epsilon\xi$. Thus, the new variables $(U,V,\psi)$ are gauge invariant with respect to the original gauge transformations modulo a gauge transformation associated to the new mass-shell constraint.
The Pauli-Lubanski pseudoscalar in twistor variables is, after using the mass-shell and spin-shell constraints,
\begin{equation}
{\cal W}= \pm m \Sigma\, , \qquad \Sigma = \frac{i}{4} \epsilon^{IJ}\psi_{IK}\psi_{JK}\, .
\end{equation}
The two independent components of $\psi_{IJ}$ can be traded for a single {\it complex} anticommuting variable $\psi$, such that
$\{\psi,\bar\psi\}_{PB}=-i$, by writing
\begin{equation}\label{psis}
\psi_{11}=-\psi_{22} = \frac{1}{\sqrt{2}}\left(\psi+\bar\psi\right) \, , \qquad \psi_{12}=\psi_{21} = \frac{1}{\sqrt{2}\, i}\left(\psi - \bar\psi\right)\, .
\end{equation}
On passing to the quantum theory, $\psi\to \hat\psi$ and $\bar\psi\to \hat\psi^\dagger$, we have $\{\hat\psi,\hat\psi^\dagger\}=1$ (in units for which $\hbar=1$)
and hence
\begin{equation}
\hat\Sigma = \hat n- \frac{1}{2}\, , \qquad \hat n = \hat\psi^\dagger\hat\psi\, .
\end{equation}
The operator $\hat n$ is a fermi number operator with eigenvalues $0,1$. The eigenvalues of the spin operator $\hat\Sigma$ are therefore $\pm 1/2$.
We thus confirm, for $3D$, that the ${\cal N}=1$ massive spinning particle action describes a particle of spin $1/2$. The
${\cal N}>1$ case was dealt with in \cite{Mezincescu:2013nta}.
\subsection{Massless limit}
For the 3D case we shall present an analysis of the $m=0$ limit. Setting $m=0$ in (\ref{3Dspinact}) changes only the mass-shell constraint, which is now $\det U=0$.
This constraint implies that the spinors $\{U^I; I=1,2\}$ are linearly dependent. Assuming non-zero $U^1$, for simplicity of presentation, we then have
\begin{equation}\label{massless1}
U^1 = U\, , \qquad U^2 = \lambda U\, ,
\end{equation}
for spinor $U(t)$ and scalar $\lambda(t)$. We may now solve the $\Lambda=0$ constraint by setting
\begin{equation}\label{massless2}
W^1 = W\, , \qquad W^2 = \lambda W + \kappa U + V\, ,
\end{equation}
for spinor $W(t)$, another scalar $\kappa(t)$, and any spinor $V(t)$ such that
\begin{equation}\label{Vpsis}
U_\alpha V^\alpha = -2\bar\psi\psi\, .
\end{equation}
A solution for $V$ exists because we are assuming non-zero $U$. We may add to $V$ any multiple of $U$ but the solution for $V$ is unique if we consider it to
represent the equivalence class for which $V$ and $V'$ are identified if they differ by a multiple of $U$.
Gauge invariance of the relation (\ref{Vpsis}) requires the following gauge transformation for $V$
\begin{equation}
\delta V= - \alpha \lambda V\, ,
\end{equation}
where $\alpha(t)$ is the scalar parameter for $SO(2)$ gauge transformations. Because of the equivalence relation on $V$, it is inert under the
transformation (\ref{atrans}) with parameter $b(t)$. Gauge invariance of the relations (\ref{massless1}) and (\ref{massless2}) requires the scalars
$(\lambda,\kappa)$ to transform as follows:
\begin{equation}
\delta \lambda = -(1+\lambda^2)\alpha\, , \qquad \delta\kappa = -2\alpha\lambda \kappa -b(1+\lambda^2)\, .
\end{equation}
This shows that we may fix the gauge invariances by setting $\lambda=\kappa=0$. At this point the only non-zero independent variables are $(U,W)$ and $\psi$, and
the action reduces to
\begin{equation}
S= \int dt\left\{ \dot U_\alpha W^\alpha + i \bar\psi\dot\psi\right\}\, .
\end{equation}
This is the twistor action for the massless 3D spinning particle. It is manifestly $Sp(4;\bb{R})$ invariant, with $(U,W)$ transforming as a 4-plet, i.e. as a 3D twistor.
Notice that the graded dimension of the phase space is $(4|2)$, which is what we should expect from a comparison with the action (\ref{masslessact}).
\section{Massive 4D spinning particle}
\setcounter{equation}{0}
We shall use a notation in which spacetime vectors are bi-spinors of $Sl(2;\bb{C})$. Specifically, for any Lorentz 4-vector V,
\begin{equation}
V^m = -\frac{1}{2}\sigma^m_{\alpha\dot\alpha}V^{\alpha\dot\alpha} \, , \qquad V^{\alpha\dot\alpha} = V^m\sigma_m^{\alpha\dot\alpha} \, .
\end{equation}
Here, $\sigma^m =(\bb{I}_2, \mbox{\boldmath $\sigma$})$ where $\mbox{\boldmath $\sigma$}$ is the triplet of $2\times2$ Pauli matrices, and
\begin{equation}\label{sigup}
\sigma_n^{\alpha\dot\alpha} := \eta_{nm}\, \varepsilon^{\alpha\beta}\varepsilon^{\dot\alpha\dot\beta} \sigma^m_{\beta\dot\beta}\, .
\end{equation}
The $\sigma$ matrices satisfy the relations
\begin{equation}
\eta_{mn} \, \sigma^m_{\alpha\dot\alpha} \sigma^n_{\beta\dot\beta} = -2\varepsilon_{\alpha\beta}\varepsilon_{\dot\alpha\dot\beta}\, , \qquad
\sigma^m_{\alpha\dot\alpha} \sigma_n^{\alpha\dot\alpha} = -2\delta^m_n\, ,
\end{equation}
where $\eta$ is the Minkowski metric, which we take to have ``mostly plus'' signature.
As (\ref{sigup}) suggests, spinor indices are raised and lowered by means of the $Sl(2;\bb{C})$ invariant alternating tensors. As in 3D, we do this according to the convention that, for any spinor $\psi$,
\begin{equation}
\varepsilon^{\alpha\beta}\psi_\beta = \psi^\alpha\, , \qquad \varepsilon^{\dot\alpha\dot\beta}\psi_{\dot\beta} = \psi^{\dot\alpha}\, \qquad
\psi^\alpha\varepsilon_{\alpha\beta} = \psi_\beta\, , \qquad \psi^{\dot\alpha} \varepsilon_{\dot\alpha\dot\beta} = \psi_{\dot\beta}\, .
\end{equation}
For any Lorentz vector $V$ we have
\begin{equation}
\eta^{mn}V_m V_n \equiv V^2 = - \frac{1}{2} V^{\alpha\dot\beta}V_{\alpha\dot\beta} = -\det V\, ,
\end{equation}
where the last equality follows from the definition of the determinant of the $2\times 2$ matrix with entries $V_{\alpha\dot\alpha}$. The factors here are a reflection of the fact that $\eta^{\alpha\dot\alpha, \beta\dot\beta} V_{\beta\dot\beta} = -2 V^{\alpha\dot\alpha}$.
In these spinor conventions, the action for the ${\cal N}=1$ spinning particle is
\begin{eqnarray}
S &=& \int\! dt \left\{-\frac{1}{2} \dot X^{\alpha\dot\alpha} P_{\alpha\dot\alpha} - \frac{i}{4} \lambda^{\alpha\dot\alpha} \dot\lambda_{\alpha\dot\alpha} + \frac{i}{2} \xi\dot\xi - \frac{1}{2} e\left(P^2 +m^2 \right) \right.\nonumber \\
&& \qquad\qquad \qquad \qquad \qquad \left.
- \, \frac{i}{2} \zeta\left(P^{\alpha\dot\alpha} \lambda_{\alpha\dot\alpha} - 2m \xi\right) \right\}\, .
\end{eqnarray}
The canonical Poisson brackets are
\begin{equation}
\!\!\!\!\!\! \!\!\!\!\!\! \left\{ X^{\beta\dot\beta},P_{\alpha\dot\alpha}\right\}_{PB} = -2\delta_\alpha^\beta\delta_{\dot\alpha}^{\dot\beta}\, , \quad
\left\{\lambda^{\beta\dot\beta},\lambda_{\alpha\dot\alpha}\right\}_{PB} = 2i \delta_\alpha^\beta\delta_{\dot\alpha}^{\dot\beta}\, ,
\quad \left\{\xi,\xi\right\}_{PB} =-i\, .
\end{equation}
The gauge transformations of the canonical variables are now
\begin{equation}\label{deltas1}
\delta X^{\alpha\dot\alpha} = aP^{\alpha\dot\alpha} -i\epsilon \lambda^{\alpha\dot\alpha}\, , \qquad \delta\lambda_{\alpha\dot\alpha}= P_{\alpha\dot\alpha}\epsilon\, , \qquad \delta\xi =m\epsilon\, .
\end{equation}
In addition to its gauge invariances, the action is also invariant under the Poincar\'e isometries of 4D Minkowski space. The corresponding Noether charges are ${\cal P}_{\alpha\dot\alpha} = P_{\alpha\dot\alpha}$ for translations, and
\begin{eqnarray}
{\cal J}_\alpha{}^\beta &=& \frac{1}{2} X^{\beta\dot\alpha} P_{\alpha\dot\alpha} -
\frac{1}{4} \delta_\alpha^\beta X^{\gamma\dot\gamma}P_{\gamma\dot\gamma} -
\frac{i}{4}\lambda^{\beta\dot\alpha}\lambda_{\alpha\dot\alpha}\, , \nonumber \\
\bar{\cal J}_{\dot\alpha}{}^{\dot\beta} &=& \frac{1}{2} X^{\alpha\dot\beta}P_{\alpha\dot\alpha} -
\frac{1}{4}\delta_{\dot\alpha}^{\dot\beta} X^{\gamma\dot\gamma}P_{\gamma\dot\gamma} -
\frac{i}{4} \lambda^{\alpha\dot\beta}\lambda_{\alpha\dot\alpha}
\end{eqnarray}
for Lorentz rotations.
To construct the twistor form of the action, we proceed as in the 3D case. We first solve the mass-shell constraint by writing $P$
in terms of the $U(2)$ doublet of commuting complex spinors $U_\alpha^I$ ($I=1,2$), and their complex conjugates $\bar U_{\dot\alpha\, I}$:
\begin{equation}\label{Pus}
P_{\alpha\dot\alpha} = \mp U_{\alpha}^I\bar U_{\dot\alpha\, I}\, , \qquad |\det U|^2 =m^2 \, ,
\end{equation}
where $\det U$ is the determinant is of the complex $2\times2$ matrix with entries $U_\alpha^I$. Observe that $|\det U|^2 = \det P = -P^2$, so the condition $|\det U|^2 =m^2$ needed to solve the original mass-shell constraint is again a mass-shell constraint, but now expressed in terms of $U$. The choice of the upper sign in (\ref{Pus}) again corresponds to positive energy.
We can now solve the fermionic constraint by writing $\lambda$ as
\begin{equation}
\lambda_{\alpha\dot\alpha} = \frac{1}{m}U_\alpha^I U_{\dot\alpha}^J \psi_{IJ} + \frac{1}{m} P_{\alpha\dot\alpha} \xi\, , \qquad \left(\psi_{IJ}= \psi_{JI}\right)
\end{equation}
where the new anticommuting variables $\psi_{IJ}$ constitute an $SU(2)$ triplet. As in the 3D case, the local supersymmetry transformation of $\lambda$ is now implied by that of $\xi$, so that $\psi_{IJ}$ is inert. We may raise and lower $SU(2)$ indices with the invariant alternating tensor, which we do using the same conventions as for $Sl(2;\bb{C})$ spinor indices. For example,
\begin{equation}
\psi^I{}_J = \varepsilon^{IK} \psi_{KJ} = \psi^{IK}\varepsilon_{KJ}\, ,
\end{equation}
which are the (anticommuting) entries of a traceless $2\times2$ Hermitian matrix.
Substituting for $P$ and $\lambda$ in the action, we find the new Lagrangian
\begin{equation}
L= \dot U_\alpha^I W^\alpha_I + \dot{\bar U}_{\dot\alpha\, I} \bar W^{\dot\alpha\, I} + \frac{i}{4}\psi^I{}_J \dot\psi^J{}_I + \frac{d}{dt} \left(\cdots\right)\, ,
\end{equation}
where
\begin{eqnarray}\label{defsW}
W^\alpha_I &=& \mp\frac{1}{2} X^{\alpha\dot\alpha}\, \bar U_{\dot\alpha\, I} \pm \frac{i}{2m^2} U^{\alpha J} \det \bar U \left(\psi_{IJ}\, \xi \mp \frac{1}{2}\psi_I{}^L\psi_{LJ}\right)\, , \nonumber \\
\bar W^{\dot\alpha\, I} &=& \mp \frac{1}{2} X^{\alpha\dot\alpha}\, U_\alpha^I\ \mp\frac{i}{2m^2}\, \bar U^{\dot\alpha}_J \det U \left(\psi^{IJ}\xi \mp \frac{1}{2} \psi^I{}_L\psi^{LJ}\right)\, .
\end{eqnarray}
Using these expressions, and the new mass-shell constraint
\begin{equation}
0= \varphi := |\det U|^2 -m^2 \, ,
\end{equation}
one may derive the identities
\begin{eqnarray}\label{Wids}
0 &\equiv&G := U_\alpha^I W^\alpha_I - \bar U_{\dot\alpha \, I}\bar W^{\dot\alpha \, I} \, , \nonumber\\
0 &\equiv& \Lambda^{IJ} := U^{\alpha\, (I} W_\alpha^{J)} - \bar U^{\dot\alpha\, (I} \bar W_{\dot\alpha}^{ J)} + \frac{i}{2}\psi^I{}_L\psi^{LJ} \, .
\end{eqnarray}
Notice that $\Lambda^{IJ}=\Lambda^{JI}$ because of the anticommutativity of $\psi_{IJ}$. In order to promote the variables $W$ and $\bar W$ to the status of independent variables, these constraints must be imposed by Lagrange multipliers, along with the constraint $\varphi=0$.
To simplify the final result, we first trade the anticommuting variables $\psi^I{}_J$ for a real anticommuting $3$-vector $\mbox{\boldmath $\psi$}$ by writing
\begin{equation}
\psi^I{}_J = \mbox{\boldmath $\sigma$}^I{}_J \cdot \mbox{\boldmath $\psi$}\, .
\end{equation}
The new action now takes the form
\begin{equation}\label{newform}
S= \int dt\left\{ \dot U_\alpha^I W^\alpha_I + \dot{\bar U}_{\dot\alpha\, I} \bar W^{\dot\alpha\, I} + \frac{i}{2}\mbox{\boldmath $\psi$}\cdot \dot{\mbox{\boldmath $\psi$}} - \ell G - s_{IJ}\Lambda^{IJ} - \rho \varphi\right\}\, ,
\end{equation}
where $\ell$, $s_{IJ}= s_{JI}$ and $\rho$ are Lagrange multipliers for the constraints. Only the constraint functions $\Lambda^{IJ}$ involve the anticommuting 3-vector $\mbox{\boldmath $\psi$}$, and they now take the form
\begin{equation}\label{LambdaSig}
\Lambda^I{}_J = \Lambda_{(bos)}^I{}_J - i \mbox{\boldmath $\sigma$}^I{}_J \cdot \mbox{\boldmath $\Sigma$} \, , \qquad \mbox{\boldmath $\Sigma$}= - \frac{i}{2} \mbox{\boldmath $\psi$} \times \mbox{\boldmath $\psi$}\, ,
\end{equation}
where $\Lambda_{(bos)}$ is the part independent of $\mbox{\boldmath $\psi$}$; it can be read off from (\ref{Wids}).
The bosonic phase space is now parametrized by two pairs of complex 2-component spinors $Z^I = (U^I,W_I)$, and each pair is a complex 4-plet of $Sp(4;\bb{C})\cong U(2,2)$.
Since $U(2,2)$ is (neglecting discrete factors) the product of $U(1)$ with the 4D conformal group, each of the $Z^I$ is a 4D twistor. The bosonic phase space is therefore parametrized
by a pair of twistors, as for 3D but its real dimension is now $2\times 8=16$ and the 4D conformal invariance is broken by the mass-shell constraint. As there are a total of
$5$ first-class constraints generating $5$ gauge invariances, the bosonic dimension of the physical phase space is $16-10=6$. There are also $3$ real anticommuting coordinates
not subject to any constraint or gauge invariance, so the graded dimension of the physical phase superspace is $(6|3)$, as it should be.
From the new action (\ref{newform}) we may read off the canonical Poisson brackets. These are
\begin{equation}
\left\{ U_\alpha^I, W^\beta_J\right\}_{PB}= \delta_\alpha^\beta\delta^I_J\, , \qquad
\left\{\bar U_{\dot\alpha\, I}, \bar W^{\dot\beta\, J} \right\}_{PB} = \delta_{\dot\alpha}^{\dot\beta}\delta_I^J\, ,
\end{equation}
and, for the components $\psi_i$ ($i=1,2,3$) of $\mbox{\boldmath $\psi$}$,
\begin{equation}
\left\{\psi_i,\psi_j\right\}_{PB} = -i \delta_{ij}\, .
\end{equation}
One can verify that the Poisson bracket algebra of the spin-shell constraint functions $(G,\Lambda^I{}_J)$ is $U(2)$. The anticommuting variables contribute only to the spin part of the $SU(2)$ generators, and one may easily check that their Poisson bracket algebra is
\begin{equation}
\left\{ \mbox{\boldmath $\Sigma$}_i ,\mbox{\boldmath $\Sigma$}_j\right\}_{PB} = \varepsilon_{ijk} \mbox{\boldmath $\Sigma$}_k \, .
\end{equation}
The constraint function $\varphi$ is manifestly $U(2)$ invariant, so it has zero Poisson brackets with the spin-shell constraints. The gauge invariance it generates has the following transformations for parameter $b(t)$:
\begin{equation}
\delta_b W^\alpha_I = b\, U^\alpha_I \det \bar U\, , \quad \delta_b\bar W^{\dot\alpha\, I} = -b\, \bar U^{\dot\alpha\, I} \det U\, , \qquad
\delta_b\rho = \dot b\, .
\end{equation}
As for 3D, it is important to take into account this gauge invariance (which is again equivalent to a time reparametrization) when considering how $W$ transforms under the original local supersymmetry. The latter can be deduced by using the transformations of $X$ and $\xi$ in the expressions of (\ref{defsW}): this gives a $b$-transformation of the above type with $2m b= i\epsilon\xi$. Thus the new twistor variables $(U,W,\psi)$ are gauge invariant with respect to all the original local symmetries modulo a gauge transformation generated by the new mass-shell constraint function $\varphi$.
Although we are calling $G=0$ and $\Lambda^{IJ}=0$ the spin-shell constraints, their relation to the particle's spin is not obvious because their inclusion in the action leads to the gauging of an apparently {\it internal} $U(2)$ symmetry. In fact, the $U(1)$ constraint $G=0$ is not directly related to the particle's spin, but the $SU(2)$ constraint is, as becomes clear when one considers
the Pauli-Lubanski spin vector. In $Sl(2;\bb{C})$ spinor notation this is
\begin{equation}\label{PL}
{\cal W}_{\alpha\dot\alpha} = i\left({\cal J}_\alpha{}^\beta {\cal P}_{\beta\dot\alpha} -\bar{\cal J}_{\dot\alpha}{}^{\dot\beta}{\cal P}_{\alpha\dot\beta}\right)\, .
\end{equation}
In twistor variables, the Lorentz Noether charges are
\begin{eqnarray}
{\cal J}_\alpha{}^\beta &=& U_\alpha^I W^\beta_I - \frac{1}{2}\delta_\alpha^\beta\left(U_\gamma^KW^\gamma_K\right)\, , \nonumber \\
\bar{\cal J}_{\dot\alpha}{}^{\dot\beta} &=& \bar U_{\dot\alpha\, I} \bar W^{\dot\beta\, I} -
\frac{1}{2}\delta_{\dot\alpha}^{\dot\beta} \left(\bar U_{\dot\gamma\, K}\bar W^{\dot\gamma\, K}\right)\, .
\end{eqnarray}
Notice that there is no longer a contribution from anticommuting variables, as expected from the fact that these are now Lorentz scalars.
When these Poincar\'e Noether charges are substituted into the expression (\ref{PL}) one finds that
\begin{equation}
{\cal W}_{\alpha\dot\alpha} = \pm\, i \Lambda_{IJ}^{(bos)} U_\alpha^I \bar U_{\dot\alpha}^J\, ,
\end{equation}
where $\Lambda_{(bos)}$ is $\Lambda$ without the ``fermionic'' term. This shows that the bosonic particle has zero spin.
For the spinning particle the additional spin term in $\Lambda_{IJ}$ is such that, when $\Lambda_{IJ}=0$,
\begin{equation}
{\cal W}_{\alpha\dot\alpha} = \mp\, U_\alpha^J\bar U_{\dot\alpha\, I}\, \mbox{\boldmath $\sigma$}^I{}_J\cdot \mbox{\boldmath $\Sigma$} \quad \Rightarrow \quad {\cal W}^2= m^2 \Sigma^2\, .
\end{equation}
In the quantum theory, $\Sigma^2$ equals $s(s -1)$ for an irreducible massive spin-$s$ representation of the Poincar\'e group, but to
make use of this fact we must first quantize.
To pass to the quantum theory we use Dirac's prescription to replace Poisson brackets of canonical variables by $-i$ times the (anti)commutator of their corresponding operators. This yields the following canonical anticommutation relation for the components of the operator $\hat{\mbox{\boldmath $\psi$}}$:
\begin{equation}
\left\{\hat\psi_i, \hat\psi_j\right\} = \delta_{ij} \quad \Rightarrow \quad \hat{\mbox{\boldmath $\psi$}} = \frac{1}{\sqrt{2}} \mbox{\boldmath $\tau$} \quad \Rightarrow\quad \hat{\mbox{\boldmath $\Sigma$}}= \frac{1}{2} \mbox{\boldmath $\tau$} \, ,
\end{equation}
where $\mbox{\boldmath $\tau$}$ are Pauli matrices. It then follows that
\begin{equation}
\hat\Sigma^2 = \frac{3}{4} \bb{I} \quad \Rightarrow\quad s= \frac{1}{2}\, .
\end{equation}
As expected, the quantum ${\cal N}=1$ spinning particle has spin $1/2$.
\subsection{Quantum theory for ${\cal N}\ge2$}
The twistor formulation of the ${\cal N}$-extended spinning particle can be found by following exactly the same procedure already explained for $D=3$.
The resulting action is
\begin{equation}\label{genN}
\!\!\!\!\! \!\!\!\!\! \!\!\!\!\! \!\!\!\!\! \!\!\!\!\! \!\!\!\!\! S = \int \! dt\left\{ \dot U_\alpha^I W^\alpha_I + \dot{\bar U}_{\dot\alpha\, I} \bar W^{\dot\alpha\, I} + \frac{i}{2}\mbox{\boldmath $\psi$}_a\cdot \dot{\mbox{\boldmath $\psi$}}_a
- \, \ell G - s_{ij}\Lambda^{IJ} - \rho\varphi - f_{ab}\, \mbox{\boldmath $\psi$}_a \cdot \mbox{\boldmath $\psi$}_b \right\},
\end{equation}
where $\Lambda^{IJ}$ is as given in (\ref{LambdaSig}) but now with
\begin{equation}
\mbox{\boldmath $\Sigma$} = -\frac{i}{2}\sum_{a=1}^{\cal N}\mbox{\boldmath $\psi$}_a \times \mbox{\boldmath $\psi$}_a\, .
\end{equation}
Proceeding as we did for ${\cal N}=1$, we now find for ${\cal N}\ge2$ that
\begin{equation}
\hat{\mbox{\boldmath $\Sigma$}} = \frac{1}{2}\left[ \mbox{\boldmath $\tau$} \otimes \bb{I} \otimes \bb{I} \otimes \cdots + \bb{I}\otimes\mbox{\boldmath $\tau$} \otimes\bb{I}\otimes + \cdots +
\bb{I}\otimes\bb{I}\otimes \cdots \otimes\mbox{\boldmath $\tau$}\right]\, .
\end{equation}
This acts on a reducible space of dimension $2^{\cal N}$. However, we still have to consider the $SO({\cal N})$ constraints; there are
${\cal N}({\cal N}-1)$ of them. One implies that the state space is annihilated by the operator
\begin{equation}
\sum_{i=1}^3 \mbox{\boldmath $\tau$}_i \otimes \mbox{\boldmath $\tau$}_i \otimes\bb{I} \cdots \otimes \bb{I}\, .
\end{equation}
However, this operator has eigenvalues $1$ and $-3$, so there is no state that satisfies the constraint. The theory is quantum inconsistent!
This result is implicit in the conclusion of \cite{Howe:1989vn} that the massless spinning particle is inconsistent for ${\cal N}>2$ in odd spacetime dimensions\footnote{In even spacetime dimensions it describes a massless particle of spin $\frac{1}{2}{\cal N}$} because of a global anomaly (of the general type discussed in \cite{Elitzur:1985xj}). As pointed out in \cite{Howe:1989vn}, the massive spinning particle in $D$ dimensions can be obtained by
a type of dimensional reduction from the massless spinning particle in $D+1$ dimensions, so we should expect the massive ${\cal N}>2$ spinning particle
to be quantum inconsistent in {\it even} spacetime dimensions. This is what we find for $D=4$.
As also pointed out in \cite{Howe:1989vn}, the global anomaly can be cancelled for $ {\cal N}=2$ by the WCS term. We shall now recover this result from our twistor formulation of the model. First, we introduce the complex anticommuting triplet
\begin{equation}
\mbox{\boldmath $\psi$} = \frac{1}{\sqrt{2}} \left(\mbox{\boldmath $\psi$}_1 + i\mbox{\boldmath $\psi$}_2\right)\, .
\end{equation}
This leads to the ${\cal N}=2$ action
\begin{eqnarray}
S&=& \int dt \Big\{ \dot U_\alpha^I W^\alpha_I + \dot{\bar U}_{\dot\alpha\, I} \bar W^{\dot\alpha\, I} + i\bar{\mbox{\boldmath $\psi$}} \cdot \dot{\mbox{\boldmath $\psi$}} - \ell G - s_{ij}\Lambda^{IJ} - \rho\varphi \nonumber \\
&&\qquad\qquad
- \, \frac{1}{4} f \left[ \left(\bar{\mbox{\boldmath $\psi$}} \cdot \mbox{\boldmath $\psi$} - \mbox{\boldmath $\psi$}\cdot \bar{\mbox{\boldmath $\psi$}}\right) + 2 c\right]\Big\}\, ,
\end{eqnarray}
where $c$ is the coefficient of the WCS term. Of course, $\bar{\mbox{\boldmath $\psi$}} \cdot \mbox{\boldmath $\psi$} = - \mbox{\boldmath $\psi$}\cdot \bar{\mbox{\boldmath $\psi$}}$ in the classical theory but the
expression $(\bar{\mbox{\boldmath $\psi$}} \cdot \mbox{\boldmath $\psi$} - \mbox{\boldmath $\psi$}\cdot \bar{\mbox{\boldmath $\psi$}})$ yields the standard fermi oscillator operator ordering in the quantum theory.
The canonical anticommutation relations of the operators $\hat{\mbox{\boldmath $\psi$}}$ and $\hat{\mbox{\boldmath $\psi$}}^\dagger$ are
\begin{equation}
\left\{ \hat\psi_i, \hat\psi_j^\dagger\right\} = \delta_{ij}\, .
\end{equation}
The $SO(2)$ constraint therefore reduces to
\begin{equation}
n_1 +n_2 +n_3 - \frac{3}{2} + c =0\, ,
\end{equation}
where $n_i$ are the eigenvalues of the fermi number operators $\hat n_i\equiv {\hat\psi}_i^\dagger{\hat\psi}_i$ (no sum over $i$), and
we have allowed for the zero point contributions of each of the three fermi oscillators. We now see that
\begin{equation}
c= \frac{3}{2} - k \, , \qquad k=0,1,2,3.
\end{equation}
For each choice of $k$ we have
\begin{equation}
\!\!\!\! \hat{\mbox{\boldmath $\Sigma$}}= -i \hat{\mbox{\boldmath $\psi$}} \times \hat{\mbox{\boldmath $\psi$}}{}^\dagger\quad \Rightarrow \quad \hat \Sigma^2 = (n_1-n_2)^2 + (n_2-n_3)^2+ (n_3-n_1)^2\, .
\end{equation}
For $k=0,3$ (and hence $|c|=\frac{3}{2}$) all $n_i$ are equal, so there is a single polarization state with $\hat\Sigma^2=0$. These two cases describe a particle of zero spin. For $k=1,2$ (and hence $|c|=\frac{1}{2}$), either one or two of the $n_i$ are zero, and both cases give three polarization states with $\hat\Sigma^2=2$, which implies a particle of spin 1. Since $c$ is non-zero in all cases, we see that the WCS term is crucial to quantum consistency.
\section{Massive 6D spinning particle}
\setcounter{equation}{0}
For the 6D spinning particle, we could use an $Sl(2;\bb{H})$ notation for spinors \cite{Kugo:1982bn} but it is simpler to use an $SU^*(4)$ notation\footnote{The $4\times4$ $SU^*(4)$ matrices are found from the $2\times2$ $Sl(2;\bb{H})$ matrices by using the $2\times2$ Pauli matrix representation of the algebra of quaternions.}. In this notation, Lorentz 6-vectors are converted into antisymmetric bi-spinors by means of a set of $6$ antisymmetric $4\times4$ matrices $\Sigma^m$
which can be chosen such that ($\alpha,\beta,\gamma,\delta=1,2,3,4$)
\begin{equation}\label{complete}
\Sigma_m^{\alpha\beta}\Sigma^n_{\alpha\beta} = \delta_m^n \, , \qquad
\Sigma^m_{\alpha\beta} \Sigma_m^{\gamma\delta} = \delta_{[\alpha}^\gamma \delta_{\beta]}^\delta \, ,
\end{equation}
where
\begin{equation}\label{Sigup}
\Sigma_m^{\alpha\beta} := \frac{1}{2} \varepsilon^{\alpha\beta\gamma\delta} \Sigma^n_{\gamma\delta} \eta_{mn} \, .
\end{equation}
For this choice\footnote{Our choice of factors differs from those of \cite{Howe:1983fr}, where other aspects of the $SU^*(4)$ spinor notation are explained.}
we have, for example,
\begin{equation}\label{Pform}
\bb{P}_{\alpha\beta} = \Sigma^m_{\alpha\beta} P_m\, , \qquad P_m = \Sigma_m^{\alpha\beta} \bb{P}_{\alpha\beta}\, ,
\end{equation}
As suggested by the definition (\ref{Sigup}), we may raise or lower antisymmetric pairs of spinor indices using the $SU^*(4)$ invariant alternating tensor. For example,
\begin{equation}
\bb{P}^{\alpha\beta} := \frac{1}{2} \varepsilon^{\alpha\beta\gamma\delta} \bb{P}_{\gamma\delta}\, .
\end{equation}
We then find, in agreement with \cite{Mezincescu:2013nta,Routh:2015ifa}, that
that
\begin{equation}
\bb{P}^{\alpha\beta}\bb{P}_{\alpha\beta} =P^2\, .
\end{equation}
In the above conventions, the action for the 6D massive spinning particle is
\begin{equation}\label{spinning}
\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! S= \int\! dt \left\{ \dot{\bb{X}}^{\alpha\beta} \bb{P}_{\alpha\beta} + \frac{i}{2}\lambda^{\alpha\beta} \dot \lambda_{\alpha\beta} + \frac{i}{2} \xi\dot\xi - \frac{1}{2} e\left(\bb{P}^2+m^2\right) +i\zeta \left(\lambda^{\alpha\beta}\bb{P}_{\alpha\beta} +m\xi\right)\right\}\, .
\end{equation}
The infinitesimal gauge transformations generated by the constraints are
\begin{equation}
\delta_\epsilon X^{\alpha\beta} = -i\epsilon\lambda^{\alpha\beta}\, , \qquad \delta_\epsilon\lambda_{\alpha\beta} =\epsilon\, \bb{P}_{\alpha\beta}\, \qquad \delta_\epsilon \xi= m\epsilon\, .
\end{equation}
The Lorentz Noether charges are
\begin{equation}
{\cal J}_{\alpha}{}^{\beta} = 2 \bb{P}_{\alpha\gamma}\bb{X}^{\beta\gamma} - \frac12 \delta_{\alpha}^{\beta}\, \bb{P}_{\gamma\delta} \bb{X}^{\gamma\delta}
+ i \lambda_{\alpha\gamma}\lambda^{\beta \gamma} \,.
\end{equation}
To pass to the twistor form of the action, we first solve the mass-shell constraint as in \cite{Routh:2015ifa} by
setting\footnote{The sign of the energy now depends on the choice of the $USp(4)$-invariant tensor $\Omega$. Also, notice the sign of $\det \bb{U}$ on the mass shell. }
\begin{equation}\label{Psq1}
\bb{P}_{\alpha\beta} = \frac{1}{2} \bb{U}_\alpha^I \bb{U}_\beta^J\, \Omega_{JI} \, ,\qquad \det \bb{U}=-m^2 \, ,
\end{equation}
where $\bb{U}$ is a 4-plet $(I=1,2,3,4)$ of $SU^*(4)$ spinors, and $\Omega$ is the antisymmetric $USp(4)$-invariant matrix (normalized such that $\det\Omega=1$). We use $\Omega$ to raise and lower indices using the same conventions that we used previously for $Sl(2;\bb{R})$ and $Sl(2;\bb{C})$. To verify that the mass-shell constraint is solved, one needs the identity $3\Omega_{I[J} \Omega_{KL]} \equiv \epsilon_{IJKL}$, where $\epsilon_{IJKL}$ is the invariant alternating tensor of $USp(4)$. The invariant tensor $\epsilon^{IJKL}$ is then defined by raising
indices, which implies that $\epsilon^{1234}=1$ given (as we assume) that $\epsilon_{1234}=1$.
As for the 3D and 4D cases, the constraint on the determinant of $U$ can be viewed as a new mass-shell constraint.
Before proceeding it is convenient to define
\begin{equation}
\bb{V}_I^{\alpha} = \frac{1}{6m} \epsilon_{IJKL}\epsilon^{\alpha\beta\gamma\delta}\bb{U}^J_{\beta}\bb{U}^K_{\gamma}\bb{U}^L_{\delta} \, .
\end{equation}
This is a new $USp(4)$ $4$-plet of commuting $SU^*(4)$ spinors of opposite chirality to $\bb{U}$, and the two are inverses of each other, up to factors, since
\begin{equation}
\bb{V}^\alpha_I \bb{U}_\alpha^J = -m\delta_I^J\, , \qquad \bb{V}^\alpha_I \bb{U}_\beta^I = -m\delta^\alpha_\beta\, \qquad (\det \bb{U} = -m^2)\, .
\end{equation}
It can be shown, again on the surface $\det \bb{U}=-m^2$, that \cite{Routh:2015ifa}
\begin{equation}
\bb{P}^{\alpha\beta} = -\frac12\, \bb{V}_I^{\alpha}\bb{V}_J^{\beta}\, \Omega^{JI} \, , \qquad (\det \bb{U} = -m^2)\, .
\end{equation}
Next, we solve the fermionic constraint by setting
\begin{equation}\label{solvef}
\lambda_{\alpha\beta} = \frac{1}{\sqrt{2}\, m} \bb{U}_{\alpha}^I \bb{U}_{\beta}^J \, \psi_{IJ} + \frac{1}{m} \bb{P}_{\alpha\beta} \xi\, ,
\end{equation}
where $\psi_{IJ}$ is antisymmetric and $\Omega$-tracefree, and hence has five independent components. As for the 3D and 4D cases, the supersymmetry transformation of $\lambda$ is now implied by that of $\xi$, so that the new anticommuting variables $\psi$ are inert. A useful alternative, but equivalent, expression for $\lambda$ is
\begin{equation}
\lambda^{\alpha\beta}= \frac{1}{\sqrt{2}\, m} \bb{V}^\alpha_I\bb{V}^\beta_J \psi^{IJ} + \frac{1}{m}\bb{P}^{\alpha\beta} \xi\, .
\end{equation}
To prove equivalence of this expression to (\ref{solvef}) one needs the relation
\begin{equation}
\psi^{IJ}= - \frac{1}{2}\epsilon^{IJKL}\psi_{KL}\, .
\end{equation}
The left hand side is defined by raising indices with $\Omega$. To show that this equals the right hand side one uses the identity
$\epsilon^{IJKL} = \Omega^{I[J}\Omega^{KL]}$ and the fact that $\psi_{IJ}$ is both antisymmetric and
$\Omega$-traceless\footnote{It is not consistent to use the alternating invariant tensor of $USp(4)$ to raise or lower antisymmetric pairs of $USp(4)$ spinor indices because a different sign would then be needed to apply this to $\Omega$ itself, as follows from identity $\Omega^{IJ} \equiv \frac{1}{2}\epsilon^{IJKL}\Omega_{KL}$.}.
Substituting for $\bb{P}$ and $\lambda$, one finds that
\begin{equation}\label{halfway}
\dot{\bb{X}}^{\alpha\beta} \bb{P}_{\alpha\beta} + \frac{i}{2} \lambda_{\alpha\beta}\dot\lambda^{\alpha\beta} + \frac{i}{2} \xi \dot \xi =
\dot{\bb{U}}_\alpha^I\bb{W}^\alpha_I + \frac{i}{4} \psi^{IJ} \dot\psi_{IJ}
+ \frac{d}{dt} \left(\dots\right)\, ,
\end{equation}
where\footnote{We choose the overall sign of $\bb{W}$ to be opposite to that chosen in \cite{Routh:2015ifa} so that the form of the action is similar to the 3D and 4D cases deduced in previous sections.}
\begin{equation}\label{newW}
W^\alpha_I =-\bb{X}^{\alpha\beta}U^J_{\beta}\Omega_{JI} - \frac{i}{\sqrt{2}\, m} \bb{V}^\alpha_K \psi^K{}_I \xi - \frac{i}{2m} \bb{V}^\alpha_K \, \psi^{KJ}\psi_{IJ}\, .
\end{equation}
This expression implies the identity
\begin{equation}
0\equiv \bb{U}^{(I}_{\alpha} \bb{W}^{\alpha J)} - \frac{i}{2} \psi^{KI} \psi_K{}^{J} \equiv \Lambda^{IJ} \, ,
\end{equation}
which becomes a constraint imposed by a Lagrange multiplier in the twistor form of the action in which $\bb{W}$ is an independent variable. This action is
\begin{equation}\label{spinaction}
S= \int dt \, \left\{ \dot{\bb{U}}^I_{\alpha} \bb{W}_I^{\alpha} + \frac{i}{4}\psi_{IJ}\dot \psi^{IJ} - s_{IJ} \Lambda^{IJ} - \rho\, \varphi\right\}\, .
\end{equation}
As anticipated, the only surviving anticommuting phase space variables are the five independent components of $\psi_{IJ}$.
The bosonic phase space is now parametrized by the spinor pair $(U^I,W_I)$, with each spinor in the $({\bf 4},{\bf 4})$ representation of $SU^*(4)\times USp(4)$; equivalently,
each spinor is a pair of $Sl(2;\bb{H})$ spinors, and the spinor pair $(U^I,W_I)$ is equivalent to a pair of $4$-component quaternionic spinors in the $({\bf 4},{\bf 2})$ representation of
$Sp(4;\bb{H}) \times U(2;\bb{H})$. A single $4$-component quaternionic $4$-plet of $Sp(4;\bb{H})$ is a spinor of the 6D conformal group,
and hence a 6D twistor, so the bosonic phase space of the massive 6D particle described by the action (\ref{spinaction}) is parametrized by a pair of twistors, exactly as we found earlier for
$D=3,4$. The real dimension of this space is now $4\times 8 =32$ but these variables are subject to $10+1=11$ first class constraints, which generate $11$ gauge invariances, so the physical bosonic dimension of phase space is $32-2\times 11 =10$. There are also $5$ real anticommuting variables, not subject to any constraints, so the graded real dimension of the physical phase superspace is
$(10|5)$, as expected from our starting point.
The new mass-shell constraint $\varphi=0$ is associated with the following gauge invariance with parameter $b(t)$:
\begin{equation}
\delta_b \bb{W}^I_\alpha = - mb V^\alpha_I \, , \qquad \delta_b \rho = \dot b\, .
\end{equation}
As shown in \cite{Routh:2015ifa}, this is equivalent to a time reparametrization, and as in the 3D and 4D cases, a $b$-gauge transformation
of $\bb{W}$ is induced by a local worldline supersymmetry transformation of $\bb{X}$ and $\xi$ in the expression (\ref{newW}). Specifically, one finds that
\begin{equation}
\delta_\epsilon \bb{W}^\alpha_I= i\epsilon\xi V^\alpha_I\, \, .
\end{equation}
The twistor variables are therefore gauge-invariant under the original gauge transformations modulo a $b$-gauge transformation with parameter $b= -i\epsilon\xi/m$.
We may simplify the action (\ref{spinaction}) by writing
\begin{equation}
\psi_{IJ} = \frac{1}{2} \left(\gamma^a\right)_{IJ} \psi_a \, ,
\end{equation}
where $\psi_a$ is an anti-commuting 5-vector, and $(\gamma^a)_I{}^J$ ($a=1,\dots,5$) are the five $4\times4$ ${\rm Spin}(5)$ Dirac matrices satisfying
\begin{equation}
\left\{\gamma^a,\gamma^b\right\} = 2 \delta^{ab}\, .
\end{equation}
For the choice $\Omega= \bb{I}_2\otimes i\sigma_2$, a basis for these matrices is
\begin{equation}
\gamma^a =\left\{ \sigma_2\otimes \sigma_1\, , \sigma_2\otimes\sigma_2\, , \sigma_2\otimes \sigma_3\, ,
\sigma_1\otimes\bb{I}_2\, , \sigma_3\otimes\bb{I}_2\right\}\, ,
\end{equation}
and the five antisymmetric matrices with entries $\gamma^a_{IJ}$ are $\gamma^a\Omega$. The action becomes
\begin{equation}\label{equivaction}
S= \int dt \, \left\{ \dot{\bb{U}}^I_{\alpha} \bb{W}_I^{\alpha} + \frac{i}{4}\psi_a\dot \psi_a - s_{IJ} \Lambda^{IJ} - \rho\, \varphi\right\}\, ,
\end{equation}
where now
\begin{equation}
\Lambda^{IJ} = \bb{U}^{(I}_{\alpha} \Omega^{J)K} \bb{W}^{\alpha}_K + \frac{i}{8} \left(\gamma^{ab}\right)^{IJ} \psi_a\psi_b \qquad \left(\gamma^{ab} = \gamma^{[a}\gamma^{b]}\right)\, .
\end{equation}
The Lorentz Noether charge in the twistor variables are
\begin{equation}
{\cal J}_{\alpha}{}^{\beta} = \bb{U}^I_{\alpha}\bb{W}^{\beta}_I - \frac{1}{4} \delta_\alpha^\beta \left(\bb{U}_\gamma^IW^\gamma_I\right)\,.
\end{equation}
As expected, there is no fermion bilinear term because the anticommuting variables are Lorentz scalars.
In the quantum theory, the Poisson bracket relations of the anticommuting variables $\psi_a$ become the canonical anticommutation relations
\begin{equation}
\left\{\hat\psi_a,\hat\psi_b\right\} = 2\delta_{ab} \quad \Rightarrow \quad \hat \psi_a= \Gamma_a\, ,
\end{equation}
where $\Gamma_a$ are another set of ${\rm Spin}(5)$ Dirac matrices. This is exactly what one finds in the non-relativistic limit for a particle
of spin $\frac{1}{2}$ in 5-dimensional Euclidean space, so we confirm that the quantum ${\cal N}=1$ 6D massive spinning particle has spin $\frac{1}{2}$.
The twistor form of the 6D massive spinning particle action for ${\cal N}>1$ can be obtained exactly in the way described earlier for $D=4$. The ${\cal N}=2$ case is the one of most interest because the ${\cal N}>2$ cases are inconsistent as quantum theories. We pass over the details since the the end results are known from the work of \cite{Howe:1989vn}. The
procedure is similar to that already described for 4D but the description of the results obtained involves consideration of the 6D Pauli-Lubanski tensors given in \cite{Routh:2015ifa}, which
goes beyond the scope of this paper.
\section{Discussion}
\setcounter{equation}{0}
In this paper we have shown how the massive ``spinning particle'' (with local worldline supersymmetry) may be reformulated in twistor variables for spacetime dimension $D=3,4,6$.
Our results duplicate those of \cite{Mezincescu:2013nta} for $D=3$ but our new construction generalises directly to $D=4,6$.
A feature of the twistorial action is that the anticommuting spin variables appear exactly as they do in the non-relativistic limit!
This is possible because {\it the twistor variables are invariant under the local supersymmetry of the original action}. This is also true for the massless spinning particle but the results are more striking for non-zero mass, partly because it is only in this case that one can consider a non-relativistic limit, and partly because the spin-shell group (which coincides, or ``almost coincides'' with Wigner's little group) is larger for massive particles.
It is also true that the original variables are invariant under the gauge transformations that act on the twistor variables. In this sense, the two formulations are dual, sharing physical content but differing in the extra variables used to ensure manifest Lorentz invariance. Actually, for massive particles both formulations share a common gauge invariance, generated by a Hamiltonian constraint, equivalent in both formulations to a time reparametrization. The mass-shell constraint in one formulation is simply exchanged for a mass-shell constraint in the other. Invariance of one set of variables with respect to the gauge invariances of the other must therefore be understood to be ``modulo'' a time-reparametrization invariance.
Because of the simple non-relativistic nature of the ``fermionic'' terms in the twistorial version of the massive spinning particle action, the analysis of the
implications for the quantum theory is simplified. We illustrated this fact by an analysis of the 4D ${\cal N}$-extended spinning particle. The results
are either known or implicit in earlier work, but we were able to simply confirm both that the ${\cal N}=2$ quantum spinning particle has either spin zero or spin one, and that the ${\cal N}>2$ massive spinning particle is quantum inconsistent in even spacetime dimensions.
Implicit in our results for the massive spinning particle is a twistor description of the {\it massless} spinning particle for $D=3,4,6$, obtained by setting the mass to zero. One would expect to be able to simplify the action in this case so as to parametrize the bosonic phase space by the components of a single twistor, and we have spelt out the details of the procedure that achieves this for $D=3$. In all cases,
the graded dimension of the physical phase space is the same as that found by taking the massless limit of the massive spinning particle in its standard phase space formulation, but this limit
does not yield the usual massless spinning particle action: there remains an additional anticommuting ``spectator'' variable. This discontinuity in the massless limit of the spinning particle
appears not to have been commented on previously.
In our twistor construction, we allowed for either sign of the energy when solving the mass-shell constraint on the $D$-momentum. A notable feature of our results for the twistorial action is that this sign choice does not appear in it. This does not happen for the superparticle, where the sign of the fermion kinetic terms is correlated with the sign of the energy, as pointed out in \cite{Gauntlett:1990xq} in the context of a comparison of gauge-fixed superparticle and spinning particle actions. In an appendix we have confirmed this correlation for the massive 4D superparticle from a supertwistor form of its action constructed along the lines of the 6D case in \cite{Routh:2015ifa}.
Our results for massive spinning particles fit nicely with the association of the spacetime dimensions $D=3,4,6$ with the division algebras
$\bb{R},\bb{C},\bb{H}$, and this suggests a possible octonionic extension to $D=10$. We expect the massive spinning particle to have a twistor formulation for which
the bosonic variables are the components of a pair of octonionic twistors, i.e. two 4-plets of $Sp(4;\bb{O})$. Appropriately defined \cite{Chung:1987in}, this is the
$D=10$ conformal group. We also expect 22 spin-shell constraints in the form of an anti-hermitian $2\times 2$ matrix over $\bb{O}$, and (from a reading of \cite{Chung:1987in})
we would expect this to imply a $U(2;\bb{O})\cong {\rm Spin}(9)$ gauge invariance (since $22+14=36$). If this is correct, and taking into account a mass-shell constraint, we would have
a physical phase superspace of bosonic dimension $64 - 2(22 +1)=18$. Given that the fermionic variables are again the entries of a traceless hermitian $2\times 2$ matrix, now over $\bb{O}$
and presumably equivalent to a ${\bf 9}$ of ${\rm Spin}(9)$, we would then have a physical phase superspace of graded dimension $(18|9)$, as required.
\section{Appendix: Massive 4D superparticle}
\setcounter{equation}{0}
\renewcommand{\theequation}{A-\arabic{equation}}
In this appendix we present the twistor form of the minimal massive 4D superparticle in the notation of this paper, following the twistor construction of the 6D superparticle in \cite{Routh:2015ifa}. The action is
\begin{equation}\label{Spartact}
S= \int\! dt \left\{-\frac{1}{2} \left(\dot X^{\alpha\dot\alpha} +
i\bar\theta^{\dot\alpha} \dot\theta^\alpha -i \dot{\bar\theta}^{\dot\alpha} \theta^\alpha\right)P_{\alpha\dot\alpha}
- \frac{1}{2} e\left(P^2 +m^2 \right) \right\}\, .
\end{equation}
Since the phase superspace has graded dimension $(8|4)$ and there is one (first-class) constraint generating a gauge invariance, the physical phase superspace has
graded dimension $(6|4)$.
The action is manifestly invariant under the spacetime supersymmetry transformations
\begin{equation}
\delta X^{\alpha\dot\alpha} =- i \bar\epsilon^{\dot\alpha}\theta^\alpha - i\epsilon^\alpha \bar\theta^{\dot\alpha}\, ,
\qquad \delta\theta^\alpha= \epsilon^\alpha\, .
\end{equation}
The anticommuting Noether charges are
\begin{equation}
Q_\alpha = P_{\alpha\dot\alpha}\bar\theta^{\dot\alpha}\, , \qquad \bar Q_{\dot\alpha} = P_{\alpha\dot\alpha} \theta^\alpha\, .
\end{equation}
There are also hidden supersymmetry charges \cite{Mezincescu:2014zba}:
\begin{equation}
\tilde Q^\alpha = m\theta^\alpha\, , \qquad \bar{\tilde Q}^{\dot\alpha} = m \bar\theta^{\dot\alpha}\, .
\end{equation}
The Poisson brackets of canonical variables follow directly from the action. The only non-zero one that we will need here is
\begin{equation}
\left\{\theta^\alpha,\bar\theta^{\dot\alpha}\right\}_{PB} =-i P^{\alpha\dot\alpha}/P^2\, .
\end{equation}
Using this, the full algebra of supersymmetry charges, manifest and hidden, is found to be the BPS-saturated ${\cal N}=2$ supersymmetry algebra
\begin{eqnarray}
\left\{Q_\alpha,\bar Q_{\dot\alpha}\right\}_{PB} &=& iP_{\alpha\dot\alpha} \, , \qquad
\left\{\tilde Q^\alpha,\bar {\tilde Q}^{\dot\alpha}\right\}_{PB} = iP^{\alpha\dot\alpha}\, , \nonumber \\
\left\{Q_\alpha, \tilde Q^\beta \right\}_{PB} &=& im\, \delta_\alpha^\beta\, , \qquad
\left\{ \bar Q_{\dot\alpha}, \bar{\tilde Q}^{\dot \beta} \right\}_{PB} = im\, \delta_{\dot\alpha}^{\dot\beta}\, .
\end{eqnarray}
To pass to the supertwistor form of the action, we solve the mass-shell constraint as we did for the 4D spinning particle.
Substitution for $P$ then yields the new Lagrangian
\begin{equation}
L= \left[ \dot U_\alpha^I W^\alpha_I + \dot {\bar U}_{\dot\alpha\, I} \bar W^{\dot\alpha\, I} \pm i\bar\mu_I\dot\mu^I \right]
\end{equation}
where
\begin{equation}
\mu^I = \theta^\alpha U_\alpha^I\, , \qquad \bar\mu_I = \bar\theta^{\dot\alpha} \bar U_{\dot\alpha\, I}\, ,
\end{equation}
and
\begin{equation}
W^\alpha_I= \mp \frac{1}{2} X^{\dot\alpha\alpha}\bar U_{\dot\alpha\, I} \mp \frac{i}{2} \bar\mu_I \theta^\alpha\, , \qquad
\bar W^{\dot\alpha\, I} = \mp\frac{1}{2} X^{\dot\alpha\alpha}U_\alpha^I \mp \frac{i}{2}\mu^I\bar\theta^{\dot\alpha}\, .
\end{equation}
From these expressions we deduce the identity
\begin{equation}
0 \equiv G^I{}_J := U_\alpha^I W^\alpha_J - \bar U_{\dot\alpha\, J} \bar W^{\dot\alpha\, I} \mp i \mu^I\bar\mu_J \, .
\end{equation}
This becomes a $U(2)$ constraint when we promote $W$ to an independent variable. This leads to the new action
\begin{equation}
S= \int\! dt \left\{ U_\alpha^I \dot W^\alpha_I + \bar U_{\dot\alpha\, I} \bar W^{\dot\alpha\, I} \pm i\bar\mu_I\dot\mu^I - s_J{}^I G^I{}_J - \rho \varphi\right\}\, ,
\end{equation}
where $\varphi = |\det U|^2 -m^2$, as for the massive spinning particle.
As a check on this action, one may verify that the (graded) dimension of the physical phase superspace is still $(6|4)$. The $SU(2)$ doublet of twistors $(U,W)$ have $2\times4=8$ complex components, giving a real bosonic dimension of 16, but there are $4$ spin-shell constraints, with spin-shell algebra $U(2)$, and $1$ further mass-shell-type constraint; all are first class so the physical bosonic dimension of $16-2\times 5 =6$. The new anticommuting variable $\mu^I$ is a complex doublet of $U(2)$, and there are no fermionic constraints, so the physical fermionic dimension is $4$.
A crucial feature of this superparticle action, which is required by spacetime supersymmetry \cite{Gauntlett:1990xq}, is the correlation between the sign of the energy and the sign of the ``fermionic kinetic term''.
\subsection*{Acknowledgments}
We are grateful to Paul Howe for helpful correspondence, and to Alex Arvanitakis and Joaquim Gomis for discussions. LM acknowledges partial support from the National Science Foundation Award PHY-1214521. PKT acknowledges support from the UK Science and Technology Facilities Council (grant ST/L000385/1). AJR is supported by a grant from the London Mathematical Society, and he thanks the University of Groningen for hospitality during the writing of this paper. LM and PKT are grateful for the hospitality of the Pedro Pascual Benasque Center for Science, where part of this work was done.
\bigskip
\providecommand{\href}[2]{#2}\begingroup\raggedright
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 8,960
|
%% bootstrap_tsdata_to_mvgc
%
% Calculate sampling distribution for conditional time-domain MVGC from time
% series data, based on a nonparametric bootstrap
%
% <matlab:open('bootstrap_tsdata_to_mvgc.m') code>
%
%% Syntax
%
% FB = bootstrap_tsdata_to_mvgc(U,x,y,p,nsamps,acmaxlags,acdectol)
%
%% Arguments
%
% See also <mvgchelp.html#4 Common variable names and data structures>.
%
% _input_
%
% U multi-trial time series data
% x vector of indices of target (causee) multi-variable
% y vector of indices of source (causal) multi-variable
% p model order (number of lags)
% nsamps number of bootstrap samples
% acmaxlags maximum autocovariance lags (default as for 'var_to_autocov')
% acdectol autocovariance decay tolerance (default as for 'var_to_autocov')
%
% _output_
%
% FB bootstrap Granger causalities (empirical distribution)
%
%% Description
%
% Returns |nsamps| samples from the empirical sampling distribution of the
% time-domain MVGC from the variable |Y| (specified by the vector of indices
% |y|) to the variable |X| (specified by the vector of indices |x|), conditional
% on all other variables in the time series data |U|. The bootstrap randomly
% samples (with replacement) residuals of the full autoregression of |U| on its
% own lags; the subsampled residuals are then added back to the corresponding
% predictors to form surrogate time series [2]. |p| is the model order; for
% other parameters see <var_to_autocov.html |var_to_autocov|>.
%
%% References
%
% [1] L. Barnett and A. K. Seth,
% <http://www.sciencedirect.com/science/article/pii/S0165027013003701 The MVGC
% Multivariate Granger Causality Toolbox: A New Approach to Granger-causal
% Inference>, _J. Neurosci. Methods_ 223, 2014
% [ <matlab:open('mvgc_preprint.pdf') preprint> ].
%
% [2] D. A. Freedman, Bootstrapping regression models, _Ann. Stats._ 9(6), 1981.
%
%% See also
%
% <mvgc_demo_bootstrap.html |mvgc_demo_bootstrap|> |
% <bootstrap_tsdata_to_pwcgc.html |bootstrap_tsdata_to_pwcgc|> |
% <bootstrap_tsdata_to_smvgc.html |bootstrap_tsdata_to_smvgc|> |
% <bootstrap_tsdata_to_spwcgc.html |bootstrap_tsdata_to_spwcgc|> |
% <var_to_autocov.html |var_to_autocov|> |
% <autocov_to_mvgc.html |autocov_to_mvgc|>.
%
% (C) Lionel Barnett and Anil K. Seth, 2012. See file license.txt in
% installation directory for licensing terms.
%
%%
function FB = bootstrap_tsdata_to_mvgc(U,x,y,p,nsamps,acmaxlags,acdectol)
if nargin < 6, acmaxlags = []; end % ensure default
if nargin < 7, acdectol = []; end % ensure default
[n,m,N] = size(U);
assert(m > p,'too many lags');
p1 = p+1;
M = N*(m-p);
np = n*p;
x = x(:)'; % vectorise
y = y(:)'; % vectorise
assert(all(x >=1 & x <= n), 'some x indices out of range');
assert(all(y >=1 & y <= n), 'some y indices out of range');
assert(isempty(intersect(x,y)), 'x and y indices must be distinct');
FB = nan(nsamps,1);
% estimate VAR coefficients
U = demean(U); % no constant term
U0 = reshape(U(:,p1:m,:),n,M); % concatenate trials for unlagged observations
UL = zeros(n,p,M);
for k = 1:p
UL(:,k,:) = reshape(U(:,p1-k:m-k,:),n,M); % concatenate trials for k-lagged observations
end
UL = reshape(UL,np,M); % stack lags
A = U0/UL; % OLS using QR decomposition
if isbad(A), return; end % something went badly wrong
% calculate predictions and residuals
m = m-p; % we lose p observations
UP = A*UL; % predictions
E = U0-UP; % residuals: so U0 = UP + E
E = reshape(E,n,m,N); % put residuals back into per-trial form
EB = zeros(n,m,N);
for s = 1:nsamps
fprintf('MVGC: bootstrap sample %d of %d',s,nsamps);
% generate bootstrap time series
for r = 1:N
EB(:,:,r) = E(:,randi(m,1,m),r); % per-trial subsample residuals with replacement
end
UB = UP + reshape(EB,n,M); % the bootstrap: add subsampled residuals to predictions
% estimate bootstrap VAR parameters
AB = UB/UL; % OLS using QR decomposition
if isbad(AB), fprintf(' *** VAR estimation failed\n'); continue; end % something went badly wrong
EE = UB-AB*UL; % bootstrap residuals (recalculate)
AB = reshape(AB,n,n,p); % bootstrap VAR coefficients
SIGB = (EE*EE')/(M-1); % bootstrap residuals covariance matrix
% calculate bootstrap MVGC
[G,res] = var_to_autocov(AB,SIGB,acmaxlags,acdectol);
if res.error, fprintf(' *** bad VAR: %s\n',res.errmsg); continue; end
FB(s) = autocov_to_mvgc(G,x,y);
fprintf('\n');
end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 9,000
|
Marsh Lane är en by i Derbyshire i England. Byn ligger 43,1 km
från Derby. Orten har 871 invånare (2001).
Referenser
Orter i Derbyshire
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,213
|
Q: Gdb wont put a break at a nop I made a simple assembly program just for the sake of learning and tried putting a break at a no operation but assembly won't listen and i rarely happen to be able to put breaks in code overall.
Would you explain me where i can put breaks and why i can't put it at the no operation address?
Dump of assembler code for function _start:
0x00000000004000b0 <+0>: nop
0x00000000004000b1 <+1>: mov $0x4,%eax
0x00000000004000b6 <+6>: mov $0x1,%ebx
0x00000000004000bb <+11>: mov $0x600124,%ecx
0x00000000004000c0 <+16>: mov $0xd,%edx
0x00000000004000c5 <+21>: int $0x80
End of assembler dump.
(gdb) break 0x4000b0
Function "0x4000b0" not defined.
A: break *0x4000b0
add a star symbol before the address
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,831
|
Q: Resample sales data by day - now unable to use polyfit - Python I have a dataframe of data with sales like this:-
sales_df
Date Sales
01/04/2020 00:03 1
01/04/2020 02:26 4
01/05/2020 02:28 3
01/05/2020 05:09 5
01/06/2020 05:16 6
01/06/2020 05:17 7
01/07/2020 05:18 3
which looks like this on sales_df.info()
0 Date datetime64[ns]
1 Sales float64
and I can perform the below and get a result
line_coef = np.polyfit(sales_df.index,sales_df['Sales'],1)
print(line_coef)
I want to do the same, but aggregated by day, so I've resampled the data like this
sales_day_df = sales_df.resample('D',on='Date').agg({'Sales':'sum'})
which results in a dataframe like this:-
sales_by_day_df
Date Sales
01/04/2020 5
01/05/2020 8
01/06/2020 13
01/07/2020 3
But when I try and perform the same
line_coef = np.polyfit(sales_by_day_df.index,sales_by_day_df['Sales'],1)
print(line_coef)
I get an error
UFuncTypeError: ufunc 'add' cannot use operands with types dtype('<M8[ns]') and dtype('float64')
I notice that I only have the one column now in my dataframe with a DatetimeIndex, is this the cause? Do I need to create a new column for the date when I resample the data?
sales_by_day_df.info()
DatetimeIndex: 30 entries, 2020-04-01 to 2020-04-30
Freq: D
|Data columns (total 1 columns):|
# Column Dtype
--- ------ -----
0 Sales float64
A: It's because when you resample, your index has to be datetime. in your code, you set the Date column as the index.
your first try work because the index still numbers (not DateTime as mentioned in the error message)
your second try didn't work because the index now is datetime
my advice is, try to reset the index then try to execute your polyfit again
you can reset your index with DataFrame.reset_index()
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 970
|
Radulf – książę Turyngii w latach 634 – 642, król w 642
Radulf II – książę Turyngia w latach 874 – 880
Radulf – biskup La Seu d'Urgell w latach 792 – 798
Radulf de Barcelona – biskup La Seu d'Urgell w latach 914 – 940
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 7,818
|
Do not conform any longer to the pattern of this world, but be transformed by the renewing of your mind. Then you will be able to test and approve what God's will is–his good, pleasing and perfect will.
The Bible is full of wisdom to help in any situation.
You can be a Christian without reading, knowing, studying, meditating, and understanding the Bible. But why would you want to? I became a Christian in my teenage years, but never understood the value of God's Holy Word.
I understand the value now!
I could have avoided so much pain, darkness, and emptiness in my life if I'd understood the value sooner.
By studying it before the adversity comes, you'll have a better understanding of God and his faithfulness. This will prepare you for any situation that arises. If you're knee-deep in adversity or even feel as if you're drowning in it, fear not. God is with you and it's not too late to start today.
The value doesn't come from reading the Bible. Reading it won't change your heart or your life. Meditating on, believing, and doing will!
So, whether you are in the midst of adversity or not, pick up that Bible today and you will never regret it. There is power in God's words.
But the power doesn't come from reading the words–it comes from being a DOER OF THE WORD. Mmm…maybe that wasn't what you wanted to hear? Maybe, you wanted the easy way? God's way is NOT the easy way, but it is the BEST way!
SHARING TIME: WHAT HAVE YOU BEEN AVOIDING BECAUSE IT'S TOO HARD?
Next What's Your God-Given Dream?
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 2,165
|
{"url":"https:\/\/www.luogu.com.cn\/problem\/P4086","text":"# [USACO17DEC]My Cow Ate My Homework S\n\n## \u9898\u76ee\u63cf\u8ff0\n\nIn your bovine history class, you have been given a rather long homework assignment with $N$ questions ($3 \\leq N \\leq 100,000$), each graded with an integer score in the range 0...10,000. As is often customary, your teacher plans to assign a final grade by discarding a question on which you received the lowest score and then averaging the remaining scores together. Unfortunately, your pet cow Bessie has just eaten your answers to the first $K$ questions! ($K$ could be as small as 1 or as large as $N-2$). After copious explanation, your teacher finally believes your story, and agrees to grade the remaining non-eaten part of the assignment the same way as before -- by removing the lowest-scoring question (or one such question, in the event of a tie) and averaging the rest. Please output all values of $K$ which would have earned you the maximum possible score according to this grading scheme, in sorted order. \u5728\u4f60\u7684\u5386\u53f2\u8bfe\u4e0a\uff0c\u4f60\u5f97\u5230\u4e86\u4e00\u4e2a\u5f88\u957f\u7684\u4f5c\u4e1a\u3002\u8fd9\u4e2a\u4f5c\u4e1a\u5305\u542b\u4e86N\u4e2a\u9898\u76ee\uff083 \u2264 N \u2264 100,000\uff09\uff0c\u6bcf\u4e2a\u9898\u76ee\u7684\u6210\u7ee9\u57280~10,000\u4e4b\u95f4\u3002 \u6309\u7167\u60ef\u4f8b\uff0c\u4f60\u7684\u8001\u5e08\u6309\u7167\u4ee5\u4e0b\u65b9\u5f0f\u8ba1\u7b97\u6700\u7ec8\u6210\u7ee9\uff1a\u53bb\u6389\u4f60\u6700\u4f4e\u7684\u4e00\u4e2a\u6210\u7ee9\uff0c\u7136\u540e\u5c06\u5176\u4f59\u6210\u7ee9\u7684\u5e73\u5747\u6210\u7ee9\u4f5c\u4e3a\u6700\u7ec8\u6210\u7ee9\u3002\u4f46\u4e0d\u5e78\u7684\u662f\uff0c\u4f60\u7684\u5ba0\u7269\u725b\u201c\u8d1d\u897f\u201d\u521a\u521a\u5403\u4e86\u524dK\u4e2a\u9898\u76ee\u7684\u7b54\u6848\uff01\uff081 \u2264 K \u2264 N-2\uff09 \u7ecf\u8fc7\u4f60\u7684\u4e00\u756a\u89e3\u91ca\uff0c\u8001\u5e08\u7ec8\u4e8e\u76f8\u4fe1\u4e86\u4f60\u7684\u6545\u4e8b\uff0c\u5e76\u4e14\u540c\u610f\u5bf9\u4f60\u6709\u7b54\u6848\u7684\u9898\u76ee\uff08\u6ca1\u6709\u88ab\u5403\u6389\u7b54\u6848\u7684\u9898\u76ee\uff09\u50cf\u4e4b\u524d\u4e00\u6837\u7ed9\u5206\u2014\u2014\u901a\u8fc7\u53bb\u6389\u6700\u4f4e\u7684\u6210\u7ee9\uff08\u5982\u679c\u6709\u591a\u4e2a\u6700\u4f4e\u6210\u7ee9\uff0c\u5219\u53ea\u53bb\u6389\u5176\u4e2d\u4e00\u4e2a\uff09\u5e76\u53d6\u5269\u4f59\u6210\u7ee9\u7684\u5e73\u5747\u6210\u7ee9\u3002 \u6839\u636e\u8fd9\u4e00\u6210\u7ee9\u8ba1\u7b97\u65b9\u6848\uff0c\u8bf7\u6309\u5347\u5e8f\u8f93\u51fa\u6240\u6709\u53ef\u4ee5\u4f7f\u4f60\u6700\u7ec8\u6210\u7ee9\u6700\u9ad8\u7684K\u7684\u503c\u3002\n\n## \u8f93\u5165\u8f93\u51fa\u683c\u5f0f\n\n### \u8f93\u5165\u683c\u5f0f\n\nThe first line of input contains $N$, and the next line contains the scores on the $N$ homework questions.\n\n### \u8f93\u51fa\u683c\u5f0f\n\nPlease output, one value per line, all values of $K$ which would have earned you the maximum possible score.\n\n## \u8f93\u5165\u8f93\u51fa\u6837\u4f8b\n\n### \u8f93\u5165\u6837\u4f8b #1\n\n5\n3 1 9 2 7\n\n### \u8f93\u51fa\u6837\u4f8b #1\n\n2\n\n## \u8bf4\u660e\n\nIf Bessie eats the first two questions, then the remaining scores are 9, 2, and 7. Removing the minimum and averaging, we get a final grade of 8, which is the highest possible.","date":"2022-12-07 17:39:16","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\": 0.6845528483390808, \"perplexity\": 1591.5442012972517}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-49\/segments\/1669446711200.6\/warc\/CC-MAIN-20221207153419-20221207183419-00308.warc.gz\"}"}
| null | null |
Members of medical community call for shift from race-based to race-conscious medicine
Anjali Mangla 1:12 am, Oct 28, 2020
Advocating for the transition of medicine away from race-based practices and toward a more race-conscious approach, Yale Medical School MD-PhD student Jessica Cerdeña GRD '21, Yale Emergency Medicine physician Jennifer Tsai and Howard University PhD student Marie Plaisime recently co-authored an editorial for The Lancet, a peer-reviewed medical journal, this month about reforming medical education for future doctors.
The editorial characterizes the current practice of medicine as "race-based," stating that physicians often infer that race has inherent biological significance, whereas in actuality race is merely a social construct. The authors say the future of medicine should move from this race-based approach to a "race-conscious" approach, with the end goal being a reduction in health inequities across racial lines. They advocated for emphasizing institutional inequities in healthcare during medical education, which they said would raise the cultural competency of future physicians.
"Race-based medicine uses and treats race as an essential biological variable that has utility in medical education and clinical practice," Cerdeña said. "Race-conscious medicine understands that race is a social and power construct that changes for political utility over time, and that it is a poor proxy for human genetic variation. Instead, the more salient variable when it comes to differences in human groups that have been socially categorized in this way is the experience of racism and racialization … This idea that there are biological differences between racial groups comes from colonization. This is how white supremacy operates."
The editorial was published in The Lancet after the prominent medical journal released a statement supporting the Black Lives Matter movement and its continuing commitment to advancing racial equality. This editorial was also published following a summer of racial unrest and protests around the country that advocated for putting an end to police brutality against Black Americans. The timing of the publication was significant to the authors.
"Certainly we were motivated by the very apparent murders of George Floyd, Ahmaud Arbery and Breonna Taylor, among others," Tsai said. "But also because this is a very long-standing problem that I think all three of us have been working on, thinking about and advocating against beforehand."
The article presented a wide range of examples in which race heavily influences physicians' medical assessment of patients, such as the Atherosclerotic Cardiovascular Disease risk calculator equation. This online tool determines a given patient's risk of having a cardiovascular event within ten years, Cerdeña said. These calculations involve categorizing the patient as either "Black" or "not Black." If the patient is Black, the predicted risk is significantly increased, and the patient is more likely to start taking a certain medication earlier than patients of other racial groups.
The prescription dosage for certain drugs can also vary based on racial groups. According to Cerdeña, medical practitioners consider East Asian people to have different metabolisms, which means that a drug like Eltrombopag, a bone marrow stimulant, is started at half the normal dose for these people. This type of race-based medicine is condemned in the article.
"You can't know someone's pharmacokinetics, or the way that they metabolize a drug, by looking at them, or by their race," Cerdeña said. "That's the problem with race-based medicine."
The Lancet piece includes different policy recommendations for researchers, clinicians and practitioners. According to Plaisime, It was crafted with care towards its intended audience of physicians, picking and choosing words that would be most accessible. The most important step in moving forward, Tsai said, is to change the curriculum of medical schools to be more race-conscious.
The authors also wrote this editorial from the perspective of their own experiences as women of color within the American healthcare system. Cerdeña is Italian and Chilean with Indigenous Mapuche ancestry, Plaisime is Haitian American and Tsai is Taiwanese American.
"As a Black woman, for sure there have definitely been times where I've been treated differently based on how I appeared in the clinical room, how I was spoken to," Plaisime said. "Also being the daughter of Haitian immigrants, I know first-hand what it's like to have your accent judged. Not just one isolated event that kind of sparked this, it's my story, and I want to make sure that all people receive equitable care."
The authors also emphasized that even research studies are subjected to racialization, despite undergoing objective screening processes instituted by peer-reviewed journals. Although race has no inherent biological significance, countless epidemiological studies include race as a critical variable when mapping out the prevalence of certain diseases.
In their article, the authors urged clinical research journals to include instructions in their publication guidelines that denounce the use of race as a proxy for biological variables such as genetics, pharmacokinetics and metabolism.
"Prestigious publications continue to allow research that [uses] problematic versions of race in their research," Tsai said. "They still allow that to be published, which means this kind of data and this kind of thinking is continually generated and perpetuated."
Plaisime, who is a medical sociologist studying the impacts of race and racism in clinical decision-making processes, explained that biologizing race is harmful. Prior to this collaboration, she had published a piece about the implications of using race in medicine.
She emphasized the need for using "evidence-based" treatments that do not rely solely on race as a factor of consideration, as this can often be detrimental to members of racial minority groups.
"The different biomarkers and tools they use aren't necessarily based on science, but more on racist assumptions," Plaisime said. "My work was based on how that kind of training impacts later on how patients receive care, and how medical students are trained."
Cerdeña and Plaisime are both Robert Wood Johnson Foundation Health Policy Research Scholars, and Tsai is completing her residency at the Yale New Haven Hospital.
Anjali Mangla | anjali.mangla@yale.edu
ANJALI MANGLA
Anjali Mangla is a Science & Technology Editor for the News. She previously covered the intersection of STEM and social justice. Anjali is a sophomore in Ezra Stiles College planning to study Neuroscience, Global Affairs and Global Health Studies.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 8,101
|
Горленко Михайло Андрійович (чернече ім'я Митрофан) — архімандрит Київського Видубицького монастиря. Походив з відомої козацько-шляхетської родини Горленків. Онук прилуцькького полковника Дмитра Горленка; син прилуцькького наказового полковника, наказового гетьмана А. Горленка, брат святителя Йоасафа Білгородського. Вихованець Києво-Могилянської академії.
Біографія
Освіту здобув у Києво-Могилянській академії.
По завершенні повного академічного курсу прийняв чернечий постриг.
Протягом 1749–1754 — ігумен Максаківського Спасо-Преображенського монастиря Чернігівської єпархії.
З 2-ї половини 50-х років XVIII століття очолив Київського Видубицький монастир як настоятель, а згодом і архімандрит.
У серпні 1763 разом з префектом Києво-Могилянської академії Мельхіседеком Орловським і вчителем піїтики Р. Петулинським, та в листопада 1764 разом з настоятелем Київського Михайлівського Золотоверхого монастиря архімандритам Модестом Стефановичем, Київського Кирилівського монастиря ієромонахом Т. Вербицьким та Ніжинського Благовіщенського Назарет-Богородицького монастиря архімандритом Є. Могилянським брав участь у роботі комісії з розмежування земель Київського Братського монастиря, на які претендувала також братія Київського Софійського монастиря (поблизу сіл Стайки та Трипілля).
Помер у Святогорській Успенській пустині, де провів останні роки свого життя.
Література
Модзалевский В. Л. Малороссийский родословник, т. 1. К., 1908.
Києво-Могилянська академія в іменах
Випускники Києво-Могилянської академії
Українські релігійні діячі
Архімандрити
Настоятелі монастирів Києва
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 3,038
|
Our mission is to build a movement to measure and incentivise business impact towards a sustainable future that works for everyone.
We envision a society that values the success of business by what it contributes to the world.
The World Benchmarking Alliance (WBA) was launched in 2018 because we believed that there needs to be real change in the way that business impact is measured to boost motivation and stimulate action for a sustainable future for everyone.
WBA identified seven transformations that need to take place to put society and the worldwide economy on a more sustainable path to achieve the SDGs. To turn these transformations into action, WBA develops in close collaboration with the Alliance a series of benchmarks assessing 2,000 of the world's most influential companies, ranking and measuring them on their contributions to the SDGs.
WBA's benchmarking journey to create a better world together
This information will be freely available to everyone. Investors, governments, civil society, individuals and the companies themselves will be empowered. Investors can influence the companies they invest in. Governments can develop better policies and civil society can direct public support and partnership efforts. Individuals can decide where to spend their money and where they choose to work.
These benchmarks will reveal both to companies and stakeholders where each company stands compared to its peers, where it can improve and where urgent action is needed to deliver on the SDGs. To turn business into a force for good. Ranking and measuring the companies will give them the guidance to drive change and create accountability for those who don't change.
How do we develop benchmarks?
Learn about the seven systems transformations we identified to achieve the SDGs.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 315
|
package org.ops4j.pax.logging.it.karaf.support;
import java.util.Dictionary;
import java.util.Hashtable;
import java.util.concurrent.CountDownLatch;
import java.util.concurrent.TimeUnit;
import java.util.function.Consumer;
import org.osgi.framework.BundleContext;
import org.osgi.service.cm.Configuration;
import org.osgi.service.cm.ConfigurationAdmin;
import org.osgi.service.event.EventConstants;
import org.osgi.service.event.EventHandler;
import static org.junit.Assert.assertTrue;
public class Helpers {
/**
* <p>Helper method that does several things:<ul>
* <li>gets current {@link org.ops4j.pax.logging} config</li>
* <li>registers {@link org.osgi.service.event.EventHandler} for configuration topic</li>
* <li>updates the configuration using passed consumer</li>
* <li>awaits for successful configuration change</li>
* </ul>
*
* <p>Simply - it synchronously changes logging configuration and waits for it to be effective.
*/
public static void updateLoggingConfig(BundleContext context, ConfigurationAdmin cm, Consumer<Dictionary<String, Object>> consumer) {
final Throwable[] pt = new Throwable[1];
try {
Configuration c = cm.getConfiguration("org.ops4j.pax.logging", "?");
final CountDownLatch latch = new CountDownLatch(1);
EventHandler handler = event -> {
if (event.containsProperty("exception")) {
pt[0] = (Throwable) event.getProperty("exception");
}
latch.countDown();
};
Dictionary<String, Object> props = new Hashtable<>();
props.put(EventConstants.EVENT_TOPIC, "org/ops4j/pax/logging/Configuration");
context.registerService(EventHandler.class, handler, props);
Dictionary<String, Object> configuration = new Hashtable<>();
if (consumer != null) {
consumer.accept(configuration);
}
c.update(configuration);
assertTrue(latch.await(5, TimeUnit.SECONDS));
} catch (Exception e) {
throw new RuntimeException(e.getMessage(), e);
}
if (pt[0] != null) {
throw new RuntimeException("Configuration problem", pt[0]);
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 733
|
Q: Does play store pre-launch report warnings delay the publication in the Beta release or in production? I have recently uploaded the app to the Play-Store after months of building it and now play store delayed publish. So, after browsing through the console found "Pre-release report", so 4 some minor issues. So, thought that they are causing the delay, so updated the app those issues removed and got now only 1 issue, which is of the before issues, which is not at all an issue actually. Because of these things I have rolled same app to the production.
So, my question is does pre-launch report really delay the publication time, even the issues are not issues actually, because the bot is flagged the issue actually.
A: No pre launch reports don't cause any delay...you are facing the delay which is currently being faced by all developers. Google has also mentioned the reason behind it that because of covid 19 pandemic they are taking more than usual review time. If it is first app for play store then it will take about 7 days or else less than 7 days. I recently published my 3rd app and it took 2 days but first one took 7 days. Similarly first app update took 2 days but 3rd apps update takes less than 1 hour may be I think now it is taking lesser time as now lockdowns have been taken off by govt. In some places.
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Bauhinia tomentosa, also known as yellow bauhinia or yellow bell orchid tree, is a species of plant in the family Fabaceae. It is found in South Africa, Mozambique, Zimbabwe, Tropical Africa, India, and Sri Lanka.
Description
Yellow bauhinia is a small tree with a maximum height of . It has drooping slender branches with multiple scrambling stems. The bark is greyish, smooth, and sometimes hairy, which gives its specific name tomentosa. Greenish leaves are deeply divided and elliptic in nature; margin entire. Flowers are bell-shaped with large, yellow petals with a dark maroon patch at the base. The fruit is a pale-brown pod. Extracts of the plant's roots have in vitro antimicrobial activity against Gram-positive bacteria.
References
tomentosa
Flora of Mozambique
Flora of Zimbabwe
Flora of India (region)
Flora of Sri Lanka
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INTELLIGENT BUSINESS MANAGEMENT SYSTEMS
OUR PERSPECTIVE
SMRs, Size matters – or does it?
Dr Janet Wilson, Senior Nuclear Consultant
If you're a nuke like me (an engineer who's spent the majority of their career in the nuclear industry) you'll be bombarded with the woes of new nuclear build; a lack of investment, massive cost overruns, construction problems, quality assurance failures, etc. You'll also have read many articles expounding the virtues of Small Modular Reactors (SMRs) which range in design from "Mini-Me" PWRs through to innovative, conceptual designs claiming to be the next generation of passively safe reactors that can be transported on the back of a truck and installed and operated with little or no nuclear expertise. So my question is – Why do I have to choose between these two options? Is there room for both? I'm no economist but here are some of my thoughts when answering these questions.
S for Small, what is the right size?
Assuming that nuclear has a place in the UK's energy mix (a debate for another time), to provide 6,000 MW you need either 6 large capacity 1,000 MW+ light water reactors or twenty 300MW SMRs. That's equivalent to a thousand 6MW wind turbines.
Conventional light water reactors such as PWRs or BWRs cost £billions to build, but can operate for at least 60 years. They are evolutionary in design, i.e. incremental safety, construction and operational improvements have been made to the original concept over the years. They are a known and understood quantity when it comes to nuclear safety, environment and security Regulators whose regulatory costs are considerable (£millions/year).
It's true to say that the cost of building any of the SMR designs out there can only be estimated but presumably they need to be less than a third of the price of conventional ones. How long they can operate for also varies. Some are "plug-and-play" and are designed to operate without refuelling and/or internal maintenance for life but it's unlikely that that life is more than 60 years. Others are simplified smaller versions of their big brothers but may have replacement refuelling modules that make them simpler to operate and maintain. Importantly, SMRs are new to Regulators and will require the same level of design scrutiny as the larger reactors and must meet the same exacting standards. Therefore, it's difficult to see how, at least initially, the costs of permissioning them will be lower. Let's see what happens when the first SMRs get their Generic Design Assessments.
Before I leave small versus large, what about input to the National Grid and speed of response to demand? It's fair to say that PWRs and BWRs are relatively inflexible in operation whereas SMRs have the potential to be more dynamic and match their power output to demand. A good argument then for both? What about innovations in electricity storage? Can stored electricity be used to respond to rapid or unexpected demand?
M for the Modular advantage.
The whole idea it seems is that these small reactors can be factory built in modules and assembled on-site thereby reducing the time and cost of construction. Great, but isn't that the way that some PWRs are heading with prefabricated modules? Well no, the prefabricated modules for large reactors face a number of obstacles. Production numbers are so low, each module can be effectively viewed as an expensive one off. The sheer scale and complexity of modules creates its own set of challenges; the number of credible suppliers is reduced as is competition, quality control is difficult and transport of very large modules can be challenging. Worse still for the supply chain, the seemingly never ending delays are savaging cash flow, so ultimately this is making big nuclear an increasingly unattractive market.
In contrast, the production of large numbers of small reactor modules appears to offer real promise on a number of fronts. Get it right and SMRs will create the opportunity to build true production lines for hundreds of standard modules. In turn this could deliver a much needed step change in production efficiency and the type of quality control we have historically seen in areas such as fuel rod production.
R for new thinking on Reactors
Technically it is interesting to consider what happens if the entire reactor is the module? The burn-up of the fuel could be considerably greater than conventional fuel cores. That means more 'nasties' at the end of life. That makes the Plutonium that is generated as the fuel 'burns' more difficult to access and so it could be considered to have higher proliferation resistance (using it to make a nuclear weapon) but there is more of it and it's in a neat, transportable package. If there needs to be the same counter-terrorist armed response presence as at other nuclear sites then how is this cheaper? Perhaps a vision of SMR farms will combat this security risk? This brings us back to the economics of whether 6 large capacity 1,000MW+ light water reactors are more or less economically viable than 20 300MW SMRs?
A range of sizes creates new options and possibilities.
Finally, Britain has some of the best Universities and Research establishments in the world and has a long and proud history of producing world class, innovative nuclear science, but it seems to me, we do the clever inventing and developing while others make the money. The struggle to build a new generation of large capacity nuclear reactors in the UK has revealed many risks and demonstrated that neither government nor the UK private sector have the appetite for investment in big nuclear.
SMR's on the other hand, present a different proposition with the potential to be produced efficiently in advanced manufacturing facilities and then deployed much more quickly. This points to the potential for SMRs to support the delivery of far better return on investment for both manufacturers and generators.
Should we therefore be supporting our nuclear scientists and engineers and maintaining our UK capabilities? Absolutely. This brings me back to my original question on whether size matter and do we need to choose between big and small reactors? Regardless of the recent delays and challenges, I can still see a place for conventional large capacity PWRs and BWRs and the carbon free baseload they will deliver. However, commercially and from a manufacturing perspective, the right size does appear to be smaller, not larger. SMRs offer the potential not only to meet the energy demands of the future, but allow for the UK to design, manufacture and export such devices, but there again I'm an engineer not an economist or a politician!
Employment Law – The Employer's Ally
Acquisitions – When to spend?
Energy Storage – Serious Implications
Fujifilm Value from Innovation
© 2019 Mercury Stone | All Rights Reserved | Sitemap | Web Design & Hosting from KCS
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\section{Introduction}
Recent events around possible discovery of pentaquarks and negative results, obtained lately,
make situation with the observation of these new type baryonic resonances quite dramatic.
Indeed, one of striking events in elementary particle physics of the last few years was
observation of baryon resonances with unusual properties (end of 2002 - 2005):
$\Theta^+(1540),\;$ strangeness $S=+1$, isospin $I=0$ (most likely), width
$\Gamma_\Theta < 10\,MeV$,
seen by different collaborations in Japan, Russia, USA, FRG, CERN;
$\Phi/\Xi_{3/2}^{--}(1862)$, strangeness $\;S=-2\;$, $\;I=3/2\;(?)$, $\Gamma < 18 \,MeV$ observed
by NA49 Collab.
at CERN\footnote{In the latest issues of PDG the state $\Xi_{3/2}$ is called
$\Phi$ \cite{PDG}, although the notation $\Xi_{3/2}$ seems to be more informative; here it will be
denoted as $\Phi/\Xi_{3/2}$ };
$\Theta^0_c(3099)$, charm $\;C=-1$, $\Gamma < 15\,MeV$ seen by H1 Collab., DESY.
Spin-parity $J^P$ of these states is not measured yet.
These states are manifestly exotic because they cannot be made of 3 valence quarks only.
There are different possibilities to have exotic baryon states:
\\
a) positive strangeness $S>0$ (or negative charm $C<0$, or positive beauty), since $s$-quark has
$S=-1$ and $c$-quark $C=+1$,
\\
b) large (in modulus) negative strangeness $S<-3B$, $\;B$ - baryon number; similar for charm
or beauty,
\\
c) large enough isospin $I> (3B+S)/2\,$, if $\;\; -3B \leq S \leq 0$, or
charge $Q\;>\;2B+S$ or $Q\;<\, -B$ in view of Gell-Mann - Nishijima relation $Q=I_3+Y/2$.
The pentaquarks $\Theta^+(1540)$ and $\Theta_c(3099)$, if it is confirmed, are just of the type
{\bf a)},
the possibility {\bf b)} is difficult to be realized in practice, since large negative strangeness of
produced baryon should be balanced by corresponding amount of positively strange kaons; high enough
energy of colliding particles is necessary here.
The state $\Phi/\Xi^{--}_{3/2}$ is of the type {\bf c)}.
The minimal quark contents of these states are:
$\Theta^+=(dduu\bar{s});\; \; \Xi^{--}=(ssdd\bar{u});\;
\Theta_c^0=(dduu\bar{c})$, and by this reason they are called pentaquarks.
The history and chronology of pentaquarks predictions and discovery
has been discussed already in
many papers, here I recall it briefly for completeness. Readers familiar with this subject can
go immediately to sections 3, 4.
$\Theta^+,\;S=+1$ baryon was observed first at
SPring-8 installation (RCNP, Japan)\cite{1}
in reaction
$\gamma ^{12}C\, \to K^+n+...$. The reported mass is $1540\pm 10\;MeV$ and width $ \Gamma < 25\,MeV$,
confidence level (CL) $4.6\sigma $. Soon after this and independently
DIANA collaboration at ITEP,
Moscow \cite{2} reported on observation of $\Theta^+$ state in
interactions of
$K^+$ in $Xe$ bubble chamber. The mass of
the bump in $K^0p$ invariant mass distribution is $1539\pm 2\;MeV, \; \Gamma < 9 \,MeV$,
confidence level a bit lower, about $4.4\sigma$.
Confirmation of this result came also from several other experiments
\cite{3,4,5,6,7,8,9,10,troyan}
mostly in reactions of photo-(electro)-production.
The reported mass of $\Theta^+$ is smaller
by several $MeV$, or even by $\sim (10-20)\,MeV$ in some of experiments \cite{5,7,8,9,10}, than first
reported value $1540\,MeV$ \cite{1}.
The CLAS Collaboration \cite{bdv} provided recently evidence for
two states in $\Theta$-region of the $K^+n$ invariant mass distribution at $1523\pm 5\,MeV$
and $1573\pm 5\,Mev$. The nonobservation of $\Theta^+$ in old kaon-nucleon scattering data provided
restriction on the
width of this state.
Phase shift analysis of $KN$-scattering in the energy interval
$1520\,-\,1560\,MeV$ gave a restriction $\Gamma < 1\,MeV$ \cite{asw}.
Later analysis of data
\cite{2}, obtained in $Xe$ bubble chamber, allowed to get the estimate for
the width of $\Theta^+$:
$\Gamma_\Theta \simeq 0.9\pm 0.3\,MeV$, and from total cross section
data $\Gamma_\Theta$ in the interval $1\,-\,4\,MeV$ \cite{gib}.
Several experiments, mostly at higher energies, did not confirm existence of $\Theta$, pessimistic
point of view was formulated, e.g., in \cite{poc}.
More complete list of references to negative
results, many of them being not published yet, and their critical discussion can be found in
\cite{hicks,azim,hic2}.
Most serious seems to be
recent negative result on $\Theta^+$ photoproduction on protons, obtained at spectrometer CLAS
(JLAB) with high statistics, where no resonance has been observed in $K^+n$ final state in
the mass interval $1520-1600\,MeV$ scanned with $5\,MeV$ steps \cite{devita}.
The doubly strange cascade hyperon $\Phi/\Xi_{3/2},\; S=-2$, probably with isospin $I=3/2$, is observed
in one experiment at CERN, only, in proton-proton collisions at $17 \,GeV $\cite{alt}. The mass of
resonance in $\Xi^-\pi^-$ and $\bar{\Xi}^+\pi^+$ systems is $1862\pm 2\;MeV$ and mass of resonance in
$\Xi^-\pi^+,\;\bar{\Xi}^+\pi^-$ systems is
$1864\pm 5\;MeV,$ width $ \Gamma < 18\,MeV$, and $CL=4.0 \sigma$.
The fact makes this result more reliable, that resonance $\Phi/\Xi^{--}$ was observed in antibaryon
channel as well.
However, this resonance is not confirmed by HERA-B, ZEUS, CDF, WA-89, COMPASS collaborations (see e.g.
\cite{poc,comp}), although there is
no direct contradiction with NA49 experiment because other reactions have been used and mostly at
higher energies, so, upper bounds on the production cross sections of
$\Phi/\Xi_{3/2}$ have been obtained in this way, see \cite{comp,spen} for compilation of these results.
The anticharmed pentaquark $\Theta_c^0,\;\; C=-1$ was observed at
H1, HERA, Germany, in
$ep$ collisions \cite{akt}, in both baryon number $B=\pm 1$ channels. The mass of resonance in
$D^{*-}p,\;D^{*+}\bar{p}$ systems is $3099\pm 3\pm 5\;MeV,
\;
\Gamma < 15\,MeV, \; CL= 6.2\sigma$.
ZEUS collaboration at HERA \cite{zeus} did not confirm the existence of $\Theta_c^0$ with this
value of mass, and
this seems to be serious contradiction, see again \cite{poc}.
There is also some evidence for existence of other baryon states, probably exotic, e.g. nonstrange
state decaying into nucleon and two pions \cite{rip}, and resonance in $\Lambda K_S^0$ system with
mass $1734 \pm 6\,MeV,\;
\Gamma \,<\, 6\,MeV$ at $CL=(3 - 6)\sigma$
which is $N^{*0}$ or $\Xi^*_{1/2}$,
observed by STAR collaboration at RHIC \cite{kab} in reaction
$Au+Au$ at $\sqrt{s_{NN}}\sim 200\,GeV$.
Several resonances in $\Lambda K_S^0$ system have been
observed recently at JINR \cite{aer}, the lowest
one has the mass $1750 \pm 18\,MeV$, not in contradiction with \cite{kab}.
Evidently, high statistics experiments on pentaquarks production are drastically needed, as
well as checking the relatively old scattering data analyzed in \cite{asw,gib}. If high statistics
experiments do not confirm existence of $\Theta^+$, it
would be interesting then to understand
why more than 10 different experiments, although each of them with
not high
statistics, using different installations and incident particles, provided
similar
positive results.
From theoretical point of view the interest to such exotic baryon states
will not dissappear in any case, because they represent the next in complexity step after baryons
made of 3 valence quarks and should most probably appear at higher masses and with greater widths.
Information about status of higher statistics experiments performed or to
be performed at JLAB (CLAS Collab.) can be found in \cite{pr,hic2}. Several reviews of existing
experimental situation appeared lately, e.g. \cite{comp,spen,azim,hic2,kab2}, and I will not
go into further details here.
In any case, the difficulties in observation of such exotic states mean that the role of these
states in hadron dynamics of moderate and especially high energies is not big and cannot be even
compared with, e.g., the role of $\Delta(1232)$ resonance in medium energy pion-nucleon interactions.
Next sections necessarily contain certain overlap with previous discussions, I hope to add some
new accent of criticism to the discussion of this interesting topic. Sections 3,4 contain short
description of the topological soliton models, in section 5 the results for baryon spectra are
presented.
In Section 6 the large $N_c$ arguments that the width of $\Theta^+$ is expected to be greater than width
of $\Delta$ resonance are criticized and ambiguity of large $N_c$ consideration is stressed, in
Section 7 a correspondence with the quark model description is established and some
difference is fixed and discussed as well. In section 8 the masses of partners of lowest pentaquark
states with different spin or isospin are estimated.
In Section 9 the multibaryons with additional quark-antiquark pairs are
discussed within chiral soliton approach, which can appear as $\Theta$ hypernuclei, or hypernuclei
with anti-charm (-beauty), and it is argued that existence of such states is a
natural property of this approach. Section 10 contains conclusions and some prospects.
\section{Early predictions}
From theoretical point of view the existence of such exotic states by itself was not unexpected.
Such states have been discussed first by R.L.Jaffe within MIT quark-bag model
\cite{j}.
The mass of these states
was estimated to be considerably higher than that reported now:
$M_\Theta \simeq 1700 \;MeV, \;\; J^P=1/2^-$.
These studies were continued by other authors \cite{hog}:
$M_\Theta \simeq 1900\,MeV$, $J^P=1/2^-$, and similar in \cite{str}.
From analysis of existed that time data on $KN$ interactions the estimate was obtained in \cite{roi}
$M_\Theta \simeq 1705\,MeV \;(I=0), 1780\,MeV \;(I=1)$ with very large width.
If the data on narrow low lying pentaquarks are not confirmed, then these earlier predictions have
more chances to be correct.
In the context of chiral soliton model the $\{\overline{10}\}$ and $\{27\}$ -plets of exotic baryons
were mentioned first in \cite{mc}, without any mass
estimates, however.
Rough estimate within
the "toy" model, $M_{\overline{10}} \,-\,M_8 \simeq 600\,MeV$,
was made a year later in \cite{bieden}. A resonance-like behaviour of $KN$ scattering phase
shift in $\Theta$ channel was obtained in
\cite{km} in a version of Skyrme model (in the limit $M_K=M_\pi$)\footnote{Recently this result has
been criticized in \cite{ikor}.}.
Numerical estimate $M_\Theta \simeq 1530\;MeV $ was obtained first by M.Praszalowicz \cite{mic}.
The mass splittings within
octet and decuplet of baryons have not been described
satisfactorily with parameters of the model accepted that time, but in the "flexible" approach
proposed in \cite{mic} 8 masses of octet and decuplet of baryons were fitted with Skyrme model
motivated mass formula, depending on 4 parameters, defined from this fit. Central value of the
mass of antidecuplet
was found equal to $1706\,MeV$.
Extension of quantization condition \cite{g} to "exotic" case was made in \cite{vk} where
masses of exotic baryonic systems ($B$ arbitrary, $N_c=3$) were estimated as function
of the number of additional quark-antiquark pairs m:
$\Delta E \sim m/\Theta_K,\;m^2/\Theta_K$.
It was neither mass splittings estimates inside
of multiplets, nor calculations of masses of
particular exotic baryons in \cite{vk}, although
it was shown that baryonic states with additional quark-antiquark pairs appear quite naturally
within chiral soliton approach as $SU(3)$ rotational excitations.
Recently more general consideration
of such states has been performed in \cite{jenm} for arbitrary numbers of colors and flavors.
First calculation with configuration mixing due to flavor symmetry breaking $(m_K \neq m_\pi)$ was
made by H.Walliser in \cite{hw} where
mass splittings within the octet and decuplet of baryons were well described, and estimate obtained
$M_\Theta \simeq 1660 \;MeV$. "Strange" or kaonic inertia $\Theta_K$ which governs the mass splitting
between exotic and nonexotic baryon multiplets was underestimated in this work,
as it is clear now (see below).
The estimate $M_\Theta \simeq 1530\;MeV$, coinciding with \cite{mic}, and first estimate of
the
width, $\Gamma_\Theta < 30\,MeV$ were made later by D.Diakonov, V.Petrov and M.Polyakov \cite{dpp}
in a variant of quark-soliton model.
It was "a luck", as stated much later by same authors:
mass splitting inside of
$\overline{10}$
was obtained equal to $540\;MeV$, greater than for decuplet of baryons, and it was
supposed that
resonance $N^*(1710)\in \,\{\overline{10}\}$, i.e. it is the nonstrange
component of antidecuplet. The
above mass value of $\Theta^+$ was a result of subtraction, $1530 = 1710\,-\;540/3$.
However, the paper \cite{dpp},
being in right
direction, stimulated successful (as we hope still!)
searches for $\Theta^+$ in RCNP (Japan) \cite{1} and
ITEP (Russia) \cite{2}.
Skyrme-type model with vibrational modes included was studied in details first by H.Weigel \cite{wei}
with a result
$M_\Theta \simeq 1570\;MeV,\;\; \Gamma_\Theta \sim \,70\,MeV$. An inconsistency in
width estimate of \cite{dpp} was noted here.
\begin{center}
\underline{Developements after $\Theta^+$ discovery.}
\end{center}
After discovery of pentaquarks there appeared big amount of papers on this subject which develop
theoretical ideas in different directions: within chiral soliton models
\cite{wk,mic2,bfk,mic3,wuma,ell,wei1,tram,mix}
and many
other; phenomenological correlated quark models \cite{kl,jw,clo,clodu,wil} and other, critical
discussion by F.Close can be found in \cite{clo2};
QCD sum rules \cite{io,dor}; by means of lattice calculations \cite{csi,ssa}, etc. It is not
possible
to describe all of them within restricted framework of present paper
(reviews of that topic from
different sides can be found, e.g. in \cite{jm,ufk}).
Quite sound criticism concerning rigid rotator quantization within chiral soliton models was
developed in \cite{coh,coh3,ikor}, but it
should be kept in mind that the drawbacks of soliton approach should be compared with
uncertainties and drawbacks of other models \footnote{It is stated in conclusions of second of
papers \cite{coh}: "this paper {\it does not} show that rigid-rotor quantization is necessarily invalid but rather that
it is not justified due to large $N_c$ QCD. It remains possible that it is justified due to some
other reason". We agree with this rather optimistic conclusion.}.
There is no regular way of solving relativistic many-body problem to find bound states or
resonances in 3-,5-, etc. quark system, and the chiral soliton approach, in spite of its drawbacks,
provides a way to circumwent some of difficulties.
The correlated quark models, diquark-triquark model \cite{kl}, or
diquark-diquark-antiquark model \cite{jw}, being interesting and predictive, contain certain,
and very substantial
, phenomenological assumptions.
\section{Topological soliton model}
In spite of some uncertainties and discrepances between different authors,
the chiral soliton approach provided predictions for the masses of exotic states
near the value observed later, considerably more near than quark or quark-bag models
made up to that time.
Here I will be restricted with this model, mainly. Situation is somewhat paradoxical:
it is easier to estimate masses of exotic states within chiral soliton models,
whereas interpretation is more convenient in terms of simplified quark model.
The topological soliton model is very elegant and attractive (to authors opinion) since it allows to
consider the families ($SU(3)$-multiplets) of baryons, nonexotic and exotic, in unique way.
At the same time, as mentioned in literature, see e.g. \cite{jw}, the apparent drawback
is that this approach does not predict anything about exotics in meson sector.
In these models the baryons and baryonic systems appear as
classical configurations of chiral ("pionic" in simplest $SU(2)$ version) fields
which are characterized by the topological or winding number identified with
the baryon number of the system \cite{sk}. This baryon number is the 4-th component
of the Noether current generated by the Wess-Zumino term in the action written in a
compact form by Witten \cite{wit}, I shall not reproduce it here. In other words,
the B-number is degree of the map $R^{3} \to SU(2)$, or $R^3 \to S^3$, since $SU(2)$
is homeomorphic to 3-dimensional sphere $S^3$:
\begin{equation}
\label{wind}
B={-1\over 2\pi^2}\int s_f^2s_\alpha I\biggl[{(f,\alpha,\beta)\over (x,y,z)}\biggr]d^3r
\end{equation}
where functions $f,\alpha,\beta$, describing $SU(2)$ skyrmion, define the direction of unit vector
$\vec{n}$ on 3-dimensional sphere $S^3$ and $I[(f,\alpha,\beta)/(x,y,z)]$ is Jacobian of
corresponding transformation.
More details can be found, e.g. in \cite{wit,wk,ufk}, see also (\ref{L}) below.
It is important that the number of dimensions
of the ordinary space, equal to $3$, coincides with the number of degrees of freedom (or generators)
of the $SU(2)$ group, and this makes possible the mapping ordinary space onto isospace.
This can be an explanation why the isospin symmetry takes place in hadronic world.
The effective chiral lagrangian describing low-energy phenomena can be obtained from underlying QCD
by means of special procedure of
bosonization \cite{de,bal,aa}, it contains infinite number of terms - powers of chiral derivatives,
and, as it is believed, is equivalent to underlying QCD. Many known features of low energy meson-meson
and meson-baryon interactions found explanation within this effective theory. In
soliton models the truncated lagrangian is used as starting point - few first
terms of this expansion are taken into account to insure solitons stabilization by 4-th, sometimes
6-th order term in chiral derivatives \cite{aj}, and to make evaluations technically possible.
Further progress in this direction is discussed in \cite{marl,marl2}.
The Lagrangian density of the model in its minimal form is
\begin{equation} \label{L}
L = -{F_\pi^2\over 16} Tr (l_\mu l_\mu) +{1\over 32\,e^2} Tr [l_\mu l_\nu]^2 +{F_\pi^2m_\pi^2\over 16}
Tr (U +U^\dagger -2),
\end{equation}
where $m_\pi,\,F_\pi$ are pion mass and decay constant taken from experiment, $e$ is the Skyrme
parameter defining the weight of the 4-th order term, stabilizing the soliton, $e\sim 4$, according
to most of latest estimates, which allows to describe the mass splittings of octet and decuplet of
baryons; $l_\mu = \partial_\mu U U^\dagger$, $U$ is unitary matrix incorporating the chiral fields,
in $SU(2)$ case $U= c_f +i \vec{n}\vec{\tau}$ and 3 components of the unit vector $\vec{n}$ are
$s_\alpha c_\beta,\,s_\alpha s_\beta,\, c_\alpha$, see Eq. (\ref{wind}) above. For each value of
baryon number, one should find the classical field configuration of minimal
energy (mass) - this is done often by means of variational minimization numerical codes. For $B=1$
configuration of minimal energy is of so called "hedgehog" type, where chiral field at each space
point can be directed along radius vector drawn from center of soliton ($\vec{n}=\vec{r}/r$,
for $B=2$ it has torus-like
form, for $B=3$ it has topology of tetrahedron, etc.
The relation takes place for configurations of minimal energy between second order term,
fourth order term and the mass term $(M.t.)$ contributions to classical mass of solitons
(known as Derrick theorem)
\begin{equation} \label{drc}
M^{(2)} + 3 M.t. = M^{(4)}.
\end{equation}
The next step is the quantization of these configurations to get spectrum of states with definite
quantum numbers, isospin $I$, strangeness $S$ or hyperchrge $Y$.
At this point the flavor
symmetry breaking $(FSB)$ terms in the Lagrangian are important which define the mass splittings
within $SU(3)$ multiplets of baryons or baryonic systems. Usually they are taken in the form
\begin{equation} \label{fsb}
L_{FSB} = {F_K^2m_K^2-F_\pi^2m_\pi^2\over 24} Tr (1-\sqrt{3}\lambda_8)(U+U^\dagger -2)-
{F_K^2-F_\pi^2\over 48} Tr (1-\sqrt{3}\lambda_8)(Ul_\mu l_\mu + l_\mu l_\mu U^\dagger )
\end{equation}
In the collective coordinates quantization procedure \cite{anw,g} one introduces the angular
velocities of rotation of skyrmion in the $SU(3)$ configuration space,
$\omega_k$, $k=1,...8$: $A^\dagger(t)\dot{A}(t) = -i \omega_k\lambda_k/2,\;
\lambda_k$ being Gell-Mann matrices, the collective coordinates matrix $A(t)$
is written usually in the form $A=A_{SU2}\,exp(i\nu\lambda_4)A'_{SU2}\,
exp(i\rho \lambda_8/\sqrt{3})$.
The Wess-Zumino term contribution into lagrangian can be calculated explicitly for this ansatz,
$L_{WZ}=-\omega_8 N_cB/2\sqrt{3}$, and so called "right" hypercharge, or hypercharge in the body-fixed
system equals $Y_R=-2\partial L/\partial \omega_8/\sqrt{3} = N_cB/3$. For any $SU(3)$ multiplet
$(p,q)$ the maximal hypercharge $Y_{max}=(p+2q)/3$, and obviously, inequality should be fulfilled
$p+2q \geq N_cB$, or
\begin{equation}
\label{m}
p+2q = 3(B+m) \end{equation}
for $N_c=3$, with $m$ positive integer. States with $m=0$ can be called, naturally, minimal
multiplets. For $B=1$ they are well known octet $(1,1)$ and decuplet $(3,0)$ \cite{g}.
States with $m=1$ should contain at least one $q\bar{q}$ pair, since they contain the $S=+1,\, Y=2$
hyperon. They are pentaquarks antidecuplet $(p,q)=(0,3)$, $27$-plet $(2,2)$, $35$-plet $(4,1)$.
The pentaquark multiplets are presented in {\bf Figure}.
\begin{figure}[h]
\label{multiplet}
\setlength{\unitlength}{1.cm}
\begin{flushleft}
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\put(2,8.3){$\{\overline {10}\}\, J=1/2$}
\put(3.1,13.1){$\Theta^+$}
\put(1.4,13.0){$(uudd\bar{s})$}
\put(3,13){\circle*{0.2}}
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\put(7,5){\circle*{0.1}}
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\put(6.5,4){\circle*{0.1}}
\put(6.5,4){\circle {0.2}}
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\put(8.5,4){\circle*{0.18}}
\put(8.6,4){$(uuss\bar{d})$}
\put(4.5,3){$(dsss\bar{u})$}
\put(6,3){\circle*{0.18}}
\put(7,3){\circle*{0.1}}
\put(7,3){\circle {0.2}}
\put(8,3){\circle*{0.18}}
\put(8.1,3){$(usss\bar{d})$}
\put(5.0,2){$(ssss\bar{u})$}
\put(6.5,2){\circle*{0.18}}
\put(7.5,2){\circle*{0.18}}
\put(7.6,2){$(ssss\bar{d})$}
\put(4.5,6){\line(1,2){0.5}}
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\put(9.5,6){\line(-1,2){0.5}}
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\end{picture}
\vglue 0.1cm
\caption{\tenrm The $I_3-Y$ diagrams for the multiplets of pentaquarks, $B=1,\;m=1$.
Large full circles show the exotic states, smaller - the cryptoexotic states
which can mix with nonexotic states from octet and decuplet. Manifestly exotic components
of pentaquarks satisfy the relation $I=(5+S)/2$ for strangeness $S \leq 0$ and have unique
quark contents shown in this figure.}
\end{flushleft}
\end{figure}
The minimal value of hypercharge is $Y_{min}=-(2p+q)/3$, the maximal isospin
$I_{max}=(p+q)/2$ at $Y=(p-q)/3$. Such multiplets as $\{27\}$, $\{35\}$
for $m=1$ and multiplets for $m=2$
in their internal points contain 2 or more states
(shown by double or triple circles in {\bf Figure}). The $28$-plet ($6,\,0$)
should contain at least two quark-antiquark pairs, as it follows from analyses of its strangeness
and isospin content \cite{ufk}, so, it is septuquark (or heptaquark)
,
although it has $m=1$, and it is not shown here by this reason.
\section{The mass formula for the rigid rotator}
The lagrangian describing baryons or baryonic system is quadratic form in angular velocities
defined above, with momenta of inertia, isotopical (pionic) $\Theta_\pi$
and flavor, or kaonic $\Theta_K$ as coefficients \cite{g}:
\begin{equation}
\label{Lrot}
L_{rot} = {1\over 2}\Theta_\pi (\omega_1^2+\omega_2^2+\omega_3^2) +
{1\over 2}\Theta_K (\omega_4^2+...+\omega_7^2) - {N_cB \over 2\sqrt{3}}
\omega_8. \end{equation}
The expressions for these moments of inertia as functions of skyrmion profile
are well known \cite{anw,g} and presented in many papers, see e.g. \cite{ufk}. The
quantization condition (\ref{m}) discussed above follows
from the presence of linear in angular velocity $\omega_8$ term in $(3)$
originated from the Wess-Zumino-Witten term in the action of the model
\cite{wit,g}.
The hamiltonian of the model can be obtained from $(3)$ by means of canonical
quantization procedure \cite{g}:
\begin{equation}
\label{ham}
H = M_{cl} + {1\over 2\Theta_\pi} \vec{R}^2 + {1\over 2\Theta_K}
\biggl[C_2(SU_3) -\vec{R}^2 -{N_c^2B^2\over 12} \biggr], \end{equation}
where the second order Casimir operator for the $SU(3)$ group,
$C_2(SU_3)=\sum_{a=1}^8 R_a^2$, with eigenvalues for the $(p,q)$ multiplets
$C_2(SU_3)_{p,q}=(p^2+pq+q^2)/3 +p+q, $
for the $SU(2)$ group,
$C_2(SU2)=\vec{R}^2 =R_1^2+R^2_2+R^2_3= J(J+1) = I_R(I_R+1)$.
The operators $R_\alpha = \partial L/\partial\omega_\alpha$ satisfy definite
commutation relations which are generalization of the angular momentum
commutation relations to the $SU(3)$ case \cite{g}. Evidently, the linear in
$\omega$ terms in lagrangian (\ref{Lrot}) are cancelled in hamiltonian (\ref{ham}).
The equality of angular momentum (spin) $J$ and the so called right or body
fixed isospin $I_R$ used in (\ref{ham}) takes place only for configurations of the
"hedgehog" type when usual space and isospace rotations are equivalent. This
equality is absent for configurations which provide the minimum of classical
energy for greater baryon numbers, $B\geq 2$ \cite{vkax}.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline
$(p,q)$& $N(p,q)$ &m &$C_2(SU_3)$&$J=I_R$ &$K(J_{max})$&$K(J_{max}-1)$\\
\hline
$(1,1)$&$\{8\}$ &0 & 3 &1/2 &3/2 &\\
$(3,0)$&$\{10\}$ &0 & 6 &3/2 &3/2 &\\
\hline
$(0,3)$&$\{\overline{10}\}$ &1&6 &1/2 &3/2+3&\\
$(2,2)$&$\{27\}$ &1&8 &3/2; 1/2 &3/2+2& 3/2+5\\
$(4,1)$&$\{35\}$ &1&12 &5/2; 3/2 &3/2+1& 3/2+6\\
$(6,0)$&$\{28\}$ &1&18 &5/2 &3/2+7&\\
\hline
$(1,4)$&$\{\overline{35}\}$ &2&12 &3/2; 1/2 &3/2+6& 3/2+9\\
$(3,3)$&$\{64\}$ &2&15 &5/2; 3/2; 1/2 &3/2+4& 3/2+9\\
$(5,2)$&$\{81\}$ &2&20 &7/2; 5/2; 3/2 &3/2+2& 3/2+9 \\
$(7,1)$&$\{80\}$ &2&27 &7/2; 5/2 &3/2+9& 3/2+16\\
$(9,0)$&$\{55\}$ &2&36 &7/2 &3/2+18& \\
\hline
\end{tabular}
\end{center}
{\bf Table 1.}{\tenrm The values of $N(p,q)$, Casimir operator $C_2(SU_3)$, spin
$J=I_R$, coefficient $K$ for first two values of $J$ for minimal $(m=0)$ and
nonminimal $(m=1,\;2)$ multiplets of baryons.}
\vglue 0.1cm
For minimal multiplets $(m=0)$ the right isospin $I_R=p/2$, and it is easy to
check that coefficient of $1/2\Theta_K$ in (\ref{ham}) equals to
\begin{equation}
\label{K}
K=\,C_2(SU_3)-\vec{R}^2-N_C^2B^2/12 \,=\,N_CB/2, \end{equation}
for arbitrary $N_C$ \footnote{For the number of colors $N_C$
different from 3 the minimal multiplets for baryons differ from octet
and decuplet. They have $[p,q]=[1,(N_c-1)/2],\; [3,(N_c-3)/2],...,\,[N_c,0]$. There are totally
$(N_c+1)/2$ multiplets of baryons with the interval $\Delta Y$ for each of them increasing from
$(N_c+1)/2$ to $N_c$, see Appendix. It is an artifact
of large $N_c$ approximation that besides the states existing in real world with $N_c=3$,
the spurious states appear, and the number of these states is infinite as $N_c\to \infty$.}.
So, $K$ is the same for all multiplets with $m=0$ \cite{vk}, see {\bf Table 1} -
the property known long ago for the $B=1$ case \cite{g}.
For nonminimal multiplets there are additional contributions to the energy
proportional to $m/\Theta_K$ and $m^2/\Theta_K$, according to (\ref{ham}).
The following expression was obtained for the energy surplus due to addition of $m$ quark-antiquark
pairs (formula (6) of \cite{vk}):
\begin{equation}
\label{old}
\delta E_{rot} = m \bigl[(3B/2 +1 +m-N)/(2\Theta_K) + (2N+1-m)/(2\Theta_\pi)\bigr]
\end{equation}
with "right isospin" $N=(p+m)/2$.
It means
that in the framework of chiral soliton approach the "weight" of quark-
antiquark pair is defined by parameter $1/\Theta_K$, and this property of
such models deserves better understanding.
{\bf Table 1} was presented previously in \cite{ufk}, here we need it also to estimate
the mass difference of partners of lowest baryon states with same quantum numbers except
spin. It follows from Table 1 that for each nonzero $m$ the coefficient
$K(J_{max})$ decreases with increasing $N(p,q)$, e.g. $K_{5/2}(35)\,<K_{3/2}(27)
\,<\,K_{1/2}(\overline{10})$. The following differences of the rotation energy
can be obtained easily:
\begin{equation}
\label{d108}
M_{10} - M_{8} = {3\over 2\Theta_\pi}, \qquad M_{\overline{10}} -M_{8} = {3\over 2\Theta_K}, \end{equation}
obtained in \cite{g,dpp},
\begin{equation}
\label{d2710}
M_{27,J=3/2}- M_{10} = {1\over \Theta_K}, \quad M_{27,J=3/2} - M_{\overline{10}} =
{3\over 2\Theta_\pi} - {1\over 2\Theta_K},
\end{equation}
\begin{equation}\label{278}
M_{27,J=3/2}- M_{8} = {1\over \Theta_K} +{3\over 2\Theta_\pi} ,
\end{equation}
which follows also from (\ref{old}) at $B=1,\;m=1$,
\begin{equation}
\label{d3527}
M_{35,J=5/2} - M_{27,J=3/2} = {5\over 2\Theta_\pi} - {1\over 2\Theta_K}.
\end{equation}
According to these relations, the mass difference between decuplet and $27$-plet is
$1.5$ times smaller than between octet and antidecuplet, by this reason the mixing
between corresponding components of decuplet and $27$-plet is large and not negligible,
although it was neglected in \cite{dpp,dp}, e.g.
If the relation took place $\Theta_K \ll \Theta_\pi$, then $\{27\}$-plet would
be lighter than antidecuplet, and $\{35\}$-plet would be lighter than $\{27\}$-plet.
In realistic case $\Theta_K$ is approximately twice smaller than $\Theta_\pi$
(see {\bf Table 2}, next section), and therefore the components of antidecuplet are lighter
than components of $\{27\}$ with same values of strangeness.
Beginning with some values of $N(p,q)$ coefficient $K$ increases strongly, as can
be seen from {\bf Table 1}, and this corresponds to the increase of the number
of quark-antiquark pairs by another unity. The states with $J\,<\,J_{max}$ have
the energy considerably greater than that of $J_{max}$ states, by this reason
they could contain also greater amount of $q\bar{q}$-pairs.
The states with $m=2$ (second floor of this building) have considerably higher energy than
states with $m=1$, and this difference defines the scale of mass splitting between partners
with higher values of spin. It can be noted from {\bf Table 1} that the $35$-plet with
$J=3/2$ has exactly the same rotation energy as $\overline{35}$-plet, $(m=2)$ with $J=3/2$:
$K=3/2+6$ in both cases (this degeneracy was noted first by H.Walliser). It is a clear hint
that states with same values of $(p,q)$ but different spin should have different
quark contents.
The formula (\ref{ham}) is obtained in the rigid rotator approximation which is
valid if the profile function of the skyrmion and therefore its dimensions and
other properties are not changed when it is rotated in the configuration space
(see next section and, e.g.
discussion in \cite{ufk}).
\section{Spectrum of baryonic states}
Expressions (\ref{ham}-\ref{d3527}) and numbers given in {\bf Table 1} are sufficient
to calculate the spectrum of baryons without mass splitting inside of $SU(3)$-
multiplets, as it was made e.g. in \cite{bieden,vk}.
\subsection{The rigid rotator model}
The mass splitting due to the presence of flavor symmetry breaking terms in the lagrangian (\ref{fsb})
plays a
very substantial role in the spectrum of baryon states.
The corresponding contribution into hamiltonian can be written in simple form \cite{schw,hw,wk}:
\begin{equation} \label{HSB}
H_{SB}=\frac{1-D_{88}^{(8)}}{2}\Gamma_{SB}={3\over 4} s^2_\nu\,\Gamma_{SB} \end{equation}
where the $SU(3)$ rotation function $D_{88}^8(\nu) =1-3s^2_\nu/2$,
\begin{equation} \label{GSB}
\Gamma_{SB}={2\over 3}\Biggl[\Biggl({F_K^2\over F_\pi^2}m_K^2 -m_\pi^2\Biggr)
\Sigma +(F_K^2-F_\pi^2)\tilde{\Sigma}\Biggr] \end{equation}
\begin{equation} \label{Sig}
\Sigma = \frac{F_{\pi}^2}{2} \int (1-c_f) d^3\vec{r}, \qquad
\tilde{\Sigma}= {1\over 4}\int c_f \Biggl(f'^2+{2s_f^2\over r^2}\biggr)d^3r,
\end{equation}
kaon and pion masses $m_K,\;m_\pi$ as well as $F_K,\,F_\pi$ are taken from experiment.
At large number of colors $\Gamma_{SB} \sim N_c$, both the soliton mass and the total mass splitting
of $SU(3)$ multiplets also are $\sim N_c$. Individual mass splittings within multiplets are
of the order of $N_c^0\sim 1$, since the change of hypercharge within multiplets $\Delta Y \sim N_c$,
see footnote in previous section.
The quantity $SC=<s_\nu^2>/2=<1-D_{88}^{(8)}>/3$ averaged over the baryon
$SU(3)$ wave function defines its strangeness content, which allows to establish a bridge between
chiral soliton approach and quark models \footnote{The $\nu$-dependent wave functions in $SU(3)$
configuration space are simple in some cases: e.g. for $\Theta^+$-hyperon $\Psi_\Theta (\nu)=
\sqrt{15} sin\,\nu \,cos^2\nu$, for the hyperon $\Omega\in \{10\}$, $\Psi_\Omega =\sqrt{5/2}sin^3\nu$.
They are normalized according to $\int |\Psi_B(\nu)|^2 4\,sin^3\nu cos\nu d\nu =1$. In most cases
the $\nu$-dependent contributions into $|\Psi_B|^2$ consist of several terms.}.
Without configuration
mixing, i.e. when flavor symmetry breaking terms in the lagrangian are
considered as small perturbation, $<s_\nu^2>_0$ can be expressed simply in
terms of the $SU(3)$ Clebsh-Gordan coefficients. The values of $<s_\nu^2>_0$
for the octet, decuplet, antidecuplet and some components of higher multiplets
are presented in {\bf Tables 2, 5}. In this approximation the components of $\{10\}$
and $\{\overline{10}\}$ are placed equidistantly, and splittings of decuplet
and antidecuplet are equal.
The spectrum of states with configuration mixing and diagonalization of the
hamiltonian in the next orders of perturbation theory in $H_{SB}$ is given in
{\bf Table 2}
(the code for calculation was kindly presented by H.Walliser).
The calculation results in the Skyrme model with only one adjustable parameter -
Skyrme constant $e$ ($F_\pi=186\,Mev$ - experimentally measured value) are shown
as variants A and B. The values of mass of $\Theta^+$ obtained in this way are close
to the observed mass. The values of $<s_\nu^2>$ become lower when configuration mixing
takes place, and equidistant spacing of components inside of antidecuplet is violated.
For the decuplet of baryons the total mass splitting increases when mixing is included,
but results obtained mimic approximately the equidistant position of its components, see also
discussion in the next section.
It should be stressed here that the chiral soliton approach in its present state
can describe the differences of baryon or multibaryon masses \cite{schw,hw,wk}.
The absolute values of mass are controlled by loop corrections of the order of
$N_C^0\sim 1$ which are estimated now for the case of $B=1$ only \cite{mou}.
Therefore, the value of nucleon mass in {\bf Table 2} is taken to be equal to
the observed value.
As it can be seen from Table 2, the agreement with data for pure Skyrme model with
one parameter is not perfect, but the observed mass of $\Theta^+$ is reproduced
with some reservation. To get more reliable predictions for masses of other
exotic states the more phenomenological approach was used in \cite{wk} where
the observed value $M_\Theta =1.54\,GeV$ was included into the fit, and
$\Theta_K,\;\Gamma_{SB}$ were the variated parameters (variant C in Table 2).
The position of some components of $\{27\}$, $\{35\}$ and $\{\overline{35}\}$-plets is shown
in Table 2 as well (they are components with largest isospin).
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
& & A & B& C & \\
\hline
$\Theta_\pi \,(GeV^{-1})$ & --- &$6.175 $& $5.556$ & $5.61$ & - \\
$\Theta_K \,(GeV^{-1})$ & --- &$2.924 $ & $2.641$ & $2.84$ & - \\
$\Gamma_{SB} \,\;(GeV) $ & --- & $1.391$ & $1.274 $ & $1.45$ & - \\
\hline
\hline
$Baryon|N,Y,I,J>$ &$<s_\nu^2>_0$& A & B & C & $Data$\\
\hline
$ N\,|8,1,{1\over 2},{1\over 2}>\,input$&$0.467$ &$\,939$ &$\,939$ &$\,939$&$\,939$ \\
$\Lambda\,|8,0,0,1/2>$ &$0.600$ & 1097 & 1082 & 1103 &1116 \\
$\Sigma\,|8,0,1,1/2> $ &$0.733$ & 1205 & 1187 & 1216 &1193 \\
$\Xi \,|8,-1,1/2,1/2>$ &$0.800$ & 1316 & 1282 & 1332 &1318 \\
\hline
$\Delta \,|10,1,3/2,3/2>$ &$0.583$& 1228 & 1258 & 1253 &1232\\
$\Sigma^*|10,0,1,3/2>$ &$0.667$ & 1359 & 1376 & 1391 &1385\\
$\Xi^* |10,-1,1/2,3/2>$ &$0.750$ & 1488 & 1489 & 1525 &1530\\
$\Omega \,|10,-2,0,3/2> $ &$0.833$& 1611 & 1596 & 1654 &1672\\
\hline
$\Theta^+\,|\overline{10},2,0,1/2>$ &$0.500$& 1521 & 1566 & 1539 &1540 \\
$ N^*\,|\overline{10},1,1/2,1/2> $ &$0.583$ & 1637 & 1669 & 1661 &1675?\\
$\Sigma^*\,|\overline{10},0,1,1/2>$ &$0.667$ & 1736 & 1756 & 1764 &1770?\\
$\Xi_{3/2}|\overline{10},-1,3/2,1/2>$&$0.750$ & 1758 & 1787 &1786 &1862? \\
\hline
\hline
$\Theta^*_1\,|27,2,1,3/2>$ &$0.571$ & 1648 & 1700 & 1688 & \\
$\Delta^*_1\,|27,1,3/2,3/2>$ &$0.589$ & 1780 & 1809 & 1826 & \\
$\Sigma^*_2\,|27,0,2,3/2>$ &$0.607$ & 1677 & 1728 & 1718 & \\
$\Xi^{*}_{3/2}|27,-1,3/2,3/2>$ &$0.714$ & 1803 & 1842 & 1850 & 1862? \\
$\Omega^*_1\,|27,-2,1,3/2>$ &$0.821$ & 1935 & 1959 & 1987 & \\
\hline
\hline
$\Theta^*_2\,|35,2,2,5/2>$ &$0.708$ & 1982 & 2060 & 2061 &\\
$\Delta_{5/2}|35,1,5/2,5/2>$&$0.438$& 1723 & 1816 & 1792 &\\
$\Sigma^*_2\,|35,0,2,5/2>$ &$0.542$& 1844 & 1926 & 1918 &\\
$\Xi^{*}_{3/2}|35,-1,3/2,5/2>$ &$0.646$& 1967 & 2037 & 2046 &\\
$\Omega^{*}_1\,|35,-2, 1,5/2>$ &$0.750$& 2091 & 2149 & 2175 &\\
$ \Gamma \;\, |35,-3,1/2,5/2>$ &$0.854$& 2216 & 2261 & 2306 &\\
\hline
\hline
$\;\; |\overline{35},3,1/2,3/2> $ &$0.562$& 2350 & 2470 & 2412 &\\
$\;\; |\overline{35},2,1,3/2> $ &$0.583$& 2403 & 2513 & 2466 &\\
$\;\; |\overline{35},1,3/2,3/2> $ &$0.604$& 2435 & 2541 & 2501 &\\
$\;\; |\overline{35},0,2,3/2> $ &$0.625$& 2437 & 2546 & 2502 &\\
$\;\; |\overline{35},-1,5/2,3/2>$ &$0.646$& 2417 & 2534 & 2480 &\\
$\;\; |\overline{35},-2,2,3/2> $ &$0.792$& 2573 & 2677 & 2643 &\\
\hline
\end{tabular}
\end{center}
{\bf Table 2.} {\tenrm Values of masses of the octet, decuplet, antidecuplet,
manifestly exotic components of higher multiplets, and highest isospin components
of the $\{\overline{35}\}$-plet ($m=2$).
A: $e=3.96$; B: $e=4.12$;
C: fit with parameters $\Theta_K,\;\Theta_\pi$ and
$\Gamma_{SB}$ \cite{wk}, which are shown in the upper 3 lines.}
\\
The experimental value of the mass of the $N^*$ candidate for antidecuplet, $M_{N^*}=1675\,MeV$,
is taken from recent work \cite{kuz}, the value $M_{N^*}\simeq 1680\,MeV$ was obtained somewhat
earlier \cite{araz} in the modified partial wave anlysis of existing data.
The accuracy of numerical calculations of masses given in Table 2 is not better than $\sim 1\%$, and
several figures are presented for convenience of different variants comparison. Small correction of
numbers for variants A and B is made, in comparison with \cite{ufk}.
The accuracy of method itself is difficult to
estimate, comparison with other quantization schemes can be useful for this.
The unexpected at first sight fact that the state $\Theta^+\in \{\overline{10}\}$ containing
strange
antiquark is lighter than nonstrange component of antidecuplet, $N^*(I=1/2)$
can be easily to understood if we recall that all antidecuplet components contain
$q\bar{q}$ pair: $\Theta^+$ contains 4 light quarks and $\bar{s}$, $N^*$
contains 3 light quarks and $s\bar{s}$ pair with some weight, $\Sigma^* \in
\{\overline{10}\}$ contains $u,d,s$ quarks and $s\bar{s}$, etc.
, see Section 7.
The mass splitting inside of decuplet is influenced essentially by its mixing
with $\{27\}$-plet components \cite{wk}, see {\bf Figure}, which increases this
splitting considerably - the effect ignored in \cite{dpp}. As a result of this mixing, the lowest
in energy state of $\{10\}$, $\Delta$-isobar, moves considerably towards lower mass, the whole
mass splitting within decuplet increases from $\sim 270\,MeV$ to $350\,-\, 400\,MeV$, but equidistant
position of states remains, roughly, since $\Sigma^*$ and $\Xi^*$ are mixed as well. The
approximate equidistant position of the components of decuplet is not an argument against
important role of mixing with other multiplets, as it is stated sometimes in literature.
The mixing of
antidecuplet with the octet of baryons has considerable effect on the position of
$N^*$ and $\Sigma^*(\overline{10})$ - their masses increase, the position of $\Xi^*_{3/2}$
is influenced
by mixing with
$\{27\}$-plet, $(J=1/2)$, and $\{\overline{35}\}$-plet, and its mass decreases. As a result of mixing, the
total mass splitting
of antidecuplet decreases slightly, opposite to the case of decuplet, and
equidistant position of its components is perturbed.
Position of $\Theta^* \in \{27\}$ is influenced by mixing with higher multiplets \cite{wk},
the components of $\{35\}$-plet mix mainly with corresponding components of septuquark
$\{64\}$-plet.
The mass of $\Theta$ hyperon is obtained in the interval $1520 - 1560\, MeV$ for the Skyrme
parameter $e$ between $3.96$ and $4.12$, in the rigid rotator approximation, so the statement made
in \cite{clo2}
that "all models appear to normalise to some feature and do not naturally explain the low mass
of the orbitally excited pentaquark" does not apply to the simple chiral soliton model which is
$SU(3)$ generalization of the original Skyrme model quantized as rigid rotator.
The flavor symmetry
breaking in the kaon decay constant, i.e. the fact that $F_K/F_\pi =1.22$ leads to certain increase
of the kaonic moment of inertia and to decrease of the $\Theta$ mass \cite{wk}
\begin{equation}
\label{thf}
\Theta_K ={1\over 8} \int (1-c_f) \biggl[ F_K^2 - (F_K^2-F_\pi^2){2-c_f\over 2} s_\nu^2 +
{1\over e^2} \biggl(f'^2+{2s_f^2\over r^2}\biggr) \biggr] d^3r,
\end{equation}
where $f(r)$ is the profile function of skyrmion, $f(0)=\pi$ at the origin, and $f(\infty)=0$.
This moment of inertia is maximal when the angle of rotation into strange direction $\nu=0$, see
Table 2, and this corresponds to rigid rotor approximation used previously and in \cite{wk}.
$\Theta_K$ decreases when $\nu$ deviates from $0$, and indeed, the masses of exotic baryons obtained
within soft, or slow rotator approximation, are considerably greater \cite{kss}.
It should be noted that predictions of the mass of $\Xi^*_{3/2}$ made in \cite{wk} half a year before
its observation at CERN \cite{alt} were quite close to the reported value $1862 \,MeV$: it was
$1786\,MeV$
for the component of antidecuplet, and $1850\,MeV$ for the $\{27\}$ component,
variant C of
{\bf Table 2}.
Predictions for masses of cryptoexotic components of $\{\overline{10}\}$
and $\{27\}$-plet are clear from {\bf Table 2} as well.
It was stated in the paper \cite{jw} that the spectrum of antidecuplet obtained
"from correlated
quark picture differs in several dramatic ways from the spectrum predicted by the chiral soliton
model", and "the prediction of light charged exotic $\Xi$'s is the most distinctive signature of
our model". The following comment is necessary here.
Indeed, it was apparent contradiction of estimates made in \cite{jw} and results
obtained in \cite{dpp} within particular variant of chiral quark-soliton model
where the total splitting of antidecuplet was found equal to $540\,MeV$ \footnote{Later, when
observation of the resonance $\Xi^{--}$ has been reported in \cite{alt}, the authors
\cite{dpp} revised their result in \cite{dp} and identified the lowest and the highest masses of
antidecuplet
with observed values, i.e. they put the total mass splitting of $\overline{10}$ equal to the value
$\sim 324\,MeV$ taken from experiment. Cryptoexotic components of antidecuplet, $N^*$ and $\Sigma^*$,
have been placed within this mass gap. The change of the experimental value of the pion-nucleon
sigma-term was important for this re-analysis, the latest and largest value of sigma-term was
obtained in \cite{pavar}.}.
As shown in \cite{wk} and above, the total splitting of anti-10
in Skyrme-type model equals to $\Delta_M(\overline{10})= 1.5\;\Gamma_{SB} \Delta_{SC}(\overline{10})
\simeq 270\,MeV$ if configuration mixing is not included, and less than
$\sim 270\,MeV$, about $250\,MeV$ if mixing is taken into account. $\Delta_{SC}(\overline{10})=1/8$
is the splitting of strangeness contents within antidecuplet, which can be expressed in terms of
Clebsch-Gordan coefficients of the $SU(3)$ group. Therefore, there is no such
dramatic difference between simplified quark model picture of \cite{jw} and chiral soliton model
predictions, as it was claimed in \cite{jw}, but results of \cite{wk}, available since April 2004,
have not been considered in \cite{jw}. Another comment is that picture of ideal mixing between
octet and antidecuplet of pentaquark states, proposed in \cite{jw}, can be disturbed by mixing
with ground state octet, as it takes place in chiral soliton approach \cite{wk,mix}.
Normally, the ground state octet contains admixture of antidecuplet (about $(5-6)\%$ in probability
for the nucleon, variant C of {\bf Table 2}),
$\{27\}$-plet ($\sim 3\%$), and smaller amounts of higher multiplets, since the number of
quark-antiquark pairs is not conserved by strong interactions.
Further developments of the correlated quark models with diquarks or triquarks are of interest,
also if the announced pentaquark states are not confirmed.
In {\bf Table 3} predictions of the mass of exotic $\Phi/\Xi_{3/2}$ state with strangeness $S=-2$
which were made {\it before} experimental evidence for this state \cite{alt}, are presented.
The paper \cite{bfk} repeated the approach of \cite{dpp}, the mass of $\Xi_{3/2} \in \{27\}$
shown in {\bf Table 3} was a new result in comparison with \cite{dpp}. The state observed in \cite{alt}
could belong just to $\{27\}$-plet, another doubly strange state from anti-10 should exist in this
case, with smaller mass and more narrow than the observed one.
Of course, this discussion becomes irrelevant if the $\Phi/\Xi_{3/2}$ state is not confirmed.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline
&DPP\cite{dpp}&WK\cite{wk}& JW\cite{jw}& BFK\cite{bfk} & P\cite{mic2} &Datum\cite{alt}\\
\hline
$\Phi/\Xi_{3/2}\in \{\overline{10}\}$&2070 &1780-1790 & 1750 & --- & 1800 & 1862 \\
$\;\;\Xi_{3/2}\in \{27\} $&--- & 1850 & --- & 2048 & --- & 1862?\\
\hline
\end{tabular}
\end{center}
{\bf Table 3.} {\tenrm Predictions of the mass of doubly strange hyperon $\Phi/\Xi_{3/2}$ in chronological
order. The value by M.Praszalowicz, $1800\,MeV$, is taken from figure in \cite{mic2} and is
approximate by this reason.} \\
The component of $\{35\}$-plet with zero strangeness and $I=J=5/2$ is of special
interest because it has the smallest strangeness content (or $s_\nu^2$) -
smaller than nucleon and $\Delta$, see {\bf Table 2}. It is the lightest component of $\{35\}$-plet,
and this remarkable
property has explanation in simplistic pentaquark model, see Section 7 below.
As a consequence of isospin conservation by
strong interactions it can decay into $\Delta\pi$, but not to $N\pi$ or $N\rho$.
Generally, the baryon resonances which belong to $\{35\}$-plet cannot be obtained in meson-baryon
interactions, or in some decay into meson (from the octet) and baryon, also from octet, due to
$SU(3)$ invariance of strong interactions, see also \cite{azim}. The components of $\{35\}$ with
highest isospin which are manifestly exotic, cannot be formed in this way also due to isospin
invariance of strong interactions, and this is essentially more rigorous prohibition.
The masses of lowest $m=2$ multiplet, $\{\overline{35}\}$-plet, are shown in Table 2 as an example:
this state is not a pentaquark, but septuquark (or heptaquark). The partners of antidecuplet
with spin $J=3/2$ are contained within this multiplet, see section 8.
\subsection{Model of the slow (soft) rotator}
An alternative method of calculation is the soft (or slow) rotator approximation developed
for the case of $B=1$ by Schwesinger and Weigel \cite{schw}, and used
in \cite{kss} to describe the strange dibaryons spectrum. It is supposed within this
approximation that for each value of the angle $\nu$ it is sufficient time to rearrange the profile
function under influence of forces due to flavor symmetry breaking terms in the Lagrangian.
Estimates show that for $B=1$ the rigid rotator approximation is better, whereas for $B\geq 2$
the soft rotator becomes more preferable. Indeed, the rotation time in cofiguration space can be
estimated as $\tau_{rot} \sim \pi/\omega$, and the angular velocity
$\omega \sim \sqrt{C_2(SU3)}/\Theta_K$ for definite $SU(3)$ multiplet, see Table 1. It is difficult
to estimate the time necessary for rearranging the profile function under
influence of FSB forces, one can state only that it is greater than
time necessary for signal propagation accross skyrmion, $\tau_{sign}\sim 2R_S$. So, we come to
the inequality $\pi \Theta_K \ll 2R_S\sqrt{C_2(SU3)}$ which should be fulfilled for the rigid
rotator approximation being valid. For $B=1$ both sides of this inequality are of the same order of
magnitude, although left side is somewhat smaller.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
\hline
$Baryon|N,Y,I,J>$ &$<s_\nu^2>$& SR & $Data$\\
\hline
$ N\,|8,1,{1\over 2},{1\over 2}>\,input$&$0.314$ &$\;\;939$ &$\;\;939$ \\
$\Lambda\,|8,0,0,1/2>$ &$0.500$ & 1110 &1116 \\
$\Sigma\,|8,0,1,1/2> $ &$0.602$ & 1220 &1193 \\
$\Xi \,|8,-1,1/2,1/2>$ &$0.740$ & 1320 &1318 \\
\hline
$\Delta \,|10,1,3/2,3/2>$ &$0.315$& 1240 &1232\\
$\Sigma^*|10,0,1,3/2>$ &$0.483$& 1415 &1385\\
$\Xi^* |10,-1,1/2,3/2>$ &$0.650$& 1560 &1530\\
$\Omega \,|10,-2,0,3/2> $ &$0.790$& 1670 &1672\\
\hline
$\Theta\;\;|\overline{10},2,0,1/2>$ &$0.380$& 1737 & 1540 \\
$\Xi_{3/2}|\overline{10},-1,3/2,1/2>$&$0.607$ & 2118 & 1862? \\
\hline
\hline
$\Theta^*_1\,|27,2,1,3/2>$ &$0.416$ & 1840 & \\
$\Sigma^*_2\,|27,0,2,3/2>$ &$0.438$ & 1880 & \\
$\Xi^{*}_{3/2}|27,-1,3/2,3/2>$&$0.594$ & 2090 & \\
$\Omega^*_1\,|27,-2,1,3/2>$ &$0.755$ & 2270 & \\
\hline
\hline
$\Theta^*_2\,|35,2,2,5/2>$ &$0.464$ & 2180 &\\
$\Delta_{5/2}\,|35,1,5/2,5/2>$ &$0.242$ & 1750 &\\
$\Sigma^*_2\,|35,0,2,5/2>$ &$0.382$ & 1990 &\\
$\Xi^*_{3/2}\,|35,-1,3/2,5/2>$ &$0.528$ & 2190 &\\
$\Omega^{*}_1\,|35,-2, 1,5/2>$ &$0.675$ & 2370 &\\
$ \Gamma \;\, |35,-3,1/2,5/2>$ &$0.854$ & 2530 &\\
\hline
\hline
$\;\; |\overline{35},3,1/2,3/2> $ &$0.442$& 2900 & \\
$\;\; |\overline{35},-1,5/2,3/2>$ &$0.477$& 3030 & \\
$\;\; |\overline{35},-2,2,3/2> $ &$0.641$& 3385 & \\
\hline
\end{tabular}
\end{center}
{\bf Table 4.} {\tenrm Values of masses of the octet, decuplet, antidecuplet and manifestly
exotic components of higher multiplets
within soft rotator (SR) approximation \cite{schw}:
$e=3.46,\; F_K/F_\pi =1.26,$ the values of $<s^2_\nu>$ are calculated with configuration mixing
included.}\\
Thus we see, that rigid rotator is really more preferable
for $B=1$, especially for exotic multiplets (since the value of $C_2(SU3)$ is greater, see Table 1)
\footnote{If we take into account connection between soliton radius and another (isotopic) moment of
inertia, $\Theta_I \sim M_S R_S^2/2$, this condition will take the form
$\Theta_K < \sqrt{\Theta_IC_2(SU3)/M_S}$.}.
With increasing baryon number left side of this inequality grows faster than right side, therefore
slow rotator approximation may become better for greater baryon numbers.
In view of conflicting experimental situation on pentaquarks
observation it makes sense to present the results for pentaquarks spectra within this approximation
as well.
A natural thing is that the masses of exotic states within soft rotator model are greater
than in the rigid rotor approximation: the strange, or kaonic inertia $\Theta_K$ becomes smaller
for slow rotator, as explained above, (\ref{thf}). However, it looks somewhat unexpected that increase
of masses is so great, up to $\sim 200\, MeV$. Anyway, for $B=1$ the rigid rotator approximation
is better justified \cite{ufk}. Strangeness contents of baryon states shown in Table 4 are calculated
with configuration mixing included, and they are considerably smaller than SC calculated in first
order of perturbation theory, Table 2. The slow rotator approximation \cite{schw} deserves more
attention if the negative results on $\Theta$ observation are confirmed.
All baryonic states considered here are obtained by means of quantization of
soliton rotations in $SU(3)$ configuration space, therefore they have positive
parity. A qualitative discussion of the influence of other (nonzero) modes
- vibration, breathing - as well as references to corresponding papers can be
found in \cite{wei,wk}. Calculation of baryon spectra with monopole excitation is made in
\cite{wei,wei1}. The realistic situation can be more complicated than
somewhat simplified picture presented here, since each rotation state can have
vibrational excitations with characteristic energy of hundreds of $MeV$.
The resonance $N^*(1440)$
is just the monopole excitation of ground state nucleon \cite{wei,wei1}.
\section{Comments on the $\Theta$ width and large $N_c$ arguments}
If the matrix element of the decay $\Theta^+\to KN$ is written in a form
\begin{equation}
M_{\Theta\to KN} = g_{\Theta KN}\bar{u}_N \gamma_5 u_\Theta \phi_K^\dagger
\end{equation}
with $u_N$ and $u_\Theta$ - bispinors of final and initial baryons, then the
decay width equals to
\begin{equation} \label{Gamma}
\Gamma_{\Theta\to KN}= \frac{g^2_{\Theta KN}}{8\pi}
\frac{\Delta_M^2-m_K^2}{M^2} p_K^{cm} \simeq
\frac{g^2_{\Theta KN}}{8\pi}
\frac{\bigl(p_K^{cm}\bigr)^3}{Mm_N}
\end{equation}
where $\Delta_M=M-m_N, \; M$ is the mass of decaying baryon, $p_K^{cm}\simeq 269\, MeV/c$ if
$M_\Theta = 1540\, MeV$ - the
kaon momentum in the c.m. frame. For the decay constant we obtain then
$g_{\Theta KN} \simeq 4.4$ if we take the value $\Gamma_{\Theta\to KN}=10\,MeV$
as suggested by experimental data \cite{2},\cite{zeus}. This should be compared
with pion-nucleon coupling constant $g_{\pi NN}\simeq 13.14$ (according to latest analysis
\cite{arbri} $g^2_{\pi NN}/(4\pi) = 13.75 \pm 0.10$). So, suppression of the decay
$\Theta\to KN$ takes place, but not
very large if the width is really close to $10\,MeV$.
Prediction of the widths of baryon resonances is not an intrinsic property of the chiral
soliton approach - in distinction from spectra of states. Additional assumptions concerning
the form of transition amplitudes are necessary \cite{dpp,mic2}.
Numerical cancellation
in the matrix element of $\Theta$ decay was obtained in \cite{dpp}, and later proved also in
large $N_c$ limit in chiral quark soliton model, for vanishing dimension of the soliton \cite{mic2}.
It would be difficult, however, to
explain the width $\Gamma_\Theta \sim 1\,MeV$ or smaller, as
suggested by scattering data
\cite{asw,gib}.
The arguments have been presented in the literature \cite{coh}, see also \cite{mic2},
that in large $N_c$ limit and in the case of chiral symmetry, i.e. when $m_\pi=m_K=0$, one should
expect that $\Theta$ width is parametrically greater than width of $\Delta (1232)$ isobar,
in contradistinction from what is seen experimentally.
As it has been observed long ago, the mass splitting between antidecuplet and octet of baryons
is of the order of $N_c^0\sim 1$, whereas that between decuplet and octet is of the order
of $N_c^{-1}$ due to the difference in rotation energy. To make these conclusions, the
identification of multiplets in our $N_c=3$ world and hypothetical large $N_c$ world is made in
definite way, and this identification is not unique in the latter case.
It is known that the artifact of large $N_c$ generalization of the chiral soliton and the quark
models is appearance of multiplets of baryons
which are absent in real $N_c=3$ world \footnote{This is not the only problem. The hypercharge for
arbitrary (but odd) $N_c$ is $Y=N_cB/3 +S$ (\cite{g}, see also \cite{ikor,coh}), and the electric
charge defined by relation $Q=I_3 +Y/2$ is integer only if $N_c$ is multiple of $3$. Another
possibility for electric charges was discussed in \cite{abb}, see Appendix.}.
For nonexotic baryons there are $(N_c+1)/2\,$ $SU(3)$
multiplets, beginning with $[p,q]= [1,(N_c-1)/2]$ which is interpreted as analogue of $N_c=3$ octet.
The next one is the multiplet with $(p,q) = [3, (N_c-3)/2]$ interpreted as "decuplet", and the
multiplet with largest $p$ is that with $(p,q)=(N_c,0)$. All multiplets
except first two are usually ignored, even not mentioned. To discuss the large $N_c$ properties
of any particular state, one should first establish correspondence between such state in real world
and in miraculous large $N_c$ world, and the way to do this depends on the principle which is
taken as leading one.
The $Y=N_c/3$ state within $(1, (N_c-1)/2)$ multiplet not only has the minimal possible for any baryon
isospin (and spin) $I=1/2$, but is also the state maximally antisymmetrized in isospin and spin
variables. It is natural to consider it as analogue of nucleon by this reason as well.
The state with $Y=1$ from $(3,0)$ multiplet in $N_c=3$ world not only is a state with isospin $I=3/2$,
but it is also a state of maximal symmetry in isospin and spin variables. So, if we take this
principle of maximal symmetry as a leading one, we should take the state with $Y=N_c/3,\;I=N_c/2$
from the multiplet $(p,q)=(N_c,0)$ as analogue of $\Delta$ in the large $N_c$ world.
The rotation energy of this state
quantized as rigid rotor is very large, $N_c(N_c+2)/(8\Theta_I)\sim N_c$, leading to parametrically
large width of $"\Delta "$ baryon. The ratio of $"\Delta" - "N"$ mass splitting to $"\Theta"-"N"$
splitting is of the order $\sim N_c$ in this case. Even if not quite convincing, this example shows
that large $N_c$ argumentation is not without ambiguity because identification of baryons of $N_c=3$
and large $N_c$ worlds is a subtle question.
The difference of masses of particular
baryons, e.g. of $\Delta \in \{10\}$ and nucleon from ground state octet contains also some
contribution due to $FSB$ terms and different values of their strangeness content. Strangeness
content of the nucleon is $SC_N=7/30$, and $SC_\Delta = 7/24$, see {\bf Table 2} and formula (\ref{HSB}).
Strangeness contents of analogues of nucleon in $[1,(N_c-1)/2]$ and "$\Delta$" in
$[3,(N_c-3)/2]$ multiplets are given in Appendix. Their difference is
$SC_\Delta - SC_N = 2(N_c+4)\bigl[1/[(N_c+1)(N_c+9)] - 1/[(N_c+3)(N_c+7)]\bigr]$. At large $N_c$
this difference decreases like $1/N_c^3$, therefore it gives negligible contribution to the
baryons mass differences.
In reality the masses of $\pi$-meson and especially of kaons are not only different from zero,
but even comparable with mass splittings - both masses are formally of the order of $N_c^0\sim 1$.
The width of $\Theta$ depends on result of cancellation of two quantities, each of them is of the
order of $N_c^0\sim 1$: $"\Theta \,-\,N"$ mass splitting and kaon mass. For the case of
$\Theta \to KN$ almost all energy release is absorbed by the kaon mass.
Therefore, the phase space suppression of the $\Theta$ decay cannot be controlled by $1/N_c$ counting
arguments only, since finally it depends on subtraction of two quantities of same order
of magnitude, $N_c^0 \sim 1$, but different nature, at least in our present understanding. The result
of this subtraction looks occasional,
it could be even negative, thus making the $\Theta$ baryon stable relative to strong interactions.
There are many examples in physics when some quantities of crucial importance
cannot be deduced from general principles \footnote{The particular values of binding
energies of nuclei or nuclear levels responsible for stability or instability of nuclear isotopes,
and for spectra of photons and neutrinos emitted by stars could be one of such examples.}.
Without any doubt, the width of exotic states is extremely important
and interesting quantity, especially if the width of the order of $1\,MeV$ for $\Theta^+$
is confirmed. The cheking of scattering data used in the analyses of \cite{asw,gib} seems to be quite
important, see also \cite{azim}. Critical review of these scattering data was made recently in
\cite{hic2} where necessity of their checking also has been emphasized.
\section{Wave functions of pentaquarks and the masses of strange quark (antiquark)}
Similar to the case of baryons and mesons made of valence quarks (antiquarks), it is convenient
to discuss the properties of new baryon resonances in terms of their quark wave functions (WF).
The question about correspondence of chiral soliton model results and expectations from the quark
models is quite interesting and even thorny.
\subsection{Quark contents of pentaquarks}
The quark contents of wave functions of {\it manifestly} exotic resonances are {\it unique}
within pentaquark
approximation, i.e. the number of quarks or antiquarks of definite flavor is
fixed by their strangeness and isospin \footnote{For pentaquarks manifestly exotic states are
defined by relation $I=(5+S)/2$ if strangeness $S\leq 0$ (any state with $S>0$ is manifestly
exotic, as discussed in Introduction).
}.
It is easy to obtain for WF of manifestly exotic components of antidecuplet (see also the {\bf Figure}):
$$ \Psi_\Theta \sim uudd\bar{s}, $$
and for 4 components of exotic $S=-2,\,I=3/2$ state
$$ \Psi_{\Phi/\Xi_{3/2}} \sim ssdd\bar{u};\; ssd(u\bar{u}-d\bar{d})/\sqrt{2};\;
ssu(d\bar{d}-u\bar{u})/\sqrt{2};\; ssuu\bar{d}. $$
Quark content of cryptoexotic states WF are not unique. Within antidecuplet:
$$\Psi_{N^*} \sim udd\,
[\alpha_- u\bar{u} + \beta_-d\bar{d} +\gamma_- s\bar{s}];\;\;
uud\, [\alpha_+ u\bar{u} + \beta_+d\bar{d} +\gamma_+ s\bar{s}], $$
$$\Psi_{\Sigma^*} \sim sdd\,[\mu_- u\bar{u} + \nu_-d\bar{d} +\rho_- s\bar{s}];\;...\;;\;
sdd\,[\mu_+ u\bar{u} + \nu_+d\bar{d} +\rho_+ s\bar{s}], $$
coefficients $\alpha_-,\;\alpha_+$, etc. depend on the particular variant of the model.\\
E.g., for the model with diquark transforming like flavor anti-triplet, $D_q \sim \bar{3}_F$
\cite{jw}
, $\alpha_-=\sqrt{1/3},\; \beta_-=0,\; \gamma_-=\sqrt{2/3}$, etc. Equidistancy within
$\overline{10}$ was obtained in \cite{clo,clodu} for this case.
Within $\{27\}$-plet only the $S=0,\;I=3/2$-state (analogue of $\Delta$-isobar) is cryptoexotic.
The states with $S=+1, I=1$ and state with $S=-1, I=2$ contain one $s$-quark field as depicted in
the {\bf Figure}, and their masses do not differ much by this reason, as it was obtained in chiral
soliton model as well, see Table 2.
Within $\{35\}$-plet {\it all} states of maximal isospin are manifestly exotic and have unique
quark content.
The state with $S=0,\;I=5/2$ (it can be called $\Delta_{5/2}$) does not contain strange quarks:
$$ \Psi_{\Delta_{5/2}} \sim dddd\bar{u};\;...\;;\; uuuu\bar{d}, $$
neither $s$, nor $\bar{s}$ quarks!
Remarkably, that within chiral soliton model this state has minimal, among all baryons, strangeness
content ($SC(\Delta_{5/2})\simeq 0.22$),
and has the lowest (within $\{35\}$-plet) mass, see Table 2 and \cite{wk}.
Evidently, besides flavor antitriplet diquark $D_q \sim \bar{3}_F$ (anti-triplet in color, singlet
$L=0$ state) discussed in this context
in \cite{jw} and called also "good" diquark \cite{wil},
the diquarks $D_q \sim 6_F$ ("bad" diquarks, transforming also like $\bar{3}$ in color, triplet
$L=0$ states) are necessary to form $\{27\}$- and $\{35\}$-plets of
pentaquarks.
Let us denote $(q_1q_2)$ the flavor symmetric diquark with spin $J=1$ ($\bar{3}_C$ in color,
triplet $L=0$ state).
Then realization of the wave function of $\{27\}$-plet of pentaquarks via diquarks is (we use same
notation $|N(p,q),Y,I,I_3>$ for the components of multiplets as in {\bf Table 2}, and present the
states with lowest value of $I_3$):
$$\Psi_{|27,2,1,-1>}\sim (d_1d_2)[d_3u_4]\bar{s}, $$
with $[u_3d_4]=(u_3d_4-d_3u_4)/\sqrt{2}$,
$$ \Psi_{|27,1,3/2,-3/2>} \sim \bigl[-(d_1d_2)[u_3d_4]\bar{u}+ (d_1d_2)[s_3d_4] \bar{s}\bigr]/\sqrt{2}, $$
other components of this $Y=1$ isomultiplet can be obtained easily with the help of isospin raising
$I^+$ operator.
States with negative strangeness have the wave functions
$$ \Psi_{|27,0,2,-2>} \sim (d_1d_2)[s_3d_4]\bar{u}, $$
$$ \Psi_{|27,-1,3/2,-3/2>} \sim (d_1s_2)[s_3d_4]\bar{u}, $$
$$ \Psi_{|27,-2,1,-1>} \sim (s_1s_2)[s_3d_4]\bar{u}. $$
The components with other projections of isospin $I_3$ are not shown here since they can be obtained
easily.
For the $\{35\}$-plet two flavor-symmetric diquarks $D_{6F}$ are necessary to form the states with
maximal isospin, according to group theoretical equality $6\otimes 6\otimes \bar 3 = \{35\} \oplus
\{27\} \oplus 2\{10\} \oplus \{\overline{10}\} \oplus 2\{8\}$.
For example, the $S=+1$ $\Theta^*$ state has wave function
$$ \Psi_{|35,2,2,-2>} \sim (d_1d_2)(d_3d_4)\bar{s}, $$
the above mentioned $\Delta_{5/2}$ has
$$ \Psi_{|35,1,5/2,-5/2>} \sim (d_1d_2)(d_3d_4)\bar{u}, $$
etc. States with other isospin projections also can be obtained easily.
The antidecuplet can be made from two symmetric diquarks $D_{6F}$ as well, e.g. its $S=+1$ component
made
of two isovector diquarks
is
$$\Psi_{\Theta^+}\sim [u_1u_2d_3d_4+ d_1d_2u_3u_4-{1\over 2}(u_1d_2+u_2d_1)(u_3d_4+d_3u_4)]\bar{s},$$
it is expected to have considerably higher energy \cite{wil}.
\subsection{Mass of strange antiquark in different pentaquark multiplets}
Here we shall compare the mass spectrum of baryons obtained within chiral soliton model (CSM)
with the quark model in pentaquark approximation, which will allow to make some conclusions concerning
masses of strange quarks, antiquarks and diquarks, necessary to fit
the chiral soliton model predictions.
The contribution of strange quark mass $(m_s)$, antiquark mass $(m_{\bar s})$ and strange
diquark mass $(m_{s\bar s})$ to masses of pentaquark states is presented in Table 5, in the lines
below notations of states.
It is easy to see that without configuration mixing (the first lines of numbers in Table 5)
there is linear dependence of masses on hypercharge of states for antidecuplet;
for $\{27\}$-plet the states with hypercharges $Y=2,\;1,\;0$ belong to one line, and states
with $Y=0,\;-1,\;-2$ - to another line; for $\{35\}$-plet 5 states with hypercharge
from $Y=1$ down to $Y=-3$ are on one line.
Such linear dependence, however, is not specific for CSM only, but is the consequence
of the special way of $SU(3)$-symmetry breaking, when FSB terms in lagrangian are proportional
to the $D_{88}$ Wigner function, or to hypercharge, which leads to the Gell-Mann - Okubo formula
\begin{equation}
\label{gmo}
\Delta M_{FSB} = a [Y^2/4 - I(I+1)] + b Y,
\end{equation}
with $a,\,b$ - some constants different for different $SU(3)$ multiplets.
For antidecuplet the relation between hypercharge and isospin takes place $I=1-Y/2$.
For $\{27\}$-plet the states $|Y,I>=|0,2>,\; |-1,3/2>$ and $|-2,1>$ are on the line $I=Y/2+2$,
the states $|Y,I>=|0,2>,\; |1,3/2>$ and $|2,1>$ belong to the line $I=-Y/2 +2 $.
For the components of $\{35\}$-plet with $Y$ from 1 to -3 similar relation takes place
$I=Y/2+ 2 $. It is easy to see that in all these cases quadratic in $Y$ term in formula (\ref{gmo})
cancels, and linear dependence of the mass on hypercharge
takes place. Similar results have been obtained recently in \cite{oh}.
Less trivial and more informative are some relations for masses of strange quarks/antiquarks
which follow from comparison with the quark model.
In what follows we shall reserve a possibility that effective masses of strange quark
and antiquark are different, as well as they are different within different $(p,\,q)$ multiplets.
This effect is known already since it takes place for ground states octet and decuplet
of baryons as well: the effective strange quark mass is $189\,MeV$ within octet and $147\,MeV$ within
decuplet, in average \footnote{When hyperfine splitting contributions are included, this difference
between strange quark masses extracted from octet and decuplet, becomes much smaller.}.
We can easily obtain within pentaquark approximation, ascribing the mass difference of different
components to the strange quark (antiquark) mass, the following relations:
\begin{equation}
\label{splaten}
\Delta_M(\{\overline{10}\}) = [2m_s - m_{\bar{s}}]_{\{\overline{10}\}}. \end{equation}
Recall that for decuplet
\begin{equation}\label{splten}
\Delta_M(\{10\}) = [3m_s]_{\{10\}}, \end{equation}
so, in oversimplified model where $m_s(\{\overline{10}\})=m_{\bar{s}}(\{\overline{10}\})=
m_s(\{10\})$ the first one should be 3 times smaller than $\Delta_M(\{10\}) $.
However, this condradiction becomes much softer and even can dissappear in more refined models
where masses of strange quark and antiquark are different, as well as they are different in
different $SU(3)$ multiplets.
The equality of mass differences between adjacent components of antidecuplet:
$$ {2\over 3}m_{s\bar s}-m_{\bar s}=m_s-{1\over 3}m_{s\bar s} $$
has a consequence that the
mass of $s\bar s$ pairs equals simply to the sum of quark and antiquark masses:
\begin{equation} \label{ss10} m_{s\bar s} = m_s +m_{\bar s}, \end{equation}
the index $\overline{10}$ is omitted for all masses.
Equality similar to (\ref{ss10}) holds for masses within $\{27\}$-plet as well.
Relations (\ref{splaten},\ref{ss10}) are the only relations which can be obtained for
masses of strange quark and antiquark within antidecuplet, leaving otherwise much freedom
for these masses.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
$|\overline{10},2,0>$&$|\overline{10},1,1/2>$&$|\overline{10},0,1>$&$|\overline{10},-1,3/2>$& &\\
\hline
$m_{\bar s}$ &$2 m_{s\bar s}/3$ &$m_s+m_{s\bar s}/3$&$2 m_s$& & \\
\hline
564 & 655 & 745 & 836 & &\\
600 & 722 & 825 & 847 & & \\
\hline
\hline
$|27,2,1>$&$|27,1,3/2>$&$|27,0,2>$&$|27,-1,3/2>$&$|27,-2,1>$&\\
\hline
$m_{\bar s}$ &$m_{s\bar s}/2$ &$m_s$&$2 m_s$&$3m_s$ & \\
\hline
733 & 753 & 772 & 889 & 1005 &\\
749 & 887 & 779 & 911 & 1048 &\\
\hline
\hline
$|35,2,2>$&$|35,1,5/2>$&$|35,0,2>$&$|35,-1,3/2>$&$|35,-2,1>$&$|35,-3,1/2>$ \\
\hline
$m_{\bar s}$ &$0 $ &$m_s$&$2 m_s$&$3m_s$ &$4 m_s$ \\
\hline
1152 & 857 & 971 & 1084 & 1197 & 1311 \\
1122 & 853 & 979 & 1107 & 1236 & 1367 \\
\hline
\end{tabular}
\end{center}
{\bf Table 5.} {\tenrm Masses of components of $\{\overline{10}\}$, and components with maximal
isospin for
$\{27\}, J=3/2$ and $\{35\},J=5/2$ -plets of exotic baryons (in $MeV$, the nucleon mass is
subtracted). The contribution of strange quarks and antiquarks is written below notation of states,
$m_{s\bar s}$ is the mass of the $s\bar s$ pair.
The first line of numbers is the result of calculation without configuration
mixing, the second line - configuration
mixing included according to \cite{wk}.
Calculations correspond to variant $C$ of {\bf Table 2}, or case $A$ of paper \cite{wk}:
$\Theta_K =2.84\,GeV^{-1},\; \Theta_\pi=5.61\,GeV^{-1},\;\Gamma =1.45\,GeV.$ } \\
More information can be obtained for strange quark/antiquark masses within higher exotic multiplets.
Linear dependence of masses of manifestly exotic components of $\{27\}$-plet allows to obtain for
the mass of strange quark $m_s\in \{27\} \simeq 117\,MeV$ (configuration mixing not included).
For $\{27\}$-plet it is also useful to fix the difference of masses between manifestly
exotic components
$|27,2,1>$ and $|27,0,2>$:
\begin{equation} \label{spl27}
\Delta_{2-0}(\{27\})= [m_{\bar{s}} - m_s]_{\{27\}} \simeq - 40\,MeV,
\end{equation}
so, strange antiquark within $27$-plet should be lighter than strange quark, according to CSM
results.
Within $35$-plet, it follows from the results for masses of the components with strangeness
$S\leq 0$ that the effective strange quark mass is about $115\,MeV$.
If we ascribe the difference of masses between $Y=2$ and $Y=1$ states of $\{35\}$-plet to the mass of
strange antiquark, we obtain that $m_{\bar{s}}\in \{35\} \simeq 295\,MeV$.
Strong interactions of the quark $s$ and antiquark $\bar{s}$ are different,
so no wonder that effective masses of quark and antiquark are different. However,
such big difference between masses of strange antiquarks in $27$ and $35$-plets seems
to be unexpected.
Configuration mixing increases the mass of strange quark within $27$-plet
up to $\sim 135\,MeV$. Within $35$-plet configuration mixing does not change the above numbers
drastically: the effective strange quark mass increases up to $125-130 \,MeV$, and the mass of
antiquark $\bar{s}$ decreases to $\sim 270\,MeV$.
The effect of configuration mixing is especially important for cryptoexotic components of
antidecuplet ($Y=1\;and\;0$) which mix with similar components of the lowest baryon octet, as a result,
their masses increase. The $\Phi/\Xi_{3/2}$ component is mixed with analogous component $\Xi_{3/2}
\in \{27\}$, and its mass moves to lower value. In summary, after mixing the total mass splitting of
antidecuplet decreases, and equidistant position of states is considerably violated, unlike the case
of decuplet.
Within $27$-plet, configuration mixing increases the mass of cryptoexotic state $|27,1,3/2>$
considerably (more than by $130\,MeV$). The identification of this state, analogue of
$\Delta (1232)$ -isobar, is not straihgtforward, see also recent analysis in \cite{azim}.
The
comparison of masses
of $\Theta^+ \in \overline{10}$ and $\Theta^* \in 27$ allows to
conclude that $6_F$ diquark is heavier
than $\bar{3}_F$ diquark by $\sim 120-150\,MeV$, if we ascribe the mass difference of
$\Theta$-resonances to the mass difference of diquarks.
It is possible to estimate the mass difference of diquarks more straightforward, in the limit
$m_K \to 0$. Then we obtain $\Delta M_{(6F - \bar{3}F)} \simeq 3/(2\Theta_\pi)-1/(2\Theta_K) \sim
100\,MeV$. This is smaller than the estimate given by F.Wilczek in \cite{wil},
$\Delta M_{(6F - \bar{3}F)} \sim 240 - 360\,MeV$.
The comparison of masses of $\Theta^* \in 27$ and $\Theta^* \in 35$, taking into account
the mass difference of strange antiquarks, allows to get for the mass difference of bad and
good diquarks, $\Delta M_{(6F - \bar{3}F)} \sim 200\,MeV$, in better agreement with estimate
of \cite{wil}.
As it follows from the consideration of negative
strangeness components of $\{27\}$- and $\{35\}$-plets, the masses of strange quarks do not differ
considerably within these multiplets, they are close to $130\,MeV$ and do not differ much
from masses of strange valence quarks within octet and decuplet of baryons.
Quite different, even paradoxical situation takes place for strange antiquark.
If we take the mass of $s$-quark in
antidecuplet about $(140-150)\,MeV$, as in decuplet, then the effective mass of strange anti-quark
should be small, not greater than few tens of $MeV$.
For $\{27\}$-plet we obtain from (\ref{spl27}) that
strange anti-quark is lighter than strange quark by $30-40\,MeV$, and in $\{35\}$-plet the mass of
strange anti-quark is about $270-290\,MeV$, or about $\sim 2$ times greater than mass of strange
quark within $\{27\}$-plet.
Detalization of the quark models could show is it really possible, or not.
To conclude this section, we note that effective masses of strange quark and especially strange
antiquark should be different for different $SU(3)$ multiplets, to make possible the link between
rigid rotator version of chiral soliton and simple quark model. This issue will be considered in
more details elsewhere.
\section{Partners of lowest exotic states with different spin}
The partners of lowest exotic states, i.e. the states with same flavor quantum numbers, isospin,
strangeness, etc., but different spin have been
discussed in the literature during latest years, after evidence has been obtained for exotic states
like $\Theta^+$ and $\Phi/\Xi_{3/2}$ \cite{clo,coh3}. Within $CSM$ the equality between spin of baryon states
and so called "right" isospin
($I_R=1/2$ for antidecuplet) follows from the fact that the lowest $B=1$ classical configuration
is of
hedgehog type, and as a result the isospin and space (or spin) rotations are equivalent.
It is not so for the states with greater values of $B$ which have generally different spin and isospin
\cite{vkax}
.
At the same time, within the quark or correlated quark models one could expect existence of
partners of states, since the spins of quarks and angular momentum of orbital motion can be summed
providing states
with different values of spin \cite{clo}. For example, according to \cite{clo} one
should expect existence of partners of $\Theta^+$ with
$J^P=3/2^+$ and the mass greater than that of
lowest states by several tens of $MeV$ \cite{clo}.
This possibility was considered as an argument against chiral soliton models since it was claimed that
such states cannot be obtained within $CSM$.
However, careful consideration of multiplets of exotic baryons in the framework of chiral soliton
approach allows to conclude that partners of lowest baryons exist within higher $SU(3)$ multiplets
of baryons. Some examples are considered here.
The partners of baryon antidecuplet ($J^P=1/2^+$) with $J^P=3/2^+$ exist within $\overline{35}$-plet,
$(p,\,q)=(1,\,4),$ exoticness $m=2$. The rotational energy of these states is greater than that
of antidecuplet, according to {\bf Table 1}, by
\begin{equation}
\label{dela1035}
M_{rot}(\overline{35},J=3/2)-M_{rot}(\overline{10},J=1/2)={3\over 2\Theta_K}+{3\over 2\Theta_\pi}
\end{equation}
which is about $750\,-\,800\,MeV$, i.e. considerably greater than quark model estimates \cite{clo}.
Some contribution to the mass difference of such partners comes also from $FSB$ mass terms, but
the mass splitting between components of $\{\overline{35}\}$ corresponding to $\{\overline{10}\}$
is smaller than that of $\{\overline{10}\}$ itself, almost twice: the value of $sin^2 \nu$ increases
from $5/8$ to $3/4$, as shown in Table 6. These states are septuquarks, at least.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
$Baryon\,|N(p,q),Y,I,J>$ &$<s_\nu^2>_0$ & A & B & C & \\
\hline
$\Theta^*\,|\overline{35},2,0,3/2>$&$0.625$&2423&2535 & 2487 & \\
$N^*|\overline{35},1,1/2,3/2> $&$0.667$&2481&2586 & 2548 & \\
$\Sigma^*\,|\overline{35},0,1,3/2>$&$0.708$&2527&2628 & 2596 & \\
$\Xi^{*}|\overline{35},-1,3/2,3/2>$&$0.750$&2557 & 2658 & 2627 & \\
\hline
\hline
$N^*\,|27,1,1/2,3/2>$ &$0.643$ &1739 &1782 & 1783 & \\
$\Sigma^*\,|27,0,1,3/2>$ &$0.679$ &1847 &1871 & 1896 & \\
$\Lambda^*\,|27,0,0,3/2>$ &$0.714$ &1829 &1861 & 1876 & \\
$\Xi^{*} |27,-1,1/2,3/2>$ &$0.768$ &1917 &1937 & 1969 & \\
\hline
$\Delta^*|35,1,3/2,5/2>$ &$0.438$&2054 & 2122 & 2137 & \\
$\Sigma^*\,|35,0,1,5/2>$ &$0.542$&2123 & 2181 & 2209 & \\
$\Xi^{*}|35,-1,1/2,5/2>$ &$0.646$&2186 & 2235 & 2275 & \\
$\Omega^{*}\,|35,-2, 0,5/2>$ &$0.750$&2244 & 2286 & 2336 & \\
\hline
\end{tabular}
\end{center}
{\bf Table 6.} {\tenrm Values of masses of the partners of the antidecuplet with $J=3/2$ within
$\{\overline{35}\}$-plet; partners of the lowest octet within the $\{27\}$-plet, $J=3/2$; and
partners of the lowest decuplet within the $\{35\}$-plet, $J=5/2$. Rigid rotator approximation
has been used here according to \cite{wk,ufk}.}\\
There are also partners of other lowest multiplets, e.g. the partners of baryons octet
$J^P=1/2^+$ with $J^P=3/2^+$ exist, the lowest one is contained within $\{27\}$-plet with $J^P=3/2^+$.
The difference of rotation energies equals to
\begin{equation}
M_{rot}(27,J=3/2)-M_{rot}(8,J=1/2)={1\over \Theta_K}+{3\over 2\Theta_\pi},
\end{equation}
so, about $580\,-\,620\,MeV$. More accurate numbers are presented in Table 6.
The partners of lowest $J=3/2$ decuplet with $J=5/2$ sit within $\{35\}$-plet and have the energies
shown also in Table 6, last 4 lines.
Generally, within complicated $SU(3)$ multiplets, like $\{27\}$ and $\{35\}$-plets, there are also
partners of iso-multiplets with same spin and different isospins. For example, within $\{27\}$-plet,
for $Y=0$
there are partners with isospin $I=2,\;I=1$ and $I=0$, spin $J=1/2$ and $J=3/2$; for $Y=1$ there are
states with $I=3/2$ and $1/2$ (see {\bf Figure}). For fixed value of spin $J=I_R$
states with different values of isospin $I$ have same rotational energy, their mass difference is
due to $FSB$
terms, only. Such partners can be obtained within other approaches, see e.g. \cite{io}.
The spectrum of baryon states, including their partners, is rich, and interesting problem is
to find correspondence with the spectrum arising from the quark models.
\section{Multibaryons with exoticness}
Numerous applications of the chiral soliton models to the properties of baryons have been widely
discussed, mostly accepted and also criticized in literature. Another branch of these applications
are the properties of states with baryon
number greater than $1$, nuclei and/or multibaryons, and this issue is much less known and accepted.
The possibility to describe real nuclei as quantized chiral solitons appeared after discovery of
classical chiral field configurations bound relative to the transition to states with smaller
baryon numbers (history of this discovery and references can be found, e.g. in \cite{hms,vkax,kz}).
One of recent results is successful description of the mass splittings of nuclear isotopes
with different values of isospin, or so called "symmetry energy" of nuclei \cite{ksm}. Some
variation of the only parameter of the model, Skyrme constant, allowed to provide good
description of data for atomic numbers up to $\sim 30$ and to predict binding energies (b.e.) of some
neutron rich nuclides \cite{ksm}, in general agreement with other, more traditional, approaches.
The binding energies of light hypernuclei also can be calculated in general agreement with data
\cite{vk1}. Therefore, one can conclude that the chiral soliton approach provides results
which are, at least, in qualitative agreement with existing nuclear physics data.
To obtain baryon states with definite quantum numbers, the quantization of classical configurations
should be performed. There are several quantization prescriptions described in the literature
to get the states with flavor quantum numbers, strangeness, charm or beauty.
Besides "rigid rotator" quantization scheme originating from works \cite{anw,g}, described and
used above, there is also bound state approach \cite{ck,kk} and its simplified and very transparent
version \cite{kk,westk} which is convenient for estimating the energies of states with lowest flavor or
anti-flavor quantum numbers. This scheme has been used recently to find the spectrum of lowest
states with positive strangeness (beauty) or negative charm \cite{ksh}.
Within this quantization scheme the energy of state consists of two contributions. One, most important,
is the flavor excitation energy which is of the order of $N_c^0\sim 1$. Second component is the
correction of the order $\sim 1/N_c$ depending on the isospin of the state (hyperfine splitting
correction).
In the leading order in $N_c$ the hamiltonian of the system can be written as
\begin{equation} \label{hdd}
H =M_{cl} + 4 \Theta_{F,B} \Pi^\dagger \Pi +
\biggl( {3\over 2}\Gamma_{SB} + {N_c^2B^2\over 16\,\Theta_{F,B}} \biggr) D^\dagger D
\end{equation}
where $\Gamma_{SB}$ is given above by Eq. (\ref{GSB}), the moment of inertia
$\Theta_{F,B}=\Theta_K$ for $B=1$, 2-component amplitude $D$ is deviation of
starting $SU(2)$ soliton into "flavor direction" which is believed to be small. Indeed, it can be
easily obtained that \begin{equation}
|D| \sim [24 \Theta_{F,B} \Gamma_{SB} +N_c^2B^2]^{- 1/4},
\end{equation}
i.e. it decreases with increasing $FSB$ mass and/or number of colors $N_c$. $\Pi$ is momentum
canonically conjugate to variable $D$.
The relation takes place, $D^\dagger D \simeq (1-D_{88})/3 \,=\, s_\nu^2/2$ which is fulfilled
with good accuracy when $\nu$ is small.
This hamiltonian can be diagonalized and written in terms of flavor or antiflavor numbers
\cite{kk,westk},
\begin{equation}\label{hab}
H = M_{cl} + a^\dagger a \omega_{F,B} + b^\dagger b \bar{\omega}_{F,B}
\end{equation}
$a^\dagger,\;b^\dagger$ being flavor and antiflavor creation operators, and flavor (antiflavor)
excitation energies
\begin{equation}
\omega_{F,B}= {N_cB\over 8\Theta_{F,B}} \bigl(\mu_{F,B}-1\bigr), \qquad
\bar{\omega}_{F,B}={N_cB\over 8\Theta_{F,B}} \bigl(\mu_{F,B}+1\bigr),
\end{equation}
\begin{equation}
\label{mu}
\mu_{F,B}=\biggl[1 + {24\Theta_{F,B}\Gamma_{SB} \over (N_cB)^2}\biggr]^{1/2}.
\end{equation}
At large $N_c$ the quantities $\mu_{F,B},\;\omega_{F,B}$ and $\bar{\omega}_{F,B}$ scale like
$N_c^0\sim 1$.
When $FSB$ is small, the expansion of $\mu_{F,B}$ can be made, and the flavor excitation energy
\begin{equation} \label{smallm}
\omega_{F,B}\simeq {3\Theta_{F,B}\Gamma_{SB}\over 2N_cB},
\end{equation}
quadratically depends on the $FSB$ mass, because $\Gamma_{SB}\sim m_K^2$.
Further details and formulas can be found in \cite{westk,ksh}.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline
B & $\bar{\omega}_s$ & $\bar{\omega}_c $& $\bar{\omega}_b $& $\Delta\epsilon_s$& $\Delta\epsilon_c$&
$\Delta\epsilon_b$\\
\hline
1 &$591$ &$1750$ &$4940$ &--- &--- &--- \\
2 &$571$ &$1720$ &$4900$ &$ 45$ & $60$ & $90$\\
3 &$564$ &$1710$ &$4890$ &$ 65$ & $40$ & $50$ \\
4 &$567$ &$1710$ &$4870$ &$ 20$ & $15$ & $50$ \\
6 &$555$ &$1710$ &$4880$ &$ 55$ & $30$ & $40$ \\
8 &$553$ &$1710$ &$4890$ &$ 70$ & $30$ & $40$ \\
12&$547$ &$1720$ &$4910$ &$ 85$ & $30$ & $30$ \\
16&$541$ &$1720$ &$4930$ &$ 95$ & $30$ & $10 $ \\
20&$538$ &$1730$ &$4940$ &$100$ & $20$ & $-10$ \\
24&$536$ &$1730$ &$4960$ &$105$ & $20$ & $-20$ \\
\hline
\end{tabular}
\end{center}
{\bf Table 7.} The anti-flavor excitation energies (in $MeV$) and binding energies changes of
anti-flavored hypernuclei in comparison with ground states of ordinary nuclei (also in $MeV$) for
baryon numbers up to $24$. \\
The energies of anti-flavors excitation and binding energies changes of flavored multibaryons
in comparison with ordinary nuclei presented in {\bf Table 7}, are taken from \cite{ksh}.
For anti-charm and anti-beauty the antiflavor excitation energies are considerably smaller
than masses of $D$ and $B$-mesons, correspondingly. It means that anti-charmed (anti-beautiful)
pentaquarks - their ground states - are bound relative to strong decays, since $1/N_c$
corrections are small for large mass of flavor (the masses of ground state pentaquarks
are $\sim 2700\,MeV$ for anti-charm and $5880\,MeV $ for $\Theta_b$ \cite{ksh}). The property
of binding of anti-charmed (-beautiful) pentaquarks is known really long ago \cite{rscoc,ohpm}.
The anti-charmed pentaquark observed recently with the mass $3099\,MeV$ \cite{akt} can be
some excitation of the ground state we discuss here, see, however \cite{karlip} where the
mass of the $\Theta_c$ was predicted to be $2985 \pm 50\, MeV$ within correlated quark model.
Some decrease of b.e. for anti-charm and anti-beauty, presented in Table 7, can be an artifact
of approximations used to calculate them (rational map approximation \cite{hms}).
For baryon numbers $B\geq 10$
the rescaled (or nuclear) variant of the model can be used, which leads to increase of b.e. in
comparison with nucleon variant of the model, by several tens of $MeV$ \cite{ksh}. It should be
kept in mind
that the mass of $\Theta^+$ hyperon within this particular variant of the model equals to $1588\,MeV$.
The accuracy of calculation is not better than $\sim 30-50 \,MeV$, but deeply bound
$\Theta$-hypernuclei should be expected for atomic numbers greater than $\sim 20$.
Similar results have been obtained also within more traditional potential or mean-field approaches
\cite{cabrera,zhong,vicen}, discussion of this issue and references can be found in \cite{lan}.
The increase of energy of exotic states in comparison with nonexotic ones was obtained for arbitrary
$N_c$ within rigid rotator model as well (Appendix of \cite{ksh}). It was found
\begin{equation}\label{odd}
\Delta E_{rot} = {N_cB+3\over 4\Theta_{F,B}}
\end{equation}
for odd $B$-numbers, and for $B=1$ this coincides with above expression, second of (\ref{d108}).
For even $B$-numbers
\begin{equation}\label{even}
\Delta E_{rot} = {N_cB+2\over 4\Theta_{F,B}}.
\end{equation}
In derivation of these expressions it was assumed that ground states of nuclei and lowest states
of flavored multibaryons belong to $SU(3)$ multiplets $(p,q)$ with the lowest possible values of
$p$ \cite{ksh}, i.e. they have lowest allowed value of isospin - in general agreement with data.
What is remarkable, the leading in $N_c$ contribution is the same as in
rigid oscillator model \cite{westk} used to make calculations in \cite{ksh}, where the difference
of anti-flavor and flavor excitation energies
\begin{equation}
\bar{\omega}_{F,B} - \omega_{F,B} = {N_cB\over 4\Theta_{F,B}}.
\end{equation}
Evidently, convergence of both quantization
methods improves not only with increasing $N_c$, but also with increasing baryon number.
It should be noted that two different methods of quantization used in present paper, the rigid
(or soft) rotator used in previous sections, and rigid oscillator method, a variant of the
bound state
approach \cite{kk,westk}, are not identical and lead to different results for $N_c=3$.
According to (\ref{smallm}), the mass
splitting of decuplet is $\Delta_M(\{10\},RO) = 3\Gamma_{SB}/2$, whereas for rigid rotator it is
8 times smaller, according to previous results, see (\ref{HSB}), Table 2 and also Appendix below.
For the octet of baryons the RO result for total
splitting is 4 times greater than the RR result. The RO method works well for exotic baryon and
multibaryon states, but meets difficulties in describing the nonexotic components of $SU(3)$
multiplets which contain exotic states.
Another issue of interest could be the properties of classical chiral field configurations at
large baryon numbers,
as obtained within the Skyrme model. Analytical evaluations performed in \cite{vk2} have shown that
these properties are quite universal: at large B-numbers multibaryons described within the Skyrme
model are spherical bubbles with the mass and B-number concentrated in their shell. The thickness
of this shell is approximately constant, about $t \sim 3.6/(F_\pi e)$, same is the average energy
density in the shell, $\rho_{shell}\sim F_\pi^4 e^2$, if the mass term in the lagrangian is small
enough. Both $t$ and $\rho$ do not depend on baryon number.
So, the bags of matter appear in this model, the properties of "material" which these bags are
made of, follow from effective chiral lagrangian \cite{vk2} (in difference from traditional bag
models where these properties are postulated, or introduced from phenomenological grounds).
Although multibaryon configuations obtained in this way differ
from ordinary nuclei, by the form of their density distribution first of all, further modifications
of the model are possible, including modifications of the mass term \cite{marl2,vk2}, but I will
not go into further details here.
\section{Conclusions and prospects}
The contradictive situation with observation of pentaquark states will be resolved, probably,
within next few years.
Even if not all reported pentaquark states are confirmed, one could state that interesting
branch of
baryon spectroscopy appeared which will enlarge
our knowledge about hadron structure.
If none of announced observed pentaquarks is confirmed, there remains still certain theoretical
interest in understanding the structure of pentaquarks and correspondence between chiral soliton
and quark model descriptions.
Such states can appear as broader resonances at higher energies, as it was discussed previously
\cite{j,hog,str,roi}.
Present discussion, certainly, puts more questions than gives answers.
The following problems and questions can be pointed out, many of them have been, of course, noted
in previous discussions \cite{hic2,azim}:
$*$ High statistics confirmation of existence of narrow pentaquarks seems to be necessary,
especially for the resonances
$\Phi/\Xi_{3/2}$ and $\Theta_c$, see \cite{pr}.
Some information about experiments performed
or to be performed is contained in \cite{pr,hicks,hic2,kab2}.
$*$ Width determination is of great importance, $\Gamma \sim 1 \,MeV$ is not excluded and suggested
by analyses of scattering data,
but would be difficult to explain it by theory: a special reason
is necessary then.
$*$ Several missing components of multiplets remain to be found, for example, of considerable
interest are:\\
in $\{\overline{10}\}$-plet: $\Phi/\Xi_{3/2}^+ \to \Xi^0 \;\pi^+,\;\; \Sigma^+\,\bar{K}^0$;\\
in $\{27\}$-plet: $\Theta^*_1\to NK$; $\Xi^*_{3/2} \to \Xi\pi$; $\Sigma_2 \to \Sigma\,\pi;\;$;
$\Omega_1 \to \Omega\,\pi,\, \Xi \bar{K},$;\\
in $\{35\}$-plet: $\Omega_1^* \to \Omega\,\pi,\; \Xi \bar{K},\; \Xi^* \bar{K}$;
$\;\Delta_{5/2}\to N\pi\pi;\;$
$\Gamma_{S=-4} \to \Omega \bar{K}$, etc.
In the latter case the complication is due to the fact that most of interesting components of
$\{35\}$-plet are not available in octet-octet meson-baryon interaction.
$*$ Studies of cryptoexotics $(N^*,\; \Delta^*,\; \Xi^*...)$ are of interest as well, to complete
the picture of pentaquarks, more detailed discussion can be found in \cite{azim,araz}.
$*$ Spin and parity are {\it crucial} for cheking the validity of chiral soliton models
predictions. Negative parity of these states would provide big difficulties for their
interpretation as quantized topological solitons, although in any model it seems unrealistic
to get a narrow resonance, with $\Gamma \leq 10\,MeV$, decaying into S-wave state of meson and baryon
with energy release about $100\,MeV$.
$*$ As a result, better understanding of the structure of baryons and their wave functions will be
reached.
The understanding of the possible important role of correlated diquarks and triquarks in the baryons
wave functions could be the first example \cite{jw,dor}. The link of the soliton approach and quark models leads to
the conclusion that the effective masses of strange quark and antiquark within baryon states should
be considerably different and depend on the particular $SU(3)$ multiplet, and this can be another
example. The difference of masses of strange antiquarks within $27$-plet and $35$-plet is so large,
that it looks as paradox.
$*$ As it was noted in literature \cite{coh,ikor}, predictions of chiral soliton models are not
completely selfconsistent from the point of view of the $1/N_c$ expansion.
In addition to problems considered in \cite{coh,ikor}, we note, e.g., that
the mass splitting between octet and antidecuplet of baryons is of the order of $N_c^0\sim 1$,
whereas the total mass splitting within octet or antidecuplet is of the order of $N_c$, as the
classical soliton mass itself.
There is also some inconsistency between rigid rotator and bound state quantization models, in
particular the mass splittings within $SU(3)$ multiplets given by these models, differ
considerably. These mass splittings
coincide at large $N_c$, in the leading in $1/N_c$ approximation, but for $N_c=3$ the bound state
approach in its present form (the rigid oscillator model, in particular \cite{westk})
gives much greater splittings when FSB mass is not large (see Appendix). In view of these difficulties,
the results obtained in the large $N_c$ limit, including e.g. some objections against chiral
soliton model results \cite{coh,ikor}, should be interpreted with great care and may not be valid for
the real $N_c=3$ world.
Predictions of chiral soliton approach should be considered as a reasonable extrapolation,
when one of states of interest is fitted. Results of this extrapolation are impressive sometime.
$*$ Other predictions of CSM are of interest besides those discussed in present paper, e.g.
supernarrow radiatively decaying dibaryon (JINR and INR experiments \cite{khr,fil}, see,
however, \cite{tam} where negative result was obtained for low values of dibaryon masses).
$*$ Chiral soliton models are good example of the field theoretical models which allow to obtain
the results of practical interest. They provide a possibility to describe not only baryons and
baryonic resonances, but also systems with large baryon numbers as "bags" of certain type,
the properties of these bags are deduced from initial lagrangian \cite{vk2}.
Some important and interesting issues have not been considered here in view of restricted size of the
paper: exotic baryons production mechanisms and their properties; determination of spin-parity
and electromagnetic properties of these baryons, etc. Discussion and references can be found in
\cite{jm,azim}.
{\it Acknowledgments.} Computer programs for configuration mixing arranged by Bernd Schwesinger and
Herbert Weigel
(soft rotator approximation) and by Hans Walliser (rigid rotator) have been used in present paper.
I'm greatly indebted to Hans Walliser also for his help in numerical calculations, useful remarks
and criticism, to Tom Cohen and Igor Klebanov for helpful discussion of large $N_c$ subtleties,
to Igor Strakovsky for reading the manuscript and useful comments on experimental data
available now, and to Andrei Shunderuk for checking of some formulas and numerical results. E-mail
conversations with Ya.I.Azimov, D.I.Diakonov, G.Holzwarth, R.L.Jaffe, S.Kabana, J.Trampetic,
H.Weigel are acknowledged, as well as discussions with A.A.Andrianov, V.A.Andrianov, L.N.Bogdanova,
K.G.Boreskov, B.L.Ioffe, B.Z.Kopeliovich, L.N.Lipatov, V.M.Lobashev, V.A.Matveev, Yu.V.Novozhilov,
L.B. Okun', V.A.Rubakov, Yu.A.Simonov, K.A. Ter-Martirosyan.\\
\section{Appendix. Some properties of the large $N_c$ baryons.}
As it was discussed above, at large arbitrary (odd) number of colors $N_c$ baryon consists of
$N_c$ quarks in color singlet state, and there are totally $(N_c+1)/2$ nonexotic $SU(3)$
multiplets of baryons, from $[p,q]=[1,(N_c-1)/2]$, to $[p,q]=[N_c,0]$.
The hypercharge for arbitrary $N_c$ is $Y=N_cB/3 +S$ (\cite{g}, see also \cite{ikor,coh}).
One possibility
for the choice of charges of quarks is as usual, $Q_u=2/3$, $Q_d=Q_s=-1/3$, see \cite{coh} e.g.
In this case the electric
charge defined by relation $Q=I_3 +Y/2$ is integer only if $N_c$ is multiple of $3$. Another
possibility for electric charges was discussed in \cite{abb}.
where the supercharged quarks
and $SU(3)$ multiplets were considered. In this case $Q=I_3+Y/2 + B(3-N_c)/6$, the charges of quarks
follow from this expression at $B=1/N_c$:
\begin{equation}
Q_u={1\over 2} + {1\over 2N_c},\qquad Q_d=Q_s=-{1\over 2} + {1\over 2N_c},
\end{equation}
and average charge of each baryonic $SU(3)$ multiplet, or supercharge, equals to $\bar{Q}=(3-N_c)B/6$.
Below strangeness contents of baryons at large number of colors are presented, which define the
mass splittings of baryon multiplets within rigid rotator approximation.
For the multiplet $[p,q]=[1,(N_c-1)/2]$ which is analogue of the $N_c=3$ octet we obtained:
\begin{eqnarray} \label{scoc}
<s_\nu^2>_{"N"} &=& {4(N_c+4)\over (N_c+3)(N_c+7)}, \qquad <s_\nu^2>_{"\Lambda"} = {6\over (N_c+7)},
\\ \nonumber
<s_\nu^2>_{"\Sigma"} &=& {2(3N_c+13)\over (N_c+3)(N_c+7)}, \qquad
<s_\nu^2>_{"\Xi"} = {8\over (N_c+7)}.
\end{eqnarray}
Evidently, the Gell-Mann---Okubo relation $M_\Sigma + 3M_\Lambda =2(M_N+M_\Xi)$ is fulfilled
for these values of $<s_\nu^2>$. The increase of $<s_\nu^2>$ per unit of strangeness within "octet"
of baryons equals, in average, at large $N_c$
\begin{equation}
\Delta(<s_\nu^2>,\delta |S|=1,"8") \simeq {2\over N_c}\left (1-{8\over N_c} \right ).
\end{equation}
For the components of "decuplet" $[p,q]=[3,(N_c-3)/2]$ we obtain
\begin{eqnarray} \label{scdec}
<s_\nu^2>_{"\Delta"} &=& {4(N_c+4)\over (N_c+1)(N_c+9)}, \qquad
<s_\nu^2>_{"\Sigma*"} = {2(3N_c+7)\over (N_c+1)(N_c+9)}, \\ \nonumber
<s_\nu^2>_{"\Xi*"} &=& {4(2N_c+3)\over (N_c+1)(N_c+9)}, \qquad
<s_\nu^2>_{"\Omega"} = {10\over (N_c+9)}, .
\end{eqnarray}
Equidistant behaviour of "decuplet" components can be noted, with a step
\begin{eqnarray}
\Delta(<s_\nu^2>,\delta |S|=1,"10")& = &2(N_c-1)/[(N_c+1)(N_c+9)] \\ \nonumber
& \simeq & {2\over N_c}\left (1-{11\over N_c}+{101\over N_c^2}\right ).
\end{eqnarray}
At large $N_c$ average splittings within "octet" and "decuplet" coincide and equal to $2/N_c$,
but preasymptotic corrections $\sim 1/N_c^2$ are different, making splitting within "decuplet"
smaller than within "octet", in qualitative agreement with observations for octet and
decuplet in real world.
For the $\Theta^+ \in "\{\overline{10}\}"$ it is easy to obtain
\begin{equation}
<s_\nu^2>_{"\Theta"} = {6\over (N_c+9)},
\end{equation}
and for the $\Theta_1 \in "\{27\}"$
\begin{equation}
<s_\nu^2>_{"\Theta_1"} = {2(3N+23)\over (N_c+5)(N_c+11)},
\end{equation}
which is slifgtly greater than for $\Theta$.
At large $N_c$ it is a matter of simple algebra to establish that there is equidistant
behaviour of strangeness contents (recall that $<s_\nu^2>_B = 2 SC_B$) for the components of
non-exotic multiplets, with not large (fixed) values of strangeness $S$:
\begin{equation}
<s_\nu^2>_{(p\sim 1,q\sim N_c/2, |S|\sim 1)} \simeq 2 {2+|S| \over N_c}.
\end{equation}
As a result, in the limit $N_c \to \infty $ the mass splittings between adjacent components of
"octet", "decuplet" and other
nearest multiplets coincide with those obtained within rigid oscillator approximation \cite{westk}.
However, $1/N_c^2$ corrections to these asymptotic values of mass splittings are large, the expansion
parameter is about $\sim 11/N_c$ or $\sim 8/N_c$. These corrections lead to the decrease of the
mass splittings
between adjacent components of these multiplets, and this effect becomes of the order 1 when
$|S| \sim N_c$. As a result, the total mass splittings of the whole multiplets are smaller than within
RO approximation by numerical factors. For the real world, $N_c=3$, the mass splitting of decuplet
is 8 times smaller for rigid rotor approximation than for rigid oscillator (when FSB mass is small
and hyperfine splitting correction of the order $\sim 1/N_c$ is not included),
and 4 times smaller for the octet. Hyperfine splitting correction as found in \cite{kk,westk}
decreases the mass splitting within RO model, but not sufficient. It is possible to modify
the next to leading in $1/N_c$ contributions to the mass splittings by means of appropriate
resolution of the operator ordering ambiguity within RO and to remove the difference from
RR model \cite{kleko}. However, it is not clear how to make extrapolation to realistic value
$N_c=3$, and what is the influence of such modification on results and conclusions of paper
\cite{ikor}. This illustrates well that
although both methods, RR and RO, converge at large $N_c$, small $m_K$ and fixed not large values of
strangeness, in real world there is considerable difference between both approaches.Recently the
paper \cite{chl} echoed the difficulties of extrapolation of results obtained in large $N_c$ world
to the realistic $N_c=3$ world, at least for some physical observables
When $m_K$ is large (as for charm or beauty quantum numbers) the flavor excitation energies for
RO method depend linearly on $m_D$, which looks much more realistic than for RR method, and the
bound state approach \cite{ck,westk} is more preferable.\\
\\
NOTES ADDED in PROOF. The higher statistics study of the positively charged kaon interactions
in the Xe bubble chamber \cite{VVB} reinforced the evidence of the DIANA Collaboration for
the production of the $\Theta^+$ hyperon, with the confidence level from 4.3 to 7.3
standard deviations, depending on the estimation method. At the same time, the CLAS Collaboration
in recent high statistics experiment \cite{BMcK} disavowed their previous result on the observation
of $\Theta^+$ in the photoproduction reaction on deuterons.
Detailed calculations of the strangeness contents of all components of exotic multiplets of
baryons (pentaquarks) have been performed recently at an arbitrary number of colors $N_c$
\cite{VBKAMS} within the rigid rotator model. The leading terms in the $1/N_c$ expansion
for the positive strangeness states coincide with those in the rigid oscillator model,
but the next-to-leading order terms differ essentially from those obtained within the
RO model in its commonly accepted version, as for the "octet" and "decuplet" of baryons
discussed in \cite{kleko} and in present paper.\\
\\
{\elevenbf References}
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"redpajama_set_name": "RedPajamaArXiv"
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Q: How to change the name of constraint or drop it that has dot (.) inside its name? I have created a constraint named version.pk while back ago on some table. Now, I want to drop it using the following query
alter table user.some_table drop constraint version.pk
However it's giving me an error saying ORA-01735: invalid ALTER TABLE option. I think it's because the constraint has dot (.) inside it and oracle does not recognize the query as a valid one. I wanted to change the name of the constraint to version_pk with the following query
alter table user.some_table rename constraint version.pk to version_pk
But again the same issue this time with different error ORA-00946: missing TO keyword . But I think the reason is the same, as it is not a valid query.
One solution that I have found for primary key type of constraints is this
alter table user.some_table drop primary key
But my constraint is foreign key type. Is there any way to refer constraint name as a literal text, something like 'version.pk', so that query remains valid?
A: Use a quoted identifier:
alter table user.some_table drop constraint "VERSION.PK";
Note: when you use quoted identifiers, you MUST use the correct case for all characters in the identifier as "VERSION.PK", "version.pk" and "VeRsIoN.pK" are three different identifiers.
Note: Single quotes are for text literals and double quotes are for quoted identifiers.
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"redpajama_set_name": "RedPajamaStackExchange"
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{"url":"https:\/\/maxsharabayko.blogspot.com\/2014\/11\/the-efficiency-of-x265-v14.html","text":"## November 17, 2014\n\n### The maturity of H.265\/HEVC video compression on the study of X265 v.1.4\n\nIn this post I share my test results on x265 coding efficiency to track the development progress. The x265 version 1.4 was used for this test, as well as the JCT-VC test sequences. It is worth mentioning that the Class E sequence set has changed, as described in JCTVC-O0022. However, for backward compatibility of the test results I still use the old test sequences set.\n\nThe two configurations of the x265 encoder are prepared. The \"ultra fast\" preset is used to measure the maximum achievable performance of the encoder. The command line arguments for this configuration are the following:\nx255 -p ultrafast -t psnr --rect --amp --keyint -1 --bframes 3 --ipratio 1.0 --pbratio 1.0 --b-adapt 0\nThe second configuration uses \"very slow\" preset to estimate the maximum quality that x265 is able to provide. The command line arguments follow.\nx265 -p veryslow -t psnr --rect --amp --keyint -1 --bframes 3 --ipratio 1.0 --pbratio 1.0 --b-adapt 0\nBoth configurations produce the same GOP structure with one P frame followed by three B frames. All the frames in a sequences are coded with the same quantization parameter, no rate control is applied.\nThe test computer is based on Intel Core i7-4700HQ CPU, 2.4 GHz and has 8GB RAM. The x265 encoder is built in x64 mode.\n\nThe compression efficiency is compared to the HM reference encoder v. 13.0. The \"Low Delay Main\" configuration file is used as the basis, and the GOP structure was changed to follow PBBB pattern. The comparison to the HM reference encoder is provided in terms of Bjontegaard delta rate (BD-RATE). To be short, the BD-RATE provides an estimation of the average increase (for positive BD-RATE values) or decrease (for negative values) of the compression bitrate of one test set over another. In this very experiment the BD-RATE means the percentage of the HM bitrate provided by the x265 encoder. For instance, the BD-RATE value of 15.89% means that x265 on average produces 15.89% bitrate overhead at the same PSNR quality level compared to the HM. The agerage YUV PSNR is calculated as follows:\n\n$$PSNR_{YUV}=\\frac{1}{8}\\cdot (6\\cdot PSNR_{Y}+PSNR_{U}+PSNR_{V})$$\n\nThe BD-Y-RATE is the bitrate change with respect to the Y-PSNR (luma) quality level. The BD-Y-PSNR is the Y-PSNR quality difference for the x265 and the HM encoders at the same bitrate value. Obviously, the BD-UV-PSNR is the UV-PSNR (average chroma PSNRs) quality difference for the x265 and the HM encoders at the same bitrate value.\nFPS stands for 'frames per second' and provides the estimation of the average compression speed.\n\nTable 1. The performance results for x265 v.1.4 in \"Very Slow\" preset\n Class Sequence Resolution to HM PBBB BD-RATE (%) BD-Y-RATE. % BD-Y-PSNR. dB BD-UV-PSNR. dB FPS A Traffic 2560\u00d71600 15.89 12.15 -0.37 -0.58 0.44 PeopleOnStreet 12.13 5.96 -0.26 -1.13 0.20 B Kimono 1920\u00d71080 7.95 1.59 -0.04 -0.65 0.53 ParkScene 20.45 15.52 -0.45 -0.77 0.74 Cactus 10.60 6.20 -0.11 -0.24 0.67 BQTerrace -2.48 -14.02 0.26 -0.75 0.75 BasketballDrive 17.75 10.54 -0.18 -0.62 0.54 C RaceHorses (C) 832\u00d7480 8.68 4.23 -0.18 -0.78 1.05 BQMall 20.13 15.95 -0.63 -1.00 2.09 PartyScene 18.33 14.06 -0.69 -1.11 1.38 BasketballDrill 21.58 18.35 -0.68 -1.00 2.11 D RaceHorses (D) 416\u00d7240 12.03 7.53 -0.39 -1.02 2.71 BQSquare 7.77 3.46 -0.14 -0.66 4.59 BlowingBubbles 16.68 13.23 -0.54 -0.86 3.62 BasketballPass 25.25 20.47 -0.90 -1.50 6.99 E Vidyo1 1280\u00d7720 29.05 24.59 -0.65 -0.74 3.58 Vidyo3 23.37 17.11 -0.51 -0.77 2.64 Vidyo4 28.92 21.47 -0.49 -0.88 2.60 F BaskeballDrillText 832\u00d7480 20.76 17.15 -0.68 -1.12 2.21 ChinaSpeed 1024\u00d7768 26.62 22.30 -1.30 -1.60 1.14 SlideEditing 1280\u00d7720 29.78 28.82 -4.23 -2.42 3.03 SlideShow 10.82 12.94 -0.89 -0.19 2.65\n\nThe performance results for \"very slow\" preset are provided in Table 1. As can be seen, the bitrate overhead varies from 8.68% for RaceHorces (C) test sequence to 29.78% for Vidyo1 test sequence. The compression speed is rather slow, but provides the ability to do file-based transcoding of the SD and maybe HD video. Nevertheless, the compression efficiency outlined by the BD-RATE estimation is significantly worse compared to the HM. It may be compensated by good rate control though.\n\nTable 2. The performance results for x265 v.1.4 in \"Ultra Fast\" preset\n Class Sequence Resolution to HM PBBB BD-RATE (%) BD-Y-RATE. % BD-Y-PSNR. dB BD-UV-PSNR. dB FPS A Traffic 2560\u00d71600 58.15 58.80 -1.50 -0.81 10.09 PeopleOnStreet 57.31 52.96 -1.89 -1.57 3.82 B Kimono 1920\u00d71080 62.10 60.37 -1.51 -1.00 8.33 ParkScene 51.18 51.72 -1.28 -0.77 16.10 Cactus 66.26 62.11 -1.06 -0.65 14.95 BQTerrace 67.79 59.40 -1.15 -0.77 20.53 BasketballDrive 75.55 69.34 -1.04 -1.08 11.74 C RaceHorses (C) 832\u00d7480 57.62 53.00 -1.89 -1.51 30.52 BQMall 66.94 64.75 -2.09 -1.46 62.34 PartyScene 62.36 59.46 -2.30 -1.70 43.72 BasketballDrill 72.62 70.14 -2.14 -1.73 60.07 D RaceHorses (D) 416\u00d7240 56.65 52.65 -2.20 -1.82 102.59 BQSquare 78.93 79.91 -2.52 -1.07 241.60 BlowingBubbles 63.45 62.16 -2.04 -1.46 146.21 BasketballPass 50.23 47.88 -1.84 -1.53 270.74 E Vidyo1 1280\u00d7720 75.05 73.47 -1.64 -0.98 93.92 Vidyo3 91.89 93.06 -2.09 -1.09 68.43 Vidyo4 85.45 82.20 -1.48 -1.26 68.51 F BaskeballDrillText 832\u00d7480 72.24 69.75 -2.26 -1.94 60.14 ChinaSpeed 1024\u00d7768 104.44 104.90 -4.37 -2.63 27.37 SlideEditing 1280\u00d7720 113.78 117.56 -11.52 -4.63 62.47 SlideShow 86.47 85.50 -4.74 -3.91 37.21\n\nTable 2 provides the performance results fot the x265 encoder in \"ultra fast\" preset. The compression efficiency is drastically worse even compared to \"very slow\" preset. This configuration does not provide the benefits of the HEVC video compression technology and may be used only to test and debug real time compression systems. On a more powerful CPU the x265 encoder in \"ultra fast\" preset is able to provide real time compression for FullHD 1080p@30 Hz video sequences.\n\nRegarding the compression performance some interesting results were found here. The encoder performance is measured on the FullHD video sequence, a trailer to the movie \"Max Schmeling\". The \"fast\" preset is used for testing, and the general x265 configuration is:\n--crf 20 --preset fast\nwhere CRF controls the quality-based VBR.\n\nTable 3. The x265 v.1.4 performance on different CPUs at FullHD video coding\n Processor model Type* Cores Freq. (GHz) RAM RAM freq. (MHz) RAM channels Average FPS x64 Intel Core i7-5960X DT 8 4.5 DDR4 3000 4 32.42 Intel Core i7-5960X DT 8 4.4 DDR4 2666 4 31.35 Intel Core i7-5820K DT 6 4.5 DDR4 2666 2 25.44 Intel Core i7-5820K DT 6 4.37 DDR4 3000 2 24.61 Intel Core i7-4930K DT 6 3.9 DDR3 1600 2 17.89 Intel Core i7-4790K DT 4 4.4 DDR3 2000 2 17.73 Intel Core i5-4670 DT 4 4.5 DDR3 2200 1 15.86 Intel Core i7-4790 DT 4 4.0 DDR3 1600 2 15.28 Intel Core i7-4770 DT 4 3,9 DDR3 1600 2 15.08 Intel Core i7-3770K DT 4 4.5 DDR3 2200 2 15.02 AMD FX-8350 DT 8 4.67 DDR3 1600 2 14.97 AMD FX-8320 DT 8 4.63 DDR3 1600 2 14.95 AMD FX-8320 DT 8 4.4 DDR3 2200 2 14.46 Intel Core i7-2600K DT 4 4.5 DDR3 1600 2 14.23 AMD FX-8320 DT 8 4.2 DDR3 1600 2 13.68 Intel Core i7-4770K DT 4 3.9 DDR3 1600 2 12.80 Intel Core i7-3770 DT 4 3.9 DDR3 1600 2 12.30 Intel Core i7-3570K DT 4 4.2 DDR3 1600 2 12.04 Intel Core i5-2500K DT 4 4.3 DDR3 2200 2 11.61 Intel Core i7-4700MQ M 4 3.4 DDR3 1600 2 11.60 Intel Core i7-2600K DT 4 3.6 DDR3 1333 2 10.69 Intel Core i5-3470 DT 4 3.6 DDR3 1600 2 9.76 AMD FX-8120 DT 8 3.4 DDR3 1333 2 9.70 Intel Core i7-860 DT 4 3.35 DDR3 1333 2 8.10 Intel Core i7-920 DT 4 2.67 DDR3 1066 3 8.01 Intel Core i3-4370 DT 2 3.8 DDR3 1600 2 7.93 AMD Opteron 6234 WS 12 2.4 DDR3 1333 2 7.88 Intel Core i5-2300 DT 4 2.8 DDR3 1333 2 7.79 Intel Core i7-2630QM M 4 2.8 DDR3 1333 2 7.43 AMD A8-7600 DT 4 3.8 DDR3 1800 2 6.12 Intel Core2 Quad Q9650 DT 4 3.0 DDR2 800 2 6.02 Intel Core i5-3230M M 2 3.2 DDR3 1600 2 5.07 Intel Core i7-3517U M 2 2.4 DDR3 1333 1 4.50 Intel Core i5-460M M 2 2.53 DDR3 1066 2 3.94 Intel Core i5-480M M 2 2.93 DDR3 1066 2 3.90 AMD A4-5300 DT 2 3.6 DDR3 1333 2 2.89 AMD Phenom II X6 1090T DT 6 3.4 DDR3 1600 2 2.84 Intel Core i5-4200U M 2 2.3 DDR3 1333 2 2.79 Intel Core 2 Quad Q6600 DT 4 3.6 DDR2 800 2 2.61 Intel Celeron 2955U M 2 1.4 DDR3 1600 2 2.36 AMD Athlon 64 X2 3800+ DT 2 2.0 DDR2 400 2 0.46\n* WS \u2014 workstation, DT \u2014 desktop, M \u2014 mobile\/notebook processor","date":"2023-03-30 12:24:06","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.3965235948562622, \"perplexity\": 8211.036823794473}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296949181.44\/warc\/CC-MAIN-20230330101355-20230330131355-00420.warc.gz\"}"}
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Q: Patch Org to update managed package Patch org is version deepened or Org depended? Means we use one patch org for one version or for all versions update?
A: A patch org is a clone of an existing version, though you can then have many versions of the patch.
So if the existing version to be patched is say 2.5, the first version created in the patch org will be 2.5.1 and then there could also be 2.5.2, 2.5.3 etc. But if it turns out that you also need to patch say version 3.8, you will need to create a new patch org of that version, so creating version 3.8.1 and so on.
The patch orgs must be compatible with the next version up so they can be upgraded to that next version up or later.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
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#ifndef SANDESHA2_PROPERTY_BEAN_H
#define SANDESHA2_PROPERTY_BEAN_H
/**
* @file sandesha2_property_bean.h
* @brief
*/
#include <axutil_utils_defines.h>
#include <axutil_env.h>
#include <axutil_array_list.h>
#ifdef __cplusplus
extern "C"
{
#endif
/**
* @ingroup sandesha2_property_bean
* @{
*/
typedef struct sandesha2_property_bean_t sandesha2_property_bean_t;
AXIS2_EXTERN sandesha2_property_bean_t* AXIS2_CALL
sandesha2_property_bean_create(
const axutil_env_t *env);
long AXIS2_CALL
sandesha2_property_bean_get_inactive_timeout_interval(
sandesha2_property_bean_t *bean,
const axutil_env_t *env);
axis2_status_t AXIS2_CALL
sandesha2_property_bean_set_inactive_timeout_interval(
sandesha2_property_bean_t *bean,
const axutil_env_t *env,
long interval);
axis2_status_t AXIS2_CALL
sandesha2_property_bean_set_inactive_timeout_interval_with_units(
sandesha2_property_bean_t *bean,
const axutil_env_t *env,
long interval,
axis2_char_t *units);
long AXIS2_CALL
sandesha2_property_bean_get_ack_interval(
sandesha2_property_bean_t *bean,
const axutil_env_t *env);
axis2_status_t AXIS2_CALL
sandesha2_property_bean_set_ack_interval(
sandesha2_property_bean_t *bean,
const axutil_env_t *env,
long interval);
long AXIS2_CALL
sandesha2_property_bean_get_retrans_interval(
sandesha2_property_bean_t *bean,
const axutil_env_t *env);
axis2_status_t AXIS2_CALL
sandesha2_property_bean_set_retrans_interval(
sandesha2_property_bean_t *bean,
const axutil_env_t *env,
long interval);
axis2_bool_t AXIS2_CALL
sandesha2_property_bean_is_exp_backoff(
sandesha2_property_bean_t *bean,
const axutil_env_t *env);
axis2_status_t AXIS2_CALL
sandesha2_property_bean_set_exp_backoff(
sandesha2_property_bean_t *bean,
const axutil_env_t *env,
axis2_bool_t exp_backoff);
axis2_char_t* AXIS2_CALL
sandesha2_property_bean_get_in_mem_storage_mgr(
sandesha2_property_bean_t *bean,
const axutil_env_t *env);
axis2_status_t AXIS2_CALL
sandesha2_property_bean_set_in_mem_storage_mgr(
sandesha2_property_bean_t *bean,
const axutil_env_t *env,
axis2_char_t *manager);
axis2_char_t* AXIS2_CALL
sandesha2_property_bean_get_permanent_storage_mgr(
sandesha2_property_bean_t *bean,
const axutil_env_t *env);
axis2_status_t AXIS2_CALL
sandesha2_property_bean_set_permanent_storage_mgr(
sandesha2_property_bean_t *bean,
const axutil_env_t *env,
axis2_char_t *manager);
/**
* return the storage manager to use. This could be either
* persistent or inmemory.
* @param property bean
* @env environment
* @return storage manager(persistent/inmemory)
*/
axis2_char_t* AXIS2_CALL
sandesha2_property_bean_get_storage_mgr(
sandesha2_property_bean_t *bean,
const axutil_env_t *env);
axis2_status_t AXIS2_CALL
sandesha2_property_bean_set_storage_mgr(
sandesha2_property_bean_t *bean,
const axutil_env_t *env,
axis2_char_t *manager);
axis2_bool_t AXIS2_CALL
sandesha2_property_bean_is_in_order(
sandesha2_property_bean_t *bean,
const axutil_env_t *env);
axis2_status_t AXIS2_CALL
sandesha2_property_bean_set_in_order(
sandesha2_property_bean_t *bean,
const axutil_env_t *env,
axis2_bool_t in_order);
axutil_array_list_t* AXIS2_CALL
sandesha2_property_bean_get_msg_types_to_drop(
sandesha2_property_bean_t *bean,
const axutil_env_t *env);
axis2_status_t AXIS2_CALL
sandesha2_property_bean_set_msg_types_to_drop(
sandesha2_property_bean_t *bean,
const axutil_env_t *env,
axutil_array_list_t *msg_types);
axis2_status_t AXIS2_CALL
sandesha2_property_bean_add_msg_type_to_drop(
sandesha2_property_bean_t *bean,
const axutil_env_t *env,
int msg_type);
int AXIS2_CALL
sandesha2_property_bean_get_max_retrans_count(
sandesha2_property_bean_t *bean,
const axutil_env_t *env);
axis2_status_t AXIS2_CALL
sandesha2_property_bean_set_max_retrans_count(
sandesha2_property_bean_t *bean,
const axutil_env_t *env,
int count);
axis2_char_t *AXIS2_CALL
sandesha2_property_bean_get_db_path(
sandesha2_property_bean_t *bean,
const axutil_env_t *env);
axis2_status_t AXIS2_CALL
sandesha2_property_bean_set_db_path(
sandesha2_property_bean_t *bean,
const axutil_env_t *env,
axis2_char_t *db_path);
void AXIS2_CALL
sandesha2_property_bean_free(
sandesha2_property_bean_t *bean,
const axutil_env_t *env);
void AXIS2_CALL
sandesha2_property_bean_free_void_arg(
void *arg,
const axutil_env_t *env);
int AXIS2_CALL
sandesha2_property_bean_get_terminate_delay (
sandesha2_property_bean_t *bean,
const axutil_env_t *env);
axis2_status_t AXIS2_CALL
sandesha2_property_bean_set_terminate_delay(
sandesha2_property_bean_t *bean,
const axutil_env_t *env,
int delay);
int AXIS2_CALL
sandesha2_property_bean_get_polling_delay (
sandesha2_property_bean_t *bean,
const axutil_env_t *env);
axis2_status_t AXIS2_CALL
sandesha2_property_bean_set_polling_delay(
sandesha2_property_bean_t *bean,
const axutil_env_t *env,
int delay);
axis2_char_t* AXIS2_CALL
sandesha2_property_bean_get_spec_version(
sandesha2_property_bean_t *bean,
const axutil_env_t *env);
axis2_status_t AXIS2_CALL
sandesha2_property_bean_set_spec_version(
sandesha2_property_bean_t *bean,
const axutil_env_t *env,
axis2_char_t *spec_version);
/** @} */
#ifdef __cplusplus
}
#endif
#endif /*SANDESHA2_PROPERTY_BEAN_H*/
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 5,623
|
\section{Introduction} \label{sec:intro}
Massive stars (M$_* \geqslant$ 8 M$_\odot$) play a vital role in shaping galaxies in all stages of their lives (e.g. \citealt{2005IAUS..227....3K}). Yet our understanding of their formation processes remains sketchy. Massive stars are rare. Their birthplaces are always hidden by distant and highly obscured dust. Only at limited wavelengths, e.g. infrared (IR), (sub)millimeter, and radio, and from their violent interactions with the surroundings can we get some hints on their early formation processes (e.g. \citealt{2011ApJ...728....6Q, 2013ApJ...767L..13R}).
In the very early stage of high-mass star formation (HMSF), the (pre-)protostellar cores are cold and are only detectable at (sub-)millimeter and far-infrared wavelengths \citep{2007ARA&A..45..339B, 2010ApJ...715..310R}. With the growth of the embedded massive young stellar objects (MYSOs), the cold dense molecular cores are heated and become observable at mid-infrared wavelengths \citep{1993ApJ...405..706O, 2007PASP..119..855W, 2010A&A...510A..89M, 2013PASA...30...57J}. The so-called ``hot cores'' \citep{2000prpl.conf..299K} formed at this stage have weak free-free emission, which is now detectable by the most sensitive radio telescopes, e.g. \textit{NSF's Karl G. Jansky Very Large Array} (VLA) \citep{1993A&A...276..489O, 2016ApJS..227...25R}.
In the next evolutionary stage, the abundant UV photons produced by the central high-mass stars begin to ionize the surrounding material, forming ultra-compact (UC) \ion{H}{2} regions \citep{2002ARA&A..40...27C}. UC \ion{H}{2} regions are strong free-free radiation emitters with diameters smaller than 0.1 pc, electron densities ($N_e$) higher than 10$^4$ cm$^{-3}$, and emission measures ($EM$) higher than 10$^7$ pc cm$^{-6}$ \citep{1989ApJS...69..831W}. Morphologically, UC \ion{H}{2} regions are also resolved to have several typical structures, which is a joint effect of the dynamics of the ionized gas, the surrounding material, and the evolutionary stages of UC \ion{H}{2} regions \citep{1989ApJS...69..831W, 2002ARA&A..40...27C, 2007prpl.conf..181H, 2010ApJ...719..831P}.
After the first discovery of UC \ion{H}{2} regions in the 1960s \citep{1967ApJ...148L..17R, 1979ARA&A..17..345H}, many radio surveys of UC \ion{H}{2} regions have been carried out with single dishes and interferometers. \citet{1982A&A...108..227W} carried out a pioneer single-dish radio continuum survey towards 85 UC \ion{H}{2} regions. \citet{1989ApJS...69..831W} and \citet{1994ApJS...91..659K} selected dozens of UC \ion{H}{2} regions from the IRAS survey and performed high-resolution VLA observations towards these regions. \citet{1998MNRAS.301..640W} carried out a survey towards hundreds of UC \ion{H}{2} regions with the ATCA. \citet{2007A&A...461...11U, 2009A&A...501..539U} and \citet{2013ApJS..208...11L} carried out the Red MSX Source Survey and observed abundant UC \ion{H}{2} regions at the resolution of $\sim$1$''$ to 2$''$ with the ATCA and the VLA, covering both the southern and northern hemispheres. More recently, \citet{2018A&A...615A.103K} has carried out an unbiased high-resolution survey and provided a catalog of more than 200 UC \ion{H}{2} regions in the Galactic plane.
A denser counterpart of UC \ion{H}{2} region, namely hyper-compact (HC) \ion{H}{2} region, was discovered during the surveys of UC \ion{H}{2} regions (e.g. \citealt{1993ApJ...417..645G, 1995ApJ...438..776G}). HC \ion{H}{2} regions have diameters smaller than 0.05 pc, $N_e$ higher than 10$^6$ cm$^{-3}$, and $EM$ higher than 10$^{10}$ pc cm$^{-6}$ \citep{2007prpl.conf..181H}. They remain unresolved or barely resolved under interferometric observations \citep{2010MNRAS.405.1560M}. Considering the expansion tendency of UC \ion{H}{2} regions, HC \ion{H}{2} regions used to be regarded as a sub-class of UC \ion{H}{2} regions that are formed at the very early stages of ionization \citep{2005IAUS..227..111K, 2019MNRAS.482.2681Y}. Yet now they are considered to be a distinct class because of their broad radio recombination line profiles (about 40--50 km s$^{-1}$) \citep{2004ApJ...605..285S, 2004ApJ...600..286D, 2011ApJS..194...44S} and probably different driving mechanisms \citep{2002ApJ...580..980K, 2004ApJ...610..351I, 2006ApJ...637..850K, 2007prpl.conf..181H}.
Besides heating and ionizing the surroundings, MYSOs drive jets and molecular outflows during their rapid accretion processes. Ionized jets and molecular outflows are ubiquitous in the formation of stars at all mass regimes \citep{1992ApJ...395..494A, 2003ApJ...587..739G} and are keys to understanding the star formation mechanisms \citep{2007prpl.conf..245A, 2014prpl.conf..451F}. Most of the ionized jets have thermal free-free emission and can be best observed in the centimeter wavelengths. For some radio jets with extreme energy, non-thermal emission can be observed \citep{1989ApJ...346L..85R, 2005ApJ...626..953R}. This non-thermal component is commonly interpreted as synchrotron radiation from shocks produced by high-velocity jets shooting into surrounding dense molecular clouds \citep{2010Sci...330.1209C, 2016ApJ...816...64C}.
Previous studies have provided abundant information about high-mass star-forming regions. Whereas the surveys aiming to cover a large area are always subject to incoherent distances and low-sensitivities; the works focusing on obtaining deep insights into a few well-observed cases are limited in statistical significance. To better characterize the radio properties of HMSF and achieve statistically significant results, it requires an unbiased survey with high sensitivity and high resolution towards an adequate number of MDCs at the same distance. We have launched such a survey in the Cygnus X star-forming complex, an ideal laboratory for HMSF studies. The Cygnus X star-forming complex is one of the nearest and most active massive-star-forming regions in our Galaxy \citep{2007A&A...476.1243M, 2012A&A...539A..79R, 2018ARA&A..56...41M}. It exhibits HMSF processes in all evolution stages and has a rich collection of \ion{H}{2} regions, OB associations, and high-mass star-forming sites \citep{1977A&A....58..197H, 1991A&A...241..551W, 2001A&A...371..675U, 2004ApJ...601..952S, 2007A&A...474..873S, 2013ApJ...772...69G}. An average distance of 1.4 kpc \citep{2012A&A...539A..79R} makes it possible to resolve the massive dense cores (MDCs) down to the sub-Jeans scale ($<$ 0.05 pc) with the high-resolution facilities such as the VLA and the Submillimeter Array (SMA). Most of the previous studies focused on the core scale and discussed the relation between the MDCs' properties and HMSF. Yet later high-resolution observations have revealed that the MDCs are more likely to fragment into condensations \citep{2010A&A...524A..18B, 2018A&A...615A..94F, 2019ApJ...878..146S}, which is in agreement with our SMA observations (Qiu et al., in preparation). Here we use ``core'' for the cloud structure of $\sim$0.1 pc, and ``condensation'' for the structure fragmented from the core with a typical size of $\sim$0.01 pc. In the hierarchical scheme of HMSF, condensation is more directly related to the formation of individual stars or binaries. Thus the studies at the condensation scale can provide us a more explicit insight into the immediate environments of HMSF. With the high angular resolution of the VLA, we are now able to study the radio properties of individual condensations.
This is the second paper of our project, the Surveys of {\bf C}lumps, Cor{\bf E}s, and Co{\bf N}den{\bf S}ations in Cygn{\bf US} X (CENSUS, PI: Keping Qiu), which aims to build a hierarchical view of the HMSF in the Cygnus X star-forming complex from 1--10 pc molecular clumps down to 0.01 pc dust condensations. This project uses the data from infrared to radio wavelengths observed by the facilities such as the \textit{Hershel Space Observatory}, SMA, JVLA, JCMT, ALMA, NOEMA, CARMA, and Tianma 65 m radio telescope. The work presented here takes advantage of the VLA data and focuses on the radio properties of the MDCs under high sensitivity and resolution.
\section{Sample Selection}\label{sec:sample}
We initially built the MDC sample based on the work of \citet{2007A&A...476.1243M} (hereafter Motte07), who identified 40 MDCs with masses higher than 30 M$_\odot$ from an extinction map of the Cygnus X star-forming complex and 1.2 mm dust continuum observations of selected high-extinction regions. The region along the direction of the OB2 association was not chosen for the MDC survey in Motte07 owing to the low extinction. We included a further 8 MDCs in this region, based on the JCMT and Herschel sub-millimeter continuum observations (\citealt{2019ApJS..241....1C}, hereafter Cao19). In a recent work by \citet{2021ApJ...918L...4C} (hereafter Cao21), over eight thousand dense cores were identified from a column density map of the Cygnus X star-forming complex using the \textsl{getsources} software. We then cross-checked and updated the sample with that in Cao21 since the column density map can better characterize the MDCs and the properties of the MDCs are derived with a uniform method. The parameters of the MDCs are also obtained from Cao21 as given in Table \ref{tab:MDC_Cao21}, except for the 24 $\mu$m flux. The 24 $\mu$m fluxes are obtained from the \textsl{Spitzer} Cygnus X Archive Catalog \citep{2010AAS...21541401K, CygnusX_Archive2011} and the MSX6C Infrared Point Source Catalog \citep{2003AAS...203.5708E, MSX6C2015}. The 21.3 $\mu$m fluxes are linear scaled to 24 $\mu$m according to the model of a B3-type embryo \citep{2019ApJS..241....1C}. The parameters of the MDCs, e.g., FWHMs (full width at half maximum), in Cao21 are slightly different from those in Motte07 and Cao19. Two dense cores, 742 ( NW01 in Motte07) and 839 (NW12 in Motte07) have masses lower than 30 M$_\odot$. We still take them for study because they have been covered by our VLA programs. We do not specifically distinguish these two dense cores from the others in the following content. Finally, we have a sample of 47 MDCs, among which eight are located in the OB2 region. Their detailed physical parameters are listed in Table \ref{tab:MDC_Cao21}.
Cao21 analyzed the 1.3 mm continuum maps of the sampled MDCs using the SMA and identified dust condensations with \textsl{getsources} from each MDC. Dust condensations are $\sim$0.01 pc-scale structures that are fragmented from the MDCs. Their spatial scales are comparable to the resolution of our VLA data, which helps to study the immediate environment of the radio sources.
\begin{longrotatetable}
\begin{deluxetable*}{c|c|c|ccccc|cccccc|l}
\tablecaption{Physical Parameters of the MDCs\label{tab:MDC_Cao21}}
\tablehead{
\colhead{MDC} & \colhead{Cao19} & \colhead{Motte07} & \colhead{RA} & \colhead{Dec} & \colhead{$D_{maj}$} & \colhead{$D_{min}$} & \colhead{PA} & \colhead{Mass} & \colhead{T$_{dust}$} & \colhead{$L_{FIR}$} & \colhead{$F_{\nu, \ 24\ \mu m}$} & \colhead{$N_{H_2}$} & \colhead{$n_{H_2}$} & \colhead{Type} \\
\colhead{} & \colhead{} & \colhead{} & \colhead{(hms)} & \colhead{(dms)} & \colhead{(pc)} & \colhead{(pc)} & \colhead{(deg)} & \colhead{($M_\odot$)} & \colhead{(K)} & \colhead{($L_\odot$)} & \colhead{(Jy)} & \colhead{(cm$^{-2}$)} & \colhead{(cm$^{-3}$)} & \colhead{}
}
\startdata
214 & C03-1 & \nodata & 20:30:29.03 & 41:15:57.1 & 0.276 & 0.179 & 133.6 & 143.64 & 21.24 & 1268.2 & 5.85 & 1.7E+23 & 3.6E+05 & Q \\
220 & N03-1 & N02 N03 & 20:35:34.17 & 42:20:10.8 & 0.287 & 0.247 & 31.0 & 383.1 & 17.75 & 1151.8 & 5.41 & 3.1E+23 & 5.6E+05 & Q \\
247 & \nodata & \nodata & 20:30:27.34 & 41:16:13.7 & 0.300 & 0.198 & 84.1 & 43.24 & 21.28 & 385.8 & 50.74\tablenotemark{a} & 4.1E+22 & 8.3E+04 & B \\
248 & N12-1 & N12 N13 & 20:36:57.55 & 42:11:35.2 & 0.267 & 0.204 & 145.5 & 202.05 & 18.17 & 698.9 & 0.97 & 2.1E+23 & 4.4E+05 & Q \\
274 & N05-2 & N05 N06 & 20:36:07.41 & 41:39:58.0 & 0.370 & 0.229 & 98.8 & 107.38 & 21.51 & 1022.1 & 122.96\tablenotemark{a} & 7.2E+22 & 1.2E+05 & B \\
302 & C08-2 & \nodata & 20:35:07.72 & 41:14:01.7 & 0.311 & 0.246 & 122.4 & 76.26 & 22.29 & 899.4 & \nodata & 5.7E+22 & 9.9E+04 & C \\
310 & NW12-1 & NW14 & 20:24:31.73 & 42:04:20.4 & 0.240 & 0.195 & 152.2 & 152.78 & 20.48 & 1084.3 & 18.21\tablenotemark{a} & 1.9E+23 & 4.2E+05 & B \\
327 & \nodata & NW02 & 20:19:40.67 & 40:57:08.4 & 0.300 & 0.222 & 95.5 & 120.74 & 20.87 & 958.6 & \nodata & 1E+23 & 1.9E+05 & Q \\
340 & C05-1, 2 & \nodata & 20:32:23.46 & 41:07:52.7 & 0.309 & 0.245 & 113.7 & 119.29 & 16.09 & 199.4 & 0.21 & 8.9E+22 & 1.6E+05 & Q \\
341 & N63-1 & N63 & 20:40:05.40 & 41:32:13.3 & 0.245 & 0.235 & 4.4 & 160.91 & 17.44 & 435.2 & 0.60 & 1.6E+23 & 3.2E+05 & Q \\
351 & S32-1 & S32 & 20:31:20.72 & 38:57:15.4 & 0.258 & 0.190 & 141.2 & 78.63 & 18.29 & 283.2 & 0.18 & 9.1E+22 & 2E+05 & Q \\
370 & \nodata & \nodata & 20:28:09.35 & 40:52:54.0 & 0.245 & 0.184 & 12.8 & 57.1 & 22.73 & 757.5 & \nodata & 7.2E+22 & 1.6E+05 & C \\
507 & S07-1 & S08 S09 & 20:20:38.43 & 39:37:45.4 & 0.322 & 0.231 & 1.2 & 372.46 & 21.4 & 3439.6 & 196.83\tablenotemark{a} & 2.8E+23 & 5.1E+05 & B \\
509 & S30-1, 2, 3 & S30 S31 & 20:31:13.29 & 40:03:12.6 & 0.341 & 0.287 & 134.6 & 300.64 & 18.18 & 1045.0 & 2.29 & 1.7E+23 & 2.7E+05 & Q \\
520 & C08-3 & \nodata & 20:35:10.60 & 41:13:11.0 & 0.362 & 0.264 & 8.1 & 81.01 & 23.43 & 1289.1 & \nodata & 4.8E+22 & 7.6E+04 & C \\
540 & S43-2, 3 & S42 S43 & 20:32:40.73 & 38:46:26.3 & 0.398 & 0.253 & 6.6 & 240.78 & 15.54 & 326.0 & 2.91 & 1.4E+23 & 2.1E+05 & Q \\
608 & \nodata & \nodata & 20:33:59.89 & 41:22:28.9 & 0.247 & 0.185 & 177.8 & 30.6 & 21.12 & 261.1 & \nodata & 3.8E+22 & 8.6E+04 & Q \\
640 & \nodata & NW04 & 20:20:30.07 & 41:22:06.8 & 0.256 & 0.190 & 160.5 & 52.79 & 18.61 & 210.9 & \nodata & 6.1E+22 & 1.4E+05 & Q \\
675 & NW04-1 & NW05 NW07 & 20:20:31.39 & 41:21:27.5 & 0.338 & 0.248 & 139.2 & 104.26 & 20.08 & 656.8 & 116.15\tablenotemark{a} & 7.1E+22 & 1.2E+05 & B \\
684 & N68-1 & N68 & 20:40:33.83 & 41:59:03.5 & 0.257 & 0.203 & 38.8 & 109.49 & 17.62 & 315.5 & 0.20 & 1.2E+23 & 2.5E+05 & Q \\
698 & DR21-9 & N56 & 20:39:17.42 & 42:16:10.4 & 0.225 & 0.190 & 109.8 & 81.14 & 16.98 & 186.8 & 5.65 & 1.1E+23 & 2.5E+05 & Q \\
699 & DR21-3, 13 & N38 N48 & 20:39:00.02 & 42:22:16.0 & 0.397 & 0.282 & 128.8 & 1283 & 20.92 & 10332.1 & 38.42\tablenotemark{a} & 6.5E+23 & 9.5E+05 & B \\
714 & N05-3 & N14 & 20:37:01.07 & 41:35:00.1 & 0.228 & 0.216 & 134.8 & 101.14 & 22.73 & 1340.3 & 26.67\tablenotemark{a} & 1.2E+23 & 2.5E+05 & B \\
723 & S29-1 & S29 & 20:29:57.75 & 40:15:54.7 & 0.328 & 0.257 & 52.2 & 123.9 & 16.02 & 201.5 & 0.32 & 8.4E+22 & 1.4E+05 & Q \\
725 & N05-1 & N10 & 20:36:52.18 & 41:36:23.8 & 0.292 & 0.238 & 146.4 & 147.64 & 24.04 & 2737.4 & 134.39\tablenotemark{a} & 1.2E+23 & 2.2E+05 & B \\
742 & NW01-1 & NW01 & 20:19:38.81 & 40:56:39.2 & 0.292 & 0.189 & 168.3 & 19.44 & 26.97 & 718.8 & 542.07\tablenotemark{a} & 2E+22 & 4.1E+04 & B \\
753 & \nodata & S06 S07 & 20:20:37.57 & 39:38:25.8 & 0.302 & 0.213 & 92.2 & 189.53 & 17.82 & 582.8 & \nodata & 1.7E+23 & 3.2E+05 & Q \\
798 & \nodata & S10 & 20:20:44.02 & 39:35:25.1 & 0.341 & 0.223 & 166.6 & 89.27 & 19.19 & 429.1 & 1.55 & 6.7E+22 & 1.2E+05 & Q \\
801 & N68-2, 5 & N64 N65 & 20:40:28.06 & 41:57:05.7 & 0.331 & 0.236 & 26.9 & 143.46 & 17.84 & 444.4 & 5.64 & 1E+23 & 1.8E+05 & Q \\
839 & \nodata & NW12 & 20:24:13.93 & 42:11:41.4 & 0.189 & 0.181 & 135.9 & 15.83 & 16.19 & 27.4 & 0.03 & 2.6E+22 & 6.9E+04 & Q \\
892 & DR15-4 & S41 & 20:32:33.85 & 40:16:58.6 & 0.226 & 0.191 & 134.3 & 31.4 & 31.64 & 3031.6 & \nodata & 4.1E+22 & 9.7E+04 & C \\
1018 & DR21-8 & N36 N40 N41 & 20:38:59.33 & 42:23:37.2 & 0.416 & 0.278 & 11.0 & 811.38 & 19.21 & 3922.3 & 0.66 & 4E+23 & 5.7E+05 & Q \\
1112 & W75N-1 & N30 N31 N32 & 20:38:36.70 & 42:37:48.6 & 0.420 & 0.369 & 109.6 & 499.31 & 28.08 & 23521.8 & \nodata & 1.8E+23 & 2.3E+05 & B \\
1179 & DR21-10 & N57 & 20:39:19.47 & 42:16:01.8 & 0.280 & 0.211 & 125.9 & 35.9 & 16 & 58.0 & \nodata & 3.4E+22 & 6.9E+04 & N \\
1201 & S106-2 & S18 S20 & 20:27:25.83 & 37:22:53.6 & 0.374 & 0.205 & 90.8 & 52.83 & 33.37 & 7012.6 & \nodata & 3.9E+22 & 6.9E+04 & C \\
1225 & DR15-1 & S34 & 20:31:57.45 & 40:18:29.3 & 0.417 & 0.290 & 74.8 & 206.54 & 14.26 & 166.7 & 0.25 & 9.7E+22 & 1.4E+05 & Q \\
1243 & DR21-4 & N51 & 20:39:02.41 & 42:25:09.1 & 0.338 & 0.251 & 12.4 & 320.2 & 19.04 & 1465.3 & 50.53\tablenotemark{a} & 2.1E+23 & 3.6E+05 & B \\
1267 & W75N-2 & N22 N24 & 20:38:05.11 & 42:39:55.6 & 0.339 & 0.288 & 116.2 & 202.54 & 15.33 & 252.7 & \nodata & 1.2E+23 & 1.8E+05 & Q \\
1454 & DR15-2, 6 & S36 S37 & 20:32:21.85 & 40:20:00.7 & 0.508 & 0.414 & 127.8 & 420.81 & 16.17 & 724.4 & 9.21 & 1.1E+23 & 1.2E+05 & Q \\
1460 & C09-1 & \nodata & 20:34:59.19 & 41:34:48.4 & 0.574 & 0.402 & 58.4 & 198.01 & 22.1 & 2216.3 & 25.00\tablenotemark{a} & 4.9E+22 & 4.9E+04 & B \\
1467 & DR21-2 & N44 & 20:38:59.64 & 42:23:06.9 & 0.341 & 0.233 & 27.6 & 257.92 & 23.4 & 4067.0 & 0.17 & 1.8E+23 & 3.2E+05 & Q \\
1528 & DR21-1, 6, 20 & N42 N46 N50 & 20:39:00.76 & 42:19:06.4 & 0.535 & 0.336 & 164.2 & 677.32 & 24.81 & 15187.4 & \nodata & 2.1E+23 & 2.5E+05 & C \\
1599 & DR21-7 & N52 N53 & 20:39:03.13 & 42:26:00.0 & 0.232 & 0.186 & 168.5 & 164.34 & 17.19 & 407.9 & 1.27 & 2.2E+23 & 5.1E+05 & Q \\
2210 & DR15-3 & S38 & 20:32:22.30 & 40:19:19.5 & 0.294 & 0.259 & 114.7 & 70.06 & 15.63 & 98.1 & 0.48 & 5.2E+22 & 9.2E+04 & Q \\
3188 & \nodata & N21 & 20:38:01.59 & 42:39:39.7 & 0.316 & 0.218 & 53.4 & 46.59 & 16.29 & 83.6 & 0.18 & 3.9E+22 & 7.1E+04 & Q \\
4797 & N68-4 & N69 & 20:40:33.32 & 41:50:46.6 & 0.587 & 0.398 & 44.5 & 378.04 & 17.26 & 960.7 & 2.13 & 9.2E+22 & 9.2E+04 & Q \\
5417 & DR21-23 & N37 N43 & 20:38:58.30 & 42:24:35.9 & 0.321 & 0.301 & 0.5 & 148.04 & 18.74 & 616.6 & \nodata & 8.7E+22 & 1.4E+05 & B \\
\hline
\enddata
\tablecomments{The coordiantes and physical parameters of the MDC sample.
The corresponding MDC names in Cao19 and the dense core names in Motte07 are provided in columns 2 and 3.
The MDC parameters are taken from Cao21 except for the 24 $\mu$m flux.
$D_{maj}$ and $D_{min}$ are the major and minor axes of the fitted FWHM of an MDC.
PA is the position angle of the fitted FWHM.
Mass and temperature are determined with a graybody thermal dust emission model.
$L_{FIR}$ is far-infrared luminosity.
$N_{H_2}$ is column density.
$n_{H_2}$ is volume-averaged density.
See Cao19 for the derivation of the parameters.
$F_{\nu,\ 24 \mu m}$ is the \textit{Spitzer} 24 $\mu$m flux.
``Type'' is a classification according to the 24 $\mu$m flux. N, Q, and B represent starless MDC candidates, infrared-quiet MDCs, and infrared-bright MDCs, respectively. C represents MDCs whose 24 $\mu$m fluxes are contaminated by external sources and cannot be obtained. The detailed definitions are given in Section \ref{sec:dis}.
}
\tablenotetext{a}{Flux scaled from \textit{MSX} 21 $mu$m flux.}
\end{deluxetable*}
\end{longrotatetable}
\section{Observations and Data Reduction} \label{sec:data}
\subsection{VLA X-Band Survey} \label{subsec:3.6}
The VLA X-band radio continuum observations (Project code: 16A--301, PI: Keping Qiu) were made on 29th June 2016 using the VLA. The observations were carried out in the B configuration with all the 27 antennas, which provided a typical angular resolution of $\sim$0$''$.6, corresponding to a linear scale of $\sim$0.004 pc at a distance of 1.4 kpc. The maximum recoverable scale (MRS) was $\sim$17$''$, corresponding to 0.12 pc at a distance of 1.4 kpc. The observations were set in full polarization mode with two 1-GHz basebands centered at 9.5 GHz and 10.5 GHz, respectively. Each baseband was uniformly divided into eight spectral windows, and each spectral window was further divided into 64 2-MHz-wide channels.
The primary calibrator 3C286 was used for bandpass and flux calibration and was observed at the beginning of each schedule block; the secondary calibrator J2007+4029 was used for complex gain calibration and was observed for 80 seconds before and after every seven or eight scans on the targets. There were a total of 22 observing fields covering 29 MDCs. The MDCs not covered were MDC 839, 1112, the eight MDCs in DR21, and the eight MDCs in the OB2 association, whose archival data had similar observational settings. For each observing field, the on-source integration time was 90 seconds, resulting in a sensitivity of $\sim$20 $\mu$Jy beam$^{-1}$.
\subsection{VLA K-Band Survey} \label{subsec:1.3}
The VLA K-band radio continuum and spectral line observations (Project code: 17A--107, PI: Keping Qiu) were made during April and May 2017 using the VLA. Here we only describe the observational settings of the radio continuum observations. The observations were carried out in the D configuration with all the 27 antennas, which provided a typical angular resolution of $\sim$4$''$, corresponding to a linear scale of $\sim$0.02 pc at a distance of 1.4 kpc. The MRS was $\sim$66$''$, corresponding to 0.5 pc at a distance of 1.4 kpc. The observations were set in full polarization mode with two 1-GHz basebands centered at 22.3 GHz and 24.0 GHz, respectively. Each baseband was uniformly divided into eight spectral windows, and each spectral window was further divided into 64 2-MHz-wide channels.
The same set of calibrators as in the K-band survey was adopted. A total of 33 observing fields were observed, in which two were mosaic fields each composed of two single-pointing fields. The entire sample except the MDCs in the DR21 and W75N regions are covered. Each observing field had an on-source integration time of 20 minutes, resulting in a continuum sensitivity of $\sim$15 $\mu$Jy beam$^{-1}$.
\subsection{Archival Data}\label{subsec:archive}
For each target, we have done an extensive search for any existing VLA observations in the archive and from the literature. The data accumulated for decades greatly replenished this work. We selected the archival data according to the following criteria:
\begin{enumerate}
\item The observations should be carried out after 1988 for a stable performance of the VLA.
\item The target MDCs should not be on the edge of the field of views (FOVs).
\item The resolutions should be higher than 14$''$, which corresponds to 0.1 pc at a distance of 1.4 kpc, the typical spatial scale of an MDC.
\item The observations should have enough bandwidth and on-source integration time for good $uv$-coverage and continuum sensitivities.
\end{enumerate}
For the targets observed by more than one project with similar observational settings, we select the ones with higher sensitivities and different resolutions.
The details of the observations are listed in Table \ref{tab:obsInfo}. The information of the data from the literature is obtained from the corresponding papers.
\startlongtable
{\catcode`\&=11
\gdef\Hunter1994{\citet{1994A&A...284..215H}}
\gdef\Molinari1998{\citet{1998A&A...336..339M}}
\gdef\Urquhart2009{\citet{2009A&A...501..539U}}}
\begin{deluxetable*}{c|ccccccp{4cm}}
\tablecaption{Observational Parameters of the Data Used\label{tab:obsInfo}}
\tablehead{
\colhead{Project Code} & \colhead{Date} & \colhead{Config.} & \colhead{Freq.} & \colhead{Flux Calibrator} & \colhead{Gain Calibrator\tablenotemark{a}} & \colhead{$F_\nu$} & \colhead{Covered MDCs}\\
\colhead{} & \colhead{(yyyy mmm)} & \colhead{} & \colhead{(GHz)} & \colhead{} &\colhead{} & \colhead{(Jy)} & \colhead{}
}
\startdata
16A--301 & 16 Jun & B & 10.00 & 3C286 & J2007+4029 & 1.98 & 220 248 274 310 327 341 351 507 509 540 640 675 684 698 714 723 725 742 753 798 801 839 892 1179 1201 1267 1454 2210 3188 4797 \\
17A--107 & 17 Apr, May & D & 23.17 & 3C286 & J2007+4029 & \nodata & The entire sample excluding the regions of DR21 and W75N\\
\hline
12B--140\_0185\tablenotemark{b} & 2012 Nov & A & 5.74 & 3C286 & J2007+4029 & 2.80 & 310 640 675 1112 \\
13A--315\_1898 & 2013 Aug & C & 43.60 & 3C286 & J2007+4029 & 1.22 & 1467\\
13A--373\_1665 & 2013 May & DnC & 23.23 & 3C48 & J2015+3710 & 4.31 & 1243 5417 \\
13A--373\_4594 & 2013 Apr &DnC & 24.37 & 3C48 & J2015+3710 & 4.52 & 1454 2210 \\
13A--373\_7871 & 2013 May & DnC & 24.70 & 3C48 & J2015+3710 & 4.72 & 1243 5417 \\
13A--373\_9583 & 2013 Mar &D & 24.37 & 3C48 & J2015+3710 & 4.65 & 1225 \\
13B--210\_6088 & 2014 Jan & B & 23.20 & 3C286 & J2015+3710 & 3.77 & 274 509\\
14A--092\_7083 & 2014 Mar & A & 44.00 & 3C286 & J2012+4628 & 0.58 & 310 640 675 1112 \\
14A--092\_9305 & 2014 Mar & A & 44.00 & 3C286 & J2012+4628 &0.65 & 640 675 714 1112 \\
14A--241\_0324 & 2014 Jul &D & 23.09 & 3C48 & J2007+4029 & 1.64 & 220 341 699 1018 1112 1467\\
14A--420\_0232 &2015 May & D & 5.80 & 3C48 & J2052+3635 & 2.95 & 4794\\
14A--420\_1115 &2015 May &B & 5.80 & 3C138 & J2007+4029 & 2.60 & 274 1460\\
14A--420\_6898 &2014 Aug & D & 5.80 & 3C48 & J2052+3635 & 2.92 & 798\\
14A--420\_6944 &2014 Aug & D & 5.80 & 3C286 & J2007+4029 & 2.58 & 892\\
14A--420\_7824 &2014 Aug & D & 5.80 & 3C286 & J2007+4029 & 2.59 & 725 \\
14A--420\_8009 &2014 Aug & D & 5.80 & 3C48 & J2052+3635 & 3.16 & 351\\
14A--420\_9375 & 2015 May & B & 5.80 & 3C286 & J2007+4029 & 2.53 & 699 1018 1112 1243 1467 1528 1599 5417 \\
14A--420\_9676 & 2015 May & B & 5.80 & 3C286 & J2007+4029 & 2.59 & 507 753 \\
14A--481\_3009 &2014 May & A & 21.88 & 3C286 & J2015+3710 & 3.81 & 327 742 \\
14B--173\_7197 & 2014 Dec & C & 30.91 & 3C48 & J2038+5119 & 3.42 & 699 1018 1467 \\
15A--059\_5602 & 2015 Feb & B & 30.91 & 3C48 & J2038+5119 & 3.42 & 699 1018 1467\\
\hline
AB515 & 1989 Apr & B & 1.46 & 3C286 & J2052+3635 & 4.94 & 892\\
AB1073 & 2003 Apr &D & 8.46 & 3C48 & J2015+3710 & 4.04 & 220 351 892\\
AC240 & 1989 Mar &B & 8.44 & 3C286 & J2007+4029 & 3.01 & 742 \\
AC240 & 1989 Mar &B & 14.94 & 3C286 & J2007+4029 & 2.87 & 725 \\
AD219 & 1988 Apr & CD & 4.86 & 3C48 & J2007+4029 & 3.40 & 327 507 742 753\\
AF362 & 1999 Jul & A & 8.46 & 3C48 & J2015+3710 & 2.51 & 1201 \\
AF381 & 2001 Apr &B & 4.86 & 3C286 & J2015+3710& 2.45 & 1112 1528 \\
AF381 & 2001 Apr &B & 14.94\tablenotemark{c} & 3C286 & J2015+3710 & 2.71 & 699 1018 1112 1467\\
AG625 & 2002 Aug & B & 8.44 & 3C286 & J2007+4029 & 2.64 & 742 327 \\
AH398 & 1990 Mar & A & 4.86 & 3C286 & J2023+3153 & 2.05 & 725 \\
AH549 & 1995 Aug &A & 4.86 & Manual\tablenotemark{d} & J2025+3343 & 2.74 & 725 \\
AH726 & 2001 Mar & B & 4.86 & 3C286 & J2015+3710 & 2.56 & 327 742 \\
AH869 & 2005 May& B & 4.86 & 3C286 & J2007+4029 & 2.31 & 1112 1528 \\
AJ239 & 1994 Jul & B & 8.44 & 3C48 & J2007+4029 &3.11 & 507 753 \\
AK355 & 1994 Jul & B & 4.86 & 3C48 & J2007+4029 & 4.39 & 725 \\
AK355 & 1994 Jul & B & 8.49 & 3C48 & J2007+4029 & 2.8 & 725 \\
AK355 & 1994 Jul & B & 14.94 & 3C48 & J2007+4029 & 2.25 & 725 \\
AK450 & 1997 Nov & D & 8.44 & 3C286 & J2015+3710 & 2.72 & 327 742 \\
AK477 & 1998 Dec & C & 8.44 & 3C286 & J2015+3710 & 2.72 & 327 742 \\
AM462 & 1995 Jan & CD &14.94 & 3C48 &J2007+4029 & 2.47 & 302 520 \\
AM432 & 1994 Jan & D& 8.44 & 3C48 & J2007+4029 & 3.12 & 274 \\
AM446 & 1994 Apr & A & 1.43 & 3C48 & J2007+4029 & 3.71 & 725 \\
AM446 & 1994 Apr & A &4.86 & 3C48 & J2007+4029 & 4.32 & 725 \\
AM446 & 1994 Apr & A & 8.44 & 3C48 & J2007+4029 & 2.71 & 725 \\
AM446 & 1994 Apr & A & 14.94 & 3C48 & J2007+4029 & 2.17 & 725 \\
AR436 & 2000 Jul & D& 4.86 & 3C48 & J2015+3710 & 1.96 & 220 \\
AR537 & 2004 Mar & C & 43.34 & 3C286 & J2015+3710 & 2.48 & 1201 \\
AS643 & 1998 Jul & AB & 8.46 & 3C286 & J2007+4029 & 2.15 & 1460\\
AS643 & 1998 Jul & AB & 8.46 & 3C286 & J2322+5057 & 1.69 & 1460\\
AS683 & 2000 May & C & 22.46 & 3C48 & J2025+3343 & 2.52 & 725 \\
AS683 & 2000 May & C & 43.34 &3C48 & J2025+3343 & 2.68 & 725 \\
AS831 & 2005 Apr & B & 8.46 & 3C286 & J2007+4029 & 1.00 & 1112 \\
\hline
Araya2009 & 2004 Nov & A & 8.46 & 3C48 & J2007+404 & 2.54 & 1467 \\
Araya2009 & 2005 May & B & 22.4 & 3C48 & J2007+404 & 1.78 & 1467 \\
CG2010 & 2006 Mar & A & 8.46 & 3C286 & J2007+4029 & 2.30 & 1112 \\
CG2015 & 2014 Mar, Apr & A & 6.0 & 3C286 & J2007+4029 & \nodata & 1112 \\
CG2015 & 2014 Mar, Apr & A & 15.0 & 3C286 & J2007+4029 &\nodata & 1112 \\
CG2015 & 2014 Mar, Apr & A & 22.0 & 3C286 & J2007+4029 &\nodata & 1112 \\
CG2015 & 2014 Mar, Apr & A & 44.0 & 3C286 & J2007+4029 &\nodata & 1112 \\
Fontani2012 & 2007 Mar & D & 22.5 & 3C286 & J2015+3710 & 1.39 & 274 \\
Gibb2007 & 1996 Nov & A & 4.86 & 3C48 & J2025+3343 & 2.80 & 1112 \\
Gibb2007 & 1996 Nov & A & 8.46 & 3C48 & J2025+3343 & 2.60 & 1112 \\
Gibb2007 & 1996 Nov & A & 44.49 & 3C48 & J2025+3343 & 2.56 & 1112 \\
Hunter1994 & 92 Nov & A & 8.44 & 3C48 & J2007+4029 & \nodata & 1112 \\
Kurtz1994 & 1989 Mar & B & 8.41 & 3C286 & J2007+4029 & 3.02 & 742 \\
Kurtz1994 & 1989 Mar & B & 14.96 & 3C286 & J2007+4029 & 3.12 & 742 \\
Masque2017 & 2014 May & A & 22.46 & 3C286 & J2015+3710 & 3.86 & 742 \\
Miralles1994 & 1989 Jul & C & 4.9 & 3C286 & J2007+4029 & 2.36 & 274 \\
Molinari1998 & 1994 Aug & CnB & 4.86 & 3C48 & \nodata & \nodata & 507 753 \\
Rosero2016 & 2011 Aug & A & 6.15 & 3C286 & J2007+4029 & \nodata & 274 \\
Shepherd2004 & 2001 Mar & B & 4.89 & 3C286 & J2012+4628 & \nodata & 1112 \\
Shepherd2004 & 2001 Mar & B & 14.96 & 3C286 & J2012+4628 & \nodata & 1112 \\
Shepherd2004 & 2000 Apr & C & 43.34 & 3C286 & J2012+4628 & \nodata & 1112 \\
Shepherd2004 & 2001 Mar & B & 43.34 & 3C286 & J2012+4628 & \nodata & 1112 \\
Torrelles1997 & 1996 Dec & A & 22.28 & 3C48 & J2023+3153 & 2.5 & 1112 \\
Urquhart2009 & 2009 Jul & B & 4.86 & 3C286 & \nodata & \nodata & 725 \\
\hline
\enddata
\tablecomments{Basic observational parameters of the data. Column 1 gives the project code or the reference of the data; column 2 gives the date of the observation; column 3 gives the configuration of the VLA antennas; column 4 gives the central frequency of the observation; column 5 and 6 give the flux calibrators and gain calibrators, relatively; column 7 gives the bootstrapped flux density of the gain calibrator, which may not be provided in the reference. Column 8 gives the MDCs covered by the observation. Projects 16A--301 and 17A--107 are the PI observations (PI: Keping Qiu).}
\tablenotetext{a}{ For easy comparison, here we list the J2000 names of the gain calibrators, which may be different from the source names originally adopted in the observational settings. See \url{https://science.nrao.edu/facilities/vla/observing/callist} for reference.}
\tablenotetext{b}{ The code after the underscore is the last four digits of the archive file ID. It helps to fast locate the specific schedule block of a project when searching the NRAO data archive (\url{https://archive.nrao.edu/archive/advquery.jsp}).}
\tablenotetext{c}{ Only the upper--band data were used for imaging.}
\tablenotetext{d}{ The \texttt{setjy} task in CASA failed by using the flux calibrators. We thus specified the flux densities and spectral indexes of the gain calibrator manually. The input values are from observations with similar settings and a close date.}
\tablereferences{
(1) \citet{2009ApJ...698.1321A}
(2) \citet{2010AJ....139.2433C};
(3) \citet{2015Sci...348..114C};
(4) \citet{2012MNRAS.423.1691F};
(5) \citet{2007MNRAS.380..246G};
(6) \Hunter1994;
(7) \citet{1994ApJS...91..659K};
(8) \citet{2017ApJ...836...96M};
(9) \citet{1994ApJS...92..173M};
(10) \Molinari1998
(11) \citet{2016ApJS..227...25R};
(12) \citet{2004ApJ...601..952S};
(13) \citet{2002ApJ...566..931S};
(14) \citet{1997ApJ...489..744T};
(15) \Urquhart2009;
}
\end{deluxetable*}
\subsection{Data Reduction}\label{subsec:reduc}
Both the historical VLA data and the JVLA data were calibrated and imaged by the Common Astronomy Software Applications (CASA)\footnote{\url{http://casa.nrao.edu}}\citep{2007ASPC..376..127M} v4.6.0 with the standard procedures. Edge channels, radio-frequency interference, and problematic data were flagged before and during data reduction. The Perley-Butler 2013 model \citep{2013ApJS..204...19P} was applied for flux calibration. Imaging was made by the task {\tt CLEAN} using the Briggs weighting with {\tt ROBUST=0.5} for a compromise between sensitivity and angular resolution. We made joint imaging for the visibilities with the same pointing centers, same frequencies, and comparable bandwidths, and performed mosaic imaging for the visibilities with close (but different) pointings and similar sensitivities. The properties of the radio continuum maps are listed in Table \ref{tab:mapInfo}. Data of the X-band survey had issues that severely affected the final product. Only the maps of MDC 274 and MDC 507 in the X-band survey were adopted.
\include{Table3_MapInfo}
\subsection{Source Identification}\label{ssec:rdetect}
Radio sources are identified in each map by searching for structures: (1) emission peak is not lower than five times the image RMS noise ($\sigma$); (2) area of the 3$\sigma$ contour is not smaller than the synthesized beam. Parameters such as position, peak flux density, and total flux density are further determined by two-dimensional Gaussian-fitting and direct measurement.
Gaussian fitting is performed using the task \texttt{IMFIT} of \textsc{MIRIAD}, which can fit one or multiple Gaussian components simultaneously on an image. This method is applied to the sources with an elliptical morphology. The fitting results include the coordinates, convolved and deconvolved sizes, peak flux densities, and total flux densities of the fitted Gaussian components, along with the corresponding fitting errors.
Direct measurement is adopted when the sources are resolved into cometary or irregular structures. This measurement is performed interactively using the task {\tt viewer} of \textsc{CASA}, with which we carefully measure the peaks and total flux densities within certain contour levels, e.g. 3$\sigma$ or 5$\sigma$. Such a direct measurement gives the coordinations of the geometric centers, peaks, and total flux densities without errors. For elliptical sources, we compare the total flux densities derived from the direct measurement with those returned from a Gaussian fitting, and the results have a typical difference of less than 10\%. For very faint sources, the difference reaches 30\% or more. This is due to a cutoff at a certain contour level in the direct measurement.
For a source covered by multiple observations, the obtained coordinates are always slightly different across the maps. In this case, we adopt the coordinates determined from the maps of the highest resolutions.
\section{Results}\label{sec:rst}
\subsection{Radio Flux density}\label{ssec:flux}
We have detected a total of 64 radio sources at $\sim$0.01-pc scale, i.e., the scale of dust condensations, and 17 relatively large-scale (0.1--1 pc) extended sources. Since our primary goal is to study the radio emission at the condensation scale, a detailed analysis of the extended emissions is beyond the scope of this work, and they will not be discussed. The detailed properties of all the detected radio sources are listed in Table \ref{tab:detection}, including the coordinates, observing frequencies, sizes, peak and total flux densities. The radio continuum maps of each MDC are presented in Figure \ref{fig:radio}.
\include{Table4_Detections}
\begin{figure}[ht!]
\plotone{214_247_K_17A-107.pdf}
\caption{Radio continuum map of MDC 214 and 247. The K-band emission is shown in both grayscale and red contours. The grayscale starts at a 3$\sigma$ level. The green ellipses represent the FWHMs of the MDCs in Cao21; the blue solid ellipses represent the dust condensations identified from the SMA 1.3 mm continuum maps. The observing frequency and the VLA configuration are labeled in the upper-right corner. The synthesized beam is shown in the bottom-left corner. The contour levels and the VLA project codes are provided below the map. MDC names are labeled by bold green indices. Radio sources associated with the MDC are marked by light green crosses and indexed by the labels nearby. The complete figure set (96 images) is available in the online journal. \label{fig:radio}}
\end{figure}
Most of the detected radio sources are faint and compact. Their K-band flux density distribution is given in Figure \ref{dist_NO}. For the radio sources with no K-band data, the flux densities at the nearest frequencies are adopted. Most of the radio sources have flux densities ranging from 0.1 mJy to 3 mJy. The distribution peaks at $\sim$0.2 mJy. A few bright sources, e.g. 507-r3 (Figure \ref{fig:radio}.12), 725-r1 (Figure \ref{fig:radio}.22 ), 742-r2 (Figure \ref{fig:radio}.7), 1112-r3 (Figure \ref{fig:radio}.28), and 1467-r1 (Figure \ref{fig:radio}.27), are resolved, and all have flux densities higher than 10 mJy.
\begin{figure}[ht!]
\epsscale{0.7}\plotone{dist_Sv_NO.pdf}
\caption{Distribution of the K-band flux densities of the radio sources. If a radio source has no K-band detection, the flux density at the nearest frequency is adopted. The histogram in white is the distribution of all the radio sources. The histograms in blue and yellow are the distributions of the newly detected sources and the previously reported ones.\label{dist_NO}}
\end{figure}
By carefully checking the literature, we confirm that 37 radio sources are reported for the first time (see the last column of Table \ref{tab:detection}). The new sources are generally more compact, being point-like or elliptical (Table \ref{tab:new}). They are fainter, with K-band flux densities distributing mainly between 0.1--1.0 mJy and peaking at $\sim$0.2 mJy (Figure \ref{dist_NO}).
\begin{table}[h!]
\renewcommand{\thetable}{\arabic{table}}
\centering
\caption{Newly detected and the reported sources\label{tab:new}}
\begin{tabular}{c|ccc|c}
\tablewidth{0pt}
\hline
\hline
& Total & New & Reported & Ratio (N/R) \\
\hline
Compact & 53 & 35 & 18 & 1.9 \\
Extended & 11 & 1 & 10 & 0.1 \\
\hline
Ratio (C/E) & 4.8 & 35 & 1.8 \\
\hline
\hline
\end{tabular}
\tablecomments{`N'' for newly detected sources; ``R'' for reported sources; ``C'' for compact or elliptical sources; ``E'' for extended sources.}
\end{table}
\subsection{Association with MDCs}\label{ssec:rate}
A radio source is considered to be associated with an MDC when it is located within or close to the FWHM boundary of the MDC, and is considered as being associated with a dust condensation when it is abutting or overlapping with the condensation. But in quantitative analyses of the radio luminosity of the MDCs, we only include the radio sources within and right on the FWHM boundaries of the MDCs. The detected 64 radio sources are associated with 34 MDCs, of which 14 MDCs are associated with more than one radio sources. Thirty MDCs have radio sources within the FWHM boundaries, in which 12 have multiple sources. Forty-four (69\%) radio sources are associated with dust condensations and 54 (84\%) are located in the MDCs. The number of radio sources associated with each MDC is given in Table \ref{tab:MDC}, in which we classify the radio sources as being in an MDC and associated with the dust condensations (``$N_A$''), being in the MDCs but associated with no dust condensation (``$N_{NA}$''), and located close but outside of the FWHM boundary of an MDC (``$N_O$''). In this table, we also noted the star-forming indicators such as outflows and masers obtained from the literature.
\startlongtable
{\catcode`\&=11
\gdef\Beuther2002{\citet{2002A&A...383..892B}}
\gdef\Edris2007{\citet{2007A&A...465..865E}}
\gdef\Motte2007{\citet{2007A&A...476.1243M}}
\gdef\Fontani2010{\citet{2010A&A...517A..56F}}
\gdef\Stutzki1982{\citet{1982A&A...111..201S}}
\gdef\Harju1998{\citet{1998A&AS..132..211H}}
\gdef\Larionov1999{\citet{1999A&AS..139..257L}}
\gdef\Palau2007{\citet{2007A&A...465..219P}}
\gdef\Gottschalk2012{\citet{2012A&A...541A..79G}}
\gdef\Duarte2013{\citet{2013A&A...558A.125D}}
\gdef\DuarteC2014{\citet{2014A&A...570A...1D}}
}
\begin{deluxetable*}{c|ccc|c|cccc|l}
\tablecaption{Radio and Infrared Properties of the MDCs\label{tab:MDC}}
\tablehead{
\colhead{MDC} & \colhead{$N_{A}$} & \colhead{$N_{NA}$} & \colhead{$N_O$} & \colhead{Type} & \colhead{Notes}}
\startdata
214 & 0 & 0 & 0 & Q & H$_2$O/CH$_3$OH maser$^{4,10,13,18,26,28}$, outflow$^{10,19}$\\
220 & 0 & 0 & 0 & Q & Outflow$^{21,23,24}$ \\
247 & 0 & 1 & 0 & B & H$_2$O/CH$_3$OH maser$^{3,20}$, outflow$^{27}$ \\
248 & 1 & 0 & 0 & Q & H$_2$O maser$^{26}$, outflow$^{21,23,24}$ \\
274 & 1 & 1 & 0 & B & H$_2$O maser$^4$, outflow$^{6,7,21}$ \\
302 & 0 & 0 & 0 & C & \\
310 & 2 & 0 & 0 & B & H$_2$O maser$^{4,16,18,20}$, outflow$^{12,19,21}$ \\
327 & 0 & 1 & 0 & Q & \\
340 & 0 & 0 & 1 & Q & \\
341 & 1 & 0 & 0 & Q & Outflow$^{21,23,24}$ \\
351 & 1 & 0 & 0 & Q & \\
370 & 0 & 0 & 0 & C & Outflow$^{25}$ \\
507 & 2 & 1 & 0 & B & H$_2$O/CH$_3$OH/OH maser$^{4,10,13,15,16,18,20}$, outflow$^{10,19}$ \\
509 & 4 & 1 & 2 & Q & H$_2$O/CH$_3$OH maser$^{8,20,26,29}$, outflow$^{7,8,14,19,29}$\\
520 & 0 & 0 & 0 & C & H$_2$O maser$^4$ \\
540 & 0 & 0 & 3 & Q & \\
608 & 0 & 0 & 0 & Q & \\
640 & 0 & 0 & 0 & Q & \\
675 & 1 & 0 & 0 & B & H$_2$O maser$^{17,21}$, outflow$^{25}$ \\
684 & 1 & 0 & 0 & Q & Outflow$^{21}$ \\
698 & 1 & 0 & 0 & Q & H$_2$O maser$^{20}$, outflow$^{21,25}$ \\
699 & 0 & 1 & 0 & B & H$_2$O/CH$_3$OH maser$^{2,5,16,20,23,24}$, outflow$^{27}$ \\
714 & 3 & 0 & 0 & B & H$_2$O maser$^{20,26}$, outflow$^{21,27}$ \\
723 & 1 & 1 & 0 & Q & \\
725 & 2 & 0 & 0 & B & H$_2$O/CH$_3$OH maser$^{13,16,18}$, outflow$^{21}$ \\
742 & 2 & 1 & 0 & B & Outflow$^{25}$ \\
753 & 0 & 0 & 1 & Q & H$_2$O/CH$_3$OH/OH maser$^{4,28}$, outflow$^{30}$ \\
798 & 1 & 0 & 0 & Q & \\
801 & 1 & 0 & 0 & Q & Outflow$^{21}$ \\
839 & 1 & 0 & 0 & Q & \\
892 & 0 & 0 & 0 & C & \\
1018 & 0 & 0 & 0 & Q & H$_2$O maser$^{13}$, outflow$^{23,24}$ \\
1112 & 3 & 3 & 0 & B & H$_2$O/CH$_3$OH/OH maser$^{4,16,20,26}$, outflow$^{5,21,25,27}$ \\
1179 & 0 & 0 & 0 & N & \\
1201 & 0 & 1 & 0 & C & H$_2$O maser$^{1,4,13,16,20,26}$, outflow$^1$ \\
1225 & 2 & 0 & 0 & Q & \\
1243 & 1 & 0 & 0 & B & H$_2$O/CH$_3$OH maser$^{20,26}$, outflow$^{25,27}$ \\
1267 & 1 & 0 & 1 & Q & \\
1454 & 3 & 2 & 0 & Q & H$_2$O maser$^{26}$ \\
1460 & 0 & 0 & 0 & B & H$_2$O maser$^4$ \\
1467 & 0 & 0 & 2 & Q & H$_2$O/CH$_3$OH/OH maser$^{2,4,17,26}$, outflow$^{22,25}$ \\
1528 & 0 & 0 & 0 & C & H$_2$O/CH$_3$OH maser$^{2,4,5,9,16}$, outflow$^{5,21}$ \\
1599 & 0 & 0 & 0 & Q & H$_2$O/CH$_3$OH maser$^{4,16}$, outflow$^{23,24}$ \\
2210 & 1 & 0 & 0 & Q & \\
3188 & 0 & 1 & 0 & Q & Outflow$^{21}$ \\
4797 & 0 & 1 & 0 & Q & Outflow$^{21}$ \\
5417 & 1 & 0 & 0 & B & H$_2$O/CH$_3$OH/OH maser$^{11,16,17}$ \\
\hline
\enddata
\tablecomments{A summary of the radio detections, infrared classifications, and star-formation indicators of the MDCs.
$N_{A}$ is the number of radio sources in an MDC and associated with dust condensations.
$N_{NA}$ is the number of radio sources in an MDC that are associated with no dust condensation;
$N_{O}$ is the number of radio sources located close but outside of the FWHM boundary of an MDC.
Column ``Type'' is the classification based on the 24 $\mu$m fluxes and is the same as that in Table \ref{tab:MDC_Cao21}.
In the ``Notes'' column, we summarized the star--formation indicators obtained from the literature. }
\tablerefs{(1) \Stutzki1982; (2) \citet{1990ApJ...364..555P}; (3) \citet{1994ApJS...92..173M}; (4) \Harju1998;(5) \Larionov1999; (6) \citet{2002ApJ...576..313K}; (7) \Beuther2002; (8) \citet{2004ApJ...608..330B}; (9) \citet{2005AJ....130..711K};(10) \citet{2005ApJ...625..864Z}; (11) \citet{2005MNRAS.356..637H}; (12) \citet{2006ApJ...643..978K}; (13) \citet{2007PASJ...59.1185S}; (14) \Palau2007;(15) \Edris2007; (16) \Motte2007; (17) \citet{2008MNRAS.384..719H}; (18) \Fontani2010; (19) \citet{2010MNRAS.404..661V};(20) \citet{2011MNRAS.418.1689U}; (21) \Gottschalk2012; (22) \citet{2012ApJ...744...86Z}; (23) \Duarte2013; (24) \DuarteC2014;(25) \citet{2015MNRAS.450.4364N}; (26) \citet{2015MNRAS.453.4203X}; (27) \citet{2015MNRAS.453..645M}; (28) \citet{2016ApJS..222...18G}; (29) \citet{2017ApJS..233....4R};(30) Yang et al., in preparation.}
\end{deluxetable*}
\subsection{Spectral Indices} \label{ssec: idx}
Radio continuum emission produced by star-forming activities can be either thermal free-free emission or non-thermal synchrotron radiation. In the centimeter wavelengths, spectral energy distributions (SEDs) of the two mechanisms both can be modeled by a power-law relation of $S _ { \nu } \propto \nu ^ { \alpha }$ \citep{1975MNRAS.170...41W}. The spectral indices of thermal free-free emission arising from UC \ion{H}{2} regions can vary from $-0.1$ to 2 depending on the optical depth \citep{1993RMxAA..25...23R, 2004ApJ...612L..69S}. The measured spectral indices of thermal ionized jets/winds range from 0.1 to $\sim$1 \citep{2018A&ARv..26....3A}. Non-thermal radiation is characterized by a negative spectral index ($\alpha < -0.1$) \citep{2005ApJ...626..953R, 2010Sci...330.1209C}.
SEDs derived from interferometric data can be affected by the spatial filtering effect, especially for the resolved sources. We use the size (in arc sec$^2$) of the source in a map as the direct indicator of the probed spatial scale. The SEDs are fitted only when there are data covering at least two VLA observing bands and the sizes of the sources vary within a factor of two. The error of flux densities is a quadrature summation of the calibration error and the measurement error \citep{2001AJ....121.1556B}: the calibration error is assumed to be 5\% at frequencies lower than 15 GHz, 10\% between 15 GHz and 35 GHz, and 15\% at higher frequencies; the measurement error is estimated as the image RMS times the source sizes in units of beam size.
Among the 64 radio sources, we are able to characterize the SEDs of 8 sources. Two of the SEDs are flat ($-0.1 \leqslant \alpha \leqslant 0.2$); four are positive ($\alpha > 0.2$); two are negative ($\alpha < -0.1$). The flat and positive spectral indices indicate thermal emission from \ion{H}{2} regions, or ionized jets and winds \citep{1986ApJ...304..713R, 2018A&ARv..26....3A}, whereas the negative spectral indices suggest the presence of non-thermal emission presumably arising from a synchrotron jet (e.g., \citealt{2017A&A...597A..43G}).
During SED fitting, we notice that for the same source, the spectral indices obtained by different works can sometimes be inconsistent, e.g. the radio sources associated with MDC 1112 (see the Appendix for a detailed discussion). Some of the differences cannot be simply explained by uncertainties but are caused by various reasons. A most common issue in interferometric observations is the spatial filtering effect, which can lead to, e.g., $\sim$60\% flux density missing \citep{2004ApJ...601..952S} and can severely affect the fitting results \citep{1999ApJ...514..232K}. Thus it is essential to use data sensitive to the same spatial scales. An additional point worth consideration is time variability. Previous observations and simulations have revealed that some of the UC \ion{H}{2} regions can show time variation in their flux densities and morphologies within a typical period of ten years (\citealt{2004ApJ...604L.105F, 2005A&A...431..993V, 2008ApJ...674L..33G, 2010RMxAA..46..253N, 2011MNRAS.416.1033G, 2012ApJ...758..137K, 2018A&ARv..26....3A} and the references therein). The time variability of radio jets has also been confirmed (e.g. \citet{2018A&ARv..26....3A, 2010AJ....139.2433C}). The VLA data we adopted have a long time span of thirty years, within which the VLA had a major upgrade from the HVLA to the JVLA. The time span is even longer considering the data taken from the literature. Besides, for the data obtained from the literature, the measurement and uncertainty estimations are carried out by different methods. We thus carefully check the probed spatial scales and refrain from using data with long time spans for SED fitting considering possible time variation.
\section{Discussion} \label{sec:dis}
\subsection{Overall Performance of the Dataset} \label{ssec:data}
We detect a large number of faint radio sources, of which more than half are new detections. We quantitatively characterize the detection capability of the entire work by looking into the observations that cover the majority of the MDCs. Projects 17A--107, 14A--241, and 13A--373 are all 23.2 GHz observations with similar sensitivities and resolutions (Figure \ref{cmp}). Together they cover the entire sample. We take them as the ``baseline data'' to assess the overall detection capability. The other data may have finer resolutions and even higher sensitivities but only cover a small number of MDCs and may have quite different observational settings. Thus those data do not significantly affect the detection rate of the whole sample. The baseline data have concentrated RMS noises of several tens of micro Janskies (also see Figure \ref{dist_rms_cmp}). A few maps have RMS noises higher than 100 $\mu$Jy because of containing bright extended sources and strong sidelobes. After excluding these maps, the average RMS noise of the baseline data is 30 $\mu$Jy/beam, corresponding to a 5$\sigma$ sensitivity of 0.15 mJy/beam. They have similar angular resolutions of about 3$''$, corresponding to 0.02 pc at a distance of 1.4 kpc (also see Figure \ref{dist_beam_cmp}). Although this is not the highest resolution the dataset has achieved, it is sufficient for detecting source multiplicity within a 0.1-pc scale and resolving positional offsets between the radio sources and the dust condensations.
\begin{figure*}[ht!]
\epsscale{0.8}\plotone{plot_rms_beam.pdf}
\caption{Comparison of the RMS and the resolution between the baseline data and the other archival data. The dots show the baseline data, and the crosses indicate the archival data. The observing bands are represented by different colors. \label{cmp}}
\end{figure*}
\begin{figure}[ht!]
\epsscale{0.8}\plotone{dist_rms.pdf}
\caption{Stacked distribution of the RMS noises. The vertical axis is the number of radio continuum maps. The histograms in blue and yellow are of the baseline data and the archival data, respectively. \label{dist_rms_cmp}}
\end{figure}
\begin{figure}[ht!]
\epsscale{0.8}\plotone{dist_beam.pdf}
\caption{Stacked distribution of the beam sizes. The vertical axis is the number of radio continuum maps. The colors are the same as in Figure \ref{dist_rms_cmp}.\label{dist_beam_cmp}}
\end{figure}
Among the 64 radio sources, 57 are detected by the baseline data, in which 34 are new detections. For the other seven sources, two are so weak that are only detected with the data of higher sensitivities; five are contaminated by the nearby extended sources and are only distinguishable in the maps that have filtered out the extended emission. Moreover, the flux density distribution peaks near the overall sensitivity limit determined by the baseline data (Figure \ref{dist_NO_withLimit}). We conclude that our work is capable of detecting radio continuum sources with 23.2 GHz peak flux densities no less than 0.15 mJy/beam and resolving multiple sources with separations larger than 0.02 pc.
\begin{figure}[ht!]
\epsscale{0.8}\plotone{dist_Sv_NO_withLimit.pdf}
\caption{Colors are the same as Figure \ref{dist_NO}. The vertical axis is the number of radio detections. The dashed line represents the overall sensitivity limit.\label{dist_NO_withLimit}}
\end{figure}
\subsection{Nature of the Radio Sources} \label{ssec:nature}
Radio continuum emission can be produced by several processes during HMSF. Thermal free-free emission is observed in \ion{H}{2} regions, ionized jets, disc-winds, and the radio knots produced by the interaction between jets and the surrounding material \citep{1986ApJ...304..713R, 2005IAUS..227..120R}. Non-thermal synchrotron components are found in the jet knots produced by jets with extremely high energy and speed \citep{2014ApJ...792L..18A, 2018MNRAS.474.3808V}. In the low-mass regime, Class I objects can produce the non-thermal gyrosynchrotron radiation \citep{2013ApJ...775...63D}. Objects such as planet nebulae (PNe) and extra-galactic objects also produce radio continuum emissions. Since the gyrosynchrotron radiation emitted by Class I objects is too weak to be detected by our data \citep{2013ApJ...775...63D}, we only inspect the possible contamination from extra-galactic objects and PNe before further discussion.
The number of possible extra-galactic objects is estimated using the models from \citet{2005A&A...431..893D}. The number density of extra-galactic objects at 23.2 GHz is interpolated using the models at 20 GHz and 30 GHz and is obtained to be 1.3$\times$10$^6$ sr$^{-1}$. Our search area is 1.5 times the total area enclosed by the FWHMs of all the surveyed MDCs, and is about $2.4 \times 10^{-6}$ sr. Thus the total number of possible extra-galactic sources is about three, which is negligible for statistical analysis.
We check the HASH PN database\footnote{http://202.189.117.101:8999/gpne/} \citep{2016JPhCS.728c2008P} for PNe with radio fluxes above our detection threshold. No record is found in our FOV. Moreover, PNe are produced during the late stages of massive star evolution. Since their surrounding dust and gas cocoons should have already dispersed, we are not likely to detect them in the dusty MDCs.
In conclusion, the contamination from extra-galactic objects and PNe is negligible. The detected radio sources in this work should be small \ion{H}{2} regions or ionized jets/winds, and a more detailed discussion in this context is presented below.
\subsubsection{\ion{H}{2} Regions}\label{sssec:hii}
A straightforward way to identify \ion{H}{2} region candidates is by morphology. In high-resolution observations, developed UC \ion{H}{2} regions are found to have several typical morphologies, including cometary, core-halo, shell-like, and irregular \citep{1989ApJS...69..831W}. We detect two cometary (699-r1, 742-r2) and three core-halo (725-r1, 1467-r1, 2210-r1) sources. Moreover, the complex radio continuum emission in MDC 1528 may be composed of at least two cometary UC \ion{H}{2} regions or a result of the interaction between the stellar wind and the surrounding material. High radio flux densities can also suggest the existence of UC \ion{H}{2} regions. In our detected radio sources, 507-r3 (Figure \ref{fig:radio}.12), 725-r1 (Figure \ref{fig:radio}.22), 742-r2 (Figure \ref{fig:radio}.7), 1201-r1 (Figure \ref{fig:radio}.29), and 1112-r3 (Figure \ref{fig:radio}.28) have radio flux densities of several tens of milli Janskies, much higher than the others. However, these diagnostics do not work for compact and faint sources. We thus look further into their physical parameters.
UC \ion{H}{2} regions have been quantitatively characterized as a pack of ionized gas with size $<$0.1 pc, $N_e \geq 10^4$ cm$^{-3}$, and $EM \geq 10^7$ pc cm$^{-6}$ and HC \ion{H}{2} regions with size $<$0.05 pc, $N_e \geq 3 \times 10^5$ cm$^{-3}$, and $EM \geq 10^8$ pc cm$^{-6}$ \citep{2010MNRAS.405.1560M}. We calculate these physical parameters of the radio sources on each map with the UC \ion{H}{2} region model of \citet{1967ApJ...147..471M} and \citet{1969ApJ...156..269S}, which assumes a spherically symmetric, optically thin UC \ion{H}{2} region of uniform density and electron temperature of 10$^4$ K. The required parameters for calculation are distances (1.4 kpc), H$_2$ column densities (see Table \ref{tab:MDC_Cao21}), observing frequencies, radio flux densities, and source sizes. The results are listed in columns 6--8 of Table \ref{tab:parameters_full}, which are $EM$, $N_e$, and the excitation parameter ($U$), respectively. The maps with UC- or HC- \ion{H}{2} region candidates are marked by one or two asterisks, respectively.
Only nine sources meet the criteria of UC- or HC- \ion{H}{2} regions in at least one map. Two of them are the most luminous radio sources in MDC 1112, whose natures have been long under debate \citep{1997ApJ...489..744T, 2001ApJ...546..345S, 2010AJ....139.2433C, 2020MNRAS.496.3128R}. Source 675-r1 reaches the criteria only on the Q-band A-configuration map, which only picks up the most compact components. The result of source 1201-r1 is consistent with the fact that it is a very dense and bright ionizing source \citep{2018A&A...617A..45S}. Moreover, this method will underestimate the parameters for the sources that do not meet the optically-thin criterion as the model requires, which can lead to some young UC/HC \ion{H}{2} regions being misclassified as unqualified. Meanwhile, the uncertainty in deriving the source size by deconvolution, especially for the barely resolved sources (e.g., 310-r2 and 1112-r6), can bring large errors.
\startlongtable
\begin{deluxetable*}{cccccccc}
\centering
\tablecaption{Physical Parameters Derived from UC \ion{H}{2} model\label{tab:parameters_full}}
\tabletypesize{\scriptsize}
\tablehead{
\colhead{MDC} & \colhead{Radio ID} & \colhead{Spectral Index} & \colhead{Frequency} & \colhead{Project Code} & \colhead{$EM$} & \colhead{$N_e$} & \colhead{$U$} \\
\colhead{} & \colhead{} & \colhead{} & \colhead{(GHz)} & \colhead{} & \colhead{(10$^{5}$ pc cm$^{-6}$)} & \colhead{(10$^{3}$ cm$^{-3}$)} & \colhead{(pc cm$^{-2}$)}
}
\startdata
248 & 1 & \nodata & 23.2 & 17A--107 & 19.57 & 13.05 & 0.98 \\
\hline
274 & 1 & $-$0.11 & 5.8 & 14A--240\_1115 & 15.22 & 17.78 & 0.53 \\
& & & 8.4 & AM432 & 1.16 & 2.18 & 0.65 \\
& & & 10.0 & 16A--301 & 13.84 & 15.11 & 0.59 \\
& & & 22.5 & Fontani2012 & 1.54 & 2.73 & 0.62 \\
& & & 23.2 & 17A--107 & 9.03 & 10.83 & 0.58 \\
& & & 23.2 & 13B--210 & 24.03 & 23.58 & 0.55 \\
\hline
310 & 1 & \nodata & 23.2 & 17A--107 & 5.26 & 6.44 & 0.67 \\
& 2 & 0.75 & 23.2 & 17A--107 & 1.35 & 3.18 & 0.44 \\
& & & 44.0 & 14A--092** & 21824.93 & 3931.42 & 0.53 \\
\hline
340 & 1 & \nodata & 23.2 & 17A--107 & 0.77 & 2.49 & 0.35 \\
\hline
341 & 1 & \nodata & 23.2 & 14A--241 & 7.42 & 8.71 & 0.64 \\
351 & 1 & \nodata & 23.2 & 17A--107 & 0.28 & 1.05 & 0.41 \\
507 & 2 & \nodata & 5.8 & 14A--420\_9676 & 38.12 & 24.53 & 0.86 \\
& & & 8.4 & AJ239 & 40.22 & 30.01 & 0.69 \\
& & & 10.0 & 16A--301 & 47.61 & 38.45 & 0.58 \\
& 3 & \nodata & 5.8 & 14A--420\_9676* & 100.76 & 30.96 & 1.67 \\
& & & 8.4 & AJ239* & 102.78 & 31.44 & 1.65 \\
\hline
509 & 1 & \nodata & 23.2 & 17A--107 & 0.9 & 2.34 & 0.45 \\
& 2 & \nodata & 23.2 & 17A--107 & 0.17 & 0.73 & 0.39 \\
& 4 & \nodata & 23.2 & 17A--107 & 0.19 & 0.82 & 0.38 \\
& 5 & \nodata & 23.2 & 17A--107 & 0.11 & 0.52 & 0.39 \\
& 6 & \nodata & 23.2 & 17A--107 & 1.6 & 2.17 & 0.88 \\
& 7 & \nodata & 23.2 & 17A--107 & 24.79 & 24.66 & 0.53 \\
\hline
675 & 1 & \nodata & 23.2 & 17A--107 & 27.67 & 17.97 & 0.9 \\
& & & 44.0 & 14A--092** & 7973.45 & 1518.3 & 0.69 \\
\hline
714 & 2 & \nodata & 23.1 & 17A--107 & 1.16 & 3.1 & 0.4 \\
\hline
725 & 1 & $-$0.01 & 1.4 & AM446 & 90.41 & 28.69 & 1.74 \\
& & & 22.5 & AS683* & 1619.91 & 182.75 & 2.4 \\
\hline
742 & 2 & $-$0.03 & 4.9 & AD219 & 16.47 & 6.3 & 2.29 \\
& & & 8.5 & AK450 & 14.57 & 5.61 & 2.32 \\
\hline
753 & 1 & $-$0.65 & 4.9 & AD219 & 13.65 & 11.6 & 0.84 \\
& & & 4.9 & Molinari1998 & 22.49 & 16.17 & 0.89 \\
\hline
839 & 1 & \nodata & 23.2 & 17A--107 & 1.64 & 3.75 & 0.43 \\
\hline
1112 & 1 & \nodata & 4.9 & Gibb2007* & 546.25 & 216.59 & 0.68 \\
& & & 5.8 & 14A--420\_9375* & 114.81 & 57.61 & 0.83 \\
& & & 8.5 & CG2010* & 240.03 & 94.29 & 0.89 \\
& & & 8.5 & Gibb2007* & 538.71 & 263.92 & 0.51 \\
& & & 14.9 & AF381* & 131.56 & 64.05 & 0.8 \\
& & & 22.3 & Torrelles1997* & 768.67 & 184.09 & 1.13 \\
& 2 & \nodata & 5.8 & 12B--140 & 75.07 & 53.04 & 0.61 \\
& & & 14.9 & AF381 & 85.19 & 52.09 & 0.68 \\
& 3 & \nodata & 4.9 & Gibb2007** & 1311.0 & 489.61 & 0.55 \\
& & & 5.8 & 12B--140* & 836.87 & 289.51 & 0.7 \\
& & & 8.5 & CG2010** & 1256.46 & 322.16 & 0.9 \\
& & & 8.5 & Gibb2007** & 1183.97 & 366.42 & 0.72 \\
& & & 22.3 & Torrelles1997** & 16808.85 & 1675.03 & 1.3 \\
& & & 43.5 & Gibb2007** & 47115.54 & 4389.09 & 0.99 \\
& 4,5 & \nodata & 5.8 & AF381 & 36.54 & 23.17 & 0.89 \\
& & & 5.8 & 14A--420\_9375 & 21.73 & 18.33 & 0.72 \\
& & & 5.8 & AH869 & 24.37 & 16.3 & 0.95 \\
& & & 8.5 & CG2010 & 88.33 & 46.15 & 0.85 \\
& 6 & \nodata & 5.8 & 12B--140* & 135.78 & 97.7 & 0.49 \\
& & & 14.9 & AF381 & 32.36 & 30.59 & 0.53 \\
\hline
1201 & 1 & 0.73 & 8.5 & AF362** & 12123.85 & 1394.39 & 1.24 \\
\hline
1225 & 1 & \nodata & 24.4 & 13A--373\_9583 & 0.61 & 2.21 & 0.33 \\
\hline
1243 & 1 & \nodata & 23.8 & 13A--373 & 3.52 & 5.82 & 0.52 \\
\hline
1267 & 2 & \nodata & 23.2 & 17A--107 & 1.44 & 4.09 & 0.34 \\
\hline
1454 & 1 & \nodata & 23.2 & 17A--107 & 0.54 & 1.7 & 0.41 \\
& & & 24.4 & 13A--373\_4954 & 0.96 & 3.08 & 0.33 \\
& 2 & \nodata & 23.2 & 17A--107 & 1.73 & 4.56 & 0.35 \\
& 3 & \nodata & 23.2 & 17A--107 & 0.29 & 1.03 & 0.42 \\
& & & 24.4 & 13A--373\_4954 & 0.98 & 2.96 & 0.35 \\
\hline
1467 & 1 & 0.61 & 7.0 & 14A--420\_9375 & 53.74 & 29.65 & 0.94 \\
& & & 30.9 & 14B--173* & 683.99 & 154.29 & 1.26 \\
& 2 & \nodata & 8.5 & Araya2009 & 94.87 & 95.18 & 0.35 \\
\hline
2210 & 1 & \nodata & 23.2 & 17A--107 & 0.11 & 0.43 & 0.52 \\
& & & 24.4 & 13A--373\_4954 & 0.18 & 0.85 & 0.34 \\
\hline
3188 & 1 & \nodata & 23.2 & 17A--107 & 1.07 & 3.42 & 0.32 \\
\hline
4797 & 1 & \nodata & 23.3 & 17A--107 & 0.15 & 0.67 & 0.39 \\
\hline
5417 & 1 & \nodata & 7.0 & 14A--420\_9375 & 74.15 & 45.42 & 0.73 \\
& & & 23.8 & 13A--373 & 9.68 & 9.58 & 0.73 \\
\hline
\enddata
\tablecomments{Physical parameters assuming that the radio detections are UC/HC \ion{H}{2} regions. Columns 6, 7, and 8 are emission measure, electron density, and excitation parameter, respectively. Project code with one or two asterisks means the parameters derived from this map meets the criteria of an ultra- or hyper compact \ion{H}{2} region.}
\end{deluxetable*}
We further inspect the Lyman continuum flux as a function of the bolometric luminosity. Lyman continuum flux is calculated with the K-band flux density, assuming an optically thin, spherical \ion{H}{2} region with an electron temperature of 10$^4$ K \citep{1974A&A....32..269M}. For the MDCs containing multiple compact radio sources, their radio flux densities are summed up or re-measured on the maps of the lowest resolutions, in order to minimize the loss of flux due to spatial filtering. Bolometric luminosity is approximated by the far-infrared (FIR) luminosity from Cao21, considering that FIR luminosity is the dominant contributor of the bolometric luminosity of MDCs at early evolution stages. This approximation have larger uncertainties for MDCs at relatively late evolution stages, e.g., when a bright UC \ion{H}{2} region has formed. Lyman continuum flux as a function of bolometric luminosity is shown in Figure \ref{fig:nly}, where we also plot the data of the UC \ion{H}{2} regions obtained from \citet{1994ApJS...91..659K} and the expected Lyman continuum flux of a single ZAMS star \citep{1984ApJ...283..165T}. The ZAMS line is a theoretical upper limit of the Lyman continuum flux produced by photoionization. Our sample and the UC \ion{H}{2} regions show clearly different distributions. The trend of our data does not follow that of the ZAMS stars, either. Thus most of our detected sources have different ionization mechanisms rather than photoionization. Moreover, this method may underestimate the Lyman continuum flux because part of the extended radio fluxes are filtered out by the interferometer \citep{1999ApJ...514..232K, 2020MNRAS.492..895D} and our sources may not be optically thin \citep{2013MNRAS.435..400U}. This means that the blue dots in Figure \ref{fig:nly} would be pushed even further above the dash-dotted line, which strengthens the conclusion that most of the detected sources are not UC \ion{H}{2} regions.
\begin{figure}[ht!]
\epsscale{0.8}\plotone{plot_NLy_Lbol.pdf}
\caption{Lyman continuum flux as a function of bolometric luminosity. The blue dots represent the data from this work; the orange dots represent the UC \ion{H}{2} regions in \citet{1994ApJS...91..659K}; the blue dash-dotted line represents the expected Lyman continuum flux of a single ZAMS star \citep{1984ApJ...283..165T}. The bolometric luminosities of the data in this work are approximated by the far-infrared luminosities in Cao21. \label{fig:nly}}
\end{figure}
\subsubsection{Radio Jets and Winds} \label{sssec:jet}
Considering the generally low radio flux densities (no more than a few milli Janskies, see Figure \ref{dist_NO_withLimit}) of the radio sources, we look into the possibility of ionized jets/winds \citep{2009A&A...501..539U}. In high-resolution observations, radio jets can be resolved into elongated or string-like structures. A typical example in our detection is source 753-r1 (Figure \ref{fig:radio}.12). However, most sources are not sufficiently resolved. Ionized jets and winds can be associated with molecular outflows and/or shock-induced water masers \citep{1995A&AS..112..299T}. A total of 32 MDCs in our sample are found to be associate with either molecular outflows or water masers (see the last column of Table \ref{tab:MDC}). Among the 34 MDCs with radio detections, 24 are associated with outflows or water masers, or both.
Statistically, an empirical relation between the radio luminosity of thermal radio jets and the bolometric luminosity of YSOs has been established by \citet{2018A&ARv..26....3A} and is valid across the entire mass regime:
\begin{eqnarray} \label{eq:anglada}
\left(\frac{S_{v} d^{2}}{\mathrm{mJy kpc}^{2}}\right)=10^{-1.90 \pm 0.07}\left(\frac{L_{b o l}}{L_{\odot}}\right)^{0.59 \pm 0.03}\ .
\end{eqnarray}
In Figure \ref{fig:radio_bol}, we plot the radio luminosity at 8.4 GHz as a function of the bolometric luminosity of the corresponding MDCs.
\begin{figure*}[ht!]
\epsscale{0.8}\plotone{plot_LrLb_corr_jet.pdf}
\caption{\label{fig:radio_bol}Radio luminosity of thermal jets at 8.4 GHz as a function of bolometric luminosity of YSO. The red inverted triangles represent the MDCs with UC \ion{H}{2} region candidates in our sample. The red crosses represent the other MDCs. All of their bolometric luminosities are approximated by the far-infrared luminosities in Cao21. The orange dots represent the UC \ion{H}{2} regions provided by \citet{1994ApJS...91..659K}; the dots in other colors represent radio jets obtained from the literature. The green star marks the highest possible radio luminosity of a jet originating from a low-mass YSO \citep{2004ApJ...612L..69S}. The blue dash-dotted line is the expected radio luminosity from a single ZAMS star, which is a theoretical upper limit of the radio luminosity caused by photoionization \citep{1984ApJ...283..165T}. The grey dashed line is the empirical correlation established by \citet{2018A&ARv..26....3A}; the red dashed line is the fitting result of our data with the UC \ion{H}{2} region candidates excluded.}
\end{figure*}
The data include our sources (red crosses and inverted triangles) as well as the UC \ion{H}{2} regions (orange dots) and radio jets (other colored dots) from the literature \citep{2008AJ....135.2370R, 2016A&A...585A..71M, 2016ApJS..227...25R, 2018A&ARv..26....3A, 2019ApJ...880...99R}. All the radio luminosities are scaled to 8.4 GHz assuming a spectral index of 0.6, which is a theoretical value for a wind \citep{1975MNRAS.170...41W}. The \citet{2018A&ARv..26....3A} relation is represented by the grey dashed line. The bolometric luminosities and radio flux densities used in this figure are the same as those used to calculate the Lyman continuum rate in Figure \ref{fig:nly}. It is clear that except the candidate UC/HC \ion{H}{2} regions (MDC 507, 725, and 742, marked by the red inverted triangles), our data well follow the radio jet trend derived by \citet{2018A&ARv..26....3A}, and a linear fit to the data yield:
\begin{eqnarray} \label{eq:our}
\left(\frac{S_{v} d^{2}}{\mathrm{mJy kpc}^{2}}\right)=10^{-1.81 \pm 0.98}\left(\frac{L_{b o l}}{L_{\odot}}\right)^{0.65 \pm 0.35},
\end{eqnarray}
a relation similar to that of \citet{2018A&ARv..26....3A}. The fitting result supports that our sources are mostly ionized jets/winds. Moreover, by comparing with a theoretical upper limit of the radio luminosity of an ionized jet originating form a low-mass YSO (see the green star in Figure \ref{fig:radio_bol}), these jets/winds are driven from intermediate- to high-mass YSOs.
\subsection{On the evolution of MDCs}\label{ssec:evolve}
Following Cao19, we classify the sample into three categories as starless, IR-quiet, and IR-bright, a supposed evolution sequence determined by the 70 $\mu$m and 24 $\mu$m fluxes. The starless (or presumably pre-stellar given very high masses) cores have no compact emissions at 70 $\mu$m, 24 $\mu$m, or protostars \citep{2014AJ....148...11K}; the IR-quiet cores exhibit 24 $\mu$m and/or 70 $\mu$m sources and their 24 $\mu$m fluxes are lower than 23 Jy, which corresponds to an 8 $M_\odot$ stellar embryo at a distance of 1.4 kpc \citep{2019ApJS..241....1C}; the IR-bright cores are MDCs with at least one 24 $\mu$m source that has fluxes exceeding 23 Jy. With strong radio continuum emission from UC \ion{H}{2} regions characterizing relatively more advanced evolution stages \citep{2002ARA&A..40...27C, 2017A&A...599A.139K}, weak radio emission from ionized jets/winds are strong indicators of ongoing star-forming activities across the pre-UC \ion{H}{2} phases.
The number of MDCs with radio detection in each category is listed in Table \ref{tab:ir}.
\begin{table}[h!]
\renewcommand{\thetable}{\arabic{table}}
\centering
\caption{Radio detections in the three types of MDCs\label{tab:ir}}
\begin{tabular}{c|c|c|c}
\tablewidth{0pt}
\hline
\hline
Type & Total & Radio Detected & Rate \\
\hline
Starless & 1 & 0 & 0\% \\
IR-quiet & 27 & 18 & 67\% \\
IR-bright & 14 & 13 & 93\% \\
\hline
\hline
\end{tabular}
\end{table}
Although there have been previous studies claiming increasing radio detection rates along with the evolutionary stages of the MDCs \citep{1994ApJS...91..659K, 1998A&A...336..339M, 2016ApJS..227...25R}, the apparent trend of the radio detections is not statistically significant in this work according to the result of the Barnard's test. However, the IR-bright MDCs have radio flux densities higher than those of the IR-quiet MDCs (Figure \ref{fig:sv_cate}).
\begin{figure}[ht!]
\epsscale{0.8}\plotone{dist_Sv_category.pdf}
\caption{Radio flux density distribution of different MDC categories at 23.2 GHz. Green, yellow, and blue histograms represent starless, IR-quiet, and IR-bright MDCs, respectively.\label{fig:sv_cate}}
\end{figure}
Starless (or pre-stellar) cores should have no radio emission because there are no star-forming activities yet. On the contrary, IR-bright cores are likely to present luminous radio continuum emission since the central young stars or protostars may have attained masses greater than 8 M$_\odot$, and thus ionizing the surroundings to form UC \ion{H}{2} regions. Among the 14 IR-bright MDCs, we have detected radio sources in 13 of them. The most luminous and extended sources are all associated with the IR-bright MDCs. For the only MDC without radio detection at 0.01 pc scale, MDC 1460 has a 0.1-pc UC \ion{H}{2} region at its center, which may prevent us from detecting radio sources at 0.01 pc scale.
As an intermediate evolution stage, we have detected radio emission in 17 of the 27 IR-quiet MDCs. We first inspect if there are any intrinsic differences between the IR-quiet MDCs with and without radio detection. Figure \ref{fig:dist_RvsQ} shows the distributions of the physical parameters between the two groups of MDCs. The inspected physical parameters are mass, column density, far-infrared luminosity, dust temperature, and luminosity-to-mass ($L_{FIR}/M_{core}$) ratio. We use the Kolmogorov-Smirnov test and Kruskal-Wallis \textsc{H}-test to test if the distributions are statistically different. As a result, the distributions of all the five parameters are statistically the same.
\begin{figure*}[ht!]
\plotone{dist_logAll.pdf}
\caption{Distributions of the physical parameters between the IR-quiet MDCs with and withoud radio detection.\label{fig:dist_RvsQ}}
\end{figure*}
To better understand the results, we inspect the radio and far-infrared environments of each IR-quiet MDC. We notice that five out of the ten IR-quiet MDCs without radio detection are located adjacent to large-scale radio sources, and their far-infrared counterparts are also affected by the large-scale structures (see Cao19). Three MDCs are associated with radio sources adjacent to the FHWM boundaries. We thus propose that, for our sample, the IR-quiet MDCs with and without radio detection are intrinsically the same; the non-detection of radio sources in some IR-quiet MDCs can be a result of the contamination from large-scale radio continuum sources and the real radio detection rate of IR-quiet MDCs are likely to be higher than what we have obtained. Comparison between the IR-quiet MDCs with and without radio sources requires a sample with clean radio backgrounds.
Finally, we briefly discuss whether radio luminosity can refine the evolution stages of the MDCs with radio detection. During the evolution of MDCs, the dominant mechanism of radio continuum emission changes from shock-ionization to photoionization \citep{2002ApJ...580..980K, 2009ApJ...699L..31S, 2016ApJ...818...52T, 2016MNRAS.460.1039P}, and the bolometric luminosity changes from accretion-dominated to radiation-dominated \citep{2018A&ARv..26....3A}. Observationally, jets/winds are direct indicators of accretion processes \citep{1996A&A...311..858B, 2013A&A...558A.125D}. We focus on the MDCs associated with candidate ionized jets/winds.
We then select three parameters to probe the evolution phases of the MDCs: the 24 $\mu$m luminosity, the 24-$\mu$m-luminosity-to-far-infrared-luminosity ($L_{24\ \mu m} / L_{FIR}$) ratio, and the $L_{FIR}/M_{core}$ ratio. The 24 $\mu$m luminosity is a strong indicator of the mass of the central YSO; the $L_{24\ \mu m} / L_{FIR}$ ratio can probe the SED of the MDC; the $L_{FIR}/M_{core}$ ratio is often adopted for a tracer of evolution stages (e.g. \citealt{2018ApJS..235....3Y}). Relations between the radio luminosity and these three parameters are shown in Figure \ref{fig:indicator}. IR-quiet and IR-bright MDCs are represented by orange and blue dots, respectively. For comparison, we also plot the MDCs associated with candidate UC \ion{H}{2} regions (blue dots centered by white crosses). MDC 753 is excluded because its 24 $\mu$m source does not associate with any radio sources in it.
The radio luminosity appears to increase with all the three probes of the evolutionary stages, as indicated by the arrows in Figure \ref{fig:indicator}. However, linear fittings to the data yield low coefficients (all less than 0.6) and large uncertainties. We then apply the Kendall's $\tau$ test to check if the general trends are statistically significant. The results ($p$-value less than 0.05) reveal that radio luminosity is positively correlated with 24 $\mu$m luminosity. All the three correlations are significant if the MDCs associated with UC \ion{H}{2} region candidates are included. This is consistent with the expectation that the MDCs harboring UC \ion{H}{2} regions are more evolved than those only associated with compact ionized jets/winds, and that the radio luminosities of UC \ion{H}{2} regions are higher than ionized jets/winds.
\begin{figure}
\epsscale{.6}\plotone{indicators.pdf}
\caption{Radio luminosity of the radio sources versus the three parameters that may probe the evolutionary stages of the MDCs. Orange and blue dots represent the IR-quiet and IR-bright MDCs, respectively. Blue dots centered with white crosses denote MDCs associated with candidate UC \ion{H}{2} regions. The arrows mark the hypothetical evolution trends. (a) Radio luminosity against 24 $\mu$m luminosity. (b) Radio luminosity against the ratio of 24 $\mu$m luminosity to far-infrared luminosity. (c) Radio luminosity against $L_{FIR}/M_{core}$ ratio.\label{fig:indicator}}
\end{figure}
Based on the above analysis, we conclude that the radio detection rate alone is insufficient to discriminate the levels of star-forming activities between the IR-quiet and IR-bright MDCs. Instead, radio luminosity is a better indicator. The relatively lower radio detection rate of IR-quiet MDCs is likely ascribed to background contamination and the limited observational sensitivity. In our sample, the detected radio sources may provide hints on the evolutionary status of the associated MDCs. During the shock-dominated phase, the radio luminosity increases along the evolution trend continuously from IR-quiet to IR-bright. At a later evolutionary phase characterized by observable UC \ion{H}{2} regions, the radio luminosity is dominated by photoionization and is on average higher than that at the shock-dominated phase.
\section{Summary} \label{sec:sum}
As the second part of the CENSUS project, we have characterized the radio continuum emission at 0.01 pc scales towards a sample of 47 MDCs with the VLA. Our results are summarized as follows:
\begin{enumerate}
\item We have detected a total of 64 radio sources, of which 37 are reported for the first time. The radio sources are mostly faint and compact, with flux densities mostly ranging from 0.1 mJy to a few mJy. The newly reported sources are even fainter, with flux densities mostly of a few tenths of milli Janskies.
\item Forty-four (69\%) radio sources are associated with dust condensations; fifty-four (84\%) are located within the FWHM of the MDCs. Twelve MDCs are observed to have multiple radio sources.
\item We have obtained the spectral indices of 8 radio sources, in which two are negative (less than $-$0.1), two are flat (between $-$0.1 and 0.2), and four are positive (higher than 0.2). By comparing our results with the literature, we notice that there can be discrepancies across different works on the same source. We suggest that cautions should be taken in fitting the SEDs of the radio sources, considering that both potential time variability of the sources and different observational settings can induce large uncertainties in the derived spectral indices.
\item We have investigated the nature of the radio sources. Only several sources can be identified as UC \ion{H}{2} region candidates. The majority of the detected radio sources are most likely to be ionized jets or winds originating from massive YSOs.
\item In our sample, the radio detection rate increases from starless to IR-quiet, and IR-bright MDCs. However, this trend is statistically insignificant. Background contaminations and limited sensitivities hamper a meaningful interpretation of the data.
\item Focusing on the MDCs all associated with candidate ionized jets/winds, the radio luminosity appears to increase with the advancing evolution phase.
\end{enumerate}
\acknowledgments
{
Y.W., K.Q., Y.C., J.L., and B.H. are supported by the National Key R\&D Program of China No. 2017YFA0402600. We acknowledge the support from the National Natural Science Foundation of China (NSFC) through grants U1731237, 11473011, 11590781, and 11629302.
Y.C. is partially supported by the Scholarship No. 201906190105 of the China Scholarship Council and the Predoctoral Program of the Smithsonian Astrophysical Observatory (SAO).
This research made use of Astropy,\footnote{http://www.astropy.org} a community-developed core Python package for Astronomy \citep{2013A&A...558A..33A, 2018AJ....156..123A}.
This research made use of APLpy, an open-source plotting package for Python \citep{2012ascl.soft08017R}.
This research made use of SciPy \citep{JonesE2001, 2020SciPy-NMeth}.
This research made use of Matplotlib \citep{4160265},.
This research made use of Numpy \citep{2011CSE....13b..22V, 2020NumPy-Array}.
This research made use of Pandas \citep{pandas_mckinney}.
This research made use of Scikit-learn \citep{scikit-learn}.
This research made use of MIRIAD \citep{1995ASPC...77..433S}.
This research made use of the Common Astronomy Software Applications package (CASA) \citep{2007ASPC..376..127M}.
This research made use of SAOImage DS9 \citep{2000ascl.soft03002S, 2003ASPC..295..489J}.
This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.
The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.
\facilities{NSF's Karl G. Jansky Very Large Array (VLA)}
\software{CASA, MIRIAD, ds9, \texttt{Astropy}, \texttt{APLpy}, \texttt{Pandas}, \texttt{SciPy}, \texttt{Matplotlib}, \texttt{Numpy}, \texttt{Scikit-learn}}
}
\section{Radio Properties of Individual MDCs} \label{sec:rprop}
\subsection*{MDC 214, 247}\label{214_274}
MDC 214 and 247 are located in the star-forming region IRAS 20286$+$4105. The condensations of the two cores linearly distribute along the inner side of a large-scale, shell-like \ion{H}{2} region. We detect a compact radio source, 247-r1, in MDC 247. It is not associated with any dust condensation and has a 5$''$.8 offset with the closest one. \citet{2005ApJ...625..864Z, 2013ApJS..208...11L, 2015MNRAS.453..645M} have reported it as an UC \ion{H}{2} region with outflow detection; \citet{2017MNRAS.465.4753R} has also reported this source and obtained a negative spectral index of -0.5$\pm$0.05, and interpreted it as a combination of synchrotron radiation and thermal free-free emission.
\subsection*{MDC 220}\label{220}
We detected no associated compact radio source in MDC 220. A large-scale shell-like radio source is found to be surrounding the dense core. Based on the infrared data provided by Cao19, the infrared counterpart of the large-scale radio emission is slightly shifted east, indicating it is polycyclic aromatic hydrocarbons(PAHs) excited by an external radiation source(s). It is unclear whether MDC 220 and the PAHs are physically related or just visually overlapped.
\subsection*{MDC 248}\label{248}
We report a newly detected radio source, 248-r1, in MDC 248. The source is bright and is associated with the central dust condensation of MDC 248. It is slightly resolved to be extended to the northwest. Limited by the resolution, it remains unclear whether the extended part of the emission is from 248-r1 or has an independent origin.
\subsection*{MDC 274}\label{274}
MDC 274 is commonly referred to as IRAS 20343+4129 \citep{2002ApJ...566..931S}. An extended radio component is located in its southwest, which belongs to an arch-like radio source \citep{1999RMxAA..35...97C, 2002ApJ...576..313K}. The relation between the MDC and the extended source remains unknown.
We detected two radio sources in MDC 274: 274-r1 and 274-r2. Radio source 274-r1 is associated with no dust condensation. It has a $\sim$3$''$ (0.02 pc) displacement with the closest condensation, which is within the typical offset between a UC \ion{H}{2} region and a millimeter core/condensation. It is slightly resolved under high resolutions (maps of projects 16A--301 and 13B--210). A flat spectral index of $-$0.11$\pm$0.09 (Figure \ref{sed:274r1}) is obtained, indicating optically thin free-free emission. This source has been reported by various works and has been identified as an UC \ion{H}{2} region with a central ionizing source equivalent to a B2 ZAMS star \citep{1994ApJS...92..173M, 2008ApJ...673..954C}. \citet{2012MNRAS.423.1691F} derived a spectral index of 0.1$\pm$0.2; \citet{2016ApJS..227...25R} obtained an index of $-$0.1$\pm$0.1. These results agree with ours within uncertainties.
Radio source 274-r2 is weak and compact and is associated with a dust condensation. \citet{2016ApJS..227...25R} built the SED with the peak intensities and obtained a positive spectral index of 0.9$\pm$0.1. The central source of 274-r2 is considered as an embedded young stellar object with the luminosity of a B3 star \citep{2008ApJ...673..954C} or a class \uppercase\expandafter{\romannumeral1} source with the bolometric luminosity $\sim$1000 L$_\odot$. A CO outflow is found to be associated with it \citep{2007A&A...474..911P}.
\citet{2012MNRAS.423.1691F} reported another radio source in MDC 274 at the position of 20$^h$36$^m$08$^s$.23, +41$^\circ$40$'$02$''$.0. However, this source is neither detected in this work nor reported by \citet{2016ApJS..227...25R}. We also notice that despite higher sensitivity, \citet{ 2012MNRAS.423.1691F} did not detect 274-r1, whose peak intensity should be above 20$\sigma$ of their map. We thus refrain from including the results of \citet{ 2012MNRAS.423.1691F} in our work.
\begin{figure*}[htpb]
\gridline{
\fig{274-r1_sed.pdf}{0.5\textwidth}{}
}
\caption{\label{sed:274r1}SED of radio source 274-r1. The solid points are points adopted for fitting. The hollow ones are excluded owing to inconsistent recoverable scales. The blue markers represent the data obtained from our PI surveys and the VLA data archive; markers with the other colors represent the data obtained from the literature. The sizes of the circles are proportional to the source sizes in arc sec$^2$ measured from each continuum map. The grey segments represent the uncertainties in flux density. The solid black line represents the fitting result. The points are in correspondence with the data in Table \ref{tab:detection}. The data used for fitting are from \citet{2016ApJS..227...25R}, project 16A--301, and 13B--210.}
\end{figure*}
\subsection*{MDC 302, 520}\label{302_520}
The condensations of MDC 302 and 520 are distribute along the edge of the UC \ion{H}{2} region G80.363 +0.449. No associated radio source of 0.01-pc scale is detected in either MDC.
\subsection*{MDC 310}\label{310}
Two radio sources, 310-r1 and 310-r2, are detected in MDC 310, both of which are associated with dust condensations. Under a very high resolution of 0$''$.04 at 44.0 GHz, radio source 310-r1 is resolved into two resembled point sources with a projected separation of 0$''$.084, corresponding to $\sim$120 AU at a distance of 1.4 kpc (map of project 14A--092). Radio source 310-r2 remains unresolved in all our maps. Meanwhile, we notice that 310-r1 is brighter than 310-r2 in the 23.2 GHz and 44.0 GHz maps (maps of project17A--107 and 14A--092). But it is undetected in the 5.8 GHz and 10 GHz maps (project 12B--140 and 16A--301) when 310-r2 can still be well detected. This implies a very steep rising SED for 310-r1. The spectral index of 310-r2 is obtained to be 0.75$\pm$0.26 (Figure \ref{sed:310r2}), indicating thermal free-free emission from a region with moderate optical depth.
\begin{figure*}[htpb]
\gridline{
\fig{310-r2_sed.pdf}{0.5\textwidth}{}
}
\caption{\label{sed:310r2}Same convention as Figure \ref{sed:274r1} for the SED of 310-r2. The data used for fitting are from project 12B--140 and 16A--301.}
\end{figure*}
\subsection*{MDC 327, 742} \label{327_742}
MDC 327 and 742 are two MDCs very close to each other. Four radio sources are detected in this region.
We detected a compact radio source, 327-r1, in the 8.5 GHz radio continuum map (project AG625). It is associated with no dust condensation and has a 1$''$.5 $\sim$0.01 pc offset from the nearest condensation. This source is also reported by \citet{2010RMxAA..46..253N}.
The infrared counterpart of MDC 742 is also known as IRAS 20178+4046. Three radio sources were detected: a cometary UC \ion{H}{2} region, 742-r2, and two compact sources, 742-r1 and 742-r3.
Radio source 742-r1 is associated with a dust condensation. It is so weak that is only detected in the maps with the highest sensitivities (project AG625 and 14A--481). This source has not been properly reported before this work. We notice that \citet{2017ApJ...836...96M} has also detected this source but confused it with VLA 4 reported by \citet{2010RMxAA..46..253N}.
The UC \ion{H}{2} region, 742-r2, presents a typical cometary morphology with its peak position coincident with an condensation. Its spectral index is $-$0.03$\pm$0.07, a typical value of UC \ion{H}{2} regions with optically thin free-free emission (Figure \ref{sed:742r2}).
Radio source 742-r3 is weak and compact. It is severely contaminated by the bright UC \ion{H}{2} region 742-r2. This source is also reported in \citet{1994ApJS...91..659K}.
\begin{figure*}[htpb]
\gridline{
\fig{742-r2_sed.pdf}{0.5\textwidth}{}
}
\caption{\label{sed:742r2}Same convention as Figure \ref{sed:274r1} for the SED of 742-r2. The data used for fitting are from project AD219, AK477, AG625, and 17A--107.}
\end{figure*}
\subsection*{MDC 340}\label{340}
MDC 340 is overlapping with an extended radio source, whose extended emission is filtered out by the interferometer and only leaves some compact clumps. A multi-band study by \citet{2017MNRAS.465.4753R} reveals that it is a commentary UC \ion{H}{2} region. At the condensation scale, we detected a compact radio source, 340-r1, associated with a dust condensation. This radio source is reported for the first time.
\subsection*{MDC 341}\label{341}
We detected a bright radio source in MDC 341. It is slightly elongated in the northwest-southeast direction and is associated with a dust condensation. This radio source is reported for the first time.
\subsection*{MDC 351}\label{351}
MDC 351 is located adjacent to a large-scale irregular radio source. One faint radio source, 351-r1, is detected to be associated with one of the dust condensations. This radio source is reported for the first time.
\subsection*{MDC 370}\label{370}
MDC 370 is located adjacent to a large-scale irregular radio source. We detected no radio source associated with the MDC at the sub-0.1 pc.
\subsection*{MDC 507, 753}\label{507, 753}
We detected three radio sources in MDC 507. Radio source 507-r1 and r2 are both compact and are associated with dust condensations. Both sources are reported for the first time. Source 507-r3 is a bright UC \ion{H}{2} region that has been reported in several works, e.g. \citet{1998A&A...336..339M, 2009A&A...501..539U}. It is not associated with any dust condensation. According to the Lyman photon rate calculated by \citet{1998A&A...336..339M}, the central ionizing source of 507-r3 is equivalent to a B3 ZAMS star.
We detected a radio source, 753-r1, to be associated with a dust condensation in adjacent to MDC 753. It is resolved to be extended towards the northeast direction. A negative spectral index of $-$0.65$\pm$0.08 is obtained (Figure \ref{sed:753r1}). Considering its jet-like morphology as well as the negative spectral index, we suggest that this radio source is a jet knot with non-thermal synchrotron radiation. It has also been reported by \citet{1998A&A...336..339M} and was identified as a possible precursor of UC \ion{H}{2} region.
\begin{figure*}[htpb]
\gridline{
\fig{753-r1_sed.pdf}{0.5\textwidth}{}
}
\caption{\label{sed:753r1}Same convention as Figure \ref{sed:274r1} for the SED of 753-r1. The data used for fitting are from project AD219 and 17A--107.}
\end{figure*}
\subsection*{MDC 509}\label{509}
We detected a total of seven radio sources associated with MDC 509. Five radio sources, 509-r1--r5, are located in the MDC and are associated with dust condensations. They are weak and are only clearly detected in the 23.2 GHz map of project 17A-107. We also notice that these radio sources are connected by weak extended emission. Source 509-r3 and r5 are reported for the first time. Two brighter radio sources, 509-r6 and r7 are detected out of the MDC and are associated with no dust condensations. In the map of project 13B--210, which has smaller MRS, most of the extended radio emission is filtered out.
\subsection*{MDC 540}\label{540}
We detected three radio sources in adjacent to MDC 540, all of which are reported for the first time. All three sources are located on the edge of the MDC. They are weak and compact. Only source 540-r3 is associated with a dust condensation.
\subsection*{MDC 608}\label{608}
MDC 608 is located near a large-scale irregular radio source. We detected no associated radio source at the sub-0.1 pc scale.
\subsection*{MDC 640, 675}\label{640_675}
MDC 640 and 675 are located closely to each other. We detected no radio source at the sub-0.1 pc scale in MDC 640.
We detected a radio source, 675-r1, in MDC 675, which is associated with a dust condensation. The radio source is resolved to be extended to the southwest. This source is reported for the first time.
\subsection*{MDC 684}\label{684}
We detected a compact radio source, 684-r1, associated with a dust condensation in MDC 684. It is weak and barely meets our detection criteria. This source is reported for the first time.
\subsection*{MDC 698, 1179}\label{698_1179}
MDC 698 and 1179 are located closely to each other. We detected a compact radio source, 698-r1, associated with a dust condensation in MDC 698. This source is reported for the first time. We detected no radio source associated with MDC 1179 at the sub-0.1 pc scale.
\subsection*{MDC 699}\label{699}
MDC 699 is located in the DR21(OH) filament. We detected an extended radio source, 699-r1, on the edge of the MDC. The radio source is associated with no dust condensation. We obtained a spectral index of 0.44$\pm$0.10, which indicates thermal free-free emission from regions with a moderate optical depth (Figure \ref{sed:699r1}). This radio source is reported for the first time.
\begin{figure*}[htpb]
\gridline{
\fig{699-r1_sed.pdf}{0.5\textwidth}{}
}
\caption{\label{sed:699r1}Same convention as Figure \ref{sed:274r1} for the SED of 699-r1. The data used for fitting are from project 14A--420\_9375, AF381, and 14B--173.}
\end{figure*}
\subsection*{MDC 714}\label{714}
The radio emission detected to be associated with MDC 714 is elongated in the northwest-southeast direction. Although visually indistinguishable, the emission can be perfectly fitted by three Gaussian components. We thus take them as three individual sources, although we do not exclude the possibility that they are one extended radio source. All three sources are associated with dust condensations and are reported for the first time.
\subsection*{MDC 723}\label{723}
We detected two weak and compact radio sources in MDC 723. Radio source 723-r1 is associated with a dust condensation; source 723-r2 is on the edge of the MDC and is associated with no dust condensation. Both radio sources are detected for the first time.
\subsection*{MDC 725}\label{725}
We detected a hierarchical radio emission system in MDC 725. At a spatial scale of 1 pc, the bright and compact radio emission associated with the MDC is connected with a faint and extended radio source in the north (see the map of project 14A--420). The extended emission has two resemblance peaks. The \textit{Spitzer} 24 $\mu$m counterpart of the extended source has been reported by Cao19, but the peak positions are not consistent with those of the radio emission.
At a scale of 0.1 pc, \textbf{two} radio source, 725-r1 and r2, are detected to be associated with the dust condensations in the MDC. In high resolution observations, radio source 725-r1 is resolved to have the typical core-halo morphology of UC \ion{H}{2} region. However, radio source 725-r2 has never been detected before and is reported for the first time. One explanation could be that its flux density has been increased in the two decades.
The SED (Figure \ref{sed:725r1}) is built from 15 datasets that covers the L, C, X Ku, K, and Q band, with angular resolutions from $\sim$0.1$''$ to $\sim$5$''$. We selected the data that can moderately resolve the source for SED fitting. The obtained spectral index is $-$0.01$\pm$0.05, a flat spectrum indicating optically thin free-free emission. Both the morphology and the spectral index support that 725-r1 is an UC \ion{H}{2} region.
The radio properties of 725-r1 have been studied by various works. It was first detected by single-dish surveys (e.g. \citealt{1970A&A.....4..378W, 1984A&AS...58..291W}), and was further observed by interferometers \citep{1994ApJS...91..659K, 2009A&A...501..539U}. OH and Class II methanol masers were detected on or close to its edge, indicating a newly formed massive star \citep{2000ApJS..129..159A, 2003A&AT...22....1M}. The radio flux density of 725-r1 was reported to be corresponding to a B0.5 star \citet{1990AJ.....99..288O}.
\begin{figure*}[htpb]
\gridline{
\fig{725-r1_sed.pdf}{0.5\textwidth}{}
}
\caption{\label{sed:725r1}Same convention as Figure \ref{sed:274r1} for the SED of 725-r1. The data used for fitting are from project AH369, AH549, AM446, AK355 (8.4 GHz and 14.9 GHz), and AC240 (8.4 GHz)}
\end{figure*}
\subsection*{MDC 798}\label{798}
MDC 798 is located adjacent to a bright $\sim$1 pc-scale champagne-like \ion{H}{2} region. The dust condensations are distributed closely along the outer rim of the radio source. A natural hypothesis is that the dust distribution of MDC 798 is affected by the ionized region, which has been reported by \citet{2005A&A...433..565D}. At the core scale, several radio clumps are observed. Although some of them have reached our criteria of source identification, considering the radio environment, they are more likely to be the compact components of the UC \ion{H}{2} region whose extended emission has been filtered out by the interferometer. One radio source, 798-r1, is confirmed to be a radio source associated with a dust condensation by its outflow signature (Yang et al., in preparation). This radio source is reported for the first time.
\subsection*{MDC 801}\label{801}
We detected a compact radio source, 801-r1, in MDC 801. It is associated with a dust condensation. This source is reported for the first time.
\subsection*{MDC 839}\label{839}
We detected a compact radio source, 839-r1, in MDC 839. It is associated with a dust condensation. This source is reported for the first time.
\subsection*{MDC 892}\label{892}
MDC 892 is located adjacent to a bright \ion{H}{2} region \citep{1980MNRAS.192..377C}. It is composed of a bright core and a weak tail extended to the east. The dust condensations of MDC 892 distribute right along the northeast leading front of the \ion{H}{2} region, suggesting that the core is possibly compressed by the expansion of the \ion{H}{2} region. No radio source is detected at the sub-0.1 pc scale.
\subsection*{MDC 1018, 1467}\label{1018_1467}
MDC 1018 and 1467 are located in the DR21(OH) filament and are close to each other. No radio source is detected in MDC 1018. Two radio sources are detected adjacent to MDC 1467, both of which are associated with the dust condensations. Radio source 1467-r1 is resolved to have a compact core and a faint irregular envelope under high resolution with moderate MRS map of project 14B--173. The dense core is further resolved to be composed of two Gaussian-like sources under even higher resolution (map of project 15A--059). \citet{2009ApJ...698.1321A} have resolved two additional weak compact sources from the envelope. The spectral index of 1467-r1 is 0.61$\pm$0.06 (Figure \ref{sed:1467r1}), indicating free-free emission from regions with moderate optical depth.Radio source 1467-r2 is weak and compact. It is only detected in the high sensitivity map (project 14B--173).
\begin{figure*}[htpb]
\gridline{
\fig{1467-r1_sed.pdf}{0.5\textwidth}{}
}
\caption{\label{sed:1467r1}Same convention as Figure \ref{sed:274r1} for the SED of 1467-r1. The data used for fitting are from project 14A--420\_9375, 14B--173\_7917, and 13A--315.}
\end{figure*}
\subsection*{MDC 1112}\label{1112}
MDC 1112 (or W75N(B)) is one of the most well-studied star-forming regions in the Cygnus X complex. It is first observed at centimeter wavelengths by \citet{1981ApJ...244...76H} and is resolved to have three bright radio continuum components by the follow-up studies (e.g. \citealt{1994A&A...284..215H, 1997ApJ...489..744T}): 1112-r1 (also know as VLA 1 or W75N(Ba)), 1112-r2 (also known as VLA 2), and 1112-r3 (also know as VLA 3 or W75N(Bb)). All of them are associated with the brightest dust condensation of MDC 1112. Another three weaker radio sources, 1112-r4, 1112-r5 (together known as W75N(Bc)), and 1112-r6 (also known as VLA 4), are detected by later high-sensitivity observations (e.g. \citealt{2001ApJ...546..345S, 2010AJ....139.2433C}). None of them are associated with dust condensations.
The nature of the radio sources has been long under debate. \citet{1997ApJ...489..744T} considered that 1112-r1 was a thermal biconical jet and 1112-r2 and r3 were both UC \ion{H}{2} regions. This conclusion was questioned by \citet{2001ApJ...546..345S} and \citet{2010AJ....139.2433C}, who claimed that 1112-r1 was insufficient to power the large-scale outflow \citep{1994A&A...284..215H} and the main powering source should be 1112-r3. The most recent works by \citet{2010AJ....139.2433C, 2015Sci...348..114C} and \citet{2020MNRAS.496.3128R} concluded that 1112-r1 was an UC \ion{H}{2} region, 1112-r2 a thermal, ionized wind, and 1112-r3 a thermal jet. They also concluded that 1112-r4, r5, and r6 were all Herbig-Haro (HH) objects with r4 and r5 together as a bright radio HH object and r6 as an obscured one.
The spectral indices of the radio sources in MDC 1112 have been provided by several works. However, these results show great inconsistencies that some may even suggest different physical mechanisms. We suggest that the inconsistencies are mainly caused by two reasons. Firstly, the radio sources are highly time-variable \citep{2010AJ....139.2433C, 2015Sci...348..114C}. The SEDs should be fitted with data obtained from the same epoch, e.g. less than five years (inferred from Figure 2 in \citealt{2010AJ....139.2433C}). Among our references, only \citet{1997ApJ...489..744T} and \citet{2015Sci...348..114C} meet this requirement. Secondly, since the sources are resolvable with moderate resolutions, it is essential to fit the SEDs with data sensitive to similar spatial scales (see Section \ref{ssec: idx}). We are not able to check the $uv$ coverages of the literature data, whereas it is possible that the data are sensitive to different spatial scales implied by the highly inconsistent beam sizes.
\clearpage
\startlongtable
\begin{deluxetable}{c|c|c}
\tablecaption{Spectral indices of the radio sources in 1112 \label{tab:1112}
}
\tablehead{
\colhead{Source} & \colhead{Spec. Idx.} & \colhead{Reference}
}
\startdata
1112-r1 & 0.7$\pm$0.1 & \citet{1997ApJ...489..744T} \\
& 0.2$\pm$0.3 & \citet{2004ApJ...601..952S} \\
& $-$1.60 & \citet{2007MNRAS.380..246G} \\
& $-$0.4$\pm$0.1 & \citet{2010AJ....139.2433C} \\
\hline
1112-r2 & $\geqslant$ 1.0 & \citet{1997ApJ...489..744T} \\
& 0.4$\pm$0.1 & \citet{2004ApJ...601..952S} \\
& 2.2$\pm$0.3 & \citet{2010AJ....139.2433C} \\
& \textbf{0.61} & \citet{2015Sci...348..114C} \\
\hline
1112-r3 & 1.5$\pm$0.1 & \citet{1997ApJ...489..744T} \\
& 0.5$\pm$0.3 & \citet{2004ApJ...601..952S} \\
& 0.79$\pm$0.15 & \citet{2007MNRAS.380..246G} \\
& 0.6$\pm$0.1 & \citet{2010AJ....139.2433C} \\
\hline
1112-r4,5 & $-$0.3$\pm$0.6 & \citet{2004ApJ...601..952S} \\
& $-$0.34 & \citet{2007MNRAS.380..246G} \\
& $-$0.2$\pm$0.2 & \citet{2010AJ....139.2433C} \\
\hline
1112-r6 & 0.4$\pm$0.5 & \citet{2010AJ....139.2433C} \\
\enddata
\end{deluxetable}
\subsection*{MDC 1201}\label{1201}
MDC 1201 is located in the S106 region. S106 is one of the best-studied bipolar \ion{H}{2} regions at a distance of 1.3 kpc \citep{2018A&A...617A..45S}. As part of the Cygnus X rift, it is believed to be physically connected with the Cygnus X complex \citep{1982ApJ...255...95S, 2007A&A...474..873S}. The most prominent radio emission in this region is a bright and compact source, 1201-r1, whose infrared counterpart is S106 IR. It has been interpreted as an extremely powerful source that powers the large-scale bipolar \ion{H}{2} outflow \citep{1983ApJ...272..154B, 1999ApJ...525..821F, 2007MNRAS.380..246G}. The radio source remains unresolved at all resolutions. We construct the SED of this source and derive a spectral index of 0.73$\pm$0.11 (Figure \ref{sed:1201r1}). It is comparable to those of \citet{1983ApJ...272..154B} (0.73) and \citet{2007MNRAS.380..246G} (0.65$\pm$0.11).
\begin{figure*}[htpb]
\gridline{
\fig{1201-r1_sed.pdf}{0.5\textwidth}{}
}
\caption{\label{sed:1201r1}Same convention as Figure \ref{sed:274r1} for the SED of 1201-r1. The data used for fitting are from project AF362 and AR537.}
\end{figure*}
\subsection*{MDC 1225}\label{1225}
We detected two radio sources in MDC 1225, each of which are associated with a dust condensation and are reported for the first time. In the 24.4 GHz map observed in 2013 (project 13A--372), both radio sources are detected and are connected by extended emission, whereas 1225-r1 is not detected in the 23.2 GHz map observed in 2017 (project 17A--107) owing to a higher RMS noise. Both radio maps are at K band with similar resolutions. We notice that radio source 1225-r2 has a dramatic increase in flux density from 0.1 mJy to 0.4 mJy in merely four years (2013--2017), which means an average increase rate of $\sim$40\% per year. It also shows a change in morphology from compact to elongated. Since 1225-r2 should be at an early evolution stage, which has low radio luminosity, no emission at 8 $\mu$m, and weak emission at 24 $\mu$m, we consider it as an ionized jet. The time variability of thermal radio jets has been observationally confirmed by various studies (see \citet{2018A&ARv..26....3A} and the references therein), most of which are no more than 20\% but some extreme cases can have flux density doubled in two years \citep{2012A&A...537A.123R}. Our data are not yet enough to reveal the mechanism of the time variation. According to the previous studies, high time variability ($>$20\%) can be caused by the periastron passage in a close binary system \citep{2018A&ARv..26....3A} or more commonly, the ejection of bright radio knots \citep{2010ApJ...712.1403P, 2012A&A...537A.123R}.
\subsection*{MDC 1243, 1599, 5417}\label{1243_1599_5417}
The three MDCs are linearly distributed in the DR21(OH) filament. We detected no radio source in MDC 1599 and one radio source in each of MDC 1243 and 5417. Both radio sources are compact and associated with the dust condensations. They are reported for the first time.
\subsection*{MDC 1267, 3188}\label{1267_3188}
MDC 1267 and 3188 are located closely to each other. MDC 1267 is associated with two radio sources: source 1267-r1 is compact and is associated with a dust condensation; source 1267-r2 is located out of the MDC. MDC 3188 has one radio source, 3188-r1. All the radio sources are reported for the first time.
\subsection*{MDC 1454, 2210}\label{1454_2210}
MDC 1454 and 2210 are located in DR15, one of the most prominent star-forming regions in the southern Cygnus X complex. We detected five compact radio sources in MDC 1454, in which 1454-r1, r2, and r3 are associated with dust condensations. All the radio sources are reported for the first time.
We detected a weak and extended radio source, 2210-r1, in MDC 2210. It is associated with a dust condensation. This source is reported for the first time.
\subsection*{MDC 1460}\label{1460}
We detected no radio emission at the sub-0.1 pc scale associated with MDC 1460. At a larger scale, the dust condensations are distributed on the outer rim of its central UC \ion{H}{2} region, G080.634+00.684. A hypothesis is that the expanding UC \ion{H}{2} region compresses the ambient material.
\subsection*{MDC 1528}\label{1528}
MDC 1528, also known as DR21, is a very bright and well-studied high-mass star-forming region. We detected no radio emission at the sub-0.1 pc scale. At larger scale, a bright extended radio source was detected on the north of the MDC. The large-scale radio source shows a very complex structure. Its major components are two patches of cometary emission: a small one in the north and a larger one in the south. Two weak and long ``tails'' extend to the east. The nature and origin of the radio emission have been studied by various works. \citet{2003ApJ...596..344C} suggested that they are two cometary UC \ion{H}{2} regions produced by wind-blowing stars moving through the molecular cloud; \citet{2013ApJ...765L..29Z} raised the hypothesis that they are the products of an explosive event related to the disintegration of a massive stellar system.
\subsection*{MDC 4797}\label{4797}
MDC 4797 is surrounded by a bright large-scale shell-like \ion{H}{2} region, whose infrared counterpart has been reported by Cao19. A compact source, 4797-r1, is marginally detected. This source is reported for the first time.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 799
|
title: "ArgData API: Setup Class"
---
[API Reference](/argdata/api/) > [0.19.1](/argdata/api/0.19.1/) > Setup
# Setup Class
Single car setup.
**Namespace:** ArgData.Entities
## Constructors
<table class="table table-bordered table-striped ">
<thead>
<tr>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td>Setup()</td>
<td>Initializes a new instance of Setup.</td>
</tr>
</tbody>
</table>
## Properties
<table class="table table-bordered table-striped ">
<thead>
<tr>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td>BrakeBalance</td>
<td>Gets or sets the brake balance value. Allowed values between -32 (Rear) and 32 (Front).</td>
</tr>
<tr>
<td>FrontWing</td>
<td>Gets or sets the front wing setting. Allowed values between 0 and 64.</td>
</tr>
<tr>
<td>GearRatio1</td>
<td>Gets or sets the ratio of the first gear. Must be 16 or greater, and less than GearRatio2.</td>
</tr>
<tr>
<td>GearRatio2</td>
<td>Gets or sets the ratio of the second gear. Must be greater than GearRatio1 and less than GearRatio3.</td>
</tr>
<tr>
<td>GearRatio3</td>
<td>Gets or sets the ratio of the third gear. Must be greater than GearRatio2 and less than GearRatio4.</td>
</tr>
<tr>
<td>GearRatio4</td>
<td>Gets or sets the ratio of the fourth gear. Must be greater than GearRatio3 and less than GearRatio5.</td>
</tr>
<tr>
<td>GearRatio5</td>
<td>Gets or sets the ratio of the fifth gear. Must be greater than GearRatio4 and less than GearRatio6.</td>
</tr>
<tr>
<td>GearRatio6</td>
<td>Gets or sets the ratio of the sixth gear. Must be greater than GearRatio5 and less than or equal to 80.</td>
</tr>
<tr>
<td>IsValid</td>
<td>Whether the values currently entered in the setup are within allowed ranges.</td>
</tr>
<tr>
<td>RearWing</td>
<td>Gets or sets the rear wing setting. Allowed values between 0 and 64.</td>
</tr>
<tr>
<td>TyreCompound</td>
<td>Gets or sets the tyre compound.</td>
</tr>
</tbody>
</table>
## Methods
<table class="table table-bordered table-striped ">
<thead>
<tr>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td>Copy(Setup <em>source</em>)</td>
<td>Copies all setup values from the source into this Setup.<br /><em>source</em>: <br /></td>
</tr>
</tbody>
</table>
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 9,677
|
<?php
function scanForReleases($releaseFolder, $exclude = []) {
$releases = array_filter(scandir($releaseFolder), function ($fileName) use ($releaseFolder, $exclude) {
return is_link("{$releaseFolder}/{$fileName}") && !in_array($fileName, ['.', '..']) && !in_array($fileName, $exclude);
});
usort($releases, 'version_compare');
return array_reverse($releases);
}
?>
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,773
|
The surface of Brazil measures 8,515,767 square kilometers, or 16 times the France!
Brazil has 196.7 million inhabitants.
Two airports provide easy access to Rio. The Antônio Carlos Jobim International Airport (Galeão), located 20 km from the center and receives flights from major cities in Brazil and the world. The taxis provide transfers for about 30 USD. And the Santos Dumont Airport, located in Guanabara Bay and near the center, which only works for domestic flights. The view from the window is breathtaking! There are 32 km from the airport of Salvador de Bahia and the city center. A taxi costs about 30 USD. In both cases, the airport shuttles serve the city centers for a fee of about 15 USD.
No vaccination required. However, the vaccine against yellow fever is recommended in case of trip in the north. For the Amazon, also think about anti-malaria treatment, and medication against malaria. Throughout the territory, avoid drinking tap water. Do not forget to bring sunblock and mosquito repellent.
Avoid taking too much money, jewelry, or any object of value when you stroll in the city. In Brazil, urban insecurity remains a problem but it should not too much exaggerate. The government has made many efforts, including at Copacabana Beach in Rio or in the Pelourinho in Salvador. In these touristic areas, the police are very present.
The language is Portuguese. The population of major cities speak English, and Brazilians in general understand Spanish.
PROCEDURES & VISAS
Any traveler must be provided with a return ticket or exit of the Brazilian territory. However, the French are exempt from visa for any stay less than 90 days.
Catholicism is the official and dominant religion in the country, with 80% of believers. Brazilians also practice Candomblé and Umbanda, cults of African origin.
The electric current is 220V.
TAXES AND TIPS
In most bars and restaurants, tips are included in the bill but it is customary to give a little more if you are satisfied with the service. If it is not included, you have to add 10% to 15%. It's better to give something to the guides and porters.
The currency is the Brazilian real (BRL). You can change your money in banks which are generally open from Monday to Friday from 10 am to 16h (these hours vary according to the state). You can also go to a currency exchange or a travel agency. Otherwise, there are counters at airports and in the center of large cities. Many hotels, restaurants and shops accept payment by credit cards. American Express, Diners Club, MasterCard and Visa are the most frequent to withdraw money in banks that also endorse travelers checks. However, the rate is rarely beneficial.
CIRCULATE ON SITE
Given the size of the country, the plane is the most recommended means of all transports. Daily airline services connect the state capitals and major cities. The bus is commonly used, also fast and economical, it is suitable for short distances. Transport networks quadrille the country (think about travelling at night). The car, on the other hand, reveals inaccessible places. It is better to have an international license to rent a car, even if it's not an obligation. The roads are well maintained but highways and expressways are proving scarce, and gas stations in some areas. In every major city, there are national and international car rental agencies. If you opt for the car: be very careful on the road because of the lawless conduct of Brazilians. Among others, remember that during the night in town, Brazilians do not stop at red lights. In the center of Rio, forget the car and take taxis crisscrossing the city. They are plentiful and cheap, but be careful anyway. Opt for the subway: faster and easier, also the safest place for tourists. Otherwise, walking is another option: a stroll in a typical old tram traversing the steep cobbled streets of the Santa Teresa neighborhood in Rio. You can also opt for an overview of the city by helicopter which is an unforgettable experience! Since 2011, Rio has the longest aerial tramway in the world: a unique experience in an urban telecabine, 3416 meters of length connecting the downtown to the northern suburbs of Rio, 17 minutes. In Salvador, it is easy to move about thanks to lifts and cable cars that can move from one neighborhood to another. In Sao Paulo, traffic is one of the densest in the world with 6 million of cars! It goes without saying that traffic jams are huge! Thus, the richer people move squarely by helicopter!
Avenida Franklin Roosevelt, 126, Sala 701/702
ZIP CODE: 20021-120 Rio de Janeiro RJ BRAZIL.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 971
|
Ru Zhijuan (), née le , morte le , est une écrivaine chinoise.
Biographie
Ru Zhijuan, la plus jeune de 5 enfants d'une famille très modeste, naît en 1925 à Shanghai de migrants de Hangzhou. Lorsqu'elle a 3 ans, sa mère meurt et son père quitte la famille. Elle et un de ses frères sont élevés par leur grand-mère. Elle ne commence l'école primaire qu'à 10 ans, et un an plus tard, elle déménage à Hangzhou avec sa grand-mère, qui meurt peu après. Elle est envoyée dans un orphelinat à Shanghai. Après un an dans une école professionnelle pour femmes, un internat missionnaire chrétien pour filles et une école de comté, elle termine ses études secondaires avec seulement quatre ans de scolarité, mais reste passionnée par l'écrit. En , à l'âge de 18 ans, elle publie dans une revue une première nouvelle, qu'elle intitule 生活 [ Une Vie ]. Elle s'engage peu de temps après, avant même la publication, dans la Nouvelle Quatrième armée chinoise. Dans ses activités militaires, elle intervient aussi dans une troupe de théâtre, et est chargée d'écrire des chants, des poèmes et des ballades patriotiques.
En 1944, elle épouse Wang Xiaoping, né à Singapour mais arrivé en Chine pour combattre les Japonais. En 1947, elle rejoint le Parti communiste chinois. En 1955, elle devient rédactrice en chef d'un magazine littéraire et artistique, le mensuel 文艺月报 et prend sa retraite en 1960 pour se consacrer à l'écriture à temps plein.
Elle publie essentiellement des nouvelles. Une de ses nouvelles, publiée en 1958, 百合花, [Fleur de Lys] est critiquée par certains pour sa « sentimentalité bourgeoise ». La qualité de l'analyse psychologique et la fraîcheur du texte contrastent en effet avec les habitudes de l'époque, et avec une littérature qui se met essentiellement au service de la politique. Mais l'œuvre est louée par le ministre de la Culture et auteur Mao Dun, et devient populaire. Pour autant, beaucoup de ses publications de cette période ont pour arrière-plan la guerre et la reconstruction, et ont le bon goût de montrer le soutien de la population à la révolution et au parti communiste : elles s'inscrivent, d'une certaine façon, dans les normes proposées par Mao Zedong aux écrivains (le « Discours de Yan'an sur la Littérature et l'Art » prononcé par Mao en 1942 uniformisant les styles et les thèmes). Une nostalgie de la qualité des relations humaines connues par l'auteure pendant les années de guerre perce également à travers ses écrits. Elle s'intéresse aussi à l'évolution de la société chinoise par rapport aux valeurs traditionnelles. Elle est considérée de fait comme une des auteures les plus importantes de l'après-guerre. Elle ne publie plus d'ouvrages pendant la Révolution culturelle, car on estimait à l'époque que son travail traitait des préoccupations des gens ordinaires, mais pas assez de questions politiques plus importantes.
Elle regagne quelques faveurs lorsque la Révolution culturelle est reconsidérée. En occident, elle est étiquetée comme ayant été une opposante à la bande des Quatre.
Elle devient secrétaire du parti pour la Shanghai Writer's Association. À partir de 1977, ses écrits adoptent un ton plus piquant. Elle mène aussi une réflexion sur la condition féminine, et elle le fait avec émotion. Elle consacre pratiquement les dix dernières années de sa vie à une œuvre autobiographique, 她从那条路上来 [Le chemin d'où je viens], qui est publiée quelques mois après sa mort et présentée par sa fille devenue également une écrivaine bien connue, Wang Anyi. Elle meurt à Shanghai en 1998, à l'âge de 73 ans.
Références
Liens externes
Femme de lettres chinoise
Naissance en octobre 1925
Naissance à Shanghai
Décès en octobre 1998
Décès à Shanghai
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,489
|
{"url":"https:\/\/campus.datacamp.com\/courses\/feature-engineering-for-machine-learning-in-python\/conforming-to-statistical-assumptions?ex=9","text":"# When can you use normalization?\n\nWhen could you use normalization (MinMaxScaler) when working with a dataset?","date":"2019-08-26 08:04:37","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\": 0.8635938167572021, \"perplexity\": 4858.062721531916}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-35\/segments\/1566027331228.13\/warc\/CC-MAIN-20190826064622-20190826090622-00127.warc.gz\"}"}
| null | null |
Yesterday, Paul Domowitch of The Daily News hosted an Eagles chat on Philly.com. He was apparently bored out of his mind, because he answered a ton of my clown questions.
I mean Asante's decent looking I guess…huh?
Yes you did! Here's the proof!
I can make two if I have to and haha, Zach.
Which means that they won't. Head for the ark!
My favorite is Nhamdhi Assumewah.
So she's advanced! I knew it!
This entry was posted in The Eagles and tagged Asante Samuel, child prodigy, clown questions, Eagles, effigy, misspellings, pet eagle, screw job, Shady. Bookmark the permalink.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 2,484
|
{"url":"http:\/\/nag.com\/numeric\/cl\/nagdoc_cl23\/html\/C05\/c05ayc.html","text":"c05 Chapter Contents\nc05 Chapter Introduction\nNAG C Library Manual\n\n# NAG Library Function Documentnag_zero_cont_func_brent\u00a0(c05ayc)\n\n## 1\u00a0\u00a0Purpose\n\nnag_zero_cont_func_brent\u00a0(c05ayc) locates a simple zero of a continuous function in a given interval using Brent's method, which is a combination of nonlinear interpolation, linear extrapolation and bisection.\n\n## 2\u00a0\u00a0Specification\n\n #include #include\nvoid\u00a0 nag_zero_cont_func_brent\u00a0(double\u00a0a, double\u00a0b, double\u00a0eps, double\u00a0eta,\n double (*f)(double\u00a0x, Nag_Comm\u00a0*comm),\ndouble\u00a0*x, Nag_Comm\u00a0*comm, NagError\u00a0*fail)\n\n## 3\u00a0\u00a0Description\n\nnag_zero_cont_func_brent\u00a0(c05ayc) attempts to obtain an approximation to a simple zero of the function $f\\left(x\\right)$\u00a0given an initial interval $\\left[a,b\\right]$\u00a0such that $f\\left(a\\right)\u00d7f\\left(b\\right)\\le 0$.\nThe approximation $x$\u00a0to the zero $\\alpha$\u00a0is determined so that at least one of the following criteria is satisfied:\n (i) $\\left|x-\\alpha \\right|\\le {\\mathbf{eps}}$, (ii) $\\left|f\\left(x\\right)\\right|\\le {\\mathbf{eta}}$.\n\n## 4\u00a0\u00a0References\n\nBrent R P (1973) Algorithms for Minimization Without Derivatives Prentice\u2013Hall\n\n## 5\u00a0\u00a0Arguments\n\nOn entry: $a$, the lower bound of the interval.\n2: \u00a0\u00a0\u2002 bdoubleInput\nOn entry: $b$, the upper bound of the interval.\nConstraint: ${\\mathbf{b}}\\ne {\\mathbf{a}}$.\n3: \u00a0\u00a0\u2002 epsdoubleInput\nOn entry: the termination tolerance on $x$\u00a0(see Section 3).\nConstraint: ${\\mathbf{eps}}>0.0$.\nOn entry: a value such that if $\\left|f\\left(x\\right)\\right|\\le {\\mathbf{eta}}$, $x$\u00a0is accepted as the zero. eta may be specified as $0.0$\u00a0(see Section 7).\n5: \u00a0\u00a0\u2002 ffunction, supplied by the userExternal Function\nf must evaluate the function $f$\u00a0whose zero is to be determined.\nThe specification of f is:\n double f\u00a0(double\u00a0x, Nag_Comm\u00a0*comm)\n1: \u00a0\u00a0\u2002 xdoubleInput\nOn entry: the point at which the function must be evaluated.\n2: \u00a0\u00a0\u2002 commNag_Comm\u00a0*\nPointer to structure of type Nag_Comm; the following members are relevant to f.\nuserdouble\u00a0*\niuserInteger\u00a0*\npPointer\nThe type Pointer will be void *. Before calling nag_zero_cont_func_brent\u00a0(c05ayc) you may allocate memory and initialize these pointers with various quantities for use by f when called from nag_zero_cont_func_brent\u00a0(c05ayc) (see Section 3.2.1 in the Essential Introduction).\n6: \u00a0\u00a0\u2002 xdouble\u00a0*Output\nOn exit: if NE_NOERROR or NE_TOO_SMALL, x is the final approximation to the zero. If NE_PROBABLE_POLE, x is likely to be a pole of $f\\left(x\\right)$. Otherwise, x contains no useful information.\n7: \u00a0\u00a0\u2002 commNag_Comm\u00a0*Communication Structure\nThe NAG communication argument (see Section 3.2.1.1 in the Essential Introduction).\n8: \u00a0\u00a0\u2002 failNagError\u00a0*Input\/Output\nThe NAG error argument (see Section 3.6 in the Essential Introduction).\n\n## 6\u00a0\u00a0Error Indicators and Warnings\n\nOn entry, argument $\u2329\\mathit{\\text{value}}\u232a$\u00a0had an illegal value.\nNE_FUNC_END_VAL\nOn entry, ${\\mathbf{f}}\\left({\\mathbf{a}}\\right)$\u00a0and ${\\mathbf{f}}\\left({\\mathbf{b}}\\right)$\u00a0have the same sign with neither equalling $0.0$: ${\\mathbf{f}}\\left({\\mathbf{a}}\\right)=\u2329\\mathit{\\text{value}}\u232a$\u00a0and ${\\mathbf{f}}\\left({\\mathbf{b}}\\right)=\u2329\\mathit{\\text{value}}\u232a$.\nNE_INTERNAL_ERROR\nAn internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.\nNE_PROBABLE_POLE\nThe function values in the interval $\\left[{\\mathbf{a}},{\\mathbf{b}}\\right]$\u00a0might contain a pole rather than a zero. Reducing eps may help in distinguishing between a pole and a zero.\nNE_REAL\nOn entry, ${\\mathbf{eps}}=\u2329\\mathit{\\text{value}}\u232a$.\nConstraint: ${\\mathbf{eps}}>0.0$.\nNE_REAL_2\nOn entry, ${\\mathbf{a}}=\u2329\\mathit{\\text{value}}\u232a$\u00a0and ${\\mathbf{b}}=\u2329\\mathit{\\text{value}}\u232a$.\nConstraint: ${\\mathbf{a}}\\ne {\\mathbf{b}}$.\nNE_TOO_SMALL\nNo further improvement in the solution is possible. eps is too small: ${\\mathbf{eps}}=\u2329\\mathit{\\text{value}}\u232a$.\n\n## 7\u00a0\u00a0Accuracy\n\nThe levels of accuracy depend on the values of eps and eta. If full machine accuracy is required, they may be set very small, resulting in an exit with NE_TOO_SMALL, although this may involve many more iterations than a lesser accuracy. You are recommended to set ${\\mathbf{eta}}=0.0$\u00a0and to use eps to control the accuracy, unless you have considerable knowledge of the size of $f\\left(x\\right)$\u00a0for values of $x$\u00a0near the zero.\n\nThe time taken by nag_zero_cont_func_brent\u00a0(c05ayc) depends primarily on the time spent evaluating f (see Section 5).\n\n## 9\u00a0\u00a0Example\n\nThis example calculates an approximation to the zero of ${e}^{-x}-x$\u00a0within the interval $\\left[0,1\\right]$\u00a0using a tolerance of ${\\mathbf{eps}}=\\text{1.0e\u22125}$.\n\n### 9.1\u00a0\u00a0Program Text\n\nProgram\u00a0Text (c05ayce.c)\n\nNone.\n\n### 9.3\u00a0\u00a0Program Results\n\nProgram\u00a0Results (c05ayce.r)","date":"2016-09-29 19:22:21","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 36, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9986594319343567, \"perplexity\": 2625.249198010466}, \"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-2016-40\/segments\/1474738661910.62\/warc\/CC-MAIN-20160924173741-00044-ip-10-143-35-109.ec2.internal.warc.gz\"}"}
| null | null |
Keep your rod and gear safe when you travel with this case which features rigid sides and padded interior. Removable dividers allow you to adjust the case to suit your needs. Remove all of the dividers to create a single large space for multiple rods. Or, use them all to provided padded protection for your reels, fly boxes and other gear. 3 interior and 3 exterior zippered pockets provide additional storage for lines, leader, tippet, etc. Made to fit 9' 4pc rod tubes.
Dimensions: 31" x 9" x 5"
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 9,334
|
Название Митровица может относиться к следующим населённым пунктам:
Косовска-Митровица (также бывш. Титова-Митровица) — город в Сербии, на севере автономного края Косово и Метохии, являющегося частично признанным государством Республикой Косово.
Сремска-Митровица — город в Сербии, в округе Срем автономного края Воеводины.
Мачванска-Митровица — город в Сербии, в округе Мачва.
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 5,418
|
\section{Introduction}
\IEEEPARstart{I}{n} metaverse the digital and physical worlds are converging by utilizing mobile augmented/virtual reality technologies, edge computing, increased data rate support in 5G and beyond networks, digital twin and the proliferation of high end devices such as head-mounted displays \cite{xu2021wireless}\cite{dong2019deep}.
Users equipped with mobile augmented reality (MAR) devices can upload and analyze their environment through augmented reality customization to achieve appropriate augmented reality objects (AROs) and access the metaverse utilizing 5G mobile edge caching/computing enabled networks \cite{xu2022full}. In this emerging ecosystem, rendering 3-dimentional (3D) AROs with the background virtual environment and updating it in the metaverse is demanding in terms of energy consumption as well as in terms of caching and computing resources \cite{xu2022full}\cite{li2020rendering}. Hence, in addition to the fact that such applications require low latency they are also energy sensitive and face challenges in ensuring user quality of experience and providing reliable interactions within the metaverse \cite{xu2021wireless}\cite{xu2022full}.
Generally speaking, a metaverse scene will in essence consisted by a background view as well as many objects in foreground interactions. The background view at a defined amalgamated virtual and physical location can be deemed as static or slowly changing \cite{xu2022full}\cite{guo2020adaptive}. A nominal background scene is the 3D model of the metaverse, a presentation of a related background virtual environment based on a certain user viewport \cite{guo2020adaptive}\cite{kato2021split}. Even though this background does not change frequently its size can reach tens of megabytes and the corresponding complexity of rendering related functionalities measured by computation load is also significant (e.g., 10 CPU cycles/bit) \cite{guo2020adaptive}\cite{yang2018communication}. On the other hand, objects related to foreground interactions (such as for example user avatars) that are embedded in the metaverse scene change much more frequently. However, those are significantly less complex than the background scene (e.g., 4 CPU cycles/bit) \cite{li2020rendering}\cite{guo2020adaptive}. But, even though those objects are less complex their frequent changes require rendering them in a timely manner so that to avoid a considerable quality of experience degradation. Thus, in this paper, rendering for both foreground and background are deployed at at edge clouds (ECs) rather than only at terminals to make a full use of advanced caching and computing resources. Noticing that uploaded information are focused in foreground interactions while background content checking consumes not only computing resources but also lots of local cache to match and integrate AROs and related models of metaverse. The metaverse application could also be decomposed into computational and storage intensive functions which serve as a chain for better assignment and resource allocation \cite{huang2021proactive}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.75\linewidth]{workflow.jpg}
\caption{The general work flow of a metaverse AR application.
}
\label{fig:workflow}
\end{figure}
The general work flow of a metaverse AR application supported by ECs is shown in Fig. \eqref{fig:workflow}. After triggered by certain behavior with foreground interactions \cite{zhang2021multi}, background contents like for example pre-cached 3D models and AROs are searched in the EC cache. If not found, the request is redirected to the metaverse region stored in a cloud deeper in the network. Finally, according to user's physical mobility and virtual orientation extracted from foreground interactions, the matched AROs and model are integrated into the frames and streamed to the user \cite{xu2022full}\cite{guo2020adaptive}. At the same time, updated information is sent to the metaverse region for synchronization so that the user could be aware of changes caused by other participants if they share the same metaverse region. Hereafter, we assume a nominal frame rate as 15 frames/second and the rendering happens at every other frame (\~ 133.2ms interval) \cite{cozzolino2022nimbus}\cite{niu2018learning}.
\begin{figure}
\centering
\includegraphics[width=0.75\linewidth]{toy.jpg}
\caption{Illustrative toy example. Case (a) mobility is not considered and (b) physical mobility of the end user and metaverse service decomposition are considered with different renderings on pro-active resource allocation.}
\label{fig: toyMetaAR}
\end{figure}
Fig. \eqref{fig: toyMetaAR} further reveals the difference between cases that consider the user mobility with service decomposition or not related to rendering requirements in the metaverse application. Clearly, when neglecting user mobility and service decomposition as shown by case (a), models, target AROs and metaverse functions are all cached close to the user's initial location.
However, when user mobility and service decomposition is enabled, as shown in case (b), then service delivery becomes more flexible and efficient in terms of assigning requests and allocating network resources. Observe that in case (a), although user A is only one (wireless) hop away from the supporting EC, it requires 3 hops (one wireless and two wireline in the access network) after the mobility event. However, when mobility and EC resources are taken into consideration, the same user A in case (b) could enjoy a better maximum delay by facing 2 hops regardless of changing the point of attachment. Hence, in a high mobility scenario, it might not always be ideal to allocate requests and services as close as possible to the user's initial location. The AR contents in the model might be similar in terms of the viewport of different users. Hence, participating users should be aware of each other's updates and could share rendering functions to save on consumed resources. In this paper, we apply Structural Similarity (SSIM) proposed by \cite{wang2004image} for user perception experience. It is a widely accepted method that measures user perception quality of a image by comparing to its original version \cite{wang2004image}. Caching more models and AROs also causes more processing and transmission delay with energy consumption \cite{xu2021wireless}\cite{xu2022full}. Hence, the the joint optimization has to accept some potential loss due to constraints of computing and storage resources. In this paper, by considering explicitly the user mobility, service decomposition and models of metaverse regions with embedded AROs, the proposed optimization framework seeks a balance between user perception quality, power consumption and service delay.
\section{System Model}
With the set $\mathbb{M}=\{1,2,...,M\}$ we express the available Edge Clouds (ECs) in the wireless network. With $r \in \mathbb{R}$, we denote the corresponding MAR service requests in the metaverse region that are generated by mobile users that are equipped with MAR devices (each user makes a single request). The starting location of the request $r$ is the access router where this user is initially connected to; this initial location is defined as $f(r)$. A user moves to a destination $k\in \mathbb{K}$ in the case of a mobility event (i.e., changing the point of attachment). In this paper, and without loss of generality, only adjacent access routers can be regarded as allowable destinations in the mobility event. A series of metaverse regions are set on ECs to interact with users. The corresponding metaverse region serving the user can be found through functions $A(f(r)), A(k)$. As explained earlier, each metaverse region is pre-deployed on an server close to the mobile network and its distance to an EC is also predefined. In this paper, As already mentioned in previous sections, a set of AROs is assumed to be embedded across the different non real time view streams. To this end, we first define a set $\mathbb{N}=\{1,2,...,N\}$ to represent the set of available AROs. The model available to each user has multiple rendering and we define them as a set $\mathbb{S}_r=\{1,2,...,S\}$. Then, the decision variable for proactively caching a model $s$ at the EC $j\in \mathbb{M}$ is denoted as $p_{sj}$. The subset $\mathbb{L}_{rs}$ represents the target AROs required by the user $r$ in related model $s\in \mathbb{S}_r$ and the size of each target ARO $l\in \mathbb{L}_{rs}$ is denoted as $O_l$. Finally, the decision variable for proactively caching an ARO required by a request $r$ is denoted as $h^s_{rl}$. More specifically, $p_{sj}$ and $h^s_{rl}$ can be written as follows,
\begin{equation}
p^{j}=\left\{
\begin{aligned}
1,&\;\text{if rendering the related model}\;s\;\text{at node}\;j, \\
0,&\;\text{otherwise}.
\end{aligned}
\right.
\end{equation}
\begin{equation}
h^s_{rl}=\left\{
\begin{aligned}
1,&\;\text{if ARO}\;l\;\text{required by request}\; r\;\text{embedded}\qquad\qquad\qquad\quad\\&\;\text{in the model}\;s\;\text{is cached}, \\
0,&\;\text{otherwise}.
\end{aligned}
\right.
\end{equation}
In addition to the above, the following constraints should also be satisfied,
\begin{equation}
\begin{aligned}
\sum_{r \in \mathbf{R}}h^s_{rl} \leqslant 1,\; \forall j\in \mathbf{M},\;\forall s\in \mathbf{S_r},\; \forall l\in \mathbf{L_{rs}} \\
\end{aligned}
\label{cons_h1}
\end{equation}
\begin{equation}
\begin{aligned}
\sum_{s\in \mathbf{S_r}}\sum_{l \in \mathbf{L_{rs}}}h^s_{rl} \geqslant 1,\; \forall r\in \mathbf{R} \\
\end{aligned}
\label{cons_h2}
\end{equation}
\begin{equation}
\begin{aligned}
\sum_{j \in \mathbf{M}}p_{sj} \geqslant h^s_{rl},\; \forall r\in \mathbf{R},\;\forall s\in \mathbf{S_r},\; \forall l\in \mathbf{L_{rs}} \\
\end{aligned}
\label{cons_h3}
\end{equation}
\begin{equation}
\begin{aligned}
h^s_{rl} \leqslant h^s_{rl} \sum_{j \in \mathbf{M}}p_{sj},\; \forall r\in \mathbf{R},\;\forall s\in \mathbf{S_r},\; \forall l\in \mathbf{L_{rs}} \\
\end{aligned}
\label{cons_h4}
\end{equation}
Constraints in \eqref{cons_h1} ensure that each ARO can be cached at most once in a related model. Constraints in \eqref{cons_h2} ensure that at least one model and an ARO is required to compose a valid request. Constraints in \eqref{cons_h3} guarantee that the ARO must be allocated to a model first before deciding to proactively cache it and constraints in \eqref{cons_h4} certify that any ARO planned to be stored in this model should not be cached when deciding not to proactively cache the model at all. Constraints \eqref{cons_h3} and \eqref{cons_h4} together ensure that either the model or ARO cannot be handled alone during the formulation.
Denote $B_j$ as the bandwidth allocated to the user's resource block and $\gamma_{rj}$ as the Signal to Interference plus Noise Ratio (SINR) of the user $r$ at the node $j$. Denote $P^{tran}_{rj}$ as the current transmit power of the user $r$ at the node $j$, $P_i$ as the base station power, $H_{rj}$ as the channel gain, $N_j$ as the noise and $a$ as the path loss exponent and $d_{rj}$ as the Euclidean Distance between the user and the access router in the cell. Furthermore, a nominal Rayleigh fading channel is utilized to model the channel between a 5G access point and the users\cite{gemici2021modeling}. In this case, the channel gain $H_{rj}$ can be written as $H_{rj}=\sqrt{\frac{1}{2}}(t+t^{'}J)$, where $J^2=-1$, $t$ and $t^{'}$ are random numbers following the standard normal distribution \cite{cho2010mimo}. Then, the SINR $\gamma_{rj}$ in a 5G wireless network can be written as follows \cite{cho2010mimo},
\begin{equation}
\begin{aligned}
\gamma_{rj}=\frac{P^{tran}_{rj}H^2_{rj}d^{-a}_{rj}}{N_j+\sum_{i\in \mathbf{M}, i\neq j}P_iH^2_{ri}d^{-a}_{ri} }
\end{aligned}
\end{equation}
Denote the data rate as $g\in\mathbb{G}$ and the decision variable $e_{rg}$ to decide whether to select the data rate $g$ for user $r$,
\begin{equation}
e^{rg}=\left\{
\begin{aligned}
1,&\;\text{if data rate}\;g\;\text{is selected}\;\text{for user}\;r, \\
0,&\;\text{otherwise}.
\end{aligned}
\right.
\end{equation}
Noticing that the chosen data rate can also be written in Shannon Formula as $B_j \log_2 (1+\gamma_{rj})$. After choosing a data rate as $ge_{rg}$ for the user, the transmit power $P^{tran}_{rj}$ can be written as follows,
\begin{equation}
\begin{aligned}
P^{tran}_{rj}=\frac{N_j+\sum_{i\in \mathbf{M}, i\neq j}P_iH^2_{ri}d^{-a}_{ri}}{H^2_{rj}d^{-a}_{rj}}(2^{\frac{ge_{rg}}{B_j}}-1)
\end{aligned}
\label{transpower}
\end{equation}
Noticing that $2^{\frac{ge_{rg}}{B_j}}=(1-e_{rg})+e_{rg}2^{\frac{g}{B_j}}$ and should satisfy the following constraint to ensure that a user could only select one data rate,
\begin{equation}
\begin{aligned}
\sum_{g\in\mathbb{G}}e_{rg}=1, \forall r\in\mathbb{R}
\end{aligned}
\label{cons_h7}
\end{equation}
In a similar manner with \cite{huang2021proactive}, computational intensive and storage intensive MAR functionalities are defined as $\eta$ and $\varrho$, respectively. In addition, the corresponding execution location for a functionality is denoted as $x_{ri}$ and $y_{ri}$ respectively \cite{huang2021proactive}. In a mobility event, $u_{f(r)k} \in [0,1]$ is defined to represent the probability of a user moving from the initial location to an allowable destination, where adjacent servers $\{f(r),k\} \subset \mathbb{M}$. Such probabilities can also be learned from historical data, which are readily available from mobile operators. The size of foreground interactions is denoted as $F^{fore}_{\eta r}$, the size of pointers inside used for matching AROs is denoted as $F_{\varrho r}$ and the size of the related model $s$ used for background content checking is $F^{back}_{sr}$ \cite{huang2021proactive}\cite{guo2020adaptive}. During the matching and background content checking process, the target AROs or background content are possibly not pre-cached in the local cache and such case is known as a "cache miss" (otherwise there is a "cache hit"). Whenever confronted with a cache miss, the request is redirected to the metaverse region stored in a core cloud deeper in the network and suffers from an extra latency $D$ as penalty. After rendering, the model and target AROs are integrated into a compressed final frame for transmission and its compressed size is denoted as $F^{res}_{sr}$.
At first, a joint optimization scheme considering the balance between the service delay, the perception quality and the power consumption is designed to track the Metaverse AR requests in the EC supported network. The cache hit/miss is captured by the decision variable $z_{rj}$ and can be written as follows,
\begin{equation}
z_{rj}=\left\{
\begin{aligned}
1 ,&\;\text{if} \sum_{l \in \mathbf{L_{rs}}}\sum_{s \in \mathbf{S_r}}p_{sj}h^s_{rl} \geqslant L_{rs}, \\
0 ,&\;\text{otherwise}.
\end{aligned}
\right.
\end{equation}
In \cite{huang2021proactive}, constraints (10b) and (10d) reveal the cache limitation and the cache hit/miss relation. In this paper, they should be rewritten as follows,
\begin{equation}
\begin{aligned}
&\sum_{r \in \mathbf{R}}\sum_{l \in \mathbf{L_{rs}}}\sum_{s \in \mathbf{S_r}} p_{sj}h^s_{rl}O_{l}\leq \Theta_j,\forall j\in \mathbf{M}\\
\end{aligned}
\label{cons_h5}
\end{equation}
\begin{equation}
\begin{aligned}
&\sum_{l \in \mathbf{N}}\sum_{s \in \mathbf{S_r}} h^s_{rl} + \epsilon \leq L_{rs} + U(1-q_{rj}) \: \forall j\in \mathbf{M}, r \in \mathbf{R}\\
\end{aligned}
\label{cons_h6}
\end{equation}
where $\Theta_j$ is the cache capacity at node $j$. In \eqref{cons_h6}, to rewrite the either-or constraint that $\sum_{l \in \mathbf{N}}\sum_{s \in \mathbf{S_r}} h^s_{rl} < L_{rs} $ or $z_{rj}=1$, we define $\epsilon$ as a small tolerance value, $U$ as a large arbitrary number and $q_{rj}$ as a new decision variable satisfying $1-q_{rj}=z_{rj}$ \cite{huang2021proactive}. Requiring more pre-cached models and embedded AROs in a request naturally lead to an extra burden for the matching function. More specifically, the processing delay of the computational intensive function can be written as,
\begin{equation}
\begin{aligned}
V_{rj}=\frac{\omega_{\eta} F^{fore}_{\eta r}}{f_V^j}
\end{aligned}
\end{equation}
Similarly, the processing delay of the matching and background content checking function can be written as,
\begin{equation}
\begin{aligned}
W_{rj}=\frac{\omega_{\varrho} (F_{\varrho r}+\sum_{l \in \mathbf{L_{rs}}}\sum_{s \in \mathbf{S_r}}p_{sj}h^s_{rl}O_l+\sum_{s \in \mathbf{S_r}}F^{back}_{sr}p_{sj})}{f_V^j}
\end{aligned}
\end{equation}
where $\omega_{\eta}$ and $\omega_{\varrho}$ (cycles/bit) represent the computation load of foreground interaction and background matching, $f^j_V$ is the virtual CPU frequency (cycles/sec), $F_{\varrho r}$ are the size of uploaded pointers of AROs in foreground interactions \cite{huang2021proactive}\cite{guo2020adaptive}.
When finding the target AROs during matching, their pointers included by foreground interactions should also be transferred to the metaverse for updating. Finally, the final frame integrating the model and target AROs of is transmitted back to the user. Hence, the wired transmission delay for each user after processed by functions can be written as follows,
\begin{equation}
\begin{aligned}
\sum_{s \in \mathbf{S_r}}\sum_{j \in \mathbf{M}}(C_{jA(f(r))}+C_{jA(k)})p_{sj}+\\
(C_{A(f(r))f(r)}+ \sum_{k \in \mathbf{K}}C_{A(k)k}u_{f(r)k})
\end{aligned}
\end{equation}
where $u_{f(r)k}$ is the moving probability from the initial location $f(r)$ to a potential destination $k$. In previous expressions, the product of decision variables $p_{sj}h^s_{rl}$ and $p_{sj}y_{rj}$ exists and creates a non-linearity. In addition, note that when executing the matching function at the location $j$ ($W_{rj}y_{rj}$), the product of decision variables $p_{sj}h^s_{rl}y_{rj}$ also appears. To linearize the expressions above, so that to utilize linear integer programming solution methodologies, new auxiliary decision variables are brought in. A new decision variable $\alpha_{rsj}$ is introduced as $\alpha_{rsj}=p_{sj}y_{rj}$ and the constraints should be added as follows,
\begin{equation}
\begin{aligned}
\alpha_{rsj} \leqslant p_{sj}, \;
\alpha_{rsj} \leqslant y_{rj},\;
\alpha_{rsj} \geqslant p_{sj}+y_{rj}-1 \label{a1}\\
\end{aligned}
\end{equation}
Similarly, a new decision variable $\beta_{rslj}$ is introduced as $\beta_{rslj}=p_{sj}h^s_{rl}$ and the constraints should be added as follows,
\begin{equation}
\begin{aligned}
\beta_{rslj} \leqslant p_{sj},\;
\beta_{rslj} \leqslant h^s_{rl} ,\;
\beta_{rslj} \geqslant p_{sj}+h^s_{rl}-1 \label{a2}\\
\end{aligned}
\end{equation}
Also, note that $p_{sj}$ is a binary decision variable and causes $p_{sj}=p^2_{sj}$. Thus, we have $p_{sj}h^s_{rl}y_{rj}=\alpha_{rsj}\beta_{rslj}$. A new decision variable $\lambda_{rslj}$ is introduced as $\lambda_{rslj}=\alpha_{rsj}\beta_{rslj}$ and the following constraints should be added as follows,
\begin{equation}
\begin{aligned}
\lambda_{rslj} \leqslant \alpha_{rsj},\; \lambda_{rslj} \leqslant \beta_{rslj},\;\lambda_{rslj} \geqslant \alpha_{rsj}+\beta_{rslj}-1 \label{a3}\\
\end{aligned}
\end{equation}
Hence, the product $W_{rj}y_{rj}$ can be rewritten as follows,
\begin{equation}
\begin{aligned}
\frac{\omega_{\varrho} (F_{\varrho r}y_{rj}+\sum_{l \in \mathbf{L_{rs}}}\sum_{s \in \mathbf{S_r}}\lambda_{rslj}O_l+\sum_{s \in \mathbf{S_r}}F^{back}_{sr}\alpha_{rsj})}{f_V^j}
\label{storage_intensive_comp}
\end{aligned}
\end{equation}
By checking whether users share the same metaverse region by $A(f(t))=A(f(r)), \{t,r\}\subset\mathbb{R}$, we can ensure the user could also view other updates happening in the same metaverse region. Based on the previous modelling of wireless channel, the wireless transmission delay in a mobility event can be written as follows,
\begin{equation}
\begin{aligned}
&\sum_{r\in \mathbf{R}}\frac{F^{fore}_{\eta r}+\sum_{t\in\mathbf{R}, A(f(t))=A(f(r))}\sum_{s\in\mathbf{S_r}}p_{sj}F^{res}_{st}}{ge_{rg}}+\\&\sum_{r\in \mathbf{R}}\sum_{k\in\mathbf{K}}u_{f(r)k}\frac{F^{fore}_{\eta r}+\sum_{t\in\mathbf{R}, A(t)=A(k)}\sum_{s\in\mathbf{S_r}}p_{sj}F^{res}_{st}}{ge_{rg}}
\label{wireless}
\end{aligned}
\end{equation}
Noticing that with the aforementioned definition of $e_{rg}$ and related constraint \eqref{cons_h7}, $\frac{1}{e_{rg}}$ can be replaced by $e_{rg}$ for linearization. By introducing a new decision variable $\phi_{rlsg}$ with following constraints,
\begin{equation}
\begin{aligned}
\phi_{rsg} \leqslant e_{rg},\;\phi_{rsg} \leqslant p_{sj},\;&\phi_{rsg} \geqslant e_{rg}+p_{sj}-1 \label{a4}\\
\end{aligned}
\end{equation}
Thus, the previous formula \eqref{wireless} can be updated as follows,
\begin{equation}
\begin{aligned}
&\frac{1}{g}\sum_{r\in \mathbf{R}}(1+\sum_{k\in\mathbf{K}}u_{f(r)k}) (F^{fore}_{\eta r}e_{rg}+\\&\sum_{t\in\mathbf{R}, A(f(t))=A(f(r))}\sum_{s\in\mathbf{S_r}}\phi_{rsg}F^{res}_{st} )
\label{wireless_new}
\end{aligned}
\end{equation}
Based on the above derivations and inline with \cite{huang2021proactive}, the overall latency can be written as follows,
\begin{equation}
\begin{aligned}
L=&\eqref{wireless_new}+\sum_{r \in \mathbf{R}}\sum_{i \in \mathbf{M}}(C_{f(r) i}+V_{ri})x_{ri}+\\
&\sum_{r \in \mathbf{R}}\sum_{i \in \mathbf{M}}\sum_{j \in \mathbf{M}} (\eqref{storage_intensive_comp}+ C_{ij}\xi_{rij}+C_{A(f(r))f(r)}+\psi_{rj}D )+\\ \\
&\sum_{s \in \mathbf{S_r}}\sum_{j \in \mathbf{M}}(C_{jA(f(r))}+C_{jA(k)})p_{sj}+ \\
&\sum_{r \in \mathbf{R}}\sum_{k \in \mathbf{K}}(C_{A(k)k}+C_{ki}x_{ri})u_{f(r)k}
\end{aligned}
\end{equation}
where $V_{ri}$ is the processing delay of computational intensive function \cite{huang2021proactive}. Note that $L_{max}$ here denotes the maximum allowed service latency and therefore the following holds, $\frac{L}{L_{max}} \in [0,1]$.
The energy cost of the system during each service time slot is measured by its total consumed power. The total power consists of the transmission power and the CPU processing power at target ECs. We denote the required CPU processing power of the user $r$ at the node $j$ as $P^{cpu}_{rj}$ and the CPU chip architecture coefficient as $k_0$ (e.g. $10^{-15}$) \cite{dong2019deep}. Then, the power per CPU cycle at the EC can be achieved through $k_0(f^j_V)^2$ (Watt/cycle) based on measurements in \cite{zhang2013energy}\cite{miettinen2010energy}. Thus, the total power consumption can be written as follows,
\begin{equation}
\begin{aligned}
P &=\sum_{r\in\mathbf{R}}\sum_{j\in\mathbf{M}}(P^{tran}_{rj}+P^{cpu}_{rj})\\
&=\sum_{r\in\mathbf{R}}\sum_{j\in\mathbf{M}}(\frac{N_j+\sum_{i\in \mathbf{M}, i\neq j}P_iH^2_{ri}d^{-a}_{ri}}{H^2_{rj}d^{-a}_{rj}}(2^{\frac{ge_{rg}}{B_j}}-1)+\\
&\quad\qquad\qquad k_0(f^j_V)^2 (W_{rj}y_{rj}+V_{rj}x_{rj})f^j_V )
\end{aligned}
\end{equation}
$P_{max}$ represents the maximum allowable total power of the system. It also has $\frac{P}{P_{max}} \in [0,1]$.
SSIM is applied to reveal the quality of perception experience. In this paper, the video coding scheme (e.g. H.264) and frame resolution (e.g. 1280$\times$720) are assumed as pre-defined \cite{kato2021split}. Then SSIM is mainly affected by data rate and a concave function could be applied to reveal the relation between them\cite{kato2021split}. Hence, the SSIM value is denoted as $c$ and consists a set for each ARO under corresponding data rate as $\mathbb{SSIM}_{l}, l\in\mathbb{L}_r$. The overall quality of perception experience $Q$ can be written as follows,
\begin{equation}
\begin{aligned}
Q=\sum_{r\in\mathbf{R}}\sum_{l\in\mathbf{L_r}}\sum_{g\in\mathbf{G}}\sum_{c\in\mathbf{SSIM}_{l}} e_{rg}c
\end{aligned}
\end{equation}
Similarly, $Q_{max}$ here denotes the maximum available quality of perception experience and satisfies $\frac{Q}{Q_{max}} \in [0,1]$.
We denote the weight parameter is denoted as $\mu \in [0,1]$ and the joint optimization problem can eventually be written as follows,
\begin{subequations}
\begin{align}
\mathop{min}
&\; \frac{\mu}{2}(\frac{L}{L_{max}}-\frac{Q}{Q_{max}})+(1-\mu) \frac{P}{P_{max}}
\label{JOP:1}
\\
\nonumber
\\
\text{s.t.}\;& z_{rj} = 1-q_{rj}, \: \forall j\in \mathbf{M}, r \in \mathbf{R}
\label{JOPcon:1}
\\
&\sum_{r \in \mathbf{R}} (x_{rj}+y_{rj})\leq \Delta_j,\forall j\in \mathbf{M}
\label{JOPcon:2}
\\
&\sum_{j \in \mathbf{M}} x_{rj}=1,\forall r\in \mathbf{R}
\label{JOPcon:3}
\\
&\sum_{j \in \mathbf{M}} y_{rj} =1,\forall r \in \mathbf{R}
\label{JOPcon:4}
\\
&\xi_{rij} \leq x_{ri}, \: \forall r \in \mathbf{R}, i,j \in \mathbf{M}
\label{JOPcon:5}
\\
&\xi_{rij} \leq y_{rj}, \: \forall r \in \mathbf{R}, i,j \in \mathbf{M}
\\
&\xi_{rij} \geq x_{ri} + y_{rj} -1, \: \forall r \in \mathbf{R}, i,j \in \mathbf{M}
\\
&\psi_{rj} \leq z_{rj}, \: \forall r \in \mathbf{R}, j \in \mathbf{M}
\\
&\psi_{rj} \leq y_{rj}, \: \forall r \in \mathbf{R}, j \in \mathbf{M}
\\
&\psi_{rj} \geq z_{rj} + y_{rj} -1, \: \forall r \in \mathbf{R}, j \in \mathbf{M}
\label{JOPcon:10}
\\
&x_{rj}, y_{rj},p_{sj}, h^s_{rl}, z_{rj}, q_j\in \{0,1\},\nonumber\\
&\alpha_{rsj},\beta_{rslj},\lambda_{rslj}, \phi_{rslg},\psi_{rj}, \xi_{rij}\in \{0,1\}, \nonumber\\
&\forall r \in \mathbf{R}, j\in \mathbf{M}, l \in \mathbf{L_{rs}}, s\in \mathbf{S_r}
\label{JOPcon:11}
\\
&\eqref{cons_h1},\;\eqref{cons_h2},\;\eqref{cons_h3},\;\eqref{cons_h4},\;\eqref{cons_h7},\;\eqref{cons_h5},\;\eqref{cons_h6},\;\eqref{a1},\;\eqref{a2},\;\eqref{a3},\;\eqref{a4}\nonumber
\end{align}
\end{subequations}
As mentioned earlier, the constraint \eqref{JOPcon:1} together with constraints \eqref{cons_h1} to \eqref{cons_h4} reveal the relation between pre-caching decisions and the cache miss/hit for each request \cite{huang2021proactive}. The constraint \eqref{JOPcon:2} is the virtual machine limitation while \eqref{JOPcon:3} and\eqref{JOPcon:4} guarantee the once execution of each function of a request at a single server as explained in \cite{huang2021proactive}. The constraints \eqref{a1} to \eqref{a3} and \eqref{JOPcon:5} to \eqref{JOPcon:10} are auxiliary and required to solve the product of decision variables for linearization.
\section{Numerical Investigations}
In this section, the effectiveness of the proposed optimization scheme, which will be referred to as Optim in the sequel, is investigated
and compared with a number of nominal/baseline schemes.
Same as in \cite{huang2021proactive}, a nominal tree-like network topology is applied with 20 ECs in total and 6 ECs being activated for the current metaverse AR service and 30 requests are sent by MAR devices. The remaining available resources allocated for metaverse AR support within an EC are assumed to be CPUs with frequency from 4 to 8 GHz, 4 to 8 cores and $[100,400]$MBytes of cache memory \cite{dong2019deep}\cite{huang2021proactive}. Each request requires a single free unit for each service function, such as for example a Virtual Machine (VM) \cite{liu2018edge}. Up to 14 available VMs are assumed in each EC, with equal splitting of the available CPU resources \cite{huang2021proactive}. Note that different view ports lead to different models of the metaverse \cite{guo2020adaptive}. Hereafter, up to 4 different models per user can be cached and are similar for each user. All target AROs must be integrated with the corresponding model and rendered within the frame before being streamed to the end user based on a matched result.
The size of pointers used for matching are only a few bytes in size and hence their transmission and processing latency are neglected in the simulations. The set of available data rates is $\{2,3,...,8\}$Mbps and its corresponding SSIM values set is $\{0.955, 0.968,...,0.991\}$ \cite{kato2021split}. The carrier frequency of a nominal 5G access point is set to 2GHz, its transmit power is assumed to be 20dBm with the maximum of 100 resource blocks and we assume, without loss of generality, that each user can utilize one resource block\cite{korrai2019slicing}\cite{li2020computing}. The noise power is $10^{-11}$W and the path loss exponent is 4\cite{korrai2019slicing}. The location of the users is randomly generated as well as the potential destinations. Furthermore, we assume that each cell has a radius as 250m in the 5G wireless network \cite{korrai2019slicing}. As mentioned earlier, we assume a predefined video coding scheme, namely the H.264 with a fixed frame resolution as 1280$\times$720 \cite{kato2021split} in RGB (8 bits per pixel). Based on the given resolution, the size of foreground interactions after decoding and compressing can be calculated by multiplying the coefficients $\frac{5}{9}$ and $10^{-3}$ \cite{guo2020adaptive}.
Three baseline schemes implementing edge caching decisions are also implemented for comparison. These are the Random Selection Scheme (RandS), the Closest First Scheme (CFS) \cite{tocze2019orch} and the utilization based scheme (UTIL) \cite{sonmez2019fuzzy}. The RandS scheme operates a random EC selection, while the other two schemes both select the closest EC to the user's initial location. The CFS scheme also accepts the second closest one as a back up choice whilst the UTIL scheme set a capacity boundary to ensure an ideal EC working state; we assume that this is 80\% occupied of available VMs \cite{tocze2019orch}\cite{sonmez2019fuzzy}.
According to Fig. \eqref{fig:W&Delay}, the service delay for each request drops, as expected, with an increasing weight $\mu$. With a larger weight, the Optim scheme tends to select a larger data rate and proactively cache fewer AROs, which lead to a smaller overall delay. Compared to the CFS scheme, for example, the gain in delay of the Optim scheme ranges from 6.4\% to 24.8\%. As shown by Fig. Table \eqref{tab:P&SSIM}, the larger data rate caused by the increasing weight also leads to an increased perception quality for each target ARO. However, the power consumption in this case shows an ascending trend as revealed in Table \eqref{tab:P&SSIM}. Thus, a trade-off exists and power consumption should be considered vis-a-vis with the gains it offers in delay and quality. By selecting a suitable weight, a balance could be achieved via the proposed Optim scheme between delay, quality and power consumption. As eluded before, the UTIL scheme has a stricter EC capacity limit and hence it is the most sensitive scheme to the weight. Fig. \eqref{fig:Back&Delay} further reveals how delay is impacted with an increase to the background model size. When the EC has sufficient resources the delay increase proportionally to the background model size. Hence, the delay of the Optim scheme is at first 6.3\% better than the CFS scheme and it increases by 2.5\% for each extra MB in background model size. But, when the EC becomes congested, the proposed Optim scheme has to accept sub-optimal solutions. However, the baseline schemes are much easier to excess the resource limit and suffer from a penalty. The gap between the CFS scheme and the Optim scheme could even reach 18.5\%. Thus, they become much worse in delay and more sensitive to the background model size.
\begin{figure}[htb]
\centering
\includegraphics[width=0.7\linewidth]{W_Delay.jpg}
\caption{Overall Delay with Weight $\mu$ (6 EC, 30 Requests, EC Capacity is 14 and total mobility probability is 1)}
\label{fig:W&Delay}
\end{figure}
\begin{table}[htb]
\caption{Average Perception Quality SSIM and Power Consumption with Weight $\mu$ }
\centering
\begin{tabular}{c|c|c|c|c|c|c|c}
\hline
\textbf{Weight $\mu$}&0&0.2&0.5&0.8&1\\
\hline
\textbf{SSIM}&0.958&0.979&0.986&0.990&0.992\\
\hline
\textbf{Power (W)}&0.88&1.09&1.32&1.41&1.45\\
\hline
\end{tabular}
\label{tab:P&SSIM}
\end{table}
\begin{figure}[htb]
\centering
\includegraphics[width=0.7\linewidth]{Back_Delay.jpg}
\caption{Overall Delay with Background Model Size (6 EC, 30 Requests, EC Capacity is 14 and total mobility probability is 1)}
\label{fig:Back&Delay}
\end{figure}
\begin{table}[htb]
\caption{Overall Delay in no mobility event \\($\mu=1$, 6 ECs, 30 requests and EC Capacity is 14)}
\centering
\begin{tabular}{c|c|c|c|c|c|c}
\hline
\textbf{Scheme}&\textbf{Optim}&\textbf{CFS}&\textbf{UTIL}&\textbf{RandS}\\
\hline
\textbf{Delay (ms)}&37.7&38.6&38.7&44.3\\
\hline
\end{tabular}
\label{tab:no_mob}
\end{table}
Observe that according to Table \eqref{tab:no_mob}, even in the case where there is no mobility (i.e., users are stationary), the proposed Optim scheme still manages to outperform other baseline schemes because its service decomposition could better avoid potential EC overloading. Therefore, the proposed Optim scheme has an obvious advantage over baseline schemes especially during network congestion episodes and a high user physical mobility environment.
\section{Conclusions}
Experiences in the metaverse are expected to be significantly demanding in terms of energy consumption, persistent high data rate support and advanced edge caching/computing capabilities in 5G and beyond networks.
In this paper, a joint optimization framework is proposed that explicitly considers the model rendering, user mobility and service decomposition to achieve a balance between power consumption, user perception quality and service delay for content rich metaverse type of applications. Compared to nominal schemes which are mobility oblivious, the proposed optimization framework is able to provide an average reduction of 11.8\% to 35.6\% in terms of delay without sacrificing quality of experience or increasing the required power consumption.
\bibliographystyle{IEEEtran}
|
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{"url":"https:\/\/www.physicsforums.com\/threads\/how-is-f-x-sqrt-x-a-valid-function.769122\/","text":"How is f(x)=sqrt(x) a valid function?\n\n1. Sep 5, 2014\n\nCuriousBanker\n\nHello\n\nMy teacher has told me the square root function is a valid function. He has also told me that a function cannot possibly have two different output for one given input. 36^1\/2 for instance has both -6 and +6 as answers. He told me to just refer to the positive square root...eh, that seems kind of sloppy to just ignore half of the answers out of convenience, no?\n\n2. Sep 5, 2014\n\nDrewD\n\n$\\sqrt x$ is defined to be the positive number $a$ such that $a^2=x$. It isn't ignoring half the answers unless you are asked for the numbers $a$ that solve the equation $a^2=x$ and give the answer $\\sqrt x$ instead of $\\pm\\sqrt x$.","date":"2018-03-18 21:41:55","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\": 0.8021783232688904, \"perplexity\": 284.17877120619704}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-13\/segments\/1521257646176.6\/warc\/CC-MAIN-20180318204522-20180318224522-00111.warc.gz\"}"}
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\section{Introduction}
EvoMan~\cite{karinemiras01} is a framework for testing competitive game-playing agents in a number of distinct challenges such as:
\begin{itemize}
\item Learning how to win a match against a single enemy
\item Generalizing the agent to win the matches against the entire set of enemies
\item Coevolving both the agent and the enemies to create intelligent enemies with increasing difficulties.
\end{itemize}
This framework is inspired on the boss levels of the game Mega Man II~\cite{capcom} created by Capcom in which the player controls a robot equipped with a simple arm cannon and must beat $8$ Robot Masters equipped with different weapons.
In the game, every time Mega Man defeats a Robot Master, it acquires its weapon making it easier to defeat the remainders bosses. This game is considered to have a high degree of difficulty among skilled players. As a personal challenge, some skilled players try to beat all Robot Masters using only the default arm cannon.
With this competition we propose the following question: can a fully automated intelligent agent defeat each one of the Robot Masters using only the default arm cannon? In more details, we challenge the competitors to evolve an intelligent agent by allowing it to train against four ($4$) of the Robot Masters but with the ultimate goal of defeating all eight ($8$) of them.
\section{The Challenge}
In this challenge, the contestants should train their agent on a set of four enemies (defined by the contestant) and evaluate how general is their learned strategy when fighting against the whole set of enemies.
Since each enemy behavior greatly differs from each other, the player should learn how to identify and react to general patterns like avoiding being shot or shoot at the direction of the enemy. Learning a general strategy capable of winning over the entire enemies set can be very challenging~\cite{karinemiras01,karinemiras02}.
The agent will have a total of $20$ sensors, with $16$ of them corresponding for horizontal and vertical distance to $8$ different bullets (maximum allowed), $2$ to the horizontal and vertical distance to the enemy, and $2$ describing the direction the player and the enemy is facing. The sensors are illustrated in Fig.~\ref{fig:sensors}.
\begin{figure}
\centering
\includegraphics[width=0.4\textwidth]{Evoman3.png}
\caption{Sensors available for the competition.}
\label{fig:sensors}
\end{figure}
The framework is freely available\footnote{\url{https://github.com/karinemiras/evoman_framework}} and it is currently compatible with Python 3.6 and 3.7 (Python 3.8 is not compatible at the moment). There is also an extensive documentation available\footnote{\url{https://github.com/karinemiras/evoman_framework/blob/master/evoman1.0-doc.pdf}}.
\section{Evaluation Criteria}
Both the agent and the enemies start the game with $100$ energy points. Every time the player or the enemy gets hit, they lose one point. Whoever reaches $0$ points loses the match.
The final performance of the agent after the end of a match is calculated by the energy gain, as a maximization problem, calculated by the difference between the player and the enemy energy:
\begin{equation*}
Gain = 100.01 + ep - ee,
\end{equation*}
\noindent where $ee$ and $ep$ are the final amount of energy of the enemy and the player, respectively. The value of $100.01$ is added so that the harmonic mean always produces a valid result.
The main goal of this competition is that a given agent perform equally good for every boss. So, each contestant agent will be tested against all of the enemies, and they will be ranked by the harmonic mean of the performance over the different bosses.
\section{Participating in the Competition}
The initial code, manual and every other needed resources are available at a Github repository\footnote{\url{https://github.com/karinemiras/evoman_framework}}. The competitors should pay attention to the following directions:
\begin{itemize}
\item Follow the installation instructions in the file evoman1.0-doc.pdf.
\item Run the demo script controller\_specialist\_demo.py to test if the framework is working.
\item Play the game using your own keyboard to understand the difficulties of the problem. Use the script \emph{human\_demo.py} for that.
\item The agent should be trained using the Individual Evolution and Multi-objective modes with the goal of beating each one of the four adversaries chosen for training.
\end{itemize}
\section{Current Results}
In~\cite{karinemiras03} different learning strategies were tested for the individual evolution mode. In this mode the algorithm creates one agent for each boss, thus generating specialist agents. The algorithms used for this test was variants of neuroevolution~\cite{neuro} strategies with $1$-layer perceptron and $2$-layers perceptron with $10$ and $50$ neurons for the hidden layer. The weights of the Neural Network was adjusted by means of a Genetic Algorithm~\cite{ga} (GAP, GA10, GA50) and LinkedOpt algorihtm~\cite{linkedopt} (LOP, LO10, LO50). The other strategy was the evolution of a Neural Network topology with their weights by means of the NEAT algorithm~\cite{neat}.
Table~\ref{tab:results} show the obtained results so far for the individual mode. These results serve as an upper bound for the proposed competition.
From this table we can see that NEAT provided the best overall results followed by the two-layer neural networks with their weights adjusted through a Genetic Algorithm.
Notice that since these results were obtained with Individual Mode they will most likely serve as an upper bound of the results obtained in this competition.
\begin{table}[t!]
\caption{Gains obtained by each tested algorithm reported in~\cite{karine03}. The \emph{mean} row is the harmonic mean of the results.}
\centering
\begin{tabular}{c|ccccccc}
\hline
Boss & NEAT & GAP & GA10 & GA50 & LOP & LO10 & LO50 \\
\hline
1 & 190.01 & 190.01 & 190.01 & 190.01 & 0.01 & 196.01 & 80.01 \\
2 & 194.01 & 190.01 & 182.01 & 178.01 & 190.01 & 182.01 & 188.01 \\
3 & 180.01 & 158.01 & 158.01 & 136.01 & 124.01 & 70.51 & 116.01 \\
4 & 194.01 & 93.51 & 118.01 & 169.01 & 73.01 & 36.51 & 119.01 \\
5 & 194.01 & 180.01 & 188.01 & 179.01 & 178.01 & 181.01 & 188.01 \\
6 & 173.01 & 79.01 & 77.51 & 103.01 & 139.01 & 128.01 & 20.01 \\
7 & 177.01 & 170.01 & 156.01 & 118.01 & 186.01 & 169.01 & 190.01 \\
8 & 186.01 & 177.01 & 183.01 & 178.01 & 0.01 & 182.01 & 183.01 \\
Mean & 185.67 & 139.64 & 143.74 & 149.43 & 0.04 & 104.01 & 79.32 \\
\hline
\end{tabular}
\label{tab:results}
\end{table}
\section{Conclusion}
This paper introduces the EvoMan competition as a new general game playing challenge based on the Mega Man II game by CAPCOM. The main goal of the competition is to evolve an intelligent agent capable of defeating each one of the eight available bosses while being able to train against a smaller subset of those enemies.
The winner of this competition will be the one agent that performs equally well on each one of the eight bosses, hopefully defeating them all.
In order to help the competitors, we provided a table with the upper bounds of the gains for each boss, obtained with the help of specialist agents.
|
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{"url":"https:\/\/techwhiff.com\/learn\/question-prelab-question-2-a-student-has-weighed\/286759","text":"# Question: Prelab Question 2: A student has weighed out 850 mg of 1-pentanol in 50 mL...\n\n###### Question:\n\nQuestion:\nPrelab Question 2: A student has weighed out 850 mg of 1-pentanol in 50 mL volumetric flask and prepared four standard solutions as described in this procedure. Calculate concentrations of 1-pentanol in mg\/mL in each of these solutions.\nWe were unable to transcribe this image\nand unkcaiculate peak area ratio of I pentanol to internal standard for all sandard solutions. Take average of two measurements of each solution. Step 3. Make a table showing all results of step 1 and 2. YOU MUST RECORD ALL CALCULATIONS IN YOUR LAB NOTEBOOK. Step 4. Prepare a standard calibration curve by plotting peak area ratios agains 1-pentanol concentrations (unit: mg\/mL). Use Excel. The computers located in 1215 Gilman are loaded with these programs for your calculation. YOU MUST ATTACH A COPY OF THIS STANDARD CALIBRATION PLOT IN YOUR LAB NOTEBOOK. Step 5. Use the slope and intercept from the regression program of the standard calibration curve to calculate the amount of 1-pentanol (in mg) in the unknown obtained from your TA. Step 6. Submit the result reporting form showing the amount of 1-pentanol (in mg) in your unknown on Canvas.\nPrelab Question #2: A student has weighed out 850 mg of 1-pentanol in 50 mL volumetric flask and prepared four standard solutions as described in this procedure. Calculate concentrations of 1-pentanol in mg\/mL in each of these solutions.\n\n#### Similar Solved Questions\n\n##### What is the difference in average daily hotel room rates between Minneapolis and New Orleans? Suppose...\nWhat is the difference in average daily hotel room rates between Minneapolis and New Orleans? Suppose we want to estimate this difference by taking hotel rate samples from each city and using a 98% confidence level. The data for such a study follow. Use these data to produce a point estimate for the...\n##### The shape of the distribution of the time required to get an oil change at a...\nThe shape of the distribution of the time required to get an oil change at a 10-minute oil-change facility is unknown. However, records indicate that the mean time is 11.5 minutes, and the standard deviation is 4.5 minutes. Complete parts (a) through (c). (a) To compute probabilities regarding the s...\n##### A client who has a retinal detachment asks the nurse if a retinal detachment in the...\na client who has a retinal detachment asks the nurse if a retinal detachment in the goid eye is likely to occur. Which is the best response In the good eyes Nike dient who has a rednal detachme which of the following re ponses by the nume s ti appropriate chances are very high that you will experien...\n##### 7. If the contract rate for a one period loan is 11.65%, the expected recovery in...\n7. If the contract rate for a one period loan is 11.65%, the expected recovery in event of default is 20%, and the financial institution requires that the expected return on the loan equal the risk free rate of 3.375%, what is the probability of default on the loan?...\n##### 2 uRove that YIx 2 Cb) Erthin\n2 uRove that YIx 2 Cb) Erthin...\n##### Come-Clean Corporation produces a variety of cleaning compounds and solutions for both Industrial and household use....\nCome-Clean Corporation produces a variety of cleaning compounds and solutions for both Industrial and household use. While most of its products are processed Independently, a few are related, such as the company's Grit 337 and its Sparkle silver polish. Grit 337 is a coarse cleaning powder with ...\n##### Cilia, flagella and microvilli are specialised cellular structures, each formed from a central core of actin...\nCilia, flagella and microvilli are specialised cellular structures, each formed from a central core of actin filaments.\u2019 Is this statement is true or false? Argue your case using examples...\n##### A 56 year old patient is being admitted to the hospital for peritoneal dialysis. a. What...\nA 56 year old patient is being admitted to the hospital for peritoneal dialysis. a. What are principals for administering peritoneal dialysis? b. What is involved with the exchange of fluids? A patient with chronic kidney disease will be doing peritoneal dialysis at home. a. Discuss the education...\n##### Are written responses from the FDA ever deemed equivalent to a meeting\nAre written responses from the FDA ever deemed equivalent to a meeting...\n##### 1) Graph the solution curve from [0,5] with step .1 2) Find the explicit solution of...\n1) Graph the solution curve from [0,5] with step .1 2) Find the explicit solution of the IVP 3) Find the interval of definition Consider the initial-value problem y\" + x(y')2 = 0, y(1) = 4, y'(1) = 2...\n##### Selected year end financial statements of Cabot Corporation follow. (All sales were on credit, selected balance...\nSelected year end financial statements of Cabot Corporation follow. (All sales were on credit, selected balance sheet amounts at December 31, 2016, were inventory. $47,900: total assets,$259,400, common stock, $89,000, and retained earnings.$34,451) CABOT CORPORATION Income Statement For Year Ende...","date":"2022-11-27 02:03:33","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\": 0.2976333498954773, \"perplexity\": 3096.2866657004397}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-49\/segments\/1669446710155.67\/warc\/CC-MAIN-20221127005113-20221127035113-00481.warc.gz\"}"}
| null | null |
What's on Joanie Leeds' iPod?
Joanie Leeds is a month away from releasing her 6th(!) kids record. Good Egg will be released on June 24th and this time around, she funded the record via KickStarter. She brings along Mista Cookie Jar (on the insanely funky 'Drummer Dan') and Jacob Stein from The Pop Ups (on the back and forth wordplay on "The World Is Your Oyster") to help out. Of course, the production from Dean Jones shines through on Good Egg.
The new record is all over the map on genres, but never does it feel contrived. She effortlessly jumps from rocking out to a breezy ukulele tune. Easily the highlight on the record, is the singing on 'Hipster In The Making." Joanie brings some clever lyrics to the table, but the harmonies from her band, the Nightlights bring to this track just shine.
But now, we find out what's on her iPod…..
Initial reaction: After a big smile and a little head bop, I noted this was the perfect song to queue up first. What a classic!
Why did you add it? I was given the 4 disk Stax Collection as a gift back in the early 2000's. What an amazing collection with artists such as Isaac Hayes, Otis Redding (my favorite!), Booker T, Mavis Staples… Sam and Dave aren't my favorites from the collection but they have some solid tunes.
What do you like about? While my favorite Stax artist is Otis Redding (My husband and I danced to 'I've been Loving you too Long' at our wedding for our first dance), Sam and Dave had some pretty catchy hits as well. When I was growing up, my mom listened to a lot of 102.7 Classic FM in Miami, Florida. Back in the day the station was full of Sam & Dave hits like 'Soul Man', 'Hold on, I'm Comin' and this one. The soulful sound that you hear in each of the instruments as they make their appearance is stellar. It's gritty and perfect.
Track 2: Campin' Tent Artist: Okee Dokee Brothers Album: Can You Canoe?
Initial reaction: Hahaha, my buddies! Justin and Joe will laugh when they hear that they came up random on my shuffle. I LOVE this album. I was actually listening to their song 'Thousand Star Hotel' from the same album last night. So freakin' clever, as is all of their music.
Why did you add it? We always exchange CDs and when an ODBros CD arrives in the mail, I am always happy to listen as add to my permanent collection. Since my library is pretty vast, I tend to keep my kids music separate and may not download to iTunes after an initial listen. This album however is added without hesitation. (GRAMMY WINNING, I might add) They are great songwriters and I've had the honor of collaborating with Justin on my last CD, Bandwagon, title track. They just sent me their new CD, 'Through the Woods' – it's very good.
Do you want to skip it? No!
What do you like about? This song, along with the entire album is a perfect collection of canoe/camping songs. I love camping and the outdoors so while I value clever lyrics as a songwriter, I can also get behind the concept as a whole. This is kids music at it's very best. "I love my campin' tent. It's my transportable, affordable apartment" – genius!
Initial reaction: Wow, I haven't listened to this album in at least a decade. After hearing The Okee Dokee Brothers, this song is such a downer!
Why did you add it? I first saw K's Choice and became a fan instantly when they threw their pick into the audience at Lilith Fair and I caught it! I bought their CD that night. I mean, I had the pick so I felt obligated. I have 3 of their albums and I much prefer the tunes from their earlier album 'Cocoon Crash'.
Do you want to skip it? Yes, a little, because I wasn't in the mood for a slow ballad but since I hadn't listened to this band in forever, I stuck with it. The lead singer's (Sarah Betten) voice is haunting and the guitar playing is pure and simple. Plus it's a live recording and you can always tell what a band really sounds like when you hear em live!
What do you like about? I love many genres- early 90's chick-rock included. Bands like K's choice, Ani DiFranco, Indigo Girls, Tori Amos and Paula Cole got me into writing my own depressing music back in college. Glad I got all of that out of my system in my teens and early 20's! Ha. No wonder I enjoy writing for children, this sad stuff can get heavy. At the same time, once a year, every girl is obliged sit in a dark room, listen to one of these bands and cry, right? Right?!
Initial reaction: YES!!! This must be one of the best song titles of all time.
Why did you add it? I found a live recording of this show on the internet… or maybe my brother did, I can't remember. I was AT THIS SHOW back in 2008 in Williamsburg, Brooklyn!
Do you want to skip it? Hell NO. It's a beautiful tune.
What do you like about? My brother is 6 years younger than me but when it comes to Indie Rock, he is the Godfather. You know those people who know every band before they get anyone else has heard of them? Like they scour and study Pitchfork with a fine tooth comb? This is my brother. He introduced me to The Mountain Goats (and about 1000 other Indie Rock Bands) in maybe 1999? I resisted because of John Darnielle's nasal tone and the fact that most of the recordings were low quality from a boom box but his lyrics are to die for and I learned to accept the low quality sound and love this band. I've seen them about 5 times and his fans are nuts. They know EVERY word and these are not your typical lyrics. They are very poetic and complicated. In this live version, you can hear everyone singing along. I met the lead singer, John, at his concerts twice. First time, I took a picture of him and my brother outside of this tiny Williamsburg bar a LONG time ago. Second time, he was standing next to me during his opener and I offered him a drink.
Initial reaction: Laughed. I thought the boys might possibly make an appearance on this list. I have more Phish in iTunes than any other band. One may conclude I'm a Phan.
Why did you add it? I have pretty much every studio album they have released and tons (and I mean TONS) of their live shows. I have 7 different versions of 'Ghost' in iTunes. This tune is very different from the rest of their music but my favorite thing about it is Mike's bass line and the pick scrape toward the end. It's the first song on the album, short sweet and it's pretty darn funky.
Do you want to skip it? Nah. It's a solid tune.
What do you like about? etc, etc… When I was at summer camp around 11 or 12 years old, I heard my first Phish album. I was hooked at Fee. Years later when I was a freshman in college, I saw my first show in upstate NY and since then, I have seen them 24 times. 25 shows total. Every Phan knows the number of shows they've seen. But 25 is nothing compared to some people I've met. It's common to meet people at shows that have been to 90, 100, 200 shows. These crazy fans put The Mountain Goat fans in the rookie column.
This entry was posted in Music, Whats on your ipod and tagged Joanie Leeds, K's Choice, Mountain Goats, Okee Dokee Brothers, Phish, Sam & Dave, Whats on your ipod on May 14, 2014 by Dan Walsh.
|
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\section{Introduction}\label{intro}
This paper studies symmetry properties of solutions of fully nonlinear equations related to
spectral properties of what, improperly, will be called the linearized operator.
The question we would like to answer is, which symmetry features of the domain and the operator are
inherited by the
viscosity solutions of the homogeneous Dirichlet problem
\begin{equation}\label{eq1}
\left\{\begin{array}{c}
-F(x, D^2u)= f(x,u)\quad \hbox{ in } \Omega\, ,\\[1ex]
u=0 \quad \hbox{ on } \partial \Omega\, ,
\end{array}\right.
\end{equation}
where $\Omega\subset {\mathbb R}^n$, $n\geq 2$, is a bounded domain and $F$ is a fully nonlinear uniformly
elliptic operator.
Starting with Alexandrov \cite{Al} and after the fundamental works of Serrin \cite{Se} and Gidas, Ni,
Nirenberg \cite{GNN} most results on symmetry of solutions rely on the moving plane method. It is
impossible to even start mentioning all the results obtained via that method, be they for semilinear,
quasilinear or fully nonlinear equations. Let us just mention here the results obtained for positive solutions of fully nonlinear equations by Da Lio and Sirakov \cite{DLS}, Birindelli and Demengel \cite{BDov} and Silvestre and Sirakov \cite{SS}.
For the purpose of this introduction, let us
emphasise its limit of application. Indeed, as it is well known by the experts, the moving plane method cannot be applied if the domain is not convex in the symmetry direction, say e.g. if $\Omega$ is an annulus, or if the nonlinear term $f(x,u)$ does not have the right monotonicity in the $x$--variable (see e.g. \cite{PR} for several counterexamples). The moving plane method does not apply also to sign changing solutions.
Of course, even when $\Omega$ is a ball and $F$ is the Laplacian, one cannot expect sign changing solutions to be radially symmetric, as it is clear exhibited by the fact that there are non radial eigenfunctions. In these cases, some other notion of symmetry is required.
In a more philosophical understanding, the moving plane method is the tool that allows to extend the symmetry of the principal eigenfunctions, which are the only constant sign eigenfunctions, to all positive solutions of nonlinear equations.
It is quite natural to wonder if this analogy can be continued, i.e.
under which conditions can one expect solutions of nonlinear equations to share the same
symmetry of other eigenfunctions, in particular of the "second" eigenfunctions.
Indeed, in balls or annuli, linear operators of the type $\Delta +c(x)$ do have nodal eigenfunctions, in particular the second eigenfunctions, which are symmetric though they are not radial. For problems in non convex domains, one can imagine, and sometimes observe numerically, that even some positive solutions, like least-energy solutions, inherit only part of the symmetry of the domain, for instance, axial symmetry. In all these cases, if the domain is rotationally symmetric, the solutions are proved to be foliated Schwarz symmetric, according to the following
\begin{definition}\label{fss} Let $B$ be a ball or an annulus in ${\mathbb R}^n$, $n\geq 2$. A function $u:\overline B\to {\mathbb R}$ is foliated Schwarz symmetric if there exists a unit vector $p\in S^{n-1}$ such that $u(x)$ only depends on $|x|$ and $\theta= \arccos \left( \frac{x}{|x|}\cdot p\right)$, and $u$ is non increasing with respect to $\theta\in (0,\pi)$ .
\end{definition}
In other words, a foliated Schwarz symmetric function is axially symmetric with respect to the axis ${\mathbb R} p$ and non increasing with respect to the polar angle $\theta$. Note that a radially symmetric function is in particular foliated Schwarz symmetric with respect to any direction $p$, and for a not radial foliated Schwarz symmetric function the symmetry direction $p$ is unique.
In the last decades, some work has been devoted to understanding under which conditions solutions of semilinear elliptic equations are foliated Schwarz symmetric. This line of research, which strongly relies on the maximum principle, was started by Pacella \cite{P} and then developed by Pacella and Weth \cite{PW} and Gladiali, Pacella and Weth \cite{GPW}, see also Pacella, Ramaswamy \cite{PR} and Weth \cite{W}. In the semilinear elliptic case, by using symmetrization techniques, some results about foliated Schwarz symmetry of minimizers of associated functionals were obtained by Smets and Willem \cite{SW}, Bartsch, Weth and Willem \cite{BWW} and Brock \cite{Br}.
Let us recall some results occurring when the diffusion operator is the Laplacian, i.e.
for solutions of
\begin{equation}\label{linear}
\left\{\begin{array}{c}
\Delta u+f(|x|,u)=0 \quad \mbox{in}\ B\, ,\\[1ex]
u=0\quad \mbox{on}\ \partial B\, .
\end{array}
\right.
\end{equation}
Under some convexity hypotheses on $f$, it was proved in \cite{P} and \cite{PW} that a sufficient condition for the foliated Schwarz symmetry of a solution $u$ of \refe{linear} is that the first eigenvalue $\lambda_1(\mathcal{L}_u, B(e))$ of the linearized operator $\mathcal{L}_u=\Delta +\frac{\partial f}{\partial u}(|x|, u)$ at the solution $u$, in the half domain $B(e)=\{ x\in B\, :\, x\cdot e>0\}$ is nonnegative, for a direction $e\in S^{n-1}$.
Furthermore, in \cite{GPW, P, PW}, it was proved that
$\lambda_1(\mathcal{L}_u, B(e))\geq 0$ for some direction $e$ if $m(u)\leq n$, where $n$ is the dimension and $m(u)$ is the Morse index of the solution $u$. We recall that
the Morse index $m(u)$ is defined as the maximal dimension of a subspace of $C^{1}_0(B)$ where the quadratic form
$$Q(\varphi)=\frac{1}{2}\int_B |\nabla \varphi|^2dx -\int_B \frac{\partial f}{\partial u}(|x|, u)\varphi^2dx $$
is negative definite, or, equivalently, as the number of negative eigenvalues
of the linearized operator ${\mathcal L_u}$.
In this line of thought, the first question is: what plays the role of the linearized operator for the fully nonlinear problem \refe{eq1}?
In the whole paper we will suppose that $F$ is uniformly elliptic (see condition \refe{ue}) and
Lipschitz continuous in $x$ (see condition \refe{lip}). Let us recall that uniform ellipticity is equivalent to
$$
\mathcal{M}^-_{\alpha, \beta} (M-N)\leq F(x,M)-F(x,N)\leq \mathcal{M}^+_{\alpha, \beta} (M -N)\quad \forall\, x\in \Omega\, ,\ M, N\in {\mathcal S}_n\, ,
$$
where $\mathcal{M}^-_{\alpha, \beta}$ and $\mathcal{M}^+_{\alpha, \beta}$ are the Pucci's extremal operators with ellipticity constants $0<\alpha\leq\beta$
(for a precise definition, see Section 2) and ${\mathcal S}_n$ is the set of $n\times n$ symmetric matrices.
This, in order, will imply
(see Lemma \ref{diffe}) that any "derivative" $v$ of $u$ will satisfy
$$
-\mathcal{M}^+_{\alpha, \beta} (D^2 v)\leq \frac{\partial f}{\partial u}(x, u)\, v\quad \hbox{ in } \Omega\, ,
$$
$v$ being only a viscosity subsolution, and not a solution as in the semilinear case.
This suggests to define as "linearized" operator the fully nonlinear operator
$$
\mathcal{L}_u(v) \, :\, = \mathcal{M}^+_{\alpha, \beta}(D^2v) +\frac{\partial f}{\partial u}(x,u)\, v\, .
$$
In this framework, it doesn't seem possible to associate a quadratic form to $\mathcal{L}_u$ in
order to define a notion of Morse index. On the other hand, the use of the eigenvalues to define it would require the knowledge of the spectrum of the
operator $\mathcal{L}_u$.
In analogy with the linear case, see \cite{BNV, BD, BEQ, II}, in a domain $D$ one may define, through the maximum principle, the principal eigenvalues $\lambda_1^+=\lambda_1^+(\mathcal{L}_u , D)$ and $\lambda_1^-=\lambda_1^-(\mathcal{L}_u , D)$.
Associated with these values, there are principal eigenfunctions $\phi_1^{\pm}\in C(\overline D)\cap C^2(D)$, defined up to positive constant multiples, which satisfy respectively
$$
\left\{
\begin{array}{c}
-\mathcal{L}_u [\phi_1^+]= \lambda_1^+\, \phi_1^+\quad \hbox{in } D\\[2ex]
\phi_1^+ >0 \ \hbox{in } D\, ,\ \phi_1^+=0\ \hbox{on } \partial D
\end{array}\right.
\quad \mbox{and}\quad
\left\{
\begin{array}{c}
-\mathcal{L}_u [\phi_1^-]= \lambda_1^-\, \phi_1^-\quad \hbox{in } D\\[2ex]
\phi_1^- <0 \ \hbox{in } D\, ,\ \phi_1^-=0\ \hbox{on } \partial D.
\end{array}\right.
$$
However, besides the principal eigenvalues and their corresponding eigenfunctions,
not much is known about other eigenvalues. A completeness result of a spectral basis
is known only for radial eigenfunctions, see Ikoma and Ishii \cite{II}, but the sign of radial eigenvalues is not relevant for the foliated Schwarz symmetry.
Nonetheless we obtain some symmetry results, by analyzing the sign of the principal eigenvalue of $\mathcal{L}_u$ in half domains.
In order to describe our results, let us introduce a few notations that will always be valid in the sequel.
$B$ will always denote a bounded radial domain, that is a ball or an annulus centered at the origin.
For any unit vector $e\in S^{n-1}$, we further denote by
$H(e)=\{ x\in {\mathbb R}^n\, :\, x\cdot e=0\}$ the hyperplane orthogonal to $e$ and by
$B(e)=\{ x\in B\, :\, x\cdot e>0\}$ the open half domain on the side of $H(e)$ which contains $e$.
Moreover, we indicate with $\sigma_e : {\mathbb R}^n\to {\mathbb R}^n$ the reflection with respect to $H(e)$, that is
the map $\sigma_e(x)=x- 2 (x\cdot e)e$. Accordingly, for any domain $\Omega$, we will set $\Omega(e)= \{ x\in \Omega\, :\, x\cdot e>0\}$.
A first simple, but useful, result that we get is a sufficient condition for the symmetry of a viscosity solution $u$ of \refe{eq1} in a domain $\Omega$ symmetric with respect to a certain hyperplane $H(e)$. More precisely, we will show that if $f(x,s)$ is convex in the $s$--variable, then the positivity of the principal eigenvalues $\lambda_1^+(\mathcal{L}_u, \Omega(\pm e))$ in both domains $\Omega(\pm e)$ implies that $u(x)=u(\sigma_e(x))$ for all $x\in \Omega$, see Proposition \ref{prop1}.
Next, our main result, concerning the foliated Schwarz symmetry of viscosity solutions of \refe{eq1}, is
\begin{theorem}\label{lam0}Suppose that $F$ is invariant with respect to any reflection $\sigma_e$ and by rotations.
Let $u$ be a viscosity solution of problem \refe{eq1}, with $\Omega=B$ and $f(x,\cdot)=f(|x|,\cdot)$ convex in ${\mathbb R}$. If there exists $e\in S^{n-1}$ such that
$$\lambda_1^+(\mathcal{L}_u, B(e))\geq 0,$$
then $u$ is foliated Schwarz symmetric.
\end{theorem}
So, under the convexity assumption on $f$, the knowledge of the sign of the principal eigenvalue $\lambda_1^+(\mathcal{L}_u, B(e))$ in one cap $B(e)$ only is sufficient for the foliated Schwarz symmetry of a solution $u$ of \refe{eq1}, for any fully nonlinear uniformly elliptic operator $F$ with ellipticity constants $0<\alpha\leq \beta$.
In any bounded domain $\Omega$, we further define
\begin{equation}\label{mu}
\mu^+_2(\mathcal{L}_u,\Omega)=\inf_{D\subset \Omega}\max\left\{\lambda_1^+(\mathcal{L}_u,D),\lambda_1^+(\mathcal{L}_u,\Omega\setminus \overline D)\right\}
\end{equation}
where the infimum is taken on all subdomains $D$ contained in $\Omega$.
Then, for $\Omega=B$, we immediately obtain
$$
\mu^+_2(\mathcal{L}_u,B)\geq 0\Rightarrow \forall e\in S^{n-1}\ \mbox{ either}\ \lambda_1^+(\mathcal{L}_u,B(e))\geq 0
\ \mbox{ or}\ \lambda_1^+(\mathcal{L}_u,B(-e))\geq 0
$$
so that, by applying Theorem \ref{lam0}, the following corollary holds.
\begin{corollary}\label{sec} Under the assumptions of Theorem \ref{lam0},
if $u$ is a viscosity solution of \refe{eq1} and $\mu^+_2(\mathcal{L}_u,B)\geq 0$, then $u$ is foliated Schwarz symmetric.
\end{corollary}
In the semilinear case, i.e. when $\mathcal{L}_u= \Delta +f'(|x|,u)$, $\mu_2^+$ is just the second eigenvalue of $\mathcal{L}_u$, and therefore the condition $\mu^+_2\geq 0$ is equivalent to require that the Morse index of $u$ is less than or equal to one, which is the condition used in \cite{P} to obtain the foliated Schwarz symmetry. It turns out that, in the currently considered fully nonlinear case, $\mu^+_2$ is not an eigenvalue for $\mathcal{L}_u$ in $B$, as shown in Proposition \ref{secn}.
We further observe that for the laplacian the first eigenvalue in the half domains $B(e)$ is the second eigenvalue in $B$. Then, it is natural to investigate if, also in the fully nonlinear framework, $\lambda_1^+(\mathcal{M}^+_{\alpha, \beta}, B(e))$ is a nodal eigenvalue for $\mathcal{M}^+_{\alpha, \beta}$ in $B$. Here and in the sequel by nodal eigenvalue we mean an eigenvalue associated with sign changing eigenfunctions. First we will prove that $\mathcal{M}^+_{\alpha, \beta}$ cannot have nodal eigenvalues below $\lambda_1^+(\mathcal{M}^+_{\alpha, \beta}, B(e))$, and then we will show several properties that a nodal eigenfunction corresponding to $\lambda_1^+(\mathcal{M}^+_{\alpha, \beta}, B(e))$ should have.
Finally, we prove an interesting connection between the sign of the principal eigenvalue of $\mathcal{L}_u$ in half domains and the nodal set
$\mathcal{N}(u)$, i.e. the closure of the zero set of $u$. Namely, we prove that if $u$ is a sign changing viscosity solution of \refe{eq1} with $f$ independent of $x$ and with $u$ and $F$ symmetric with respect to an hyperplane $H(e)$, then the non negativity of the eigenvalue $\lambda_1^+(\mathcal{L}_u, \Omega(\pm e))$ implies that the nodal set $\mathcal{N}(u)$ intersects the boundary of $\Omega$, see Proposition \ref{prop2}. As a consequence of the above result, we obtain that for any radial sign changing solution $u$ one has
$\lambda_1^+(\mathcal{L}_u, B(e))< 0$ for any direction $e$, see Corollary \ref{rad-}.
In ${\mathbb R}^2$, the above result can be extended to a larger class of domains, i.e. domains which are symmetric with respect to
two orthogonal directions and convex in those directions. Interestingly, besides the ball, the only two
dimensional domains for which the eigenvalues of $\mathcal{M}^+_{\alpha, \beta}$ are known explicitly have these symmetry, see \cite{BL}.
Let us finally point out that our symmetry results apply to viscosity solutions, and not only to classical solutions, of \refe{eq1}. This is essential in view of the fact that, in general, axially symmetric viscosity solutions of fully nonlinear equations may not be of class $C^2$, as proved by Nadirashvili and Vl\u{a}du\c{t} \cite{NV}.
The paper is organized in the following way. The hypotheses and some preliminaries are recalled in the next section. In the third section we prove some symmetry results. Foliated Schwarz symmetry is then studied in the fourth section. Finally, in the last section, we give some applications, in particular to the study of spectral properties.
\section{Preliminaries on fully nonlinear elliptic equations}\label{sec1}
We assume that
$F:\Omega\times \mathcal{S}_n\to {\mathbb R}$ is a continuous function, with $\mathcal{S}_n$ denoting the set of symmetric $n\times n$ matrices equipped with the usual partial ordering
$$
M\geq N \Longleftrightarrow M-N\geq 0 \Longleftrightarrow (M-N)\xi \cdot \xi \geq 0\quad \forall\, \xi\in {\mathbb R}^n\, .
$$
We will always assume that $F$ is uniformly elliptic, that is
\begin{equation}\label{ue}
\alpha \, {\rm tr}(P)\leq F(x, M+P)-F(x, M)\leq \beta\, {\rm tr}(P)\, ,\quad \forall\, x\in \Omega\, ,\ M, P\in {\mathcal S}_n,\ P\geq 0\, ,
\end{equation}
for positive constants $0<\alpha\leq \beta$. Let us recall that condition \refe{ue} is equivalent to
$$
\mathcal{M}^-_{\alpha, \beta} (M-N)\leq F(x,M)-F(x,N)\leq \mathcal{M}^+_{\alpha, \beta} (M -N)\quad \forall\, x\in \Omega\, ,\ M, N\in {\mathcal S}_n\, ,
$$
where $\mathcal{M}^-_{\alpha, \beta}$ and $\mathcal{M}^+_{\alpha, \beta}$ are the Pucci's extremal operators defined respectively as
$$
\begin{array}{c}
\displaystyle \mathcal{M}^-_{\alpha, \beta} (M)= \inf_{A\in \mathcal{A}_{\alpha, \beta}} {\rm tr} (AM)= \alpha \sum_{\mu_i>0} \mu_i + \beta\sum_{\mu_i<0} \mu_i\\[1ex]
\displaystyle
\mathcal{M}^+_{\alpha, \beta} (M)= \sup_{A\in \mathcal{A}_{\alpha, \beta}} {\rm tr} (AM)= \beta\sum_{\mu_i>0} \mu_i + \alpha \sum_{\mu_i<0} \mu_i
\end{array}
$$
where $\mathcal{A}_{\alpha,\beta}=\{ A\in \mathcal{S}_n\, :\, \alpha\, I_n\leq A\leq \beta\, I_n\}$, $I_n$ being the unit matrix in $\mathcal{S}_n$, and $\mu_1, \ldots ,\mu_n$ being the eigenvalues of the matrix $M\in \mathcal{S}_n$.
Thus, Pucci's extremal operators act as barriers for the whole class of uniformly elliptic operators, and for a detailed analysis of the crucial role they play in the regularity theory for elliptic equations we refer to \cite{CaCa}. Clearly, $F(x, M)=\mathcal{M}^+_{\alpha, \beta}(M)$ or $F(x, M)=\mathcal{M}^-_{\alpha, \beta}(M)$ are special cases which can be considered as our model cases; in particular since they are invariant with respect to rotation and reflection.
From now on, we intend the ellipticity constants $\beta\geq \alpha$ fixed once and for all, and we will write just $\mathcal{M}^-$ and $\mathcal{M}^+$ for the Pucci's operators with ellipticity constants $\alpha$ and $\beta$.
As for the dependence on $x$ of $F$, we assume Lipschitz continuity, i.e. the existence of $L>0$ such that, for all $x, y \in \Omega$ and $M\in {\mathcal S}_n$,
\begin{equation}\label{lip}
|F(x,M)-F(y,M)|\leq L\, \|M\||x-y|\, .
\end{equation}
On the zero order nonlinearity $f$ we assume that it is of class $C^1$ on $\Omega\times {\mathbb R}$.
By a solution of the Dirichlet problem \refe{eq1}, we always mean a viscosity solution $u\in C(\overline B)$. For the reader's convenience, we recall that a solution in the viscosity sense is both a viscosity subsolution and a viscosity supersolution, as defined below.
\begin{definition} A viscosity subsolution (supersolution) of problem \refe{eq1} is an upper (lower) semicontinuous function in $\overline \Omega$ such that $u\leq(\geq) 0$ on $\partial \Omega$ and for any $x_0\in \Omega$ and $\phi\in C^2(\Omega)$ such that $u(x_0)=\phi(x_0)$ and $u(x)\leq (\geq) \phi (x)$ for $x\in \Omega$, one has
$$
-F(x_0, D^2\phi (x_0))\leq(\geq) f(x_0, u(x_0))\,.
$$
\end{definition}
We refer to \cite{CaCa, CIL} the reader not familiar with the viscosity solutions theory for fully nonlinear equations.
In the following, all the differential inequalities we are going to consider are always understood in the viscosity sense.
Let us further recall that in the current assumptions, by standard elliptic regularity theory (see \cite{CaCa, S}), any viscosity solution $u$ of problem \refe{eq1} is of class $C^1(\overline \Omega)$, provided that $\Omega$ is of class $C^1$. As far as existence of solutions is concerned, we refer to \cite{FQ, QS}.
In the subsequent symmetry results a crucial role will be played by the principal eigenvalues of linear perturbations of Pucci's operators. In particular, given a Lipschitz domain $D\subset {\mathbb R}^n$ and a function $c\in C(\overline D)$, let us consider the uniformly elliptic operator
$$
\mathcal{L} =\mathcal{M}^+ +c(x)\, .
$$
In analogy with the linear elliptic case, see \cite{BNV}, one may define
$$
\lambda_1^+(\mathcal{L} , D) \, := \sup \{ \lambda \in {\mathbb R}\, :\, \exists\, \varphi \in C(\overline D)\, ,\ \varphi>0 \hbox{ in } D\, ,\ -\mathcal{L} [\varphi]\geq \lambda\, \varphi \hbox{ in } D\}
$$
and
$$
\lambda_1^-(\mathcal{L} , D) \, := \sup \{ \lambda \in {\mathbb R}\, :\, \exists\, \varphi \in C(\overline D)\, ,\ \varphi<0 \hbox{ in } D\, ,\ -\mathcal{L} [\varphi]\leq \lambda\, \varphi \hbox{ in } D\}\,.
$$
As it is well known, see \cite{BD, BEQ, II}, associated with these values, called principal eigenvalues, there are principal eigenfunctions $\phi_1^{\pm}\in C(\overline D)\cap C^2(D)$, defined up to positive constant multiples, which satisfy respectively
\begin{equation}\label{eigenf+}
\left\{
\begin{array}{c}
-\mathcal{L} [\phi_1^+]= \lambda_1^+(\mathcal{L} , D)\, \phi_1^+\quad \hbox{in } D\\[2ex]
\phi_1^+ >0 \ \hbox{in } D\, ,\ \phi_1^+=0\ \hbox{on } \partial D
\end{array}\right.
\end{equation}
\begin{equation}\label{eigenf-}
\left\{
\begin{array}{c}
-\mathcal{L} [\phi_1^-]= \lambda_1^-(\mathcal{L} , D)\, \phi_1^-\quad \hbox{in } D\\[2ex]
\phi_1^- <0 \ \hbox{in } D\, ,\ \phi_1^-=0\ \hbox{on } \partial D.
\end{array}\right.
\end{equation}
When no ambiguities arise, the eigenvalues will be denoted by $\lambda_1^{+}$ or $\lambda_1^-$, and in certain cases we will only specify either the domain $D$ or the choice of the operator.
A few known properties concerning these eigenvalues are used in the paper, we list them here.
\begin{proposition}\label{prl} With the above notations, the following properties hold:
\begin{itemize}
\item[(i)] If $D_1\subset D_2$ and $D_1\neq D_2$, then $\lambda_1^\pm(D_1)>\lambda_1^\pm(D_2)\, .$
\item[(ii)] For a sequence of domains $\{D_k\}$ such that $D_k\subset D_{k+1}$, then
$$\lim_{k\to +\infty}\lambda_1^\pm(D_k)=\lambda_1^\pm(\cup_k D_k)\, .$$
\item[(iii)] If $\alpha<\beta$ then $\lambda_1^+<\lambda_1^-\, .$
\item [(iv)] If $\lambda\neq \lambda_1^\pm$ is an eigenvalue then every corresponding eigenfunction changes sign.
\item[(v)] $\lambda_1^+(D)>0 \ (\lambda_1^-(D)>0)$ if and only if the maximum (minimum) principle holds for $\mathcal{L}$ in $D\, .$
\smallskip
\item[(vi)] $\lambda_1^\pm(D)\to +\infty$ as ${\rm meas}(D)\to 0\, .$
\end{itemize}
\end{proposition}
Let us recall that the operator $\mathcal{L}$ satisfies the maximum (minimum) principle in $\Omega$ if for every function $u$ upper (lower) semicontinuous in $\overline \Omega$ satisfying $-\mathcal{L} [u] \leq 0$ in $\Omega$ and $u\leq 0$ on $\partial \Omega$ (resp. $-\mathcal{L} [u]\geq 0$ in $\Omega$ and $u\geq 0$ on $\partial \Omega$) one has $u\leq 0$ in $\overline \Omega$ ($u\geq 0$ in $\overline \Omega$).
Finally we recall that the principal eigenfunctions are the only positive (negative) supersolutions of \refe{eigenf+}(subsolutions of \refe{eigenf-}) and that the following proposition, which will be used frequently in the sequel, holds true.
\begin{proposition} \label{key} Assume that there exists $u$ lower semicontinuous and positive such that
$$ -\mathcal{L}[u]\geq 0\ \ \mbox{in}\ \Omega\, . $$
If there exists a function $v$ upper semicontinuous in $\overline \Omega$ satisfying $-\mathcal{L}[v]\leq 0$ in $\Omega$, $v\leq 0$ on $\partial \Omega$, and such that $v(\hat x)>0$
for some $\hat x\in\Omega$,
then, for some $t>0$,
$$v\equiv t\, u\ \mbox{and}\ -\mathcal{L}[u]= 0.$$
\end{proposition}
For the proof we refer to \cite{BNV, Pat}.
\section{First symmetry results}
Here and in the sequel we set
$f'(x,s)= \frac{\partial f}{\partial s} (x,s)$ and we use the notations fixed in the Introduction. Moreover,
for any two linearly independent unit vectors $e, e'\in S^{n-1}$, we denote by $\Pi(e,e')$ the plane
spanned by $e$ and $e'$, and by $\theta_{e,e'}$ any polar angle coordinate in $\Pi(e,e')$. If $u:B\to {\mathbb R}$ is a differentiable function, we set $u_{\theta_{e,e'}}$ to indicate the partial derivative of $u$ with respect to $\theta_{e,e'}$, defined as zero at the origin if $B$ is a ball.
The following technical lemma is the starting point of all our symmetry results.
\begin{lemma}\label{diffe} Assume that $F$ satisfies \refe{ue} and \refe{lip} and let $u\in C(\overline \Omega)\cap C^1(\Omega)$ be a viscosity solution of \refe{eq1}
\begin{itemize}
\item[(i)] Assume that $\Omega$ is symmetric with respect to the hyperplane $H(e)$, $F$ is invariant with respect to the reflection $\sigma_e$, i.e.
\begin{equation}\label{sime}
F\left(\sigma_e(x), (I_n-2e\otimes e)M(I_n-2e\otimes e)\right)=F(x,M)\quad \forall\, x\in \Omega\, ,\ M\in \mathcal{S}_n\, ,
\end{equation}
and that $f$ satisfies
\begin{equation}\label{f}
f(\sigma_e(x), s)=f(x, s)\, ,\quad f(x, \cdot) \hbox{ is convex in ${\mathbb R}$}\, , \quad \forall\, x\in \Omega\, ,\ s\in {\mathbb R}\, .
\end{equation}
Then, the function $w=u-u\circ \sigma_e$ satisfies
$$
-\mathcal{M}^+ (D^2 w)\leq f'(x, u)\, w\quad \hbox{ in } \Omega
$$
in the viscosity sense.
Moreover, if $f(x,\cdot)$ is strictly convex, then either $w\equiv 0$ or $w$ is a strict subsolution.
\item[(ii)] Assume that $\Omega =B$ is a bounded radial domain, $F$ is invariant by rotations, i.e. for every orthogonal matrix $O$ one has
\begin{equation}\label{ri}
F(O^t x, O^t MO)= F(x, M) \quad \forall\, x\in B\, ,\ M\in \mathcal{S}_n\, ,
\end{equation}
and that $f$ is radially symmetric in $x$.
Then, for any pair of linearly independent unit vectors $e,\ e'\in S^{n-1}$, the functions $u_{\theta_{e,e'}}$ and $-u_{\theta_{e,e'}}$ both satisfy
$$
\begin{array}{c}
-\mathcal{M}^+ (D^2u_{\theta_{e,e'}})\leq f'(|x|,u)\, u_{\theta_{e,e'}}\quad \hbox{ in } B\\[1ex]
-\mathcal{M}^+ (D^2(-u_{\theta_{e,e'}}))\leq f'(|x|,u)\, (-u_{\theta_{e,e'}})\quad \hbox{ in } B
\end{array}
$$
in the viscosity sense.
\item[(iii)] Assume that $f$ does not depend on $x$. Then, for every $1\leq i\leq n$ both the partial derivative $u_i=\frac{\partial u}{\partial x_i}$ and $-u_i$ satisfy
$$
\begin{array}{c}
-\mathcal{M}^+ \left( D^2u_i\right)\leq f'(u)\, u_i\quad \hbox{ in } \Omega\\[1ex]
-\mathcal{M}^+ \left( D^2(-u_i)\right)\leq f'(u)\,(- u_i) \quad \hbox{ in } \Omega
\end{array}
$$
in the viscosity sense.
\end{itemize}
\end{lemma}
\proof (i) Let $u\in C(\overline \Omega)$ be a viscosity solution of \refe{eq1}. By the invariance of the equation with respect to the reflection $\sigma_e$, $u\circ \sigma_e$ is also a viscosity solution of \refe{eq1}. Then, the difference
$w=u-u\circ \sigma_e$ is a viscosity subsolution of
\begin{equation}\label{subs}
-\mathcal{M}^+ (D^2 w)\leq f(x, u)-f(x, u\circ \sigma_e)\quad \hbox{ in } \Omega\, .
\end{equation}
If $u$ and $u\circ \sigma_e$ are classical solutions of \refe{eq1}, then \refe{subs} is an immediate consequence of the uniform ellipticity of $F$. In the general case, this follows from assumptions \refe{ue} and \refe{lip} by means of the standard regularization procedure by sup/inf--convolution, in the spirit of Theorem 5.3 of \cite{CaCa}. For a detailed proof we refer to the proof of Proposition 2.1 in \cite{DLS}. By \refe{subs} and the convexity of $f(x, \cdot)$, we immediately get the conclusion.
(ii) Let us fix $e, e', \theta_{e,e'}$ as in the statement.
We aim at "differentiating" with respect to $\theta_{e,e'}$ the equation satisfied by $u$. Let us fix $\theta_0\in {\mathbb R}$, and let us denote by $\mathcal{R}_0:{\mathbb R}^n\to {\mathbb R}^n$ the rotation that maps any point $x$ having cylindrical coordinates $(r,\theta,\eta)$ with respect to the plane $\Pi(e,e')$ into the point $\mathcal{R}_0(x)$ with cylindrical coordinates $(r, \theta+\theta_0,\eta)$. Let us further set $u_0(x)=u(\mathcal{R}_0(x))$. Then, by the rotational invariance of $F$ and $f$, we have that both $u$ and $u_0$ satisfy
$$
-F(x, D^2 u)=f(|x|, u)\, ,\quad -F(x, D^2u_0)=f(|x|, u_0)\quad \hbox{ in } B\, .
$$
By uniform ellipticity, arguing as in the proof of (i), we get that the difference $u_0-u$ satisfies, in the viscosity sense,
$$
-\mathcal{M}^+ (D^2(u_0-u)) \leq f(|x|, u_0)- f(|x|, u)\quad \hbox{ in } B\, .
$$
Next, by the homogeneity properties of $\mathcal{M}^+$, we also have that for all $\theta_0>0$
$$
-\mathcal{M}^+ \left( D^2\left( \frac{u_0-u}{\theta_0}\right) \right)\leq \frac{f(|x|, u_0)- f(|x|, u)}{\theta_0}\quad \hbox{ in } B\, ,
$$
whereas, for all $\theta_0<0$,
$$
\mathcal{M}^+ \left( -D^2\left( \frac{u_0-u}{\theta_0}\right) \right)\geq \frac{f(|x|, u_0)- f(|x|, u)}{\theta_0}\quad \hbox{ in } B\, .
$$
By letting $\theta_0\to 0^\pm$, and using the stability properties of viscosity subsolutions and the fact that $\frac{u_0-u}{\theta_0} \to u_{\theta_{e,e'}}$ locally uniformly in $B$, we finally obtain both
$$
\mathcal{M}^+ (D^2u_{\theta_{e,e'}}) + f' (|x|, u)\, u_{\theta_{e,e'}}\geq 0 \quad \hbox{ in }B\, ,
$$
and
$$
\mathcal{M}^+ (D^2(-u_{\theta_{e,e'}})) + f' (|x|, u)\, (-u_{\theta_{e,e'}})\geq 0 \quad \hbox{ in }B\, ,
$$
in the viscosity sense.
(iii) The proof runs as for (ii).
\hfill$\Box$
\begin{remark}\label{concave}
{\rm In statement (i), if $f(x,\cdot)$ is assumed to be concave, then one has
$$
-\mathcal{M}^- (D^2 w)\geq f'(x, u)\, w\quad \hbox{ in } \Omega\, .
$$}
\end{remark}
We are now ready to prove our first symmetry result for viscosity solutions. If $u$ is a viscosity solution of \refe{eq1}, we denote by $\mathcal{L}_u$ the "linearized" fully nonlinear operator
$$
\mathcal{L}_u \, :\, = \mathcal{M}^+ +f'(x,u)\, ,
$$
and by $\lambda_1^\pm(\mathcal{L}_u, \Omega(e))$, $\lambda_1^\pm(\mathcal{L}_u, \Omega(-e))$ the principal eigenvalues of $\mathcal{L}_u$ in the domains $\Omega(\pm e)=\Omega \cap \{ x\cdot (\pm e)>0\}$.
\begin{proposition}\label{prop1} Assume that $\Omega$ is symmetric with respect to the hyperplane $H(e)$, $F$ satisfies \refe{ue}, \refe{lip} and \refe{sime} and that $f$ satisfies \refe{f}. Let $u$ be a viscosity solution of \refe{eq1} and assume further that either
\begin{itemize}
\item[(i)]
$\lambda_1^+(\mathcal{L}_u, \Omega(\pm e))>0$
\end{itemize}
or
\begin{itemize}
\item[(ii)]
$\lambda_1^+(\mathcal{L}_u, \Omega(\pm e))\geq 0$ and $f$ is strictly convex.
\end{itemize}
Then, $u$ is symmetric with respect to the hyperplane $H(e)$.
\end{proposition}
\proof Let us set $w=u-u\circ \sigma_e$ and observe that, by definition, $w$ is antisymmetric with respect to $H(e)$ and satisfies $w=0$ on $\partial \Omega(\pm e)$. By Lemma \ref{diffe}, $w$ is a viscosity subsolution of
$$
\left\{
\begin{array}{c}
-\mathcal{M}^+ (D^2w) \leq f'(x,u)\, w \quad \hbox{ in } \Omega(\pm e)\\[1ex]
w=0 \quad \hbox{ on } \partial \Omega(\pm e)
\end{array}\right.
$$
If $\lambda_1^+(\mathcal{L}_u, \Omega (\pm e))>0$, then by the maximum principle both $w\leq 0$ in $\Omega(e)$ and $w\leq 0$ in $\Omega(-e)$, so that, by antisymmetry, $w\equiv 0$ in $\Omega$. If one of the eigenvalues is zero, say $\lambda_1^+(\mathcal{L}_u, \Omega (e))=0$ and $\lambda_1^+(\mathcal{L}_u, \Omega(-e))>0$ and, by contradiction, $w\not\equiv 0$, then $w<0$ in $\Omega(-e)$ by the strong maximum principle. Therefore, $w>0$ in $\Omega(e)$ and by Proposition \ref{key} $w$ satisfies
$$
-\mathcal{M}^+ (D^2w)= f'(x,u)\, w\quad \hbox{ in } \Omega(e)\, ,
$$
a contradiction to the strict convexity of $f$ by Lemma \ref{diffe} (i).
Analogously, if both $\lambda_1^+(\mathcal{L}_u, \Omega(\pm e))=0$, then, either $w\leq 0$ in $\Omega(\pm e)$, and then again $w\equiv 0$ in $\Omega$, or, otherwise, $w$ is a solution either in $\Omega(e)$ or in $\Omega(-e)$, in contrast with the strict convexity of $f$.
\hfill$\Box$
\begin{remark}{\rm Since $\lambda^-(\mathcal{M}^-+f^\prime(x,u),D)=\lambda^+(\mathcal{M}^++f^\prime(x,u),D)$ for any domain $D$, by Remark \ref{concave} the same conclusion of Proposition \ref{prop1} holds if $f$ is concave.}
\end{remark}
In the remaining part of this section we will exhibit a sufficient condition for the eigenvalue
$\lambda_1^+(\mathcal{L}_u, \Omega(e))$ to be negative when $u$ is a sign changing viscosity solution symmetric
with respect to the hyperplane $H(e)$.
Let us fix, for simplicity, $e=e_1=(1,0,\ldots ,0)\in S^{n-1}$ and let $\Omega$ be a smooth bounded domain symmetric with respect to $H(e_1)$ and convex in the $x_1$--direction, i.e. for any two points in $\Omega$ having the same $x_1$--coordinate, the segment joining them is also contained in $\Omega$. We are going to consider a viscosity solution $u\in C^1(\overline \Omega)$ of the problem
\begin{equation}\label{eq2}
\left\{\begin{array}{c}
-F(x, D^2u)= f(u)\quad \hbox{ in } \Omega\, ,\\[1ex]
u=0 \quad \hbox{ on } \partial \Omega
\end{array}\right.
\end{equation}
Note that in \refe{eq2} $f$ does not depend on $x$.
We recall that the nodal set $\mathcal{N} (u)$ of a solution $u$ of \refe{eq2} is defined as
$$
\mathcal{N}(u) \, := \overline{\left\{ x\in \Omega\, :\, u(x)=0\right\}}\, .
$$
\begin{proposition}\label{prop2}
Let $u\in C^1(\overline \Omega)$ be a sign changing viscosity solution of \refe{eq2}, with $F$ satisfying \refe{ue}, \refe{lip} and \refe{sime} with $e=e_1$ and assume that $u$ is even with respect to $x_1$. Then
$$ \lambda_1^+(\mathcal{L}_u, \Omega(\pm e_1))\geq 0\quad \Longrightarrow \quad \mathcal{N}(u)\cap \partial \Omega\neq \emptyset \, .
$$
\end{proposition}
\proof We follow the argument used in \cite{AP} for semilinear equations, and we prove the equivalent implication
$$ \mathcal{N}(u)\cap \partial \Omega= \emptyset \quad \Longrightarrow \quad \lambda_1^+(\mathcal{L}_u, \Omega(\pm e_1))< 0 \, .
$$
Let us consider the continuous function $u_1=\frac{\partial u}{\partial x_1}$ in the cap $\Omega(e_1)$. We notice that $u_1=0$ on $H(e_1)\cap \overline \Omega$ and that $u_1$ does not change sign on $\partial \Omega \cap \partial \Omega(e_1)$. Indeed, if there were points $Q_1\,,\ Q_2\in \partial \Omega \cap \partial \Omega(e_1)$ such that $u_1(Q_1)>0$ and $u_1(Q_2)<0$, then, since $u=0$ on $\partial \Omega$, there would exist a sequence of points $\{ x_k\}\subset \Omega$ such that $u (x_k)=0$ for every $k$ and dist$(x_k, \partial \Omega)\to 0$. This would be a contradiction to the hypothesis $\mathcal{N}(u)\cap \partial \Omega=\emptyset$. Hence, either $u_1\leq 0$ or $u_1\geq 0$ on $\partial \Omega \cap \partial \Omega(e_1)$. We can assume without loss of generality to be in the first case, since otherwise we can consider, by the symmetry of $u$, the opposite cap $\Omega(-e_1)$.
We further observe that, by Lemma \ref{diffe} (iii), $u_1$ satisfies in the viscosity sense
\begin{equation}\label{equ1}
-\mathcal{L}_u[u_1] \leq 0\quad \hbox{ in } \Omega\, .
\end{equation}
Furthermore, since $u$ is zero on $\partial \Omega$, changes sign in $\Omega$ and is symmetric in the $x_1$--variable, we deduce that $u_1$ must change sign in $\Omega(e_1)$. Then, by the previous consideration on the sign of $u_1$ on $\partial \Omega \cap \partial \Omega(e_1)$, we conclude that there exists an open connected domain $D\subset \Omega(e_1)$ such that $u_1>0$ in $D$ and $u_1=0$ on $\partial D$. Thus, if by contradiction $\lambda_1^+ (\mathcal{L}_u, \Omega(e_1))\geq 0$, then $\lambda_1^+(\mathcal{L}_u, D)>0$ and, by \refe{equ1}, the maximum principle would imply the contradiction $u_1\leq 0$ in $D$.
\hfill$\Box$
When $\Omega=B$ is a ball, $F$ satisfies \refe{ri} and $u$ is a radial sign changing solution of \refe{eq2} with a finite number of nodal regions, then the assumption $\mathcal{N}(u)\cap \partial B=\emptyset$ is obviously satisfied. Hence, we can apply Proposition \ref{prop2} for any direction $e\in S^{n-1}$.
Analogously, if $\Omega=B$ is an annulus, though it is a domain not convex with respect to any direction, a proof similar to that of Proposition \ref{prop2} can be applied (see \cite{AP} for more details). Actually, we have the following result.
\begin{corollary}\label{rad-}If $B$ is a bounded radial domain, $F$ satisfies \refe{ue}, \refe{lip} and \refe{ri} and $u$ is a radial sign changing viscosity solution of \refe{eq2}, then
$$
\lambda_1^+ (\mathcal{L}_u, B(e))<0\quad \forall\, e\in S^{n-1}\, .
$$
\end{corollary}
\proof If $u$ has a finite number of nodal regions, then the conclusion follows directly from Proposition \ref{prop2} and the above considerations. If not, there exists a radial subdomain $\mathcal{B}\subset B$ in which $u$ has exactly two nodal regions. Hence, $\lambda^+_1(\mathcal{L}_u, B(e))<\lambda^+_1(\mathcal{L}_u, \mathcal{B}(e))<0$.
\hfill$\Box$
Finally, some extra considerations can be done for the special case of planar domains $\Omega\subset {\mathbb R}^2$ which are symmetric and convex with respect to two orthogonal directions, say $e_1=(1,0)$ and $e_2=(0,1)$. Note that this kind of domains need not to be convex, but they can be easily proved to be star--shaped with respect to the origin.
Let us call doubly symmetric a continuous function $u$ which is symmetric with respect to both directions $e_i$, $i=1,2$, i.e. a continuous function $u$ which is even in the variables $x_1$ and $x_2$. For such functions we have the following result.
\begin{lemma}\label{ds} Let $\Omega\subset {\mathbb R}^2$ be a domain symmetric and convex with respect to $e_i$, $i=1,2$, and let $u\in C(\overline \Omega)$ be a sign changing, doubly symmetric function with two nodal regions. Then, $\mathcal{N}(u)\cap \partial \Omega=\emptyset$ and $0\notin \mathcal{N}(u)$, that is the nodal line of $u$ neither touches $\partial \Omega$ nor passes through the origin.
\end{lemma}
\proof Let us define $\Omega^+=\{ x\in \Omega\, :\, u(x)>0\}$ and $\Omega^-=\{ x\in \Omega\, :\, u(x)<0\}$. By assumption, both $\Omega^\pm$ are connected open sets, hence connected by arcs, and symmetric with respect to $H(e_i)$, $i=1,2$.
Let us consider a point $P_1\in \Omega^+\setminus \left( H(e_1)\cup H(e_2)\right)$ and let $P_2, P_3, P_4\in \Omega^+$ be the reflected points of $P_1$ with respect to $H(e_1)$, $H(e_2)$ and to the origin. Then, there exists a simple, closed curve $\gamma^+$ joining $P_1$, $P_2$, $P_3$ and $P_4$ and contained in $\Omega^+$, so that $u>0$ on $\gamma^+$. Obviously we can choose $\gamma^+$ not passing through the origin. By the Jordan curve theorem, ${\mathbb R}^2\setminus \gamma^+$ has two connected components, which we call $D_1$ and $D_2$, $D_1$ being the connected component containing the origin and $D_2$ the one which contains $\partial \Omega$. Since $u$ has only two nodal regions, it follows that either $\Omega^-\subset D_1\cap \Omega$ or $\Omega^-\subset D_2\cap \Omega$. In the former case we immediately deduce that $\mathcal{N}(u)\cap \partial \Omega=\emptyset$. In the latter case, we can repeat the above construction in $\Omega^-$, that is we take in $\Omega^-$ four distinct symmetric points $Q_i$, $i=1,2,3,4$ as before, and select a simple closed curve $\gamma^-\subset \Omega^-$ passing through them. Again the Jordan curve theorem implies that ${\mathbb R}^2\setminus \gamma^-$ has two connected components, say $A_1$ which contains $\partial \Omega$, and $A_2$ which contains both $\gamma^+$ and the origin. Then, $\Omega^+$ must be contained in $A_2$, so that $u$ is negative in a neighborhood of $\partial \Omega$ and, again, $\mathcal{N}(u)\cap \partial \Omega=\emptyset$. A similar argument shows also that $0\notin \mathcal{N}(u)$.
\hfill$\Box$
As a consequence of the previous lemma and Proposition \ref{prop2} we deduce the following
\begin{corollary}\label{ds1}
Assume that $u\in C^1(\overline \Omega)$ is a viscosity solution of \refe{eq2}, with $u$ and $\Omega$ as in Lemma \ref{ds} and $F$ satisfying \refe{ue}, \refe{lip} and \refe{sime} for $e=e_i$, $i=1,2$. Then
$$
\lambda_1^+(\mathcal{L}_u, \Omega(\pm e_i))<0\quad \hbox{ for } i=1,2\, .
$$
\end{corollary}
\section{Foliated Schwarz symmetry for viscosity solutions}\label{sec2}
The aim of this section is to establish either full radial symmetry or partial symmetry properties, such as foliated Schwarz symmetry, for viscosity solutions of fully nonlinear elliptic equations in bounded radial domains. Thus, we focus on solutions of the problem
\begin{equation}\label{eq3}
\left\{\begin{array}{c}
-F(x, D^2u)= f(|x|, u)\quad \hbox{ in } B\, ,\\[1ex]
u=0 \quad \hbox{ on } \partial B\, ,
\end{array}
\right.
\end{equation}
and the operator $F$ will be always assumed to satisfy \refe{ue}, \refe{lip} and \refe{ri}.
As a first result, which easily follows from Lemma \ref{diffe} (ii), let us prove the radial symmetry of the usually called "stable" solutions.
\begin{theorem}\label{stable} Let $u$ be a viscosity solution of problem \refe{eq3} such that $\lambda_1^+(\mathcal{L}_u, B)\geq 0$. Then, $u$ is radially symmetric in $B$.
\end{theorem}
\proof Let us fix any pair of linearly independent unit vectors $e, e'\in S^{n-1}$, and let us set $\theta=\theta_{e,e'}$. Then, by Lemma \ref{diffe} (ii) and the boundary condition in \refe{eq3}, the derivative $u_\theta$ satisfies, in the viscosity sense,
$$
\left\{\begin{array}{c}
-\mathcal{L}_u[u_\theta] \leq 0\quad \hbox{ in } B\\[1ex]
u_\theta=0 \quad \hbox{ on } \partial B
\end{array}\right.
$$
The assumption $\lambda_1^+(\mathcal{L}_u, B)\geq 0$ implies that either $u_\theta\leq 0$ in $B$, or, by Proposition \refe{key}, $u_\theta>0$ in $B$. Moreover, in the first case, by the strong maximum principle, either $u_\theta<0$ in $B$ or $u_\theta \equiv 0$ in $B$. Therefore, three are the possible cases: $u_\theta<0$, $u_\theta>0$ or $u_\theta\equiv 0$ in $B$. But since $u$ is $2\pi$--periodic with respect to $\theta$, its derivative $u_\theta$ has to vanish somewhere in $B$. Hence, $u_\theta\equiv 0$ in $B$, and the arbitrariness of $e$ and $e'$ implies that $u$ is radially symmetric.
\hfill$\Box$
The definition of foliated Schwarz symmetric functions was recalled in the Introduction, see Definition \ref{fss}. Let us now
give some characterizations.
\begin{lemma}\label{fssc0} A function $u\in C(\overline{B})$ is foliated Schwarz symmetric if and only if for every $e\in S^{n-1}$ one has either $u(x)\geq u(\sigma_e(x))$ in $B(e)$ or $u(x)\leq u(\sigma_e(x))$ in $B(e)$. More precisely, $u$ is foliated Schwarz symmetric with respect to the direction $p\in S^{n-1}$ if and only if $u(x)\geq u(\sigma_e(x))$ for all $x\in B(e)$ and for every $e\in S^{n-1}$ such that $e\cdot p\geq 0$.
\end{lemma}
This property was first stated in \cite{Br} and for a detailed proof we refer to \cite{W}. A different proof for solutions of semilinear elliptic equations can be found in \cite{GPW} (see also \cite{PR}).
On the other hand, for differentiable functions, the foliated Schwarz symmetry can be characterized as a sign property of the derivative $u_{\theta_{e,e'}}$, for linearly independent unit vectors $e, e'\in S^{n-1}$.
\begin{proposition}\label{fssc1} A function $u\in C^1(B)\cap C(\overline{B})$ is foliated Schwarz symmetric if and only if there exists a direction $e\in S^{n-1}$ such that $u$ is symmetric with respect to $H(e)$ and for any other direction $e'\in S^{n-1}\setminus \{\pm e\}$ one has either $u_{ \theta_{e,e'}} \geq 0$ in $B(e)$ or $u_{\theta_{e,e'}}\leq 0$ in $B(e)$.
\end{proposition}
Let us recall that the sufficiency of this condition was already observed in \cite{DGP} and \cite{PW}, but let us include the proof for the sake of completeness.
\proof Let $u\in C^1(B)\cap C(\overline{B})$ be foliated Schwarz symmetric with respect to a direction $p\in S^{n-1}$, and let us fix $e\in S^{n-1}$ such that $e\cdot p=0$. Then, $u$ is clearly symmetric with respect to $H(e)$. Moreover, let $e'\in S^{n-1}$, with $e'\neq \pm e$. In order to show that either $u_{\theta_{e,e'}}\geq 0$ or $u_{\theta_{e,e'}}\leq 0$ in $B(e)$, we can assume that $e'\cdot e=0$ and that $\theta_{e,e'}\in [-\pi,\pi]$ is the angle formed by $e'$ and the orthogonal projection of $x$ on the plane $\Pi(e,e')$. We claim that if $e'\cdot p\geq 0$ then $u_{\theta_{e,e'}}\leq 0$ in $B(e)$, whereas if $e'\cdot p\leq 0$ then $u_{\theta_{e,e'}}\geq 0$ in $B(e)$.
Indeed, using cylindrical coordinates with respect to $\Pi(e,e')$, let $x=(r, \theta, \eta)$ and $x'=(r, \theta', \eta)$ be in $B(e)$, for some $r>0$, $\eta\in {\mathbb R}^{n-2}$ and $0<\theta \leq \theta'<\pi$. Then, there exists $\nu\in S^{n-1}\cap \Pi(e,e')$ such that $x'=\sigma_\nu(x)$ , $\nu\cdot x>0$ and $\nu\cdot p>0$ if $p\cdot e'>0$, whereas $\nu\cdot p<0$ if $p\cdot e'<0$. Hence, by Lemma \ref{fssc0}, one has $u(x)\geq u(x')$ and therefore $u_{\theta_{e,e'}}\leq 0$ in $B(e)$ provided that $p\cdot e'\geq 0$, as well as $u_{\theta_{e,e'}}\geq 0$ in $B(e)$ if $p\cdot e'\leq 0$.
Conversely, assume that there exists $e\in S^{n-1}$such that $u$ is symmetric with respect to $H(e)$, and for every $e'\in S^{n-1}\setminus \{ \pm e\}$ the derivative $u_{\theta_{e,e'}}$ does not change sign in $B(e)$. Up to a rotation, we can assume that $e=e_2=(0,1,\ldots ,0)$. Again by Lemma \ref{fssc0}, we have to prove that for any $e'\in S^{n-1}$ either $u(x)\geq u(\sigma_{e'}(x))$ or $u(x)\leq u(\sigma_{e'}(x))$ for all $x\in B(e')$. By assumption if $e'=\pm e_2$ then $u(x)=u(\sigma_{e'}(x))$ , so we can assume $e'\neq \pm e_2$. Moreover, again up to a rotation around the $e_2$-axis, we can suppose that $e'$ lays on the $x_1x_2$-plane, with $e'=(\cos \theta_0, \sin \theta_0,\ldots ,0)$ for some $\theta_0\in \left( -\frac{\pi}{2}, \frac{\pi}{2}\right)$. Thus, the plane $\Pi (e, e')$ coincides with the $x_1x_2$-plane and let us denote just with $\theta\in [-\pi,\pi]$ the polar angle coordinate $\theta_{e,e'}$ given by the angle formed by the projection on the $x_1x_2$-plane with $e_1$. By assumption, we have that either $u_\theta (x)\geq 0$ or $u_\theta (x)\leq 0$ for all $x\in B$ with $x_2>0$. Moreover, using polar coordinates in the $x_1x_2$-plane, the reflection map $\sigma_{e'}$ may be written as
$$
\sigma_{e'}(r\cos \theta, r\sin \theta, \tilde{x})= (r\cos (2\theta_0-\theta+\pi), r\sin (2\theta_0-\theta+\pi), \tilde{x})\, ,
$$
with $\tilde{x}=(x_3,\ldots,x_n)\in {\mathbb R}^{n-2}$.
Now, we claim that $u(x)\leq u(\sigma_{e'}(x))$ in $B(e')$ if $u_\theta \geq 0$ in $B(e_2)$, whereas $u(x)\geq u(\sigma_{e'}(x))$ in $B(e')$ provided that $u_\theta \leq 0$ in $B(e_2)$. Indeed, assume that $u_\theta \geq 0$ in $B(e_2)$, and let us take first $x\in B(e')\cap B(e_2)$. Thus, we have $x=(r\cos \theta, r\sin \theta, \tilde{x})$ for some $\theta \in (0,\pi)$ such that $|\theta-\theta_0|<\frac{\pi}{2}$. This implies that the angle coordinate of the reflected point satisfies $2\theta_0-\theta+\pi>\theta>0$. Two cases are possible: either $\theta\geq 2\theta_0$ or $\theta<2\theta_0$. In the first case, both $x$ and $\sigma_{e'}(x)$ belong to $\overline{B(e_2)}$ and, by the non decreasing monotonicity with respect to $\theta$, it follows that $u(x)\leq u(\sigma_{e'}(x))$. In the latter case, by periodicity, symmetry and monotonicity, we again obtain
$$
\begin{array}{ll}
u(\sigma_{e'}(x)) & = u(r\cos(2\theta_0-\theta+\pi), r\sin (2\theta_0-\theta+\pi), \tilde{x})\\[2ex]
& = u(r\cos(2\theta_0-\theta-\pi), r\sin (2\theta_0-\theta-\pi), \tilde{x})\\[2ex]
& = u(r\cos(-2\theta_0+\theta+\pi), r\sin (-2\theta_0+\theta+\pi), \tilde{x})\geq u(x)\, .
\end{array}
$$
Assume now that $x\in B(e')\setminus B(e_2)$, so that $\theta \in (-\pi, 0]$. Observe that we also have $2\theta_0-\theta -\pi <\theta\leq 0$. Again, we distinguish two cases: either $\theta \leq 2\theta_0$ or $\theta>2\theta_0$. In the former case, since $u_\theta \leq 0$ in $B(-e_2)$ by symmetry and both $x$ and $\sigma_{e'}(x)$ belong to $\overline{B(-e_2)}$, we immediately obtain
$$
u(x)\leq u(r\cos(2\theta_0-\theta -\pi), r\sin (2\theta_0-\theta -\pi), \tilde{x}) =u(\sigma_{e'}(x))\, .
$$
On the other hand, if $\theta>2\theta_0$, by symmetry and monotonicity as before, we have as well
$$
\begin{array}{ll}
u(\sigma_{e'}(x)) & = u(r\cos(2\theta_0-\theta+\pi), r\sin (2\theta_0-\theta+\pi), \tilde{x})\\[2ex]
& = u(r\cos(-2\theta_0+\theta-\pi), r\sin (-2\theta_0+\theta-\pi), \tilde{x})\geq u(x)\, .
\end{array}
$$
Hence, the inequality $u(x)\leq u(\sigma_{e'}(x))$ is proved in all cases. The same arguments can be used to show that
$u(x)\geq u(\sigma_{e'}(x))$ if $u_\theta\leq 0$ in $B(e_2)$ and this concludes the proof.
\hfill$\Box$
By Proposition \ref{fssc1} and Lemma \ref{diffe} (ii) we can easily deduce a first symmetry result for viscosity solutions of \refe{eq3}, which is the fully nonlinear extension of an analogous result for semilinear elliptic equation, see Proposition 2.3 in \cite{PW}.
\begin{theorem}\label{simandlam}
Let $u$ be a viscosity solution of \refe{eq3} and assume that there exists a direction $e\in S^{n-1}$ such that $u$ is symmetric with respect to $H(e)$. If $\lambda_1^+(\mathcal{L}_u, B(e))\geq 0$, then $u$ is foliated Schwarz symmetric and if $\lambda_1^+(\mathcal{L}_u, B(e))> 0$, then $u$ is radially symmetric.
\end{theorem}
\proof Let us show that, for any $e'\in S^{n-1}\setminus \{ \pm e\}$, $u_{\theta_{e,e'}}$ does not change sign in $B(e)$. By Lemma \ref{diffe} (ii), by the boundary condition in \refe{eq3} and by the assumption of symmetry of $u$ with respect to $H(e)$, the function $u_{\theta_{e,e'}}$ satisfies
$$
\left\{
\begin{array}{c}
-\mathcal{L}_u[ u_{\theta_{e,e'}}] \leq 0\quad \hbox{ in } B(e)\\[1ex]
u_{\theta_{e,e'}}=0 \quad \hbox{ on } \partial B(e)
\end{array}\right.
$$
Now, if $\lambda^+_1(\mathcal{L}_u, B(e))>0$, then the maximum principle holds true for operator $\mathcal{L}_u$ and we deduce $u_{\theta_{e,e'}}\leq 0$ in $B(e)$. On the other hand, if $\lambda^+_1(\mathcal{L}_u, B(e))=0$, then either $u_{\theta_{e,e'}}\leq 0$ in $B(e)$ or, by Proposition \ref{key}, $u_{\theta_{e,e'}}>0$ in $B(e)$. In any case, $u_{\theta_{e,e'}}$ does not change sign in $B(e)$. Then, by Proposition \ref{fssc1}, $u$ is foliated Schwarz symmetric.
Moreover, if $\lambda^+_1(\mathcal{L}_u, B(e))>0$, again by Lemma \ref{diffe} (ii) and the maximum principle, we obtain also $-u_{\theta_{e,e'}}\leq 0$ in $B(e)$. Hence, $u_{\theta_{e,e'}}\equiv 0$ in $B(e)$, and by the arbitrariness of $e'$ it follows that $u$ is radially symmetric.
\hfill$\Box$
We are now ready to prove Theorem \ref{lam0}, which states that the a priori symmetry assumption on $u$ in Theorem \ref{simandlam} can be dropped, provided that $f(|x|,\cdot)$ is convex in ${\mathbb R}$.
{\it Proof of Theorem \ref{lam0}}. Let $e$ be the direction for which $\lambda_1^+(\mathcal{L}_u, B(e))\geq 0$ and
let us set $w_e(x)=u(x)-u(\sigma_e(x))$. If $w_e\equiv 0$, then $u$ is symmetric with respect to $H(e)$, and we reach the conclusion by Theorem \ref{simandlam}. Therefore, we assume in the following $w_e\not\equiv 0$. By Lemma \ref{diffe} (i) $w_e$ in particular satisfies, in the viscosity sense,
$$
\left\{
\begin{array}{c}
-\mathcal{L}_u [w_e]\leq 0 \quad \hbox{ in } B(e)\\[1ex]
w_e=0\quad \hbox{ on } \partial B(e)
\end{array}\right.
$$
Now, if $\lambda_1^+(\mathcal{L}_u, B(e))>0$, by the maximum principle one has $w_e\leq 0$ in $B(e)$ and then, by the strong maximum principle, $w_e<0$ in $B(e)$. If $\lambda_1^+(\mathcal{L}_u, B(e))=0$, then, by Proposition \ref{key}, either $w_e\leq 0$, and then again $w_e<0$ in $B(e)$, or $w_e>0$ (and $\mathcal{L}_u[w_e]=0$ in $B(e)$). Thus, in any case, we have two possibilities: either
$w_e<0$ or $w_e>0$ in $B(e)$.
Next, in order to prove that $u$ is foliated Schwarz symmetric, we cannot apply directly Proposition \ref{fssc1}, since we are not able to find a fixed vector $\tilde{e}\in S^{n-1}$ such that $u$ is symmetric with respect to $H(\tilde{e})$ and for any other $e'\in S^{n-1}$, the function $u_{\theta_{\tilde{e},e'}}$ does not change sign in $B(\tilde{e})$. On the other hand, we can
repeat the argument of the proof of Proposition \ref{fssc1}: for any $\nu\in S^{n-1}$, in order to show that either $u(x)\geq u(\sigma_\nu (x))$ or $u(x)\leq u(\sigma_\nu(x))$ in $B(\nu)$, it is enough to show that there exists $e'\in S^{n-1}\cap \Pi(e,\nu)$ such that
$u$ is symmetric with respect to $H(e')$ and the derivative $u_{\theta_{e,e'}}$ (or $u_{\theta_{e',\nu}}$) does not change sign in $B(e')$. Thus, the proof will be completed if we show that for any plane $\Pi$ through $e$, there exists $e'\in S^{n-1}\cap \Pi$ such that $u$ is symmetric with respect to $H(e')$ and the derivative $u_{\theta_{e,e'}}$ does not change sign in $B(e')$.
We first consider the case $w_e<0$ in $B(e)$. Without loss of generality, we assume that $e=(0,1, \ldots ,0)$ and that $\Pi$ is the plane spanned by $(1,0, \ldots, 0)$ and $e$. For $\theta\geq 0$, let us consider the direction $e(\theta)=(\sin \theta, \cos \theta, 0, \ldots, 0)\in \Pi$, so that $e(0)=e$. We apply the rotating plane method in order to find $\theta'\in (0,\pi)$ such that $u$ is symmetric with respect to $H(e')$ with $e'=e(\theta')$. We set
\begin{equation}\label{tetap}
\theta' \, :=\sup \{ \tilde{\theta} \in [0,\pi)\, :\, w_{e(\theta)}< 0\ \hbox{in }\ B(e(\theta))\, ,\ \forall\, \theta\in [0, \tilde{\theta}]\}\, .
\end{equation}
We notice that $\theta'$ is well defined since $w_e<0$ in $B(e)$, and, by continuity, $w_{e(\theta')}\leq 0$ in $B(e(\theta'))$. This implies $\theta'<\pi$, since $w_{e(\pi)}=w_{-e}=-w_e\circ \sigma_e>0$ in $B(-e)$. We claim that $w_{e(\theta')}\equiv 0$, i.e. $u$ is symmetric with respect to $H(e(\theta'))$. For, assume by contradiction that $w_{e(\theta')}\not\equiv 0$, so that, by the strong maximum principle, $w_{e(\theta')}<0$ in $B(e(\theta'))$. In this case, we can find $\epsilon>0$ small enough such that the inequality $w_{e(\theta)}< 0$ in $B(e(\theta))$ holds true for all $\theta \in [0, \theta'+\epsilon)$, and this contradicts the definition of $\theta'$. Indeed, for $\epsilon$ sufficiently small, we can select a compact set $K\subset \bigcap_{\theta'\leq \theta<\theta'+\epsilon} B(e(\theta))$ such that, for all $\theta\in [\theta',\theta'+\epsilon)$ the measure of the set $B(e(\theta))\setminus K$ is so small that the operator $\mathcal{L}_u$ satisfies the maximum principle in $B(e(\theta))\setminus K$. Moreover, by assumption, there exists $\eta>0$ such that $w_{e(\theta')}\leq -\eta$ in $K$ and then, for $\epsilon$ small enough, we have $w_{e(\theta)}\leq -\eta/2$ in $K$ for all $\theta\in [\theta', \theta'+\epsilon)$. Thus, by the maximum principle and the strong maximum principle, we have $w_{e(\theta)}< 0$ in $B(e(\theta))\setminus K$, and then $w_{e(\theta)}< 0$ in $B(e(\theta))$ for all $\theta\in [0, \theta'+\epsilon)$, in contrast with the choice of $\theta'$.
We further observe that, by Hopf's lemma, for all $\theta \in [0, \theta')$, one has
$$
\frac{\partial}{\partial e(\theta)}w_{e(\theta)}=2 \, Du\cdot e(\theta)<0\ \hbox{ on } H(e(\theta))\cap B\, ,
$$
$e(\theta)$ being the inner unit normal vector to $B(e(\theta))$ on $\partial B(e(\theta))\cap B$. This implies that, with respect to the cylindrical coordinates $x=(r\cos \theta, -r\sin \theta, x_3,\ldots, x_n)$, one has
$$
u_\theta = \left\{ \begin{array}{ll}
-r\, Du\cdot e(\theta)>0 & \hbox{ in }\ B(e')\setminus B(e)\\[1ex]
r\, Du\cdot e(\theta)<0 & \hbox{ in }\ \overline{B(e)}\setminus \overline{B(e')}\\[1ex]
\pm r\ Du\cdot e(\theta')=0 & \hbox{ in }\ H(e')\cap B
\end{array}\right.
$$
By using also Lemma \ref{diffe} (ii), it then follows that $u_\theta$ in particular satisfies
$$
\left\{ \begin{array}{c}
-\mathcal{L}_u[-u_\theta]\leq 0 \quad \hbox{ in } B(e)\cap B(e')\\[1ex]
-u_\theta \leq 0 \quad \hbox{ on } \partial\left( B(e)\cap B(e')\right)
\end{array}\right.
$$
Since $\lambda_1^+\left(\mathcal{L}_u, B(e)\cap B(e')\right)>\lambda_1^+(\mathcal{L}_u, B(e))\geq 0$, we can apply the maximum principle, and then the strong maximum principle, in order to deduce $-u_\theta < 0$ in
$B(e)\cap B(e')$. Summing up, we have proved that $u_\theta >0$ in $B(e')$, and this concludes the proof in the case $w_e<0$ in $B(e)$.
On the other hand, if $w_e>0$ in $B(e)$, one has $w_{-e}<0$ in $B(-e)$ and we can apply again the rotating plane method starting with $e(0)=-e$ and considering the directions $e(\theta)=(\sin \theta, -\cos \theta, \ldots, 0)$ for $\theta\geq 0$.
By defining $\theta'\in (0,\pi)$ as in \refe{tetap}, we find a unit vector $e'=e(\theta')\in S^{n-1}$ such that $u$ is symmetric with respect to $H(e')$ and $w_{e(\theta)}<0$ in $B(e(\theta))$ for all $\theta\in [0, \theta')$. By means of Hopf's lemma as above, we also deduce that, again with respect to the cylindrical coordinates $x=(r\cos \theta, -r\sin \theta, x_3,\ldots, x_n)$, one has
$$
u_\theta = \left\{ \begin{array}{ll}
-r\, Du\cdot e(\theta)>0 & \hbox{ in }\ B(e')\setminus B(-e)\\[1ex]
r\, Du\cdot e(\theta)<0 & \hbox{ in }\ \overline{B(-e)}\setminus \overline{B(e')}\\[1ex]
\pm r\, Du\cdot e(\theta')=0 & \hbox{ in }\ H(e')\cap B
\end{array}\right.
$$
Then, the maximum principle applied to $u_\theta$ in $B(e)\setminus \overline{B(e')}$ yields $u_\theta<0$ in $B(-e')$, so that, by symmetry, $u_\theta>0$ in $B(e')$.
\hfill$\Box$
\begin{remark} {\rm Let us observe that the only assumption that there exists a direction $e\in S^{n-1}$ such that $\lambda_1^+(\mathcal{L}_u, B(e))>0$, i.e. the positivity of the principal eigenvalue in just one cap $B(e)$, does not imply the radial symmetry of $u$. This is somehow in contrast with the assertion of Theorem \ref{simandlam} in the case when $\lambda_1^+(\mathcal{L}_u, B(e))> 0$; however one should note that in Theorem \ref{simandlam} the symmetry of $u$ with respect to $H(e)$ was assumed. A counterexample in the case when the symmetry assumption is dropped can be obtained by considering the least--energy (positive) solution of the semilinear problem
$$
\left\{\begin{array}{c}
-\Delta u=u^p\quad \hbox{ in } A\\[1ex]
u=0 \quad \hbox{ on } \partial A
\end{array}\right.
$$
where $A$ is an annulus in ${\mathbb R}^n$, $n\geq3$ and $p<\frac{n+2}{n-2}$ is close to the critical exponent $\frac{n+2}{n-2}$. It has been shown in several papers that $u$ is foliated Schwarz but not radially symmetric. On the other hand, it is easy to see that there are directions (indeed, infinitely many!) $e\in S^{n-1}$ such that $\lambda_1^+(\Delta +p\, |u|^{p-1}, B(e))>0$ whereas $\lambda_1^+(\Delta +p\, |u|^{p-1}, B(-e))<0$ and, obviously, $H(e)$ is not a symmetry hyperplane for $u$ (see \cite{PR} for more details).}
\end{remark}
By Theorem \ref{lam0}, at least for convex nonlinearities $f$, the condition
$\lambda_1^+(\mathcal{L}_u, B(e))\geq 0$ for some $e\in S^{n-1}$ is sufficient for $u$ to be
foliated Schwarz symmetric. Concerning necessary conditions, we have the following result.
\begin{theorem}\label{lam-} Assume that problem \refe{eq3} has a solution $u$ which is not radial but foliated Schwarz symmetric with respect to $p\in S^{n-1}$. Then, for all $e\in S^{n-1}$ such that $e\cdot p=0$, one has
$$\lambda^-_1(\mathcal{L}_u, B(e))\geq 0\, .$$
\end{theorem}
\proof For $e\in S^{n-1}$ orthogonal to $p$, let us denote by $\theta$ the polar angle coordinate $\theta_{p,e}$ defined as the angle formed by $p$ and the orthogonal projection of $x$ in the plane $\Pi(p,e)$. By Proposition \ref{fssc1} and by Lemma \ref{diffe} (ii), $u_\theta$ satisfies
$$
\left\{ \begin{array}{c}
-\mathcal{L}_u[u_\theta]\leq 0\, ,\ \quad \hbox{ in } B(e)\\[1ex]
u_\theta\leq 0 \ \hbox{ in } B(e)\, ,\ u_\theta=0 \quad \hbox{ on } \partial B(e)
\end{array}\right.
$$
The strong maximum principle implies that either $u_\theta <0$ or $u_\theta\equiv 0$ in $B(e)$. Since $u$ is not radially symmetric, we deduce $u_\theta<0$ in $B(e)$ and therefore, by its very definition, $\lambda_1^-(\mathcal{L}_u, B(e))\geq 0$.
\hfill$\Box$
\begin{remark}\label{necelam+}
{\rm We notice that, if $u$ is not radial but foliated Schwarz symmetric with respect to $p$, then, for any $e\in S^{n-1}$ such that $e\cdot p=0$, we have $\lambda_1^+(\mathcal{L}_u, B(e))\leq 0$ by Theorem \ref{simandlam}. Thus, in the semilinear case for which $\alpha=\beta$ and $\lambda_1^+(\mathcal{L}_u, B(e))=\lambda_1^-(\mathcal{L}_u, B(e))$, Theorem \ref{lam-} yields that if $u$ is a not radial foliated Schwarz symmetric solution, then necessarily
$$
\lambda_1(\Delta +f'(|x|,u), B(e))=0
$$
for all $e\in S^{n-1}$ orthogonal to the symmetry axes of $u$.}
\end{remark}
\section{Applications and spectral properties.}\label{sec4}
The main symmetry result of Theorem \ref{lam0} was based on the assumption that there exists some direction $e\in S^{n-1}$ such that $\lambda_1^+(\mathcal{L}_u,B(e))\geq 0$. We wish to comment on this eigenvalue and its role in providing bounds for the eigenvalues of the operator $\mathcal{M}^+$.
Let us start by recalling that in the introduction, we introduced the value
$\mu_2^+=\mu^+_2(\mathcal{L}_u,\Omega)$ defined in \refe{mu} for any bounded domain, and we showed that its
non negativity, when $\Omega=B$ is a radial domain, easily implies, by Theorem \ref{lam0}, that $u$ is foliated Schwarz symmetric. It would be very interesting to study the sign of $\mu^+_2$ for positive solutions of \refe{eq3}, in particular for those found in \cite{QS}.
Let us observe that when $\alpha=\beta$, i.e. when $F$ is the Laplace operator, $\mu^+_2$ is the second eigenvalue of $\mathcal{L}_u$, hence the inequality $\mu_2^+\geq 0$ just means that $u$ has Morse index less than or equal to one. On the contrary,
in the fully nonlinear case the following proposition holds.
\begin{proposition}\label{secn}
If $\alpha<\beta$, then $\mu^+_2(\mathcal{L}_u,\Omega)$ is not an eigenvalue for $\mathcal{L}_u$ in $\Omega$ with corresponding sign changing eigenfunctions having exactly two nodal regions.
\end{proposition}
\begin{proof}
Suppose by contradiction that $\mu_2^+=\mu^+_2(\mathcal{L}_u,\Omega)$ is such an eigenvalue.
Hence, there exists a sign changing function $\psi$ solution of
$$\left\{\begin{array}{c}
\mathcal{M}^+(D^2 \psi)+(f^\prime(|x|,u)+\mu^+_2)\psi=0 \quad \mbox{in}\ \Omega\\[1ex]
\psi=0\quad \mbox{on}\ \partial \Omega\, ,
\end{array}
\right.
$$
such that $\Omega^{-}=\{x\in \Omega\, :\, \psi(x)<0\}$ and $\Omega^{+}=\{x\in \Omega\, :\, \psi(x)>0\}=\Omega\setminus \overline{\Omega^-}$ are subdomains of $\Omega$. Since $\alpha<\beta$, Proposition \ref{prl} yields
$$\lambda_1^+(\mathcal{L}_u,\Omega^-)<\lambda_1^-(\mathcal{L}_u,\Omega^-)=\mu^+_2=\lambda_1^+(\mathcal{L}_u,\Omega^+).$$
By these inequalities and using again Proposition \ref{prl}, one can choose $D$ containing $\Omega^+$ but sufficiently close to it so that
$$\lambda_1^+(\mathcal{L}_u,\Omega^-)<\lambda_1^+(\mathcal{L}_u,\Omega\setminus \overline D)\leq\lambda_1^+(\mathcal{L}_u,D)<\lambda_1^+(\mathcal{L}_u,\Omega^+)=\mu^+_2\, ,$$
and this contradicts the fact that by the definition (\ref{mu}) we have $\mu^+_2\leq \lambda_1^+(\mathcal{L}_u,D)$.
\end{proof}
\begin{remark} {\rm The proof of Proposition \ref{secn} leads to believe that a natural candidate for being the second eigenvalue of $\mathcal{L}_u$ should be
$$
\gamma^+_2(\mathcal{L}_u,B)=\inf_{D\subset B}\max\left\{\lambda_1^+(\mathcal{L}_u,D),\lambda_1^-(\mathcal{L}_u,B\setminus \overline D)\right\}\geq \mu_2^+(\mathcal{L}_u, B)\, .
$$
It would be also interesting to know whether the non negativity of $\gamma^+_2(\mathcal{L}_u,B)$ would imply that $u$ is foliated Schwarz symmetric.}
\end{remark}
\smallskip
Let us remark that Proposition \ref{secn} holds for any operator of the form $\mathcal{L}[\varphi]=\mathcal{M}^+(D^2\varphi)+c(x)\varphi$. For simplicity we will, from now on, suppose that $c(x)=0$, i.e. we concentrate on the Pucci operator $\mathcal{M}^+$.
Let us now state a few results related to eigenvalues higher than the principal ones that can be deduced as consequences of the symmetry result of Theorem \ref{lam0}. We wish to emphasise that in \cite{A}, Armstrong defined
$$\Lambda_2=\inf\{\lambda>\lambda_1^- \, :\, \lambda\ \mbox{ is an eigenvalue of $\mathcal{M}^+$}\ \}.$$
He then proved that $\Lambda_2>\lambda_1^-$ and that for any $\mu\in (\lambda_1^-,\Lambda_2)$ and for any
continuous $f$ there exists a solution of the Dirichlet problem
$$\left\{\begin{array}{lc}
\mathcal{M}^+(D^2 u)+\mu u=f & \mbox{in}\ B\\
u=0& \mbox{on}\ \partial B.
\end{array}
\right.
$$
Hence the importance of any estimate on $\Lambda_2$.
Let us call \emph{nodal eigenvalues} the eigenvalues that are not the principal ones, since $\lambda_1^+$ and $\lambda_1^-$ are the only ones having eigenfunctions that do not change sign.
For simplicity, let us also denote by $\tilde{\lambda}_1^+=\lambda_1^+(\mathcal{M}^+,B(e))$, i.e. the principal eigenvalue in any half domain $B(e)$ (since it clearly does not depend on $e$), and by $\lambda_2^r$ the smallest radial nodal eigenvalue in $B$.
\begin{theorem}\label{lame}
The following inequalities hold
$$\lambda_2^r>\tilde{\lambda}_1^+\quad \hbox{and}\quad \Lambda_2 \geq \tilde{\lambda}_1^+\, .$$
\end{theorem}
\proof Remark first that Corollary \ref{rad-} implies that if $\lambda$ is any nodal radial eigenvalue, then, for any $e\in S^{n-1}$,
\begin{equation}\label{y}
\lambda_1^+(\mathcal{M}^++\lambda, B(e))< 0\, .
\end{equation}
But
$$\lambda_1^+(\mathcal{M}^++\lambda, B(e))=\tilde{\lambda}^+_1-\lambda\, ,$$
so that the first inequality of the statement follows.
Next, in order to prove the second inequality, suppose by contradiction that for some
$
\lambda<\tilde{\lambda}_1^+
$
there exists $\psi\neq0$ sign changing solution of
$$\left\{\begin{array}{lc}
\mathcal{M}^+(D^2\psi)+\lambda \psi=0 & \mbox{in}\ B\\
\psi=0 & \mbox{on}\ \partial B.
\end{array}
\right.
$$
Then
$$\lambda_1^+(\mathcal{L}_\psi, B(e))=\lambda_1^+(\mathcal{M}^++\lambda, B(e)))=\tilde{\lambda}^+_1-\lambda>0\, .
$$
By Proposition \ref{prop1} it follows that $\psi$ is radially symmetric and then (\ref{y}) holds true, a contradiction.
\hfill$\Box$
Let us observe that if it happens that $\lambda_1^-$ is larger than $\tilde{\lambda}_1^+$, then the estimate $\Lambda_2\geq \tilde{\lambda}_1^+$ provided by Theorem \ref{lame} is not relevant. However, when the ellipticity constants $\alpha$ and $\beta$ are sufficiently close to each other, this is not the case. It would be interesting to estimate the gap $\lambda_1^--\lambda_1^+$ in dependence of $\alpha$ and $\beta$ and the relation between $\lambda_1^-$ and $\tilde{\lambda}_1^+$.
In the two dimensional case, Theorem \ref{lame} can be extended to a larger class of domains, precisely to domains $\Omega$ which are symmetric and convex with respect to two orthogonal directions, say $e_1=(1,0)$ and $e_2=(0,1)$, i.e. the same kind of domains considered in Section 2.
Following the same notation, we consider the eigenvalues $\lambda^+_1(\mathcal{M}^+,\Omega(e_1))$ and
$\lambda^+_1(\mathcal{M}^+,\Omega(e_2))$.
By using Proposition \ref{prop1} and Corollary \ref{ds1}, the analogous result to Theorem \ref{lame} is
\begin{theorem} Let $\Omega$ be as in Lemma \ref{ds} and
let $\lambda$ be a nodal eigenvalue for $\mathcal{M}^+$ in $\Omega$ associated with an eigenfunction $\psi$ having two nodal regions. Then:
\begin{itemize}
\item[(i)] $\lambda\geq \min\left\{ \lambda^+_1(\mathcal{M}^+,\Omega(e_1)), \lambda^+_1(\mathcal{M}^+,\Omega(e_2)) \right\}\, ;$
\smallskip
\item[(ii)] if $\psi$ is doubly symmetric, then
$$\lambda>\max\left\{ \lambda^+_1(\mathcal{M}^+,\Omega(e_1)), \lambda^+_1(\mathcal{M}^+,\Omega(e_2)) \right\}\, .$$
\end{itemize}
\end{theorem}
The proof proceeds as the one of Theorem \ref{lame}.
\medskip
To conclude, we observe that a question which remains open is whether $\tilde{\lambda}_1^+$ is a nodal eigenvalue for $\mathcal{M}^+$ in $B$, as for the laplacian, or not. Note that if this was the case, then, by Theorem \refe{lame}, $\tilde{\lambda}_1^+$ would be the smallest nodal eigenvalue of $\mathcal{M}^+$ in $B$.
Next we describe some qualitative
properties that a corresponding eigenfunction should have.
\begin{proposition}\label{pis}
Assume that $\tilde{\lambda}_1^+$ is a nodal eigenvalue for $\mathcal{M}^+$ in $B$ and that $\psi_2$ is a corresponding eigenfunction, i.e.
$$\left\{\begin{array}{c}
\mathcal{M}^+(D^2\psi_2)+\tilde{\lambda}_1^+ \psi_2=0 \quad \mbox{in}\ B\\[1ex]
\psi_2=0 \quad \mbox{on}\ \partial B
\end{array}
\right.
$$
Then
\begin{itemize}
\item[(i)] $\psi_2$ is not radial;
\item[(ii)] $\psi_2$ is foliated Schwarz symmetric;
\item[(iii)] the nodal set of $\mathcal{N}(\psi_2)$ does intersect the boundary;
\item[(iv)] if $\alpha<\beta$, then, for any $e\in S^{n-1}$, $B^+:=\{x\in B\, :\, \psi_2>0\}\neq B(e)$.
\end{itemize}
\end{proposition}
\proof (i) is just the first inequality in Theorem \ref{lame}, and (ii) follows directly from Theorem \ref{lam0}. Then, (ii) and Proposition \ref{prop2} yield (iii).
Finally, in order to prove (iv), suppose by contradiction that, for some $e$, $B(e)=B^+$. This implies that $B^-=B(-e)$. Hence, $\lambda_1^-(\mathcal{M}^+,B(-e))=\lambda_1^+(\mathcal{M}^+,B(e))=\tilde{\lambda}^+_1$. On the other hand, the symmetry of the domain implies
$\lambda_1^-(B(-e))=\lambda_1^-(B(e))>\lambda_1^+(B(e))$, if $\alpha<\beta$. The contradiction proves the claim.
\hfill$\Box$
Let us denote by $\psi_1^+$ a positive eigenfunction in $B(e)$ corresponding to $\tilde{\lambda}_1^+$. Then, statement (iv) of Proposition \ref{pis} implies that $\psi_1$, the sign changing function constructed by odd reflection of $\psi_1^+$, is not an eigenfunction for $\mathcal{M}^+$ provided that $\alpha<\beta$, contrarily to the case when $\alpha=\beta$. The same argument shows that, if $\alpha<\beta$, then $\mathcal{M}^+$ cannot have a nodal eigenfunction antisymmetric with respect to $H(e)$ for some $e\in S^{n-1}$ and such that $B^+=B(e)$.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 2,935
|
I was reminded of this sweet fact when you had your last day today at Beach Babies. I was surprised at just how sad I felt about it-- this was the dreaded "Day Care"- the place that I thought I would die of sadness by sending you here when I went back to work in October. But here it is, just 4 1/2 months later, and I have to swallow away the lump of tears in my throat as I go to pick you up.
changed?" and I would joke, "I'm good right now. Thanks." I was a little embarrassed that I wasn't ready to leave you alone and I fully admitted that I knew you would transition just fine- It was me that I was worried about. They joked that I should wear their uniform T-shirt because I was there so much. Even after you started I would stop by whenever I could. The first few weeks I would go at lunch every day, just to be with you. I wanted to really know all the women that worked there. I needed them to know me too. I needed the place to feel like home to me. I needed them to see just how much I love you, for them to see how close you and I are, how precious you are to me- because I thought if they saw all of this- then they would take extra special loving care of the most important little boy in the world of mine.
Beach Babies made me feel like an honest to goodness card carrying parent at your Halloween Show and Christmas Pageant. I can't explain the excitement I felt, sitting in the audience, waiting for my boy to take the stage!
that lots of people miss you when you aren't around, not just family members. It reinforced what I already knew- you possess these tangible and intangible things that all together make you Greyson, and gives you your Greyson-ness and I was just so overwhelmed with pride and love and emotion I almost burst.
So although this is a sad goodbye, we've got so many new and exciting hello's right around the corner.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 483
|
Skagafjorden er en fjord i økommunen Dønna i Nordland fylke i Norge. Fjorden går 7,5 kilometer mod nordøst til bebyggelsen Hølen i bunden af fjorden.
Fjorden starter på den sydvestlige ende af øen Dønna mellem Staulen i syd og Grytøya i nord og er en fortsættelse af Sildøyfjorden som ligger længere mod sydvest. Fjorden ligger på sydsiden af Skagalandet, hvor bebyggelsen Skaga, som fjorden er opkaldt efter, ligger. Bebyggelsen Sandstrak ligger på sydsiden af fjorden. Inderst i fjorden deler den sig i to smalle og dybe vige. Øyvågen er den nordligste og Hølvågen ligger på sydsiden.
Fjeldet Dønnamannen på 858 meter over havet ligger på sydsiden af fjorden.
Fylkesvej 828 går langs sydsiden af fjorden.
Kilder og henvisninger
Fjorde i Nordland
Dønna
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 1,543
|
what is a pequin pepper?
This dried pepper is also known as chile pequeño or "small chile" in Spanish. Its thin skin is orange-red, and they're shaped like an oval arrowhead, only 1/2" long or less. The flavor is sweet and smoky with citrus, corn and nutty overtones. Heat is 8-9 out of 10 on the Scoville heat scale.
Grind or crush to use in fresh salsas, soups and sauces.
Store in a cool, dry place up to 2 months.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 9,785
|
package com.hubspot.singularity;
import com.fasterxml.jackson.annotation.JsonCreator;
import com.fasterxml.jackson.annotation.JsonIgnore;
import com.fasterxml.jackson.annotation.JsonProperty;
public class SingularityRack extends SingularityMachineAbstraction<SingularityRack> {
public SingularityRack(String rackId) {
super(rackId);
}
@JsonCreator
public SingularityRack(@JsonProperty("rackId") String rackId, @JsonProperty("firstSeenAt") long firstSeenAt,
@JsonProperty("currentState") SingularityMachineStateHistoryUpdate currentState) {
super(rackId, firstSeenAt, currentState);
}
@Override
public SingularityRack changeState(SingularityMachineStateHistoryUpdate newState) {
return new SingularityRack(getId(), getFirstSeenAt(), newState);
}
@JsonIgnore
@Override
public String getName() {
return getId();
}
@JsonIgnore
@Override
public String getTypeName() {
return "rack";
}
@Override
public String toString() {
return "SingularityRack{} " + super.toString();
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,737
|
Table of Contents
Title Page
Copyright Page
Dedication
PART ONE - PRINCESS
Chapter One
Chapter Two
Chapter Three
Chapter Four
Chapter Five
Chapter Six
Chapter Seven
Chapter Eight
Chapter Nine
Chapter Ten
PART TWO - WARRIOR
Chapter Eleven
Chapter Twelve
Chapter Thirteen
Chapter Fourteen
Chapter Fifteen
Chapter Sixteen
Chapter Seventeen
Chapter Eighteen
PART THREE - QUEEN
Chapter Nineteen
Chapter Twenty
Chapter Twenty-One
Chapter Twenty-Two
Chapter Twenty-Three
Chapter Twenty-Four
Chapter Twenty-Five
Afterword
**NOVELS BY MERCEDES LACKEY available from DAW Books:**
**THE NOVELS OF VALDEMAR:**
_THE HERALDS OF VALDEMAR_
ARROWS OF THE QUEEN
ARROW'S FLIGHT
ARROW'S FALL
_THE LAST HERALD-MAGE_
MAGIC'S PAWN
MAGIC'S PROMISE
MAGIC'S PRICE
_THE MAGE WINDS_
WINDS OF FATE
WINDS OF CHANGE
WINDS OF FURY
_THE MAGE STORMS_
STORM WARNING
STORM RISING
STORM BREAKING
_VOWS AND HONOR_
THE OATHBOUND
OATHBREAKERS
OATHBLOOD
_THE COLLEGIUM CHRONICLES_ FOUNDATION
BY THE SWORD
BRIGHTLY BURNING
TAKE A THIEF
EXILE'S HONOR
EXILE'S VALOR
_VALDEMAR ANTHOLOGIES_ :
SWORD OF ICE
SUN IN GLORY
CROSSROADS
MOVING TARGETS
CHANGING THE WORLD
Written with **LARRY DIXON:**
_THE MAGE WARS_
THE BLACK GRYPHON
THE WHITE GRYPHON
THE SILVER GRYPHON
_DARIAN'S TALE_
OWLFLIGHT
OWLSIGHT
OWLKNIGHT
**OTHER NOVELS:**
GWENHWYFAR
THE BLACK SWAN
**THE DRAGON JOUSTERS**
JOUST
ALTA
SANCTUARY
AERIE
**THE ELEMENTAL MASTERS**
THE SERPENT'S SHADOW
THE GATES OF SLEEP
PHOENIX AND ASHES
THE WIZARD OF LONDON
RESERVED FOR THE CAT
And don't miss:
THE VALDEMAR COMPANION
Edited by John Helfers and Denise Little
Copyright © 2009 by Mercedes R. Lackey.
All rights reserved.
Leatherbound book: Getty (RM) Dorling Kindersley.
Gold background: Gerrit Greve/Corbis.
DAW Books Collector's No. 1489.
DAW Books Inc. is distributed by Penguin Group (USA).
All characters in the book are fictitious.
Any resemblance to persons living or dead is strictly coincidental.
eISBN : 978-1-101-14933-1
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First Printing, October 2009
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Dedicated to Russell Galen, without whom none of this would be possible.
**PART ONE**
**PRINCESS**
**Chapter One**
**The talk at** the hearth of the high hall of her father's castle was all of magic that wild evening. Harvest-time had come and gone, and Samhain not far off; the old men and women were muttering about a hard winter ahead. Truly, it had turned bitter very quickly, and the harvest, while not scant, was also not bountiful. All that little Gwen knew, though, was that tonight it sounded as if everything cold and evil in the world was trying to get in. She was glad that Castell y Cnwclas was all of stone. Nothing mortal could get past those thick walls and nothing uncanny past the women gathered at the hearth, especially tonight.
Outside, the wind whined around the stone walls, and made the seats farthest from the hearth almost as cold as if the poor fellows relegated to them were sitting out on the walls. They were making up for the cold by drinking plenty of ale and mead. Inside, the drafts made flames of the torches on the walls flatten and dance, and even the huge open fire on the hearth in the center of the hall flickered this way and that, sending streamers of smoke into peoples' faces unpredictably. Gwen was glad she was sitting on the stone floor, a bit of old sheepskin between her and the flags, where she was below the smoke. She hugged her knees to her chest and listened to the women of her mother's circle with the wide eyes of a young owl. Firelight illuminated familiar faces and made them strange with shifting shadows and hectic light.
The Hall was the biggest room in the castle, and served many purposes. By day it was in turn her father's audience chamber, the place where meals were served, and the scene of most domestic work that wasn't done in the kitchen. By night, her father's men and servants slept there. The walls were as thick as Gwen's arm was long, broken only by narrow windows too small for anyone but a child to climb through. Right now, heavy wooden shutters closed off the worst of the winds. The hearth-fire in the center gave most of the heat and light, supplemented by the torches on the walls. The stone floor was covered with rushes—newly changed just two days ago, so the herbs strewn among them were still sweet and the floor beneath still clean. The ceiling was lost in darkness and further obscured by the smoke rising to the louvered hole above the hearth.
It smelled of dampness, of spilled ale, of herbs and cooked meat, of sweaty bodies and wet wool. Faintly, because it had only been two days since it had been swept clean, there was a taint of urine from the dogs and cats that ran free in here. But above all it smelled of smoke.
The women had claimed the hearth itself, sitting about the fire on benches and stools or, like Gwen and her sisters, on the floor, and the men did not challenge them. No sane man challenged a Wise Woman, much less a gaggle of them. Behind them, on the mead-benches, were the men of her father's following. He was Lleudd Ogrfan Gawr, called "The Giant," and unchallenged king of these parts. There were no more Romans to contest his rule. The Romans had come and now gone from here; they mined their tin, lead, and gold no more, and the amphitheater they had built for their so-called games now echoed only to the wail of wild cats at night. And good riddance, said her mother. Her father's words were more pithy and profane.
The good-natured growling and grumbling of the men sounded like a muttering chorus of sleepy bears on the edge of hibernation, fat with autumn berries and nuts, and thinking mostly about sleep. Partly, that was the mead and ale of her mother Eleri's brewing. She put herbs in it—she said to flavor it, but the women all knew it was to make the men calm and sleepy, and that was a secret that would never be breathed to the men, not even to the king her husband. There was little argument on Ogrfan Gawr's mead benches, and no hot-tempered quarrels that could break into blood feud. Eleri the Queen was a Wise Woman in the sense of knowing the ways of herbs as well as of magic, and she reckoned it worth the effort to keep the men from making more grief than there already was in the world. Bronywn, who served as her right hand and the children's nurse, was the keeper of her secrets.
Hunting and fighting and tall tales were the order of business on the mead-benches tonight. With the harvest over, it was hunting that would help keep the men busy until spring, and hunting would be needed to keep the hall fed if the winter was a harsh one. Magic was the subject on the hearthstone; it was the provenance of women—and a very few, very select group of men. The Druids. The bards. The occasional hermit-healer. Eleri had told Gwen that this was because men spent too much time around Cold Iron; wearing it in the form of weapons, crafting it, cherishing it. "Magic shuns Cold Iron," she had said, with a decided nod. "Men might have the Gift, but while they cling to Cold Iron, they'll never have the Power."
Gwen most especially watched her mother, listened to her words, for the Queen was also the chief sorceress here and high in the Councils of the Wise. Eleri had the Power and had it in abundance. Gwen had watched her, by full moon and waning, by Midsummer sun and Midwinter dark, weaving her Power into the spells that were the weapons _she_ wielded to defend, protect, and nurture their people. There were two thrones in Lleudd Ogrfan Gawr's High Hall: the one at the mead benches and the one at the hearth. And both were equal. The king guarded the people with his sword. The queen did so with Power.
There were those that said the queen was Fae-touched. Certainly, despite having given birth to Gwen and all her sisters, she often seemed as young as any of the maids at her hearth. There were those that said the two youngest of the brood, Gwen and her younger sister, took after her. But those that said it did so with a touch of pride, not fear; if they were Fae-touched, then, that would be a good thing.
Gwen's sisters sat beside her, watching and listening just as raptly. Gynath who was almost twelve summers, Cataruna who was fourteen, and Gwenhwyfach a mere eight, the sister enough like her to have been Gwen's twin, all listened and remained very, very quiet, lest they be remembered and sent off to bed. All the sisters had much the same look about them; they got their looks from their mother, who was slim and very fair—a rarity among dark people—and not the king, who was burly and, even rarer, had a head of hair like copper wire. They had a visitor this night, who would stay through Samhain to give their rites especial power. Eleri was concerned that the old men and women were right, that this would be a hard winter, and she would do whatever it took to keep her people safe through it.
But it was not talk of the winter to come and the Samhain rites that occupied them now. It was talk of Arthur, the High King, and his court at Celliwig.
". . . and so the High King takes a bride, and the Merlin is making sure the land-rites are performed," the lady visitor was saying; she was very important, a priestess _and_ a sorceress, from the great school at the Well of the Cauldron.
"And not afore time, too," muttered old Bronwyn. "Asking for trouble it was, leaving it for so long! It'll be a hard winter, thanks to all this dallying. As the king goes, so goes the land, and that's a fact." She made a sour face as the rest of the women nodded. "If the king be wifeless and childless, how can the land be anything but cold and hard? All very well to say the Merlin could make up for it, but he's only a man, one man, and—"
"Hush," Eleri interrupted, chiding her woman, and the visitor nodded with approval.
"What's done is done; the land hasn't suffered. The land has a long memory and longer patience. One hard winter will not ruin the land, and the Merlin has brought him round to the bride and the rites." The woman sighed. "And now I am here to ask you, has the High King's half-sister been among you?"
"Morgana?" Eleri shook her head. "You surely do not mean Anna Morgause . . . I have not seen her in a year or more. The Orkney clan does not favor us with their attention, much. Why?"
The visitor shrugged, but looked troubled. "It is Anna Morgause I mean. Morgana is hardly more than a child, for all her power, and she heeds the Merlin and the Council of the Wise. But Morgause . . . Anna is a woman grown, with four sons she would fain see raised high. She has the power and the willfulness, and she is wedded to Lot, who speaks the High King fair but watches through his fingers. And Morgause speaks the Council fair, but . . ."
But Eleri shook her head. "Rhianu, be careful of what you say. Have you anything other than gossip and your own suspicions? Has the Cauldron shown a vision of the future?"
The visitor looked away a moment. "No and no," she admitted. Eleri smiled slightly. "Have done, then, and tell us of the bride. If gossip there will be, let it be of bright things and not dark, truth and not suspicion. Anna of the Orkneys will do as she does, and if the Cauldron gives you no visions, then that is the will of the Goddess."
Gwenhwyfar pondered the visitor. She did not seem like someone who would gossip to make trouble, and normally Eleri would have deferred to her judgment, since she was older and a very powerful Wise Woman indeed, one of the Nine who served the Cauldron of the Goddess. But her mother must know _something_ that made her say what she had. Perhaps there was bad blood between Rhianu and Queen Morgause, and perhaps Eleri knew about it.
Rhianu pursed her lips, then seemed to resign herself. "Well, her name is Gwenhwyfar, like your own daughter, and the name suits her, for she is very like to all of you, as fair as a Saxon and slender as a reed. She was not our first choice, but Arthur came to the aid of her father, Leodegrance, saw her firing arrows from the walls, with her fine gown kilted up and fire in her eye." She shrugged. "He was smitten, and she is of the right bloodline and of our teaching. But—"
Eleri raised an eyebrow. "But?"
"She is her father's only child. We question whether his blood grows thin. The Good Goddess knows Uther's line—"
Eleri looked speculative. "Hmm. One child only, Arthur himself—"
"And never a by-blow by leman or lover, and it took the Merlin's magic to quicken Arthur in Ygraine's womb." Eleri nodded. "Still, at least now Arthur has found a woman he _wants,_ and all else is suitable. Passion has a magic all its own, and the rites themselves should ensure that there is at least one child."
Rhianu coughed. "We intend to make certain of that," she said, and significant glances were shared among the women.
"That is chancy, meddling in those matters," Eleri murmured softly. "Have a care that your enterprise does not miscarry."
Gwen shivered at that moment, as an icy finger traced itself along her spine.
"Has anyone troubled to scry the results?" Eleri continued, as Gwen shivered again.
"There will be a son born to Arthur, within the proper season," Rhianu replied, with confidence. "At least one."
"Sons!" said the king, cheerfully, coming up behind his wife. "Oh, sons are all very well, but a king's wealth is in his daughters! A son may run off and pledge his service to another man in another crown, but a daughter remembers what is due her sire—what is that old saw, my sweet?" He set both hands on Eleri's shoulders, and she reached up to squeeze one with affection.
" 'A son is a son 'till he takes a wife, but a daughter's a daughter for all of her life,' " Eleri responded, tilting her head back to look at him and being rewarded with a kiss.
"There, you see?" the king beamed at their visitor. "And there is my wealth. Fair daughters, strong and comely, and I know they will remember their duty to land and sire. If the High King wants loyal allies, let him have daughters to cement those bonds. If he wants magic to safeguard his kingdom, let him have daughters to spin him spells and speak for him to the gods. And if he is very lucky, he will also have a daughter that is a warrior-woman, for they make the most loyal shield-bearers."
Gwen noticed at that moment, that the queen looked as if she were harboring a pleasant secret.
But she said nothing, only again squeezed the king's hand, and the king chuckled and went back to his men.
"But what of Anna Morgause?" Eleri asked after a moment. "If there is anything about her you should be warning us against, it is your duty to make it plain."
The visitor grimaced with distaste, then looked pointedly down at Gwen and her sisters. Gwen sighed. If she had been just a little off to the side, there was a chance that the visitor would not have noticed her. That happened a lot. Then she tried concentrating very, very hard on not being noticed. Sometimes that worked—more and more as she got the knack of it. But not tonight,
Much to Gwen's dismay, her mother took the hint.
"Off with you," she said in a quiet voice that nevertheless brooked no argument. "Time for bed." The girls didn't even try to dissuade their mother, they just picked up whatever they had been sitting on and trudged off to the private rooms behind the dais.
This was a grand, grand castle indeed. Behind the dais, through a wooden door, was a set of two small rooms where the royal family and their immediate servants slept, away from the tumble of bodies in the Great Hall. A pair of rushlights, one left burning in each room, lit the way just enough that the girls didn't stumble over anything.
The first room was theirs; it was smaller than the second, and it had just enough space for the big bed where they all slept and their clothing chests lining the walls. Mag, the servant woman they all shared, who had been their nursemaid when they were smaller, helped them pull off their outer clothing and fold it neatly, each on top of her own chest. Then they clambered into the big bed, which Mag had warmed with a stone she'd put near to the fire earlier. They had their own particular order for this. The two most restless, Gwenhwyfar and Gwenhwyfach, on the outside, and Cataruna and Gynath on the inside. The bed, with its woolen blankets woven by Eleri and her women, its fur coverlet from bearskins of the bears killed by their own father, could easily have slept two more. They even had a feather mattress, an immense luxury.
Gwen was the last to climb in, and Mag shut them in with the bed-curtains, leaving them in the close darkness.
Gwen was always the last to climb in, because if she didn't wait, her sister Gwenhwyfach, the baby of the family, would find some sly way to torment her. Poke, prod, pull hair, pinch—they were as alike as twins, everyone said so, and no one could understand why Gwenhwyfach hated her sister so. When Little Gwen was in a fine mood, she was enchantingly beautiful, and she bewitched everyone around her. Her hair, like Gwen's was as light a gold as sunlight, her eyes large and a melting blue when she wanted something. She put Gwen in mind of the tale of the maiden made of flowers sometimes, she was so slender and graceful, even when she was up to mischief. In fact, her real name wasn't Little Gwen at all, but everyone insisted they looked so much alike, the name had stuck and no one even remembered what name she'd been given at birth anymore. Perhaps that was why—perhaps she sorely resented that they were so much alike. It certainly wasn't because Little Gwen was deprived. If anything, being the youngest _and_ so pretty, she was spoiled.
Then again, maybe it upset her that there was anyone who could be said to be as pretty as she was, much less that it was her older sister.
Even Gwenhwyfar was at a loss; she didn't remember doing anything that would have warranted this. If their positions had been reversed, had Gwenhwyfar been the youngest, there would be some cause for that resentment. But no, it had been Little Gwen who had usurped the position of "youngest" from her year-older sister, and she'd scarcely begun to toddle when she made her enmity known. From that day, Gwen's life had been a struggle to avoid her clever sister's tiny tortures.
One thing she had learned early on: never strike back. Little Gwen was never caught, at least not by an adult, and retribution on Gwen's part only brought down the wrath of an adult. Gwen was the older; logic said that when there was a quarrel, she was the aggressor, for why would a smaller child bully a larger? When Gwen displayed bruises, she was told that was what she deserved for picking on her younger sibling.
Her older sisters knew what was going on, of course, but protests to an adult only got them told not to take sides.
That was the other reason for having a Gwen on either side of the bed, with two sisters in between. It stopped the fighting.
Well, mostly.
"It's all your fault," Little Gwen whispered in the dark. "You got us sent to bed, Gwenhwyfar. We could still be there if not for you."
"Me? What did I do?" Gwen demanded as both her sisters sighed with exasperation.
"You weren't quiet enough. You made the queen look at you. You were fidgeting. You always fidget." This, from the person that Mag always checked for fleas, since by the nursemaid's way of thinking, anyone who squirmed that much must be harboring a host of fleas.
"Did not!"
"Did so!"
"Did no such thing!"
"Did so!"
"Give over!" snapped Gynath, the eldest of them all. "Gwen did no more fidgeting than you, and she was a deal less obvious about wanting to hear every word about the Queen of the Orkneys. Now go to sleep!"
"I can't," Little Gwen whined. "I'm cold. Gwen stole all the covers."
Since Gwen was barely covered by the drape of the blankets, this was obviously a lie. "Did not!"
"Did so!"
"Couldn't have," Gynath said smugly. "I tucked them under the featherbed on your side. You're a liar, and that just proves you're a changeling. I knew it! The Fair Folk took the real baby and left you in her place! No wonder you're a little horror!"
"Am not!" Little Gwen said, furiously. "And she stole the covers! Ow!"
This last punctuated the thump on the head her older—and much larger—sister gave her.
"Give over," Gynath repeated. "Go to sleep, or I'll tip you out and you can lie on the floor with the dogs all night."
"I'm lying with bitches now," Little Gwen muttered, and Gynath thumped her again for her pains, and, at last, she subsided.
Gwen turned on her side, her back to her sisters, and stared at the place where the curtains met. Stealthily—because if Little Gwen knew what she was doing there would be whining about letting the draft in—she parted the curtains with a finger and peered across the room at the light visible through the gaps between the door and doorframe, straining her ears to make out something besides the indecipherable muttering of voices. She had wanted to hear more too, but not about Anna Morgause.
She wanted to hear about magic and the Power. Hearing about or watching someone working magic always gave her a shivery good feeling. She couldn't wait until she came into her own Power.
She wondered what it would be. Some, like Eleri, could do just about anything in reason. Some were just healers, some could command the weather, or see into the past or the future.
She wanted to be able to do it all, though. Well, who wouldn't? _And_ she wanted something else. She wanted to be a chariot-driver, and a warrior. There had to be a way to keep the Power and still wield Cold Iron. Sometimes she felt torn in two, wanting both those things—
But there was no doubt, no doubt at all, that when she came into her Gift, she _would_ be sent to the Ladies. The doubt came about whether the King would be willing, no matter what he said, for a daughter to take up weapons. There were not many warrior-women, and most girls who tried the life soon gave it up.
That wasn't the only reason she strained to listen to the talk at the hearth. Besides hearing about magic, she wanted to hear about this new queen with the same name as her.
She wondered what life was like, for this slender, fair young woman. Did her father have a castle like this one? Clearly, if she was a good archer, he let her train with the warriors. Oh, how Gwen wanted to do that, too—
Well, maybe. She would have to be careful that the Power didn't desert her because she handled Cold Iron too much. But there had to be a way! _That_ Gwenhwyfar had done it!
_But if there isn't . . . which do I want? To be a warrior, or to have the Power?_
Did she have sisters? Probably not, and probably not brothers either, if she had been on the walls, shooting arrows at her father's enemies. Brothers were funny about things like that. Gwen had overheard plenty of fights when some of the boys tried to keep their sisters from training with the warriors and the like. No, from the sound of it, she was an only child . . .
Oh yes, Gwen remembered now. Something about the blood being thin and only the one daughter in the line. So there it was.
Gwen envied her. It must be wonderful, to be an only child. No having to share everything. No big sisters who thumped your head nor horrible little teases of younger sisters. She'd have gotten the best of everything; only children got spoiled, everyone knew that. And now, to be marrying the High King, to be his equal in all things . . . she would have her own court; everyone knew that the power of the land went through the queen as well as the king. She was trained by the Ladies, so she would probably be the one in charge of all things having to do with the Power, subject to the Merlin, of course. She would have her own horses to ride and not have to share one elderly pony with three sisters.
And, oh, the clothing. Probably enough to fill chests and chests. She would have new clothing, not things that had been cut down from adult garments and then passed down until by the time Gwen got them, they had lost any color they had once had, and any trimming had long since been pulled off. In fact, with three sisters handing down the same clothing, it was Little Gwen who actually had the best of it, since by the time Gwen was done with what Gynath handed down to her, it was suitable only for padding, patches, and baby's clouts. Little Gwen got true second-hand, just like the eldest of them.
There would be fur linings to that Gwenhwyfar's cloak and hood. There would be embroidered hems to her gowns, and her shifts would be the softest lambswool and linen. She would dress like Eleri did on rare feast days, only she would do so every day, because she was High Queen. All her clothes would be colored, and she'd never have to wear anything faded or plain again. Except her shifts. Her shifts would be linen so blinding white they'd think she was a spirit. In fact . . . in fact, she would have one gown that was that white, too, whiter than snow, whiter than clouds. Everything she wore would be soft, too. No scratchy linens for her, no itchy wool.
And no shoes she had to wear three pairs of stockings with to keep them on. Shoes would be made to fit her feet, and hers alone.
She'd have the best food, too. Whatever she wanted, like as not. The best cuts of meat, the slices from the middle of the loaf, succulent cakes and pies whenever she liked. Goose, oh, lovely goose and the rich fat to dip her bread in. They'd let her have all the sweet mead she wanted. Apples, pears, plums, cherries and berries of every sort.
She would have a stable full of horses, one of every color there was. And a falcon, a real one, not just a little sparrow hawk, a real peregrine or a goshawk. And a coursing hound, with an elegant, long eared head. She would go hunting whenever she felt like it, and no one would tell her that she couldn't.
There would be a bard all the time in the court, too, and jugglers and gleemen and all sorts of things. She could hear whatever tales she wanted, whenever she wanted, and if she woke up in the middle of the night and wanted to hear one, well, she could.
And she would, of course, have great Power and command the most serious of magic. The High Queen was also the chief of all of the Wise, and at the most important of the rituals of the year, she was the avatar of the Lady for all of the land. Gwen had seen Eleri coming back from the Great Rites, face flushed, eyes shining, exultant, and more alive than at any other time. Gwen wanted to feel like that one day.
Well, one day, she would. Eleri had promised as much. One day she, Gwen, would be leading the rituals, making the magic happen.
Suddenly, though, amidst all her envy, something else occurred to Gwen . . . would it be worth all those wonderful things to have to go far away from home? To never know if you were ever going to see your mother or father again? To have nothing around you but strangers?
Maybe . . . not.
Unable to hear anything meaningful, Gwen let the bed-curtains fall closed and wriggled closer to her sister. The bed was soft, and warmed by the heat of four bodies. They were all safe in here, and tomorrow the bird hunters were going out, and there would, almost certainly, be goose. And then there would be stories and maybe some rough music, and their visitor would talk more about magic.
And Gwen would be able to look up from her place on the hearth, look around her, and know every face in the Hall.
Maybe being High Queen wasn't so wonderful after all.
**Chapter Two**
**Gwen had not** meant to overhear her mother and the priestess, indeed she hadn't. It was a cold, bright day, and she had been given sacks of goose and swan feathers to pick over and sort, for the king and his men had gone out bird-hunting and brought back a plentiful catch. Eleri was strict about idleness; there was to be none if there were tasks to be done, and Gwen was deft enough to be trusted with this one. She wouldn't lose a single feather, she wouldn't sort where the wind could carry them off, and she wouldn't leave dirt on any of them. Not even Gynath picked feathers as clean as Gwen could.
She knew better than to sort inside; a chance draft might send the precious feathers into the fire. So she circled the castle and grounds and came to one of her favorite spots, just below the window of her parents' room, on the south wall. This spot got sun all day and was sheltered from the wind; the lush grass made a good place to sit, and no one was likely to disturb her.
So she slowly picked through the feathers. Precious down feathers went into one sack, for making the softest of pillows and featherbeds.
Body feathers went into a second, for featherbeds of lesser quality. Longer feathers went into a third sack, to be used as needed, and the primary and secondary wing feathers went into a fourth, to be used for fletching arrows and very occasionally for quill pens, although there was no one here who could write more than reckonings. Dirty feathers had to be carefully picked clean, but her reward was that she could have any feathers she liked from the third sack. She had already made plans for a feather skirt for her doll and maybe a feather cloak too. It was not hard work, nor difficult to understand, but it was painstaking. Gwen was clever and dexterous, and besides, she loved the silky feeling of the feathers, the subtle plays of grays and whites and browns, so she never complained about getting this chore.
Despite the cold, the sun had baked warmth into the turf and the stones at this spot. She put her back up against the stones and set to work.
She was halfway through the second sack when she heard voices. She quickly recognized Eleri and the visitor, who must have sought out the privacy of the solar in order to keep their words from the ears of the inveterate gossips. She concentrated very hard at that moment, willing them not to look out of the window, even though Eleri knew she was picking feathers and that this was her favorite place to do so.
"Now tell me what you would not say in public about Anna of Orkney," Eleri demanded, in what Gwen thought of as her "queenly" voice. "If there is danger to this realm from her, I want to know about it."
"That is the trouble, the things that I know are as hard to hold to as water," the priestess replied. "The priestesses great and small are not of one mind on this. Some think Anna of Orkney is dangerous, some think her ambition will be held in check by the High King and the Merlin, and some think that nothing will hold her if she reaches beyond her current status. I know that she holds to the Old Ways, and under any other circumstances, I would be inclined to her for that alone. But . . . but . . ." She sighed. "I know that Lot is ambitious. I know that his wife is equally ambitious, and I believe that there is not much either of them would scruple at to advance their ambitions. I know that she has the Power, and I know that she will use it to further her own ends rather than the welfare of the land. But how far she would go? I cannot say with any degree of certainty."
"The High King has a son," said Eleri, sounding irritated. "He has a son by the girl called Lionors. Lorholt, she calls him. Does he need more?"
The priestess made a _tsk_ ing sound. "But she was not his wife. And it is only we of the West that still hold to the Old Ways, at least publicly. If your husband had a son by another than you, and he chose to make that son his heir, and you put your blessing upon it, no one here would think it amiss. But in the lands where the Romans once held full sway, The High King must have a son by a true wife, one wedded to him by a Christian priest, as well as promises, and sealed in betrothal. The Old Rites do not signify." Gwen listened to this carefully. This seemed very strange to her. There were plenty of couples among her father's people who had never even seen a Christian priest, nor had any priest or priestess say any words over them whatsoever, and yet no one doubted they were husband and wife. Jumping the fire at Beltane, jumping the broom among friends, that was enough for most. Only those with land, or with some title of honor seemed to need the formality of vows and blessings. Blessings were for babies, who needed every help they could get, and the proof of that was that there were four small graves with other daughters of Eleri in them, who did not live to see the full turn of the seasons.
But the priestess was continuing. "The truth is, young as he is, the High King has many sons, but none of them are . . ." A pause. "Suitable, to us, to the others. None were sired on a girl to whom he had any true tie, none has he accepted as his heir. None were sired on girls that the servants of the Goddess approve of, girls of the proper bloodline, with the Powers. All are . . ." Again, a pause. "Inferior. They are of no importance. Attempts to see into their futures show nothing of note, not a hint that the Goddess cares for them any more or less than she cares for any other of her daughters. They are toys for the young High King's bed. Their sons will be numbered among his warriors but will never be outstanding. They are ordinary. The High King's heir cannot be ordinary."
Eleri snorted. "So. The High King must breed him a son on a girl acceptable to us and to the followers of the White Christ. A girl with the Powers. A young woman like this Gwenhwyfar he is wedding. So?"
The priestess responded reluctantly. "The scrying bowl shows me nothing I can make sense of. I see a son of Arthur vying for the throne, not one holding it unopposed. And I see the Merlin, and blood, connected with that son, but I cannot make out what that means." She hesitated. "I see the death of many children associated with the birth. And yet I see him surrounded by all the signs that says he has the right to the throne, and I see him as a man of the Powers. I think . . . it would be wise to avoid the wedding."
Eleri sniffed. "We could not go in any case. Arthur has our pledged fealty from his coronation, and he scarcely needs it a second time. That is a very long way to go with winter coming on, and all for a feast that we could as well hold ourselves. Which, to show our loyalty to the king, we shall, with bonfire and all. There will be nothing to complain of in our demonstration of fealty." Suddenly her tone changed. "Do you see Morgause's ambition spreading to these lands?"
"Not directly," the priestess said, though reluctantly, and Eleri breathed a sigh of relief.
"Then hear me out. The magic to make the High King a son will be a powerful one, and I am minded to sip at that same cup," Eleri continued. "My man speaks highly of his daughters, and he loves them true, but—"
"But a man wants a son, and a king wants a son more than most men." The priestess sighed. "To answer your question, that cup will indeed be overflowing, and if you, as the Chief Priestess here, were to open yourself to what is not needed, you likely will find yourself graced with the same gift. But Eleri . . . there is danger there. There may be a reason why the Goddess has seen fit to give you all daughters. It may be because of the Blessing in your blood. We cannot know that, or, if it is true, what that reason is. If you flout Her will in this, there may be consequences."
"The Goddess has seen fit to give me a husband I have come to love, to love enough to give him something he wants and will not ask for." Oh, Gwen knew that tone. The queen was not to be denied. This was what would be, and woe betide whoever stood between her and the goal.
"Then, for what it is worth, my blessing be upon you." The priestess sounded resigned. "In this, I cannot speak for the Goddess."
"You have given me leave, and that is enough," Eleri said firmly. Gwen heard their footsteps leaving.
Gwen continued to pick through and clean the feathers, trying to piece together what this all meant. All that talk of sons and the High King only puzzled her; she couldn't imagine what these Christian priests had to do with who the High King picked as his heir. But then again, that didn't matter. The High King was very far away, and what he did in Celliwig hardly even caused a ripple here. But what Eleri was up to—that troubled her, though she could not have said why. She knew very well where babies came from; her mother was midwife as well as queen, and the Great Hall, where all the rest of the court slept, was open to any sleepless child who would rather go outside than use a chamber pot. Gwen had seen the dogs and cats, the chickens and ducks and geese, her father's famous horses, and no few of her father's men and her mother's maids coupling with pleasurable abandon and no regard for privacy. So she knew where babies came from and what made them, and she had also known most of her life, in that vague sense that put parents in some mental place other than "everyone else," that the king and queen did this same thing in their great bed. Well, they must have, to have produced Gwen and all her sisters.
But this sounded more portentous than that. Magic would be involved. And her mother was going to try to make a son for the king.
Gwen turned that thought over and over in her mind. She wasn't sure she liked this idea, not sure at all. She felt more than a twinge of jealousy. A boy-child would get all the attention, right from the start. He'd be the king one day. He'd be able to order his sisters about in every place but the Circle of the Goddess and the hearth. Her father would take all the attention he now paid his daughters and lavish it on this newcomer.
And why was her mother doing this? Because, she had said, she loved the king. Yes, but didn't she love her daughters? Didn't she realize how they would feel, how they would be made to take second place?
A boy would get a pony as soon as he could walk; she was still waiting for hers, one that she didn't have to share with her sisters. He'd get a real horse as soon as he had mastered the pony. He would get lessons in the sword and the bow without ever having to ask for them, much less beg. When the time came for chores, he would get the interesting ones, not weaving or spinning, picking feathers or sewing. He would get hunting, hawking, mending weapons, fletching arrows, making bowstrings . . .
How could she not be jealous? But also, there was curiosity. Not about the wished-for son but about the magic that would make him.
It was magic for the High King, and Eleri was going to share in it . . . and that did not sound right. Surely that was not right. That magic should go to the High King only, and not someone else, even if that someone was her mother.
It was magic, from the sound of it, that would be made in Circles across the land. The High King might not even be aware this was going to happen, but nevertheless, it was magic that would stretch through every little kingdom that owed allegiance to Arthur. And that . . . it seemed wrong, very wrong, for Eleri to steal some of that away. If it had only been their kingdom, it would have been different, for Eleri was the priestess here, and the magic that was made here should benefit this land and its priestess. But it was not. Eleri had no right to it. Did she?
But this was her mother, the priestess, and the queen. If anyone would know if this was right or not, surely it would be Eleri.
Gwen continued to turn these things over and over in her mind, and finally she sighed and gave up. Besides, the topic had turned to something even more interesting.
"Gynath seems to have little Gift," the priestess was saying. "She should have come into it by now. Cataruna, though, has come on a great deal since I last saw her and should already be serving by you in the rites."
"She is," Eleri replied, with satisfaction. "And that is why I would rather not send her to you. I need her here, and she is not going to be so very powerful that I cannot teach her myself. But Gwen—"
"Already has the signs on her." The priestess's voice was firm with conviction. "And do not think that you are not powerful, for you are; whichever daughter you teach will be as powerful. You must send either Cataruna to us now, or Gwen as soon as she becomes a woman. Either will be suitable."
"That is my intent," the Queen said, then hesitated. "But . . ."
"What?" the priestess asked, sharply.
"Gwen yearns for the Power. But she also yearns for the reins and the sword. And you heard her father, he favors warrior women." The Queen sighed. "I do not know if that is mere words, and I do not know if this is some childish longing, but if there must be a choice, I would rather it was a sure one."
The priestess chuckled. "The king may well not wish to truly see one of his girls going to war. Or if he allows the training, she may tire of it. Even if she began tomorrow, the Power would not leave her overnight in any case, and by the time she is old enough to send, she will be old enough to understand that choice." The priestess's voice took on a shrewd tone. "After all, when a maiden begins to be interested in young men, suddenly all the things of war become much less attractive."
Eleri chuckled. "I bow to your wisdom."
They turned their talk to things in which she had no interest—other kings, other queens, people she didn't know or care about. Gwen went back to concentrating on the feathers.
There were some things she would certainly do. If there was going to be a baby brother, she was going to spend more time begging her father for those things she wanted. She would redouble her efforts to be good. She would do everything she had been asked and some things she hadn't, all so that her father would note what a good and obedient daughter she was. And she would take good care to ask him for those things she wanted—the pony (oh, a pony, she was almost sick with wanting one!), the lessons in sword and bow—at times when he was feeling well content. She would think very hard about convincing arguments why she should have these things, too.
That way, if there was a brother coming, she would have secured her booty before the baby claimed the king's attention.
Making the feather skirt for the doll was easy; just a bit of string to bind the feathers around doll's waist. The feather cloak, however, was proving a bit more problematic. She was old enough to be trusted with a bone needle of her very own, but sewing the feathers to a bit of rag was not working out as well as she had thought. She sat at old Mag's feet with the feathers in her lap, the needle and cloth in her hand, and her tongue in the corner of her mouth as she concentrated, but the feathers just pulled out of the stitches she made. Finally she put the needle back in its keeper and gave up on the idea; the feather skirt was pretty enough. And after a moment of thought, she took the feathers she would have used for the cloak and went to the bedroom. In a corner she found Little Gwen's doll and bound a similar skirt on it. Not out of kindness, out of self-defense. The moment Little Gwen saw the skirt, she would want one for her doll, and if she did not get one—she would hardly trouble to make one for herself—she would ruin Gwen's the first chance she got. It had happened too many times before; Gwen had made flower crowns and skirts for her doll in the spring and summer, and Little Gwen had torn the fragile garments off in a fury when no one would make them for her poppet. Gwen had made a bow and arrow for her doll, and Little Gwen had stepped on them out of spite. Gwen had made a horse out of straw for her doll and Little Gwen had thrown it into the fire. Just for good measure, Gwen braided the yarn hair of Little Gwen's doll and stuck some remaining feathers in the braids. _She_ thought it looked ridiculous, but it was something Little Gwen's doll had that Gwen's wouldn't, and that would satisfy her fractious younger sibling.
Wrapping her own doll carefully in a scrap of hide, and putting her away, Gwen considered what she could do to curry favor with her father. What would he like? What would he notice?
Perhaps a nice basket of nuts. She knew of one or two spots that hadn't been picked over yet, mostly because tangled underbrush full of nettles and briars made the trees hard to get to. But she was small and clever about getting into and out of such spots; she got a sack and trudged out into the sunny afternoon.
At the door, she stood considering what she should do, as she watched the horse keepers exercising her father's famous beasts; the old men ran the horses around them in circles on the end of long tethers. She watched them pacing at the end of their leads, their muscles rippling under their rough winter coats, their necks arched, and their eyes bright. Once again, she felt sick with longing for one of them. You didn't ride these horses to exercise them, not if you were old and not as agile as you used to be, or crippled. You needed every bit of your wits and strength to handle them. They were warhorses, trained for war, pulling the dangerous war chariots or charging into the fray, and not for casual riding. All horses were beautiful, all horses were desirable, but these—oh, these—these were kings and queens among horses. When she watched them, all her desire for the Power faded.
Finally she turned away. These horses were not for her, not yet anyway. And if she wasted her time standing there yearning after them, they never would be.
All her father's men and a few of the women were out hunting in this fine weather, for in a few days there would be a great feast, both for Samhain and for the High King's wedding, and a great deal of meat would be needed. Should there be any excess, it would be smoked and salted against the winter. This was also the time when the herd beasts were culled for the winter, but in that case, with the exception of a single ox, it would only be the things that couldn't be preserved that would add to the feast.
You didn't risk the warhorses in that sort of hunting. At least one party had gone out after boar, one had gone fowling, the rest, in pursuit of deer. She hoped there would be a lot of success with the fowling party; just once she would like to be able to eat so much goose that she didn't want any more.
In theory, she wasn't supposed to go out into the forest alone. Well . . . she wouldn't be alone, even though none of her mother's women would care to go scrabbling for nuts. But she wasn't going to take any of the other, older children either.
Instead she marched off to the kennel, and loosed Holdhard, one of the boarhounds. All the dogs loved her, and Holdhard seemed to regard her as his special charge whenever he was let off his rope. With the formidable dog trotting alongside her, she made her way over the hill and down into the valley, where the little copse of hazelnut trees was what she had in mind. Holdhard knew to be quiet when she wanted to slip away; the two of them moved stealthily enough until she was well into the woods.
She avoided the oaks, and not just because they were sacred and dangerous. A thick layer of leaves and acorns carpeted the ground beneath them, and that meant the wild pigs could be feeding in there. Even a young pig could be dangerous to a child, and a grown sow or boar could easily kill a man. Holdhard sniffed at the air and growled as they went past; Gwen called him sharply to her. Whatever he scented had to be dangerous, but it would likely leave the two of them alone if they left it alone. At this time of year, like men, the beasts' priority was to lay up food against the cold. In the case of the beasts, that meant eating everything they could to get fat against the days of starvation.
As a precaution against the nettles she had taken more rags with her; when they reached the nut trees, she wrapped them around her hands and pulled the stinging nettles aside so that Holdhard could worm his way in with her.
Once inside the ring of nettles, thistles, and briars, it was as if she were in a different world. There wasn't a breath of wind; the branches above her were bare and let the sunlight through to warm this place as thoroughly as her little nook against the castle wall. The ground was thickly carpeted with crisp brown leaves that crackled as she sifted through them for the nuts. The air was full of the scent of them, a scent of dying, a little stuffy, with a suggestion of immense age.
It was soporific, and as Gwen felt through the leaves for the hard, round nuts, with the sun on her back, Holdhard flopped down into a sun-dappled spot and began to doze.
Slowly the sack filled. Holdhard snorted and snored and twitched. There was no other sound; there didn't seem to be any birds at all in this part of the woods. The sun didn't seem to move at all, and Gwen worked in a drowsy dream.
And then a snort that did not belong to Holdhard made her look up, and she froze.
Through the screen of nettles, she watched in numb fear as a bear shambled out of the underbrush. He swung his head from side to side, as if he was trying to find something, and finally he reared up on his hind legs to sniff the breeze.
Holdhard continued to sleep. She knew that she did not dare to move, for if she did, she knew that the bear would see or scent her.
The bear dropped down onto all fours and snorted fretfully. Gwen prayed silently to the Goddess, her lips and mouth dry with terror, that the great beast would continue to be oblivious of her presence.
Her fear made everything preternaturally sharp and clear, and she saw in that clarity the gray patches on the bear's muzzle, saw that his eyes were dim rather than bright.
Then those dim eyes brightened, and the bear growled, a deep rumbling that emerged from its chest and filled the air like thunder. Fear turned to horror as Gwen saw what it was that the bear had spotted.
Gliding out of the deepest shadows among the bushes came a serpent.
But this was an impossible creature. It was long, long . . . long enough that if it had its head in the king's bedroom, its tail would still be sticking out the main door of the castle. At the thickest point, its body was as big around as the chest of one of their horses, its wicked wedge-shaped head was as big as a barrel, and its glittering eyes were the size of her fist. It could as easily have swallowed one of the horses as a grass snake swallowed a frog. And it was black, an oily, glistening black, from the tip of its snout to the end of its tail. Even its flickering, forked tongue was black.
The bear reared up on its hind legs and roared at it. Gwen smothered a scream as the serpent raised itself as tall as the bear's head, hissed angrily, and struck.
It sank its fangs into the bear's shoulder; the bear roared with anger and pain and raked its head with terrible claws, laying the flesh open in four long, bleeding furrows. Gwen clapped her hands over her ears as the snake briefly released the bear, then struck again. This time the snake cast two coils around the bear and began to squeeze. Its eyes red with rage, the bear wheezed, but it raked the serpent again and again with vicious swipes of its claws and tore at it with it long white teeth.
As Gwen watched breathlessly, the two combatants rolled and thrashed, tearing up the ground and the underbrush in their struggle. And aside from the sounds of combat, it was a silent struggle; the bear roared no more challenges, and the snake did not utter a single hiss.
Suddenly there was a tremendous _crack;_ Gwen jumped and screamed.
For a long moment, serpent and bear were frozen together into a knot of fur and scales and torn flesh and blood.
Then, slowly, the serpent's coils fell away from the bear, dropping limply to the forest floor.
The bear had broken its spine.
But the bear had not escaped unscathed.
It stood there, swaying from side to side for a long, long moment, bleeding from a hundred wounds. Gwen gathered herself to try to creep out of the grove and escape, when the bear looked up and _looked_ at her.
She froze. There was something in its eyes. Something . . . desperate. Something with a hint of recognition . . .
The bear held her with its gaze, _looking_ at her, making her feel that it was trying, somehow, to tell her something.
Then it moaned once, its legs buckled, and it toppled clumsily to the ground.
There was a roaring in Gwen's ears; little black specks danced before her eyes, then grew, then covered everything with blackness, a darkness that she fell into, and forgot bear and blood and serpent and all . . .
When she opened her eyes again, there was no sign of the bear, nor of the serpent. The forest floor was undamaged, the underbrush rustled undisturbed, and Holdhard snored on, as if nothing whatsoever had happened.
Gwen was silent all through the meal, even when her father petted and praised her for the treat she had brought him. She smiled up at him as Little Gwen seethed, but the smile was only on her lips; her mind was still on that terrible fight in the forest, trying to understand how it could have happened, and then—not happened. She had not been dreaming. She was very sure of that. She had not been asleep.
That meant it could only be one thing: a vision.
She didn't want to tell her mother about it, somehow. She really didn't want to tell _anyone_ really, but she had to know what it meant, and if she could not tell her mother, there was only one person she could unburden herself to.
Provided that person would listen to her.
After the meal was over, and the women had gathered at the hearth as the men gathered at the mead benches, instead of sitting at her mother's feet as she usually did, Gwen allowed Little Gwen to usurp her place without a murmur. Instead, she settled away from the warmth of the fire, just in the shadows, and fixed her gaze on the priestess, silently willing the woman to _look_ at her. If it worked to will people not to look at her, the opposite should be true too, shouldn't it?
For the longest time, the priestess seemed oblivious to Gwen's gaze. The usual talk went on, of the luck of the hunt that day, of the feast to come on Samhain, of those who were expected to pledge to each other by leaping the fire that night. Of the thickness of the wool, the taste of the wind, speculation on how hard the winter to come might be.
But finally, slowly, the priestess turned her head and looked into Gwen's eyes. Her solemn gaze met Gwen's anxious one, and, finally, she nodded once, then indicated the door with a little inclination of her head.
Gwen got up and headed for the door, as if she were going to relieve herself at the privy. But she lingered beside the door, shivering in the cold with her cloak around her, waiting for the priestess.
She did not have long to wait. The priestess slipped through the door and shut it against the wind, then reached down and gripped Gwen's shoulder.
"Your eyes were burning holes in my back, child," she said, calmly. "What is your trouble? For surely you have one, if you gave up your place at the hearth and hardly smiled at your father's thanks."
"I—I saw something!" Gwen blurted. Then the words came tumbling out of her, like an avalanche of pebbles, as she described the battle of serpent and bear. When she was finished, she waited in silence.
"I do not know what this means," the priestess said, after a long silence, in which the cold wind whipped their cloaks about them. "That it is a vision, and one portentous for you, I have no doubt. But I cannot tell what it means."
"Oh," Gwen said, in a small, and disappointed, voice.
"But I will meditate on this," the priestess continued. "And if the Goddess sends me enlightenment, I will tell you." The hand on Gwen's shoulder relaxed, and the priestess gave her a little pat. "You did well to tell me, Gwenhwyfar. Such visions are rare; your mother has never had one. Should you have another such, do not fear to confide it to a priestess."
"I won't," said Gwen, and that seemed all there was to say. Feeling vaguely cheated, she went back inside and spent the rest of the evening on the edge of the cluster of her sisters, shivering, until the queen sent them all to bed.
**Chapter Three**
**The morning of** Samhain dawned as perfect as anyone could have asked for. The sun was warm enough for pleasure but not so warm as to make the old people grumble about summer-out of-season and bad omens. A cloudless sky and not even a hint of wind meant that the fires would send their smoke straight up, not into anyone's face. A hard frost three days ago had killed the flies, and the hunts had been outstanding; in short, everything was as perfect as one could want to celebrate the High King's wedding, the harvest, and the rites of the Lady of the Fields and the Lord of the Wood.
Gwen and her sisters were rewarded for much hard work in the days before by being given a holiday today. They couldn't stay abed though; the moment the sun was up, so were they, getting their hair braided, putting on their best gowns and shifts. The castle hall was full of people already; folk had been coming for days, and every little space where someone could lay his head had been taken up by someone. There were even tents pitched all about the castle and people sleeping in them.
When the girls left their room, the sleepers had already been cleared from the Great Hall, and trestle tables were set up along the wall, laden with bread and autumn fruit and honey for folk to break their fast on, and ale for drinking. For the girls, however, there was a tastier treat of sops-in-wine and watered wine with honey to sweeten it. All of them helped themselves to apples once they had cleaned their bowls, both figuratively and literally. It was only dawn and a long time to dinner.
Already there was activity everywhere, in the Hall and especially out on the green and about the village. Great cauldrons of soup were cooking, and ovens were fired up with the first baking of the day; the boar's head, the baked meats, fish and fowl, the fruit pies, the cakes and baked vegetables that would be served at dinner. The second baking would be for meat pies for supper and more fish and fowl. There was a whole ox roasting at one fire and a whole wild boar at another. Samhain was not a religious festival, although tonight there would be the Great Working for the High King—it was the Equinox that was the significant date, when the Winter King slew his rival, the Summer King, as the Spring Equinox was when the Young Stag slew the Old. Samhain was the celebration of the end of harvest and the time when those animals who were to be killed for winter meat were culled out. Anything that could not be preserved must be eaten, so why not make a festival out of it? The butchered beasts were already rendered into quarters and in the pickling vats, the smokehouse, or the salt packs. Sausages were already made up and curing. The brewing was done, the ale and mead in their casks.
Still the women were hard at work, tending to the cooking. Innards and bones, hooves and vegetable scraps had gone into pies and soup, for nothing was wasted. The common folk would get their portion of the ox and the boar—everyone got at least a small share of meat—but mostly they would be eating their fill of the soup. It was the guests of the king who would feast on the choicer stuffs.
So this was mostly celebration for the menfolk. The hard work of farming was over, and the year was about to descend into the dark. Not a bad time of year to handfast, for the sharing of a bed now could mean a fine babe in the summer, and a bed was warmer with two in it. This would be the last time of abundance before the hoarding of winter.
Gwen's father made a point to bring in all his warriors for the days of feasting, organizing contests and games. There were even musicians, and not just the ones from the village.
He was a surprisingly tenderhearted man as well where children were concerned; as this was the time of year when many a lamb grown into a sheep, gosling now big and gray and honking, or pink piglet grown fat went under the knife, he saw to it that there were plenty of things to occupy the children who had made these creatures into pets. So when the former pet became quarters, ham, and sausages hanging in the smokehouse, it was all done when the child was occupied with dancing or gaming or stuffing himself with unaccustomed treats.
As Gwen headed purposefully out with her pockets bulging with apples, she did not follow after her older sisters, who were making straight toward the field where some of the older boys were engaged in wrestling, archery and sling contests, and the hurling of woolsacks.
She also made sure to lose Little Gwen at the moment when her younger sister was distracted by a game of tag. Little Gwen could not bear to be left out of anything that promised attention, and once the child's attention was fully occupied, Gwen took advantage of a couple of geese being chased to get away.
Gwen didn't want to play tag or hoops, to run races for prizes or watch the older boys and men compete at feats of strength. She wasn't interested in the quieter pursuits of playing with poppets or merrils, and she certainly wasn't interested in the mock handfasting that was going on, nor the flirtations of her oldest sister.
She made her way with quiet determination to where the horses had been tethered.
She knew better than to approach them; handling the warhorses was strictly the work of those who were given that privilege—sometimes boys and rarely girls, but mostly fully grown men and the occasional woman. But feast days like these were the only time she ever got to see them do the sorts of things they had been trained to do.
At the moment, they were being readied for the chariot races. The Romans had introduced the chariot to the tribes, and once they had seen chariots in action, there was no stopping the tribes from adopting the vehicle. But unlike the Roman races, which were held in the coliseums on round or oval tracks, and were consequently hideously dangerous for driver and horses alike, these races, like the ridden ones that would come later, were held on the straight. From the line out to some distant spot, then a turn, and back to the start. Horses were too valuable to lose to accidents that could easily be prevented.
The chariots were light wicker affairs, never pulled by more than two horses. The wheels had iron rims and iron fittings, and the wicker cars themselves were open in front, with a curved wall behind. The chariot that their father used for important occasions had seats; these racing chariots did not. Nor did they have the scythes on the wheels that the war chariots had.
The war chariots were fearsome things, and Gwen had never (of course) seen them in use in battle. But these races would demonstrate some of the skill of the charioteers and the warriors who fought with them.
There were four in the first race, which was a very special challenge match; two of them were her father's horses and were driven by his men. The other two belonged to two of his war chiefs. The king was well known to be a generous winner and a gracious loser; no one would hold back for fear of displeasing him. These would be excellent races.
Much as Gwen yearned after the horses like one gone lovesick, there was one pair and their driver that Gwen particularly wanted to watch, and they were not her father's horses. They belonged to Hydd ap Kei, one of the king's oldest friends, and the chariot driver was a woman.
Her name was Braith, and Gwen had watched her race a score of times. She was amazing in the races, and Gwen wondered what she would be like in battle. She seemed to be absolutely fearless, she was known for running out onto the pole, standing on the yoke to help balance for a fast turn, running back to the chariot again. Precious time could be lost in the turns, precious in a race, and, Gwen supposed, precious in a fight, too. Running the pole like that helped in a turn. Gwen had even, once, when the chariot had hit an unseen rock and shattered, seen Braith leap onto the horses' backs and drive them with one foot on each horse, her hair coming loose from its braids and streaming behind her like the horses' tails.
She'd been disqualified, for after all, in a chariot race it is expected that there be a _chariot_ behind the horses, but people were still talking about the feat.
Braith was indeed in the first race, and Gwen edged as near as she dared, watching her idol crooning to and soothing her team. They weren't a matched team, like the king's two; the left-hand one was a dark chestnut, the right-hand a dun. Braith combed her fingers through their coarse manes, ran her hands along their stocky necks, and whispered into their short, broad ears, standing between them as if she were a third horse in the traces. Gwen watched her with raw envy, her fingers itching and twitching with longing to touch those soft noses, scratch those warm necks. She wasn't allowed near the warhorses, ever. "Too dangerous," her father said. He didn't mean dangerous for _her,_ he meant dangerous for the horses. She might move suddenly, the wrong way, or do something else that would startle them, he said. They could sprain a muscle or make a misstep and hurt themselves some other way.
So Gwen could only watch from afar as the bettors circled the chariots, eyed the great beasts knowingly, and conversed in mutters.
Gwen thought that Braith looked exactly like her team; she was stocky, weather-beaten, rough. Her bright brown eyes peered out from under a kind of forelock of coarse, dark hair that looked as if she had hacked it off with her own knife in a fit of impatience. Her voice had the same intonation as a horse's whinny, and when she laughed, it was loud and sudden and exactly like a neigh. Gwen adored her.
If there was anyone in the world she would have liked to grow up to be, it was Braith. Power? Braith _had_ Power! If anyone doubted, all they had to do was see her with her horses! That was Epona's Power, and if Epona was a lesser goddess, well, perhaps she was closer to those who served her.
The race was to begin at the sacred oak grove, and Gwen pressed herself against the bark of one of the great trees, hoping her brown gown would blend in with the bark, and yearned after Braith and her team with a passion she never felt for the gods.
Suddenly those bright brown eyes caught sight of Gwen and locked on her. As if pulled by their reins, her horses turned to look at what Braith was looking at, so now there were three pairs of eyes gazing thoughtfully at her. Slowly, Braith smiled. And Gwen felt a jolt of something that took her breath away.
Then she went back to whispering to her team. But now and again, she looked over at Gwen and smiled.
No one else seemed to notice—or if they noticed, care that Gwen was there. Her ability to be quiet and unobtrusive was working even in this crowd. So she was allowed to watch with the rest as the drivers got into their chariots, as the chariots maneuvered into a roughly straight line, and then, at the shout from the king, reins slapped on backs, whips snapped, and the teams plunged out onto the rough sward for the outward leg of the race.
Gwen would have swarmed up the tree, but she was wearing her one good gown, and she _knew_ what her nurse _and_ the queen would have to say about it if the garment was ruined before it was even dinner.
So she just ran to stand in front of the shouting, cheering men, who were now so focused on the race that they didn't even notice her.
The hoofbeats didn't sound anything like thunder—more like rocks tumbling down a cliff. Thunder wouldn't make the ground shake; thunder didn't make her heart pound or her throat dry with excitement. Four lines of rising dust followed the teams, but the colors painted on the chariots made it easy to tell which was which. What you could _not_ tell, until they turned at the opposite end, was who was in the lead.
That was signaled by the servants at the end, who raised a pole with the owner's pennant on it as soon as the chariot made the turn.
And the first pennant up was for Braith's team. Gwen gave a squeal of glee, and jumped up and down, her hands clasped under her chin. She knew better than to pray to Epona, the goddess of horses, for Braith to win—that was _frivolous_ use of prayer, which was important; the queen had made that very clear to all her daughters. If you pestered the gods with petitions all the time, they'd grow tired of hearing from you, and when you needed them to answer, the prayers would be ignored. But she could hope, and she could wish, and she wished with all her might.
But right behind Braith's team was her father's, a pair of handsome grays out of his warhorse herd. If the Romans had still been here, he'd have lost them for certain. The Romans would have whisked them away for tribute before you could say "knife."
The other two teams were lost in the dust, but the king's, and Braith's, were so close that Gwen held her breath; it looked from here as if they were literally one team of four horses. The tension was incredible; she clasped her hands so tightly together that the knuckles hurt.
And then Braith did the unthinkable. She leaped out onto the pole and ran up between her pair, reins wrapped loosely around her wrist, to stand between them, an arm over each neck, shouting encouragement in their ears. Behind her, the empty chariot bounced and bucked; other horses might have shied, but her team paid it no heed. From some depth within them, they found new strength and surged ahead, crossing the finish line a full chariot-and-team length ahead of the King's. The men roared approval at this daring move, even the king whooping and clapping. Gwen's heart was beating so fast she felt faint.
They shot past as Braith ran back to the chariot and began, slowly, to rein her team in and turn them about.
When they pulled up again before the crowd, Gwen hung back to keep from being noticed, but Braith was having none of that. "Young Gwenhwyfar!" she called, beckoning to her. "Come ye here."
Gwen started at the sound of her name, but at her age, she was supposed to obey any adult, and although her father looked surprised to see her there, he didn't forbid it. She eased through the forest of towering men and came to the side of Braith's chariot. The horses steamed, their sides moving strongly, although they were not heaving for breath. "Nah, my beauties have just run themselves to sweat, so what is it we do with them?" Braith asked, looking straight down at her.
"Walk them so they do not founder nor stiffen," Gwen said promptly.
"And water?" Braith prompted.
"Only a mouthful at a time." Gwen knew all this very well; on the rare occasions that the sisters could get their fat pony to work up a sweat, she was the one left to walk him cool. Not that she minded. She just wished he was a horse, but she was fond of him, and a pony, even a shared pony, was better than no horse at all.
"Here ye be then." And to Gwen's astonishment, as well as that of the rest of the crowd (including several adolescent boys who gaped at her with raw envy) Braith put the looped-up reins in her hands. "Be walking them cool, please ye."
Gwen didn't hesitate. She took the reins as the two horses bent to sniff the top of her head. Then, with her heart feeling so full of happiness she thought she would burst, she began walking toward the stream, the team ambling obediently behind her, with the chariot wheels rumbling and swishing through the grass. She let them have the allotted mouthful of water when they reached the stream, then turned and began walking them back. In the distance she could see Braith talking with the king and the rest of the men. The prize was already in her hands, a pair of beautiful bridles with bronze ornaments for the team, a silver torque for her. The team's owner got a drinking horn bound in silver, with silver feet; he seemed well pleased.
Without being prompted, Gwen stopped short of the crowd, reached up under the nearest horse's mane as high as she could, and felt the shoulder. He was still sweaty, so she turned back around and made another trip to the stream. Again, she let the horses have a mouthful of water, and she tried not to feel self-conscious as everyone but Braith seemed to be casting glances at her.
This time when she returned, the horses were cool. It had only been one race, after all; this was nothing to the exertion they would get in a battle. She waited politely until Braith "noticed" her, then held up the reins.
Braith checked the horses herself. "Well done, young Gwenhwyfar," she said, gravely. "Now, will ye be doing me the kindness of stepping into my chariot?"
Now totally astonished, Gwen did as she had been asked.
"And now be running out on the pole and back." Braith did not ask if she _could_ do so, she simply acted as if it were just a matter of course that Gwen would be able.
Of course she could; it wasn't as if she hadn't been practicing just such a thing all summer. Not on a chariot with _horses_ hitched to it, of course, but on an old one with a broken axle. She flexed her toes and then, fixing her eyes not on the pole but straight ahead, ran out along the limber pole, between the warm sides of the horses and back to the chariot.
"Ah, king," sighed Braith. "It is a pity this is your daughter, for I'd be taking her back with me this day and leaving you the torque in her place."
"And for what purpose, lady?" the King asked, with a chuckle.
"To make a charioteer of her, as I was." Braith turned her head to the side and looked at the king from under her shag of hair. "And I tell you this: Be giving her a horse now, and not a pony, and of her own. A wise old warhorse, too old for battle; let the old horse teach the young rider. And be giving her training; now is the time to do it, while she's fearless. Do that, and you'll have a warrior out of her."
The king pulled at his lip. "And the queen will have a Wise Lady out of her—"
Braith shook her head. "The mark of Epona is on this one; there's two goddesses in this one, but Epona is the stronger. 'Tis a waste to make her go to the Ladies." Braith shrugged. "But if it is your will to send her, still, give her the horse and as much of the training as she can get before she goes; I never heard it said that warrior training did a Lady any harm. She's only nine summers. Maybe, when she is a woman, Epona will let her go. If not, be sure you will know. The Power won't leave her in that time, and I never heard the Ladies say otherwise."
"Nor I," the king agreed, to Gwen's joy and delight. "It will be done as you advise."
She was going to get everything she had wanted! A horse, a real horse and not a pony! Training with bow and knife and sword! Oh, and lance as well, because a charioteer used the lance too! She felt dizzy with happiness, more dizzy than she had the time she'd filched someone's forgotten cup of mead.
In her rush of happiness she did not forget her manners. "Thank you, Father," she said, with a little bow. "And thank you, Warrior." The king beamed down on her, his ruddy hair and beard glowing in the sunlight, his strong shoulders stretching the leather of his tunic, and the gleam of silver at his throat, wrists, and around his head.
She watched the rest of the morning races in a glow of happiness; none of them were as exciting as the first one. Braith won all the ones she cared to enter, but she held back a good deal of the time. The chariot races alternated with ridden races, to give all the horses a chance to rest. The king didn't enter his horses that often either; Gwen had been given tacit approval to stay, so stay she did, at the king's side, but not getting into the way, listening as hard as she ever could as the king and Braith and the king's war leaders discussed the horses and their drivers. They talked not about the race itself but about how the teams might perform on a hill, maneuvering around other chariots, when encountering slippery grass or mud. They talked of the riders, of whether man and horse seemed of one mind, whether a horse was uncertain of his rider, or the rider of his horse; such uncertainty could mean balks and spills on the battlefield. They discussed whether the horses had been seasoned to the sounds of combat. It was then that she realized that these weren't just races for the sake of the holiday; this was the opportunity for the king to see his war chiefs' best drivers and pairs, the best riders and mounts, so that he would know where to put them in a battle.
Perhaps the only race that actually had been nothing but a race had been the one between his team and Braith's. And even then—
"Your pair is steadier than last year," the king said.
Braith nodded. "Last year I'd not have run out on the pole. They'll go through fire and ice for me now. I reckon two more years, maybe three, before they start t' slow, and five or six before I need be training a new pair, then another brace of years before the new pair will be ready." She laughed. "And mebbe then 'twill be me that's out t'pasture."
The King laughed. "You are as ageless as the hills. No pasture for you!"
The rest of the war chiefs laughed and asked Braith's opinion on this or that team. Gwen became aware that not only was Braith _her_ hero, her opinion was held in high esteem by all of these men.
_I want to be like that,_ she thought, looking worshipfully up at the woman. _I want people to talk to me like that._
The sound of a horn warned them all that dinner was ready; this would not be a formal feast of the sort that was held in the Great Hall, but as Gwen knew from earlier years, she and her sisters, her mother and her chief ladies, the king's particular guests and war chiefs, and the king himself would be seated at the trestle tables hauled outside and given the best. Everyone else would help themselves. There would be more than enough; anyone not competing in the afternoon games would probably be stuffed and dozy.
The press of people around the king was too great for her to walk beside him to the tables, and she had an idea that her mother would think it forward of her to do so. She eased herself away, and trotted back toward the open-air "kitchen" where the queen was supervising the last preparations. Before she got even that far, her eldest sister, Cataruna, spotted her, and rounded her up like a straying goose.
"Now you sit here—I put Little Gwen on the other side there, so unless she starts flinging things at you across mother and father, things should be quiet enough—" Her sister paused, and turned her around to look her up and down critically. "—I don't believe it! No dirt, no leaves and grass in your hair, nothing torn—are you a changeling? Did someone make away with the real Gwen?"
Gwen laughed. "I was watching the races."
"And you didn't climb a tree to see them better?" her sister shook her head. "I shall expect a hen to crow, next, and a gander to lay an egg. All right, sit down, and mind your manners."
Gwen had every intention of minding her manners. She was not going to give her father the least little excuse for taking back what he had promised.
Dinner was uneventful, except for Little Gwen trying to command attention at her side of the table, boasting and being self-important. And it was irritating, but most of those around her seemed to find it amusing. Men and boys, particularly, fell under her naughty charm. By contrast, Gwen kept very quiet, didn't grab for the best portions, and didn't even complain when the boys on either side of her and across from her did. She watched wistfully as most of the goose went into those boys, and the juiciest bits of the roast pork, the best baked apples, the center part of the bread. Her reward was the approving nod from her mother. The king didn't notice; what children did or did not do was not something that concerned him when he was busy speaking with his guests.
The boys on either side of Gwen quickly stuffed themselves and as quickly sped off to whatever game or competition had claimed their interest. That was when the queen passed down the remains of the very special dishes that the adults had shared. Little Gwen had also already dashed off on a quest of her own at that point, so Gwen was able to enjoy her feast in peace. And she did, indeed, for the first time in her life, get enough goose that she didn't want any more and enough tasty goose-liver paste to spread on a bread-end.
The king also lingered, when he saw that Gwen was still there, and awkwardly cleared his throat, getting the queen's attention.
"It's Braith's mind that Gwen's ready for a horse and for warrior training," he said, abruptly.
The queen stared at him as if she hadn't quite heard him correctly. She licked her lips and twined the end of one of her braids about her fingers for a moment; she looked, at that moment, very conflicted. "Braith is a very competent trainer and warrior," she said carefully.
"And you trust her judgment."
The king nodded. "Braith says it's Epona's hand that's on her. She entrusted her own team to Gwen for cooling down, and I saw it myself. The girl has horse sense. And good sense about horses . . ."
"Pardon, Father, Mother?" Cataruna, Gwen's eldest sister, paused in fetching away the precious silver-rimmed drinking horns for safe-keeping. "Gwen is the one that always takes first care of the pony. And he never kicks or bites her, which is more than I can claim. Ask your horse keeper, he knows."
The Queen sucked her lower lip in a little. "I suppose there's no harm in it. But Little Gwen will want a horse and training too . . ."
The king began to roll his eyes, but then, narrowed them. "Then she shall have them. And when the horse is left neglected and her nurse has to march her down to the stable to tend him, or she cries because he's too tall, and pouts because she got a bruising, or because it stepped on her foot, you shall make her beg you to let her off."
Eleri the queen nodded, then looked past the king at Gwen. "And you will do none of these things," she said to Gwen, who nodded solemnly at what was clearly an order. "Very well then. Let it be as you wish. She has some years before she will go to the Ladies, at any rate, and I suppose no harm ever came of a girl getting warrior training before she went to the Cauldron Keepers."
"Exactly what Braith said," the king replied, with open relief. He sprang to his feet. "Then, by your leave, I'll have her with me for the rest of the races. She can't see too much of them, and perhaps she can make herself useful with the boys."
"Wait—" The queen beckoned to Mag. "Put Gwen into a good tunic and short kirtle, or trews if you can find them to fit her. She's to help with the racers by the king's command."
"I'll help you look!" Gwen exclaimed, her cauldron of happiness overflowing. She pulled up her skirts and ran back to the castle.
Gwen spent the remainder of the day at her father's side, being quiet, obedient, doing exactly what she was told, even though what she _wanted_ to do was to poke her nose into everything. She was occasionally allowed to lead horses to cool them as she had for Braith, but most of the time she kept strictly in her father's shadow and said nothing at all unless it was "Aye, sir" or "No, sir." And even though she got hungry and thirsty, she didn't run back to the tables, not even when the wind brought aromas that made her stomach growl. She kept her ears open too, to the opinions of the owners and drivers about various pairs or horse and rider. The races made her forget her growling stomach, even if they weren't as exciting as Braith's were, and she tried to see what it was that others had talked about as the horses thundered down to the turn and back again. As the afternoon went on, the horses pounded the grass on the improvised track to fragments, and raised more and more dust every time they ran. The horses were covered in a fine coat of the stuff, which streaked as they worked up a sweat. The King's grays would have looked a sad sight if they'd still been racing.
There were prizes for every race, but Gwen came to understand that the one that Braith had won was very special and had been arranged far, far ahead of time: the king's two pairs against the two finest pairs of those of his war chiefs who cared to match him. The rest were races among whoever brought a team and cared to challenge.
Finally the ridden races were over, and the best four pairs of all battled for the prize of the day: for the horses, silver bridle and harness ornaments; for the driver, a silver torque like the one Braith had won and a plain silver cloak-brooch; for the owner, if he was not the driver, a cloak-brooch worked in the image of Epona in her White Horse aspect, with a gemstone for an eye. Truly fine prizes, and there were many comments of admiration as they were passed around.
Gwen expected Braith to race for these as well, but to her surprise, the warrior was nowhere to be seen, and her horses must have been taken away for they were no longer at the picket line.
"I am surprised Braith is not here," said one of the war chiefs, echoing Gwen's surprise.
"I asked her not to run," replied Hydd ap Kai, the chief to whom the pair belonged. "It's said there might be trouble on our border before the snows fall, and I'd not have my best pair or driver not at my disposal if there is. This last race is dangerous. Drivers are like to push their pairs because it _is_ the last race, and horses are tired."
The king nodded sagely. "That is why my grays are not running," he said. And then laughed. "Besides, I would not have it whispered behind hands for the rest of the year that my pair won only because the other horses were tired!"
All the men laughed at that. "And another good reason for Braith not to run," agreed Hydd. "Whoever takes the prize will know he took it fairly, and those who lose will know they lost it fairly."
The last four teams lined up, and the crowd fell silent. The four drivers leaned forward a little, knees loose, eyes on the turn at the far end of the course. Their teams had all been given a rest and been wiped down. And now it was not just the men who were gathered to watch the race; word had spread that this was the prize race, and the boys and young men had come from the contests, the older women from their cooking and talk, the maidens and the few maiden warriors from their dances and flirtations and contests of their own. They lined the side of the course nearest the camp, leaving the other free so that a team in trouble had a side to pull off to without endangering the spectators. The tension in the air made Gwen's heart race, and her mouth felt as if it were full of dust.
The king solemnly stepped forward; with deliberation, he eyed each of the drivers in turn, then, looking at the sky so that he could not have been said to have cued a driver before time, waited until all was so still that only the distant metallic clatter of the rooks on the castle roof broke the silence, and then he shouted.
The teams shot off, showing no sign of being weary. Without Braith driving, without her father's precious grays at risk, Gwen was able to simply watch them with the same excitement as everyone else.
The cheering started immediately, and did not abate; even if someone had not had a favorite before this race began, he'd picked a favorite by the time the horses were halfway to the grove.
The flags went up and the teams turned; it was a close race, so close that at this point anyone could win.
And then one of the two centermost teams stumbled.
The crowd gasped as one; for a moment the heads of the horses vanished under the dust, and Gwen's heart stopped. Had they fallen? Had one of the horses, Epona forbid, broken a leg? That would be a terrible omen as well as a disaster—and worse still would be if the chariot had gone over, the driver thrown, to break a leg, an arm—a back—his head—
That had happened once a few years ago; she had been too little to be allowed near the course, but she remembered it, the wails of the women, the lamenting around the body, brought back to lie in solemn state on a swiftly cleared table. And that had been a horrible winter too—
But her heart leaped as the horses' heads appeared again, far behind the others but not down—they moved slowly off the course, the off-side one limping, but that was the worst of it, pulled up lame.
She turned her attention back to the remaining teams, who thundered on, until with one tremendous effort, the team that had been farthest behind leaped forward, while the crowd screamed. Gwen shouted; the horses strained, and at the very last moment, they pulled a head-length in front of the team that had been winning.
The three teams pounded past as the drivers slowed them, turning them in a great circle to bring them back to the king and his men. The rest of the company swarmed around the winner as soon as it was safe; they gathered up the driver on their shoulders, and Gwen reckoned that if they could have gathered up the horses as well, they would have.
No one seemed to take thought for the poor loser leading his horses back to the picket line. Gwen's eyes flicked between him and the winner for a moment. Then she ran as fast as her legs would take her for that lonely driver and pair.
"I'll take them and walk them," she called as soon as she was near enough for him to hear. "You find the king's horse leech. He won't watch the races, he's at the ale tuns."
"Epona's blessings on you, little one," the man said gratefully, giving the reins to her. Then, despite his own weariness, he ran.
She led the poor drooping things slowly; it wasn't just the off-side horse that was limping. The stumble must have pulled the other over enough to lame him too. They wanted to stop, but she knew that if she let them, they'd cool too fast, and that might make their hurts worse.
But the driver was back in mere moments with the king's horse healer; not needed now, she handed back the reins and walked away quickly. If it was very bad news . . . she didn't want to be there to hear it or to see the driver's face.
**Chapter Four**
**Supper was what** had been left over from the rest of the day for the common folk and baked meat pies and baked fowl for the king's guests. Gwen had thought she had eaten all the goose she could possibly eat. She discovered, to her pleasure, that she was wrong. And this time, the boys, given the option of savory meat pies dripping with rich gravy, merely picked at the goose, leaving most of it to her.
The sun was setting as supper began; it was fully dark and the torches and bonfire had been lit by the time the last of the guests rose from the table, and the servants and Gwen and her sisters (all but Little Gwen, who had disappeared as usual) carried the valuable cups and knives back to their coffers in the castle.
The queen and her women were long gone. No one mentioned this; no one would say anything about it later. _They_ had gone off to make magic for the High King to ensure a son from the marriage that had been made this day. That was woman's work, and men were not even supposed to know about it.
Nor were little girls, so Gwen pretended that she didn't and settled down to enjoy the music and dancing. Little Gwen finally put in an appearance; it seemed she had bullied or cajoled some of the village children to make her a Harvest Maiden, and they were parading about with her at the head of them, in a wreath of leaves and vines, with a stalk of weed as a scepter. The real Harvest Maiden chosen by the women was at the Working, of course. And last year, Gwen probably would have been irritated at Little Gwen's showing off. But she was full of goose and the knowledge that she was going to be given a horse and training in a few days and that Little Gwen would surely get her come-uppance if she tried to wheedle and pout and cry her way into the same.
"Be wary of that one," said a voice in her ear. Gwen turned to see Braith settling down next to her, a horn of mead in one hand, and a pottery cup in the other. She handed the cup to Gwen; it held hot cider.
"Why?" Gwen asked, casting a dubious glance after her sister.
"Because there's power in her." Braith nodded at the chain of children. "Look at her. Look at who's following. Boys, mostly. A few girls. Even young as she is, she has that power over the males. Who indulges her? Men and boys. Who persuades women not to punish her? Men and boys. With one like that, there's no reasoning with the menfolk; when she gets older and learns her Power, and make no mistake, she has _Power,_ in her presence their eyes will glaze over and their reason fly out the window. The _glamorie,_ that's what she's got, a true Power, make no mistake. Anna Morgause has it. I've seen her, and she's but to bend a finger and nine men of ten will come to sniff at her hem. And they say that young Morgana has it too, though more subtle than Anna Morgause. So be wary of her, for once she's woman grown, what she wants, she'll have, and if someone else has it, she'll take it, and the men will stand in line to get it for her."
A strange chill ran up Gwen's back, and she shivered. It seemed absurd to look at Little Gwen lording it among the other small children and talk about her in the same breadth as Lot's queen. And yet . . .
She watched Little Gwen, and despite the absurdity of the crown and the troupe of little boys about her . . . there was no doubt. Her sister was more than just pretty. When you put aside what you knew about her, and just let your eyes follow her, she had something about her that made everything about her a little _more._ Both of them had white blond hair, but Little Gwen's was glossier, and even when tousled, it looked pretty instead of messy. They both had blue-green eyes, but Little Gwen had a way of looking sideways out of them that made you think she was looking at you in particular. Her cheeks were the pink of wild roses, her chin adorably pointed. And that was now, as a little girl. What would happen when she got to be Cataruna's age?
She sipped her cider and wondered why Braith was telling her all this.
"I tell you this because I had a sister like her. By the time we were twelve and eleven summers, she had the best in the house, and the rest of us got what she didn't want or hadn't a use for. 'Twas a rare good thing for me, she didn't like the horses and they didn't like her; every lad one of us fancied, she took, only to toss aside for the next. M'brothers, m'parents, they fair doted on her." Braith shook her head. "When I got taken up by Chief Hydd's horse tamer, no one even noticed I was going. Never went back, not even t'visit, but I've no doubt she made plenty'f mischief before fever took her. An' she was only a farmer's get. Reckon what mischief yon'll make, bein' the king's." Braith sipped thoughtfully at her mead. "So... best get ye gone from here, afore there's summat ye hold dear that she comes t'fancy. Or be doin' somethin' she never will."
After that, Braith seemed to have nothing more to say, and they sat in silence. Gwen watched the dancing and listened to the music for a while, then when she looked up again, Braith was gone, leaving as quietly as she had come.
By that time the long day and a full stomach were both catching up with her. She was having trouble keeping her eyes open, and she finally decided that going to bed was a better idea than nodding off and having someone have to put her to bed like an overtired baby.
Besides, the queen and her women had just come back from the Working, and the queen had a strange, wild look about her. Gwen wasn't sure she liked the way her mother looked right now: eyes as bright as someone a-fever, cheeks flushed, looking scarcely old enough to be the mother of one, much less a brood. If you didn't know her, you'd take her for Cataruna's sister, not her mother. And the way her father was looking back at her . . . made her very uncomfortable for reasons she really didn't understand.
So as the queen drew the king into the dancing, taking his hand and pulling him up from his seat as if he was light as a bit of down, then pressing close against him, Gwen picked herself up and turned her back on the fire and her face to the castle.
The Great Hall was full of murmurings in the shadows; she took the straightest path through the middle of it and ignored what was going on; really, the only difference between tonight and every other night was that the Hall was a great deal fuller.
The bed was cold, and she shivered for a while before her body warmed up the hollow; she was almost asleep when half-running footsteps, murmurs, playful growls and breathless giggling heralded the passage of the king and queen into their bedchamber. The sounds made her uncomfortable all over again, but it wasn't just the sounds, and it wasn't just knowing that her mother and father were going to do what all those people in the shadows were doing. It was something else, something she couldn't put a finger on, a feeling that . . . that something was turning wrong that had been right. Like a blight on grain; this wasn't just a matter of her parents, it was bigger than that.
The feeling held her pinned in her bed—
Until she woke suddenly to find that it was dawn, and her sisters were all curled up with her, and, as usual, Little Gwen had stolen the covers.
The king was in a rare good mood; after breakfast he gathered up Gwen—with Little Gwen predictably trailing behind, unasked—and took her down to his horsemaster. "Braith says the lass is ready to be trained and to give her a wise old warhorse to train her," he told the old man. The horsemaster looked down at her critically. Gwen looked him in the eyes. There were scars all over him, at least, everywhere that she could see, and a pair of spectacular knife- or sword-cuts marred a craggy face still further. "I know ye," he said, finally, his voice a low growl. "And a goodly work ye make of the pony. Braith thinks ye ready for a horse now?"
Gwen nodded. "Aye, sir," she said quietly.
_"I_ want a horse!" Little Gwen interrupted imperiously. The horsemaster turned to look at her, then Gwen saw him suddenly look up at her father. Something passed between them, and the horsemaster smiled. Gwen got a shiver of pleasure when she saw that smile. It promised that Little Gwen was going to get what she wanted and not like it.
"Well, then, ye'll have a horse," the horsemaster said, "An ye'll follow me?"
Gwen followed obediently at his heels. Little Gwen marched imperiously in front of them all. When they got to the stables, the horsemaster addressed Gwen in a quiet voice while Little Gwen surveyed the horses in the paddock as if she owned all of them.
"And which of these do ye think suits ye," he asked.
Gwen ducked her head deferentially. "You should pick, sir," she said. "Braith said, old and wise. I don't know which are old and wise."
He smiled. "Then pick I shall—" he began, when Little Gwen interrupted.
"I want _that_ one!" she declared, pointing at a showy young gray. The king made a choking sound. Gwen caught the horsemaster making a soothing motion with his hand.
"All right," he replied agreeably. "Let's us get him saddled, then."
He ordered the astonished grooms to catch, saddle and bridle the high-tempered beast, and put a lead line on the bridle. Little Gwen was practically bouncing with excitement, but she frowned at the line. "I don't _need_ that!" she announced grandly. "I can ride!"
"Indeed," the horsemaster said, but kept the rope clipped to the bridle. "But every rider needs the lead to try the paces." He swung her up onto the saddle, where she perched as if she were on the old pony, legs slack, hands clenched on the reins. The horse reacted poorly to the latter; he tossed his head, and his mane lashed her face, cutting right across her eyes.
She shrieked. The horse reacted to _that_ by lurching into a run.
Or trying to. The horsemaster had been ready for that. He kept a tight grip on the lead and pulled inward while pivoting on one heel, which forced the horse to stay in a trot in a tight circle around him. Little Gwen bounced in the saddle in a way that made Gwen wince for what seemed a very long time, her shrieks now coming out as painful _"Ah! Ah! Ah! Ah!"_ sounds as she bounced and hit the saddle. Three times she went in a circle around the horsemaster, each time making more and more noise and making the horse try to break into a run. How the horsemaster kept him to a trot, Gwen could not imagine.
It was a relief when she fell off.
She immediately scrambled to her feet, face red with pain and rage. She looked about for something to hit the horse with but fortunately found nothing. The horsemaster pulled up on the lead and soothed the ruffled stallion, but he made no move to soothe Little Gwen.
Interestingly, neither did the king.
Neither man said anything to her as she stared at them in a fury. Gwen prudently backed away from everything and everyone until she had a horse or two between her and her sister. Best to not remind her just who had inspired this desire to have a horse.
Finally, Little Gwen erupted in the tantrum that Gwen knew was inevitable. "I don't _want_ your old horses!" she screamed, making every horse in the paddock shy or lay its ears back. "I _hate_ horses! You should kill them _all_ and make _soup_ out of them!"
Then she burst into angry tears and ran off. Gwen slowly emerged from hiding. The king and his horsemaster were both shaking their heads. "She's not hurt, is she?" the king asked.
"Only a bit of bruising." The old man gestured at the straw-strewn paddock. "That be why I kept her on the lead. And I grant ye, I could've made a longer affair of this, picked a horse fit for her, tried to get her to tend it as I know yon girl _will,_ an' the end of that'd be more work for _me_ when she didn't. So instead, I cut across country, give her what she wanted, and—"
He shrugged. The king laughed ruefully.
_She'll find something to take this out on,_ Gwen thought sourly. But then the horsemaster turned to see her standing there, and she tried to make her expression pleasant. "Nah, Braith's girl, let's find ye a proper horse."
In the end, it came to two, and the horsemaster couldn't make up his mind which. One was a mare, one of the cavalry duns; the other was a stallion of the famous gray line, now almost a pure white, that had been both a chariot horse and a mount. After looking them both over for a long time, the horsemaster sighed and threw up his hands. "Naught for it," he said. "Mun let _them_ choose."
He put Gwen at one end of the paddock and turned the two horses loose. "Call 'em, Braith's girl," he told her, and stood away from her so that they would not react to his presence but to hers.
Now alone in the paddock with them, her mouth went a little dry. They were _very_ big, twice the size of the pony. She swallowed, licked her lips, and made the little chirruping sounds she made to call the pony to her.
They both looked at her, ears and heads up.
"Come!" she urged. "One of you has to teach me, now, so come!"
The stallion snorted; the mare shook her head. Both of them started forward at the same time, but before they were halfway across the paddock, the dun mare shouldered the stallion aside with a snort of her own and laid-back ears. She picked up her feet in a trot that brought her to Gwen while the stallion slunk sheepishly off to one side.
Gwen held out her hand and the mare nuzzled it, then put her head down and butted Gwen in the chest, blowing hay-scented breath into her tunic, surprising a delighted laugh out of her.
The horsemaster brought saddle and bridle but waited while Gwen put them on, only giving her a hand when something was too far for her to reach. "Ye mun find ways t'be doing this on yer own, Braith's girl," he told her gravely. "I dun help the boys, I shan't help ye."
She nodded. That was reasonable. So taking the hint, once the mare—Adara was her name—was saddled and bridled, on her own she took her over to a stump that had been incorporated into the paddock fence and used that to get herself into the saddle. Once there, she found it not as dissimilar to the pony as she had feared. She was a _lot_ higher off the ground, it was true, but the pony was so fat that his girth wasn't a great deal smaller than Adara's. She couldn't imagine why Little Gwen hadn't been able to sit the saddle better, unless it was that her youngest sister really hadn't learned to ride properly. She fitted her feet into the leather stirrups and was relieved that the horsemaster had judged the length right. She was even more pleased when he didn't clip a lead rope to her bridle.
Since he was waiting expectantly, she chirruped to Adara, tightened her legs in the right places, lifted the reins a trifle, and nudged her a little with her heels. Adara moved out in a walk, circling the paddock, then increased her pace from a faster walk into a trot.
Gwen bounced for a few paces before she found her seat again. Adara's ears flicked back and forth and she looked over her shoulder with what _looked_ like amusement, and she moved into a canter.
Now this was the fastest she had ever ridden, and it was both thrilling and terrifying. The pony had never gone this fast, not even at a gallop. But the mare had another pace in her, and without Gwen doing anything, she lengthened her stride into a gallop.
The world blurred. All Gwen was conscious of was her own breathlessness, her heart racing, and the horse moving under her. And it was glorious. Like flying.
The mare gave her only a taste of this before slowing, first to the canter, then the trot again, and finally into the walk. She stopped on her own at the side of the horsemaster.
"Ye'll do," was all he said. Then he left her to make sure the mare was walked cool, unsaddled and unbridled, rubbed down, and put up in her stall with her tack with her. Gwen moved in a kind of happy dream. She had thought that yesterday was the best day of her life. But no. Today was.
One of the grooms came to tell her when she was finished that she was to report to the novice trainer. She thanked him and trotted off to the yard where all the boys, and the odd girl or two, got their first lessons in warcraft. Or rather, their first lessons in making their bodies strong enough for weapons; it seemed that handling a sword or a bow or even a knife was a long way off. Gwen had never thought of herself as lazy, but after what seemed like an age of lifting small leather pails of water over and over, of swinging weighted sticks against a padded pole over and over, and many other similar exercises, she was hot and sore and grateful to be dismissed for the day to go back to the paddock and commence another round of riding, this time under the eagle eye of one of the grooms, in the company of the rest of the beginners. She got no help in saddling and bridling this time, but neither did the others. No help, that is, from the _groom;_ she was not the only undersized person among the beginners, and they helped each other reach girths under bellies, pass breastbands around chests, and persuade the canny old horses to bend their heads for the bridle. Gwen was especially good at the latter, so no one begrudged her the help it took to get a saddle that seemed a hundred times heavier than it had been this morning onto Adara's back.
Then they lined up, head to tail, along the paddock fence, and the groom called out what they should do. Oh, not for _their_ benefit; it was very clear to Gwen that she wasn't in control of Adara right now, and it looked to her as if the rest of the beginners were in a similar case. No, no. It was the horses who responded to the commands, and they, the riders, were doing their pitiful best not to fall off, to learn how to move as one with the horse, and not merely balance there.
Ride in a circle; walk, trot, canter, then drop back to a walk. Wheel and do the same in the other direction. Repeat until the horses' muscles were sufficiently warmed up. Wheel, so that they were all facing the same direction. Charge the fence at a trot, pull up, wheel in place and charge the fence on the other side. Repeat until the young riders were starting to get the rhythm of things. Go back to riding in a circle. Split into two groups, charge each other, making sure no one collided. Wheel and repeat. Go back to riding in a circle. Trot to the fence and stop, then back. Wheel in place and repeat.
Then the groom ordered them all out of the paddock, and Gwen thought they were going to be allowed to just _ride,_ on a jaunt across the grazing meadows, as she used to on the pony—but no. The groom directed them to another part of the training field where there were padded poles set up down the middle, and when Gwen saw them, she knew what they were going to be doing. As she expected, the groom set them to weaving through the poles, down and back, first at a walk, then a trot, then a canter. They didn't go up to a full gallop, but right next to them was another set of poles, around which another set of slightly older warriors-in-training _were_ riding at an all-out gallop, and with the reins in their teeth and their hands held out to the side, keeping their seats only through superb balance!
All this was taking an entirely different set of muscles than she used in riding the stolid little pony. She could feel every pull and strain and knew she was going to be very, very sore. And yet—she would not have traded this for _anything._ And no matter how sore she was, it was going to be worth it.
The groom finally led them back to their original paddock, but of course, the work was not over. The horses had to be unsaddled, walked cool, rubbed down, and put in their proper stalls, with saddle arranged on a stand and bridle hung on a peg. Then, and only then, were they allowed to go.
It was sunset, and suppertime, by the time she limped back to the Great Hall. The servants had brought in the kettles of stew and the remains of last night's feast, and people were settling onto the benches and tucking in. The Hall was nowhere near as crowded as it had been last night; at least half the guests had packed up and headed homeward this morning, and the rest would leave tomorrow. Gwen was not altogether sorry to see them go; she was already tired of being polite and always on her good behavior even when some of the boy guests behaved outrageously.
Her father and mother were already seated at the High Table—on the day after a feast, no one really stood on ceremony—when a shriek and a wail arose from the back of the hall where the bedrooms were, and a moment later Gynath and Cataruna came storming out of the room, the one angry, the other lamenting, with ruin in their hands.
"My best slippers!" shouted Cataruna, her cheeks aflame with rage.
"My belt! I just finished embroidering it! I only wore it once!" wept Gynath, consumed with grief.
The pretty leather slippers had, very clearly, been given to the dogs to play with. They were chewed to shapelessness, and the seams had come half unsewn.
As for the belt, someone had taken it out and trodden it into the mud until nothing of the bright colors that Gynath had so painstakingly sewn into beautiful patterns could be seen for the dirt and stains.
A sinking feeling in her stomach, Gwen walked slowly to the bedroom. She dreaded what she would find. Which of _her_ possessions had been taken and ruined? Behind her, she could hear her sisters telling their parents how they had found their things—and Cataruna added shrilly that Little Gwen was nowhere to be found.
_Little Gwen._ Of course it was her. She'd wanted something, gotten it, and didn't like it—so her first thought was to take whatever her sisters took pleasure in and ruin it. Gynath's new belt had been the admiration and envy of the other girls, for Gynath was the best needlewoman in the castle. And Cataruna's slippers had made her feet look very handsome indeed in the dancing; more than one young man had said something about them in ways that had made the blood rise to Cataruna's cheeks last night.
". . . it was no accident, Father!" Cataruna snarled. "The slippers were in my chest, on top of my kirtle, right where I put them last night. She took them and gave them to the dogs, then put them back!"
Gynath was sobbing too hard to be coherent. She had been working on that belt all summer. Gwen didn't blame her for weeping.
But Gwen didn't have to look far to find Little Gwen's revenge on _her._ There in the corner where she had been left was Gwen's poppet. Or rather, what was left of her poppet.
The doll had been torn limb from limb, scalped, and decapitated. Her clothing had been shredded. Mutely, Gwen gathered up the pitiful remains in both hands, and went out into the hall where her mother was trying to soothe a disconsolate Gynath, and her father to placate Cataruna with promises of a new pair of slippers even prettier than the ruined ones. She waited until Gynath's sobs had quieted into sniffs and hiccups, and Cataruna had run out of names to call their sister. That was when the king and queen finally became aware that she was standing there. When their eyes fell on her, she silently held out her hands. It took them a few moments to realize what it was—or had been.
"Oh, no—" It was Gynath who realized it first, and it came out in a moan. "Oh, no, oh, Gwen, your poppet, your poor doll!"
Cataruna's cheeks flamed anew. "That—that—" she spluttered. "Oh! I am going to _shake_ that brat until her head falls off and her teeth fall out!"
Eleri's eyes narrowed with anger. The king put up a hand. "You'll not touch her. When she's found, she _will_ be whipped, and she'll be living on bread and water for a fortnight, and put to whatever work Bronwyn deems suitable. There will be no playtime for her until the snow flies, and perhaps not even then if I am not convinced of her repentance." He looked to his queen. "I've spoiled and indulged her overmuch, as you said time and again, and this is what comes of it. I am sorry that you, my _good_ daughters, have fallen victim to her mischief."
"And her poppet will be yours, Gwen," the Queen began—
"Lady Mother—no," Gwen replied, feeling dimly that if she were given something of _Little Gwen's_ rather than just a replacement, her youngest sister would only see it as a reason for more vengeance. She straightened her back, gently piled the pathetic remains of the doll on the table, rubbed the back of her hand across her stinging eyes, and looked up at her mother and father. "I'm a warrior now. Warriors don't need poppets. I won't have time to play with it, anyway."
Her mother gave her a skeptical look, but her father relaxed and beamed his approval. "Well said," was all he replied, but Gwen felt that approval fill her and ease some of the sadness she felt at losing her plaything.
"Bronwyn," Eleri directed, "Take these things and see what, if anything, can be done with them. The belt especially. Then look for Gwenhwyfach, and when you find her, see she is put in the guard closet to await our pleasure. And let us eat. There is no reason for a nasty child to spoil our supper, nor make us wait until our meat is cold."
Gwen ate slowly, feeling the ache of every overworked muscle, every bruise. She actually didn't mind it; concentrating on that made everything else secondary. And while Eleri consoled Gynath and Cataruna with the most golden-crusted of the pies and the last of the honeycakes, the king directed his server to give Gwen all of the leftover goose and with his own hand poured her cup full, not of cider, but of honey-mead. "You'll be aching, young warrior," he said in an undertone. "This will help you sleep."
The mead was sweet but with a fire under it. It burned its way pleasantly down her throat as she slowly ate slivers of goose, spread a surprise bit of goose liver on some bread, and sopped up the last of the goose fat with the rest of the bread. And it did start to make the aches go off into the distance and give her a warm and soft-edged feeling, as if she were falling asleep. Halfway through dinner, Bronwyn returned and reported that a sulky and unrepentant Gwenhwyfach had been put in the guard-closet, with one of the turnspits as a guard on the door.
The guard-closet was a tiny little windowless niche in the stone walls, with a single hard stone bench in it, that the king used to keep single wrongdoers in while he debated what punishment to mete out to them. From time to time all of the girls had been confined there for mischief, but never had he done what he did now.
"Here," he said, carefully picking out the hardest and most stale piece of trencherbread and a leather cup that he filled with water. He handed both to Bronwyn. "Give her those, and tell her she will be staying in the closet until morning. In the morning, my dogmaster will whip her. And then for the next fortnight, she will sleep in the rushes with the dogs and the scullions. I'll not have her sharing a soft bed that she did nothing to deserve. I'll not have her sleeping comfortable beside the sisters she wronged. When she is repentant and ready to act like a king's daughter instead of a low-born brat, we will see if she may sleep like one."
Gwen's astonishment woke her up from a half-drowse. Eleri nodded approval.
"I put you in charge of her, Bronwyn, to direct her as you like," the king continued. "While she sleeps on the hearth, you will give her work to do so that she learns the evil of idleness. She'll have nothing but bread and water. At the end of that time, she will apologize, and if I am convinced she is repentant, she may go back to the bed and the board."
Bronwyn bowed silently, took the bread and water, and disappeared into the shadows.
Gwen sopped up the last of the fat, ate the last bite of bread, drank the last swallow in the bottom of her cup. She felt the fatigue of the day settle on her like a weight; she begged permission to leave and plodded back to the bedroom.
On the way there she passed the turnspit guarding the door to the guard-closet. There were muffled sobs coming from inside. But they didn't sound repentant, or frightened, or sorrowful.
They sounded angry.
**Chapter Five**
**Winter did not** stop the training. Even when conditions were too foul to ride, it was the responsibility of the warriors-in-training to take the horses out to the paddock, turn them loose, clean the stalls, then give their feet a thorough cleaning and put them up again. Normally the grooms did this, but when the horses were confined to the stable, rather than running loose, the stalls fouled that much faster. A horse standing in a fouled stall was in danger of thrush. And a horse with thrush was in danger of having to be put down. As the horsemaster told them all sternly the first time they were set to this task, "Every horse in this stable's worth three of the likes of you, an' ne'er ye forget it."
It was true, too. So foul weather only meant another sort of work with the horses.
As for warrior training . . . well, foul weather meant that some of their "training" involved ax work . . . against the firewood. The trainers had very clever ways of making sure that every stroke accomplished some wood-splitting. Gwen built quite a set of muscles over the winter. And once they could be safely trusted with bows and arrows, they became part of the army of hunters that provided meat for the king's table. And a miss there, against rapidly moving targets, had more serious consequences than a miss at a wand. Gwen learned to appreciate every bite of rabbit pie and to look on goose, duck, venison, and boar with an appreciation she'd never felt before.
After a month of punishment, Little Gwen finally broke down and repented . . . or at least made the motions of repentance. Gwen was expecting some other form of retaliation, but at least where she was concerned, nothing happened. In fact, Little Gwen left her alone for the first time in memory. Perhaps it was nothing more than the fact that from Gwenhwyfach's perspective, Gwen's training regimen was worse than any sort of revenge. It hardly mattered, really; the only time she ever saw her little sister was at meals and bedtime and often not even then. Gwen ate early, rose early and went to bed early, so tired from the physical work that she was dead asleep from the moment she got under the blankets.
But once back in the king's good graces, Little Gwen seemed to be putting most of her effort into becoming his favorite—and to making herself as unlike Gwen as possible. She began walking and talking as daintily as any girl trying to catch the eye of a boy, kept herself fastidiously neat, and for the first time volunteered to do things, as long as they were womanly. The king found this very amusing; as for Eleri, she was too preoccupied with her own matters to pay much attention. And Gwen was just relieved that Little Gwen had finally found something to keep her from plaguing her older sisters.
The winter was not as harsh as everyone had feared, and most took that as a sign that the High King's marriage had had the desired result on the land. Certainly at the Year Turning and Fire Kindling, the Midwinter Solstice, word crept across the kingdoms that the new queen was properly increasing, and that was a good omen indeed.
Someone else was increasing as well, although the queen had kept it to herself until almost February, revealing it only when her women threatened to tell the king themselves. But again, this had little impact on Gwen's life; now one of the warriors-in-training, she was effectively out of Eleri's household.
Strangely enough, now that she spent less time _within_ the household, she came to know more of her older sisters. In many ways, she saw them now through the eyes of the older boys, hearing things from them she would never have guessed. That made her watch them, pay attention to them, in a way she had not before.
All four of the girls were fair, like their mother. This alone set them apart among most of the darker-haired people her father ruled. And now that she came to think about it . . . it was very possible that Eleri's blood was all, or part, Saxon. But if that was true, no one even whispered it; she was the queen and their Wise One, and those two facts eclipsed any mere question of blood.
Or . . . just maybe . . . there was other blood entirely in her. But if that was the case, no one would even whisper about it.
Gwen and Little Gwen were the fairest of the lot, with Gwen's hair now mostly shorn off, and Little Gwen's waist-length locks being tightly braided every morning by old Bronwyn. Cataruna had more than a flavoring of their father's red hair, but she did not have the high temper to go with it. She also had his square face, where Gwen and Little Gwen had inherited their mother's pointed chin and tiny nose, and Gynath had something in between. Cataruna was usually grave and quiet; Gynath was usually merry, and while not a flirt exactly, had discovered that young men were very interesting a year before her older sister did so.
And both of the older girls fitted into the domestic and busy life of the household as Gwen, increasingly, did not.
She found she did not miss it; she did not wish herself back in skirts nor regret trading the chores she used to do for the harder—in the physical sense—labor of the training and the sort of work the boys were expected to do. Even in the worst weather, cleaning the stable, cleaning out her horse's hooves with bare, freezing hands, chopping wood as she practiced her ax swings, she would not have traded this for sitting and learning the making of clothing, how to weave, spin, and embroider, the lore of herbs (other than those needed for battlefield medicine and horse doctoring), the management of a household. No, not even for learning magic.
She found that last growing less and less attractive with every day that her body strengthened, her skills with weapons sharpened, and her ability to understand her horses deepened. Not that magic revolted her, far from it—but where once she had longed to see herself in the rites, taking the part of the Maiden in the Circle beside her mother, learning to control and use the Power . . . now that grew distant. Just as she could look at Little Gwen playing with a lapful of poppets and feel not even a twinge of envy, now she would watch her mother beckon Cataruna off into a conversation with the other Wise Women and no longer even wonder for very long what they were talking about.
Perhaps her mother was right. Perhaps it was being around so much Cold Iron in the form of the swords and axes had blunted her need for magic. Perhaps it had even driven the magic from her.
Or perhaps Braith was right, and she never really was suited for that sort of magic in the first place.
And on the Midwinter Solstice, that change in her position was solidified, when she celebrated the night with the other young would-be warriors and not among the women. She thought her mother looked obscurely disappointed, but the queen had two other daughters both of an age to go to the Ladies. Three, if you counted Little Gwen.
And after Midwinter Solstice, Cataruna's demeanor toward Gwen changed.
Mostly, the eldest of the siblings had ignored Gwen, which was fine. They weren't even close in age, after all. Even before Gwen had gone to the squires, they hadn't had much in common. But now, as if the Solstice had signaled some change in Cataruna's mind, she began to do small kindnesses for her sister. When Gwen came in with half-frozen hands, Cataruna would beckon her over to a pot of warmed water to thaw them. When she went to bed, far earlier than anyone else, all worn out with the work, she found that Cataruna had put a fire-warmed stone in her place. When it was her turn to serve at table, Cataruna saw to it that her portion was kept warm at the fire and kept Little Gwen's greedy fingers off it. Some might have been by Eleri's orders, but not all of it. Gwen found herself exchanging grateful and slightly conspiratorial smiles with her eldest sister, and she got them in return. Cataruna's square face seemed unaccountably happier this winter than Gwen had ever seen it before. Whatever was the reason for it, it made Gwen unaccountably happy too.
While the days lengthened again, and winter lost its grip on the countryside, Gwen found herself outstripping the group of youngsters she'd started with. Not drastically, but enough that by Gwyl Canol Gwenwynol, the Spring Equinox, she was given her second horse.
All warriors had more than one horse. Charioteers needed two, of course, but riders had more than one as well. If your horse was lamed, or killed, or ill, you couldn't count on one of the chariot drivers to be able to take you to the battlefield. The chariot was already considered by some old-fashioned, although Gwen's father used it, and used it well. Many commanders were slowly abandoning it in favor of purely mounted cavalry, following the lead of the High King, who fought Roman fashion. Chariots broke, they needed highly skilled drivers, when accidents occurred they could be terrible and generally involved more than just the driver and his horses. And a single mounted man was always faster than a chariot.
Nevertheless, King Lleudd wanted his cavalry trained in chariot work, and that required two horses. All the more reason for every warrior to have two, or more than two, if he or his lord could afford it. So just before the Equinox, the horsemaster Bran came himself for her and presented her and her mare with the gray stallion that had been one of his two original choices for Gwen.
This time when she called him across the paddock, the mare was at her side. The stallion stepped carefully toward them both and diffidently bowed his head a little at the mare. Adara looked the poor fellow over with thinly veiled arrogance, as was to be expected in a lead mare of the herd, then snorted and perfunctorily touched noses with him. The stallion Dai was to be permitted to partner with Gwen. It was very hard for Gwen to keep a sober face and not laugh out loud at the two of them, but poor Dai had been humiliated once by Adara, and he wasn't going to forget that in a hurry.
So now Gwen would learn chariot driving and the trick of switching from one horse to another when riding. The High King Arthur had made a name for himself with his mounted knights who could move swiftly to any part of the land where trouble was brewing by doing just that—stopping for only the briefest periods, or not at all, by switching from a tiring horse to one that was fresher. Though her father might favor the chariot, he was no fool, and as a good commander he could easily see the advantage this brought him.
This was a well-omened time for her to have such recognition, for along with the rites of the seed blessings, the Spring Equinox was the moment when the young god of Light took up his weapons for the first time, and slew his rival of Darkness, the young Prince of Spring eliminating the killer of his father, ridding the world of the murderous Winter King. As such, Gwen's father generally called for another feast like the one at the Fall Equinox. It was not yet time for planting—the ground was still too cold, and the frosts still too certain for that—which meant that the men were not yet bound up in the sowing and tending. Lambing time was mostly over, and though calving and foaling time was on them, such were the responsibilities of horsemasters and herdsmen, not the warriors. So it was a good time to take stock of what the winter had taken and trade news and rumors.
The women, of course, and the Druids, all had magic to do. So it was a good time for them to gather also. There were the seed blessings . . . and there were other things.
For this feast, Gwen was not required to do any of the hearth chores, although she did, in fact, pitch in. With the other squires, she went to gather fallen wood in the forest. She gathered cress and the young sprouts of the cattail plants, which were delicious when quickly dunked in boiling water. She caught and cleaned fresh fish. There was, of course, little fresh game at this feast—this was the time of year when birds were about to nest and animals were giving birth, and careful custodian of his lands that the king was, he forbade any springtime hunting except for the very old—and those made for tough eating, and required stewing.
But mostly Gwen did the chores that her warrior band did—endless wood chopping for the cook fires and ovens, the hauling of water, which was regarded by their trainers as yet another fine way to build their strength, building temporary paddocks for the visitors' mounts, and a thorough cleaning out of the stables down to the bare earth, which was then sprinkled with lime to sweeten it before sand was brought in to cover the lime, and straw laid down over that.
The castle underwent a thorough cleaning too, with the winters' rushes hauled out, the stone floor scrubbed, and new rushes brought in, but that was mostly the work of the servants.
And Gwen had learned that for her, at least, the time of the celebration itself was going to mean still more work.
Peder ap Duach, Gwen's chief instructor and one of her father's most trusted captains, called all of his particular charges together just before the first visitors were to arrive. "I've assignments for some of ye," he said, shortly, looking them all over with a stern eye. "And no whinging do I want to be hearing. Not all the king's honored guests will be bringin' their own pages and squires, and that'll be the job ye'll be doin'. 'Tis a great honor to be chosen, an' a great trust. So here now. Here'll be the ones that'll be servin'."
Never in a thousand years would Gwen have thought she'd be picked, but to her astonishment, she heard her name called; she would be serving Hydd ap Kei, Braith's lord.
She didn't question the assignment, however, nor did she complain about being put to work when some of the others were free to enjoy the relative freedom they'd have while the celebrations were afoot. For one thing, it gave her rather a thrill to have been picked over those older than she. For another, well, this was _Braith's_ liege lord, which meant that she would almost certainly be spending a lot of time in the company of the real warriors and chariot drivers, without needing an excuse to try to hang about.
So as soon as it was possible to do so, once Hydd had arrived, she presented herself to him as his page. Since the weather was fine, he'd set up a tent, as had many of the lords and captains. She didn't blame them; sleeping conditions in the Great Hall were beyond "crowded." His bodyguard nodded at her and pulled the canvas flap aside for her.
"Lord Hydd, I am to be your page," she said, as the man turned away from something he had been unpacking from a small chest to look at her.
"Peder sent ye?" he asked. She bowed, as was proper, and kept her eyes on her toes, as was also proper. The king's daughter could look boldly into the face of a High Lord and one of the king's favored captains, but a page had to be respectful and show humility. "Then go to the king and give him my compliments, an' ask when he wishes me t' attend him. Bring me back his answer. Is Lord Gwyddian here yet?"
"Aye, milord, I will," she replied immediately. "I don't know about Lord Gwyddian, my lord."
"Then unless the king wants me urgent, go to him and tell him we need to speak about that handfasting at his leisure. Find out about Lord Gwyddian. Then return with the king's word; I'll have more work for ye then."
She bowed again, and ran off at high speed; she suspected sending her to her father was on the order of a test; if she _hadn't_ been sent by Peder, and was only trying to find a way to lurk about and eavesdrop on the adults, this would uncover the ruse. But of course, she had been; so she'd pass the test, if test it was.
Her father returned the compliments, as impassively as if she had been anyone but his daughter. There was no urgency, he would gladly receive Hydd at supper. Lord Gwyddian was not yet arrived. She ran back as quickly as she could—without arriving in an unseemly, untidy, and panting condition.
Hydd accepted the answers she brought back without comment, and immediately put her to work in truth. Mostly the work involved a lot of fetching and much more message-taking. In fact, by the time darkness fell she was about run off her feet.
Her duties to Hydd _should_ have included serving at his side at table, but she hadn't yet been trained in that, and with a chuckle he dismissed her. "Go and sup with yer family, little page," he told her, kindly. Near starving, she was nothing loathe to obey him.
She found herself seated between the same two boys as at the Samhain feast, but this time word had mysteriously spread that she was now one of their peers. Instead of ignoring her, they included her in their chatter, and despite the long day, she found herself having a lively conversation with them about tricks they had all learned for managing their horses. Though she was younger than they, she discovered she had great status in their eyes, not because she was the king's daughter but because she was "Braith's girl." And that she could entirely understand. Sometimes the fact that Braith had singled her out made her feel giddy.
She _had_ learned how to pour, so when the last of the supper was carried away and the tables set to the side, she stood behind Hydd and saw to it that his flagon was never empty. It was ale, not mead, they were drinking tonight; serious drinking would happen later.
The talk was of nothing particularly serious; that, too, would wait until the morrow, when all the guests would be here. The only thing that Gwen heard of any interest was that Braith would not be racing tomorrow; the best of Hydd's mares were all in foal (the king looked envious), her team included.
Long before the men were prepared to take to their beds, Gwen and the other pages began to droop. She was willing to hold out as long as she had to, or at least to try, but the king took pity on them all and dismissed them. "My own servants can see our cups stay full," he said with a laugh. "And we'll get no work out of these youngsters tomorrow if they cannot keep awake."
As was usual now, Gwen was the first into the big bed. Now she _could_ have claimed the choice spot in the center, but she kept to her old place instead. This endeared her to her older sisters, who in their turn saw to it that Gwenhwyfach got not so much as a hope of interfering with her. Little Gwen might have outwardly reformed, but it was clear that Cataruna and Gynath were not convinced of her sincerity,
Nor was Gwen, but since her return to the king's good graces, Little Gwen seemed to have wormed her way back into the position of "indulged baby." Gwen didn't much care, given that she _had_ everything she could ever have wanted, but the two older girls were not so happy about it.
And in fact, they woke her up when the three of them came to bed, arguing about it.
". . . Father thinks it's amusing," Gynath was saying, the disapproval so thick in her tone that it surprised Gwen into complete wakefulness. "But it's a disgrace. You shame all of us, acting like that. You're too young to be putting on such a show and old enough to know better."
"But Father likes it," Little Gwen said insolently. "So _you_ have nothing to say about it! I'm his favorite, and I can do what I want! You heard him!"
"We heard him," Cataruna said darkly, then laughed. "But you won't be his favorite for much longer, you wicked little changeling. You just wait till harvest. Ha!"
"Why?" Little Gwen's tone was suspicious.
"I'm not going to tell you!" Cataruna taunted. "Because you are so full of yourself that you haven't paid any attention to what's going on right under your nose!"
"Tell me!" Little Gwen demanded. "Tell!"
"Oh, tell her before they hear her out in the Hall and we all get in trouble," Gynath interrupted, crossly. "Oh—never mind. Brat, by the time harvest comes around, Mother will have had a baby, and it's going to be a boy. Which means not only will you not be the youngest anymore, Father won't care a straw about what you want. Not when he has a prince to fuss over. So there! Chew on that a while, and enjoy yourself while you can, because by this time next year you'll be lucky if he even notices you!"
The bed creaked and moved as the two eldest girls got in.
"You're lying!" Little Gwen finally burst out. "I don't believe you!"
"And I don't care. We're going to sleep. You can stand there all night stamping your foot if you want, it's not going to change the truth." The bed bounced and shook a little more as both of the older girls turned their backs on the youngest. Little Gwen stood there for several moments longer, before finally coming to bed herself. But she said nothing, so Gwen fell quickly asleep.
In the morning she was the first awake, and none of the other three even stirred as she slipped out of bed. They must have come to bed much later than she had supposed, and far past their usual bedtime. Could that have been the cause of the quarrel? Or had it been something else?
Well it hardly mattered. Gwen had work to do.
The first thing was to make sure her horses were properly tended for the day. The grooms would ordinarily take care of that, but they would have their hands full with all of the visitors' horses. So Gwen got into her older clothing first and went out to make sure they were fed, watered, groomed, and turned out for the day. Then she returned to the castle, changed into her good clothing, ate quickly, and went to present herself to Lord Hydd.
She spent the rest of the day in a state between anxiety and bliss. Anxiety because she was terrified lest she do something wrong and disgrace herself, or worse, her trainers and her father. Bliss because of the company she was in and all the things she was hearing. She didn't understand more than a quarter of it, as the talk ranged from politics to horse breeding, but she tried to consign as much of it to memory as possible.
Again, at dinner and again at supper, Lord Hydd sent her to sup at the High Table with her family rather than waiting on him. She had assumed that tonight, the night when the women would gather to work the magic that would bless the seeds and the soil, she would be expected to serve as cup bearer. But no, once the remains of supper were cleared away, all the pages were dismissed as her father and his chief lords took themselves to the solar and closeted themselves away from any and all ears, including those of the pages.
Full of nervous energy, for she had keyed herself up to see the night through and not get sent to her bed like a sleepy baby, she was at a loss as to what to do with herself. This not being a great festival like Midsummer or even Beltane, and not being a feast of plenty like the Autumn Equinox, there were no bards, nor even itinerant musicians, only those among her father's men and the villagers who could play a few tunes. That was good enough for dancing, but she had no interest in dancing. Some of her own lot of young warriors were taking advantage of the absence of their elders to dip as heavily into the ale and mead as they could; that held no appeal for her either. Cataruna and Gynath were each enjoying the attentions of several boys, an activity that seemed a pointless waste of time.
Then it occurred to her.
She could spy on the rites.
It wasn't precisely forbidden; she wouldn't have dared such a thought if there was any chance that the gods would take offense at her curiosity—so why not? In a few years she would be old enough to participate anyway, so what was the harm? Even if you weren't one of the Wise Women, there was always a place in the Circle for you.
It certainly wasn't going to be difficult to find them. All rites were held at the stone circle not far from the thicket where she had seen the bear and serpent fight.
She took a quick glance around the hall, and saw no one—no adult at any rate—who was paying much attention to what the youngsters were doing. She got up and walked out as if she had some errand she had been sent on.
No one stopped or questioned her, and once she got out past the tents and the fires, she made a sharp turn towards the stone circle. Once away from the fires, she looked back to make sure she was not being followed, waited for her eyes to adjust to the darkness, then carried on. With all the people about, she was not concerned with wild beasts; all the noise had probably frightened most of them into hiding, and the rest would be very cautious.
She saw the light of the fires within the circle reflecting up on the stones long before she caught sight of the figures within the circle or heard their voices. She knew where there would be a good vantage point, and as silently as a stalking fox, she slipped into it. Her heart raced with excitement; she had never seen any of the rites before, and she was hoping that there would be real magic.
Somewhat to her surprise, for she had thought that only women were permitted at the rites, she saw that there were two men and a boy within the circle. One of the men was cloaked and hooded, and stood well back from the rest. The others seemed to be a bard and his apprentice. The bard was speaking as she moved into place, and she held her breath to listen to him, when her mother answered him, but in a voice full of Power.
Now, she had heard the tale of Gwydion and Arianrhod, of Lleu and of Goronwy, often enough to know within hearing a few words that this was what they were playing out, with Eleri taking the part of Arianrhod and these men the other parts. But then something happened—
The world about her shifted.
She felt incredibly dizzy, hot and cold at the same time, as if she had struck her head in a fall. Everything blurred for a moment.
It was no longer night, but broad day. And she was not on her father's lands near the stone circle; she was on the top of a bluff that fell off abruptly to end in the sea. At least, she thought it was the sea, though she had never seen it herself; there was water to the horizon, an unfamiliar tangy scent in the air, and a roaring sound from the waves coming to shore below her. On top of the bluff was a castle easily five times bigger than Castell y Cnwclas; maybe ten times, it was so big she couldn't rightly judge. And the woman standing before the castle was so beautiful she took Gwen's breath away.
Her hair was a ruddy gold and fell to her feet; her eyes were bluer than the sky, and her face was terrifying in its perfection. She wore a rich gown of some shining, red stuff that Gwen couldn't identify; there was silver at her wrists and her throat, a silver chain served her as a belt, and she wore a silver filet in her air.
Before her was a man as like to her as could be; vaguely Gwen realized that if this was Arianrhod, then he must be Gwydion, her brother. With him was a boy, hovering on the edge of manhood. Both the boy and Gwydion were clothed in rough, churlish clothing with the leather aprons of cobblers.
Arianrhod was angry; but more than angry, she was near tears. And no wonder. This boy was her son, and his birth had been the cause of her shame, for she had been thus exposed by the magic of Math, Gwydion's king, to all as being no longer virgin. It was Gwydion who was the cause of that, so small wonder she was angry at him and angry at his bringing before her the boy, who had until this moment been nameless and whom she had repudiated, abandoned, and denied. "He shall get no name unless he gets it from my own lips, and that will never be!" she had told her brother.
And now he had tricked her again. She had called him "the bright and clever handed," which served very well as a name, so now he was Lleu Llaw Gyffes.
She had just at this moment seen through the deception. "Oh, perfidy!" she cried, and Gwen could see how hard it was for her not to cry. She was so angry with her brother for raising this child, for presenting the source of her shame to her, that she could scarcely form the words. "You have tricked me twice, but there shall come no third time, and this your protégé shall never be a _man."_ She all but spat the word. "Hear my will on this! You have got him a name by trickery, but he shall never bear arms unless I give them to him with my own hands! Now go! And find him a fit place among the churls or the women!"
A darkness passed over the scene as Gwen shuddered at the misery in Arianrhod's voice. She sensed how deeply wounded the goddess was, how it wounded her that this beautiful boy, whom she would gladly have cherished, was the cause of the worst experience of her life. And when the darkness faded into light, the scene remained the same, but it was clear some time had passed. Two bards, an old, old man and his apprentice, approached the castle and were welcomed inside. Somehow Gwen found herself in the Great Hall with them, as if she were some sort of bodiless spirit. And while part of her knew that the bard and his companion were, in fact, Gwydion and Lleu in disguise, _she_ could not see it and, clearly, neither could Arianrhod.
Gwydion was a famous bard in actuality, something that his sister seemed to have forgotten as he regaled her and her court of mostly women with song and story. But behind the storytelling, there was magic afoot; Gwen felt the Power stirring, could almost see it as Gwydion wove it into the tales of battle and tragedy that he chanted. She felt the Power stretching the very fabric of the air tight, as a drumhead was stretched tight, until at last it took shape from those very same tales just as Gwydion had intended.
The roar of an assaulting army shook the walls of the castle; startled into panic, Arianrhod and her women screamed in fear—as well they might considering how few men were in Arianrhod's retinue. In terror, Arianrhod turned to the "bard," who could be expected to have some idea who might be attacking her all unprovoked and who might well have some strong magic to defend his hostess. "I have given you my hearth and bread!" she cried. "I beg you, help me!"
Gwydion had only been waiting for this, and he thrust Lleu toward the queen. "This fellow is a doughty fighter," he said, "Worth ten of any normal man. Arm him, my lady, and I will strive to make magic in your aid."
Arianrhod called for a sword and armor to be brought, and with her own hands buckled sword and scabbard onto Lleu. In that moment, the clamor from outside ceased, and the seeming dropped from both Lleu and Gwydion, and Arianrhod's fear turned to fury.
"Three times tricked!" she spat. "But this, I swear, will pay for all. _Never,_ Lleu Llaw Gyffes, will you have lover or leman or wife that is a mortal woman! Enjoy that sword you got of me, for that is all the bedfellow you shall ever have!"
But Lleu did not care, for now, at last, he had the arms he needed to slay the man who had tried to slay him. His face was alight with a fierce exaltation, so that it outshone the sun, and his eyes burned so brightly that for a moment, Gwen was blinded.
When her sight came back, the scene had changed. A dark but handsome man cowered before Lleu, the treacherous Goronwy, who had plotted with Lleu's faithless wife to slay him.
But now it was Goronwy's turn to be slain. Standing where Lleu had stood, he pleaded for his life. "I have no magic to protect me as you did!" he was begging, as Gwen took in the scene. "Let me at least have a paving stone between us!"
Lleu laughed. "Never let it be said that I was less than fair!" he replied mockingly. "You may have your stone."
Desperately Goronwy pulled up a flat stone and huddled behind it, as if behind a shield. And Lleu stretched his arm back—
_As the sun stretches his strength come the Year Turning—_
And flung his spear with all his strength—
_As the warming spring is flung against the cold and weakening winter—_
—and the spear hit the flagstone so hard that it pierced straight through and killed Goronwy in the instant.
Lleu's shout of triumph shattered the world into a thousand, thousand bright splinters.
And with that, Gwen fell back into herself and found herself once again hiding in the shadows of three massive oak trees, watching the rite take place within the circle of standing stones.
**Chapter Six**
**Driving a chariot—merely** _driving_ it, and not doing any of the tricks that the experienced drivers did—was a lot harder than it looked.
To begin with, there were two sets of reins, each set going to a different horse, each of whom had its own ideas about how a good driver handled those reins. Then there was the fact that you were standing on something that was moving, so your balance was constantly shifting, and that caused tugging on the reins if you weren't careful, and _that_ gave the horses signals to do things you hadn't intended.
She was just lucky that her pair were so experienced, so steady, so calm. They reacted to bad signals not by obeying them but by stopping dead in their tracks and waiting patiently for her to sort herself (and them) out.
Gwen had never been happier. Braith was right. This was what she had been born to do.
There was so much more to learn! She'd had no idea, not really, when she first started down this path, how much there was to it. She supposed now that it was all a matter of seeing . . . that she'd only really paid attention to the warriors, who were the end of all the training, and not to the milling lot of half-finished people still in training. But now that she was in the middle of it all, she had at least a sense of how much more there was to being a warrior.
And even knowing how much work there would be, how far she had to go, she still wanted to learn it all.
Today she guided her team carefully around a course laid out by the horsemaster; they'd been at the walk, then the fast walk, then the trot. Now he signaled to them to move straight into a full charge. She slapped the reins on their backs and shouted, bracing herself against the chariot back as they surged forward in the traces.
The chariot bounced and bucked; she kept her knees flexed as she had been taught and kept her balance, although it was a fight to do so. Here is where it was so important for the young warrior to be "trained" by old, experienced horses. If she fell, she knew she could count on them to stop _dead,_ because they had done just that in the early stages of her driving training. She got bruised, but she didn't get as badly hurt as she would have if the team had kept going.
This was far more frightening than riding. Anyone with any sense would be terrified, with the flying hooves of the horses so close to you, with the chariot bouncing like the featherweight thing that it was, and you trying to guide the horses around turns that slung it sideways as well as sending it bounding into the air.
And for that reason it was all the more exciting and exhilarating.
The horsemaster let them run the course three times before signaling her to slow, then stop. He walked up to them and slid his hand up the shoulder of the mare under her mane and nodded with satisfaction. She was no warmer than she should be; she showed none of the signs of fighting with her driver. Without a word, he waved Gwen off and signaled to the next to come onto the course. She hopped down out of her chariot, her legs wobbly with fatigue but determined not to show it, and walked them back to the paddock, where she backed her chariot into its place in line, unhitched them, and led them off to cool. Once they were fit to turn loose, she unharnessed them, gave them a quick rubdown, and let them out into the field. She turned then, to find her mother at the fence, waiting patiently for her to be finished. She looked in her pregnancy like the pregnant Goddess must look: ridiculously young, face glowing and beautiful as the sun.
She was startled to say the least. Not that Eleri was an utter stranger to the stable; she had driven a chariot herself in the past, though she hadn't done so in several years and certainly could not in her current state. She was, perhaps, two moons from giving birth, which made it even odder that she should have come down here to the stables, when her increasing girth made such a long walk uncomfortable. And there was no doubt who she had come to see; Gwen was the only person here at the moment.
She recollected herself quickly. _Here_ she was not the queen's daughter; here she was nothing more than a warrior-in-training, and as such, she bowed low and did not raise her eyes. "My lady," she said, and nothing more. It was for Eleri to give an order and for her to obey it without question.
"Gwen, walk with me." The queen's voice made that a command. A gentle one, but nevertheless, a command. Obediently, Gwen went to her mother's side and set her pace to the queen's slower one.
The did not go far, only to a bit of stone outcropping overlooking the chariot course that made a convenient seat. Eleri eased herself down onto it, while Gwen remained standing until her mother patted the stone beside her. Still puzzled, but grateful, Gwen took a seat beside the queen, and Eleri put one arm around her daughter, hugging Gwen close, and with that gesture, Gwen became the princess again, and not the young warrior.
"I'm sending Cataruna to the Ladies," Eleri said, out of nowhere. "I know you wanted that yourself, and perhaps in time we shall send you, but—your mentors tell us that you are doing well. So well that they have urged me not to send you until you are much older, and your training is complete." Gwen turned her head up to look at her mother in astonishment, to see the queen gazing down at her with an anxious look in her eyes. "This kingdom needs as many with the Blessing as powerful as I have been given, as Cataruna has been given, as we can manage to get properly trained. Cataruna leaves today, in fact, in company with two of the village girls who also have the Blessing; the king and I wanted to send her off before she made any serious attachments to a boy, and there are several now with whom she might. I hope you are not upset."
Now Gwen was even more astonished. "No!" she blurted. "Braith was right. This is what I want!"
Eleri sighed, and her face took on an expression of regret. "Your father said that you would say that."
Gwen's brows creased. "Is that bad?"
The queen hugged her again. "Not at all. But you know that the hand of the goddess was strong on you when you were born, and I was sure that there was nothing that you would want more than to take up the Power. Now—" she sighed more deeply "—now you are around Cold Iron so much that the power is fading. I begin to think, as Braith does, that there were two goddesses bestowing their Blessing on you, and one of them was Epona. I cannot fault you at all for choosing her. And I know I will not have to ask you twice; you want this, more than anything."
Gwen nodded solemnly.
"Then my blessing on you, and Cataruna will take your place. There is Cataruna, and perhaps your other sisters." The queen got ponderously to her feet. "I have been watching you at your training, and your mentors are right; your hand was made for the chariot reins, for the bow, and perhaps for the sword. I will sleep well of nights, knowing that you will be a strong guardian to your little brother as he grows."
"I promise!" she said firmly. In fact, she could not think of anything more delightful. She would guard him until he was old enough to take up these first lessons himself, and then she would help to teach him. And when he was a man, she would be one of his chosen Band, and fight at his side.
The queen's hand rested briefly, caressingly, on her head, warm and tender. "Go back to your lessons, young warrior," she said fondly. "Be wise as the salmon, crafty as the fox, valiant as the wolfhound, and fierce as the hawk."
Then she turned, and as she did, Gwen felt something quite peculiar, a sense that something had been loosened between them. Not broken—not at all—but it felt very much as if the queen had opened a door to her and was letting her go through it all on her own, like the first day a young falcon was taken off the creance and allowed to fly free.
She looked up into her mother's eyes. "I will," she repeated, making a pledge of it. "You'll be proud of me."
"I already am," her mother replied, and turned to make the slow journey back to the castle.
Gwen couldn't stand to be indoors that night, sandwiched in the big bed with her sisters. She wanted to be completely alone with her thoughts, she wanted nothing to interrupt, and above all, she did not want Little Gwen to sour everything with poking and prodding—
Little Gwen had an uncanny instinct for when Gwen wanted to think. During the day, of course, Little Gwen didn't come anywhere near her. But during the day, Gwen was too busy to stop to think. That moment when the queen had come to speak to her had been the only pause in the entire day, and Gwen was pretty certain she would not have had that much if it had not been the _queen_ who had taken her aside. Gwen's day, like that of her fellows, always began before anyone else but the servants were up, and it was filled with chores, exercises, practices, lessons, and duties. It only ended when the steward, who was the one in charge of Gwen and her fellow squires and pages, said that the day was over.
But she loved it. Not every moment of it, of course—but even in the most tedious parts, the knowledge that _after this, I'll have archery practice_ or _we'll be learning to wheel in formation_ kept her willing to work through the tedious, or the difficult, or the downright onerous. Or she would be thinking hard about something she was supposed to master, which made the time pass so much faster when she was mucking out, or grooming, or cleaning weapons and armor. And of course, when she served at table, she had to stay on her toes. The Great Hall was a lot more crowded when you were counted among the servitors. Not that all the squires served _every_ night, far from it. Most meals were very informal. But they all took it in turn to serve at the High Table to keep in practice. Gwen was never allowed to serve the king—the steward told her from the beginning that a squire was never, ever allowed to serve someone he was closely related to. But at some point or other, she did serve each of the other men at the king's side of the table—his three captains, the steward himself, and any important guests he might have.
That, too, put her out of Little Gwen's reach. And usually she was so tired by the time the Steward dismissed them all that she went straight to bed and was asleep by the time Little Gwen—who was always trying to put off her bedtime—came back to the room. But on those rare occasions when Gwen wasn't exhausted and did want to lie awake thinking for a while, Little Gwen seemed to sense, somehow, that she was feigning sleep and would poke and prod her, "accidentally," or pretend to be tossing and turning, interrupting her thoughts.
So tonight she took a sheared sheepskin rug and a blanket out to that little sheltered corner where she used to pick over the feathers. She nodded at the sentry standing guard at the door. "Too hot to sleep inside," she told him, and he grinned and nodded. Of course he wouldn't have grinned and nodded if she had been old enough for boys to be interested, as they were in Cataruna. He would have asked quite sternly if the king knew she intended to sleep out, and if she was sleeping alone, and then he would have made certain that the king _did_ know and knew who she was with. Not all her willing him not to see would have stopped him from spotting her if she had been Cataruna's age. Although things were changing elsewhere, it was still the expected thing here that boys and girls, even when the girl was the king's daughter, would make their first fumblings together without there being any formal promises binding them. A swelling belly generally meant a wedding, of course, but Gwen knew vaguely that there were ways of preventing such a thing. If there hadn't been, there would have been a great many more princesses than just four. In the village, at least, the girl that went to her marriage a virgin was a rarity.
Nevertheless, for the king's daughters . . . there were some things expected. You might keep the identity of the boy you were with from your parents if you were an ordinary girl, but the king's daughter—well, there were always going to be complications. That had been carefully explained to them once they were old enough to notice that not all the bodies in the great hall of nights were quiet ones. If you went with a boy, Mother and Father had to know about it, know who he was, and to that end, the king's men would be asking questions if you went slipping out to meet one. And you had better go to your betrothal, if not your wedding, still virginal or at least able to pretend to that state.
But she was still young enough that it didn't matter. He probably thought that he was going to go meet up with some of the squires for an illicit berry feast, perhaps, or some night fishing, or even for the sharing out of too much stolen ale or mead. He still had to know, of course, and he followed her for a bit. But under his watchful eye, she went right where she said she was going, laid the hide down over the grass, rolled up the blanket into a pillow, and laid herself down to stare up at the night sky. Satisfied, he went back to his post.
What the queen had told her still warmed her heart and gave her a thrill of pride. It was one thing to have her father beaming at her—she was doing just what he had hoped one of his children would, she had joined the ranks of the warriors, she was doing well at her duties, and it was only natural that he was proud of her. Perhaps it was a mild surprise that it was Gwen in particular, but Braith was a trusted member of his elite fighting force, and the last thing he would do would be to prevent Gwen from following in the footsteps of such a valued warrior and driver.
But she was doing precisely the opposite of what the queen had planned for her. She'd avoided thinking about it, but underneath everything, she'd been certain that Eleri must be disappointed in her. Maybe angry.
But she wasn't—so not only was Gwen proud and happy, she was relieved. It wasn't often that Eleri changed her mind or her plans; it wasn't often that she needed to. Gwen had felt the weight of Eleri's expectations weighing her spirit down with dread; now that weight was gone, and she felt light enough to fly up to the moon.
Underneath all that was one thing more; the farther her duties took her from the women's side of castle life, the less time she had to spend in Little Gwen's company. That was a relief too. In fact, it was entirely possible that at some point she would be expected to move from that comfortable bed to a pallet in the great hall with the others. Little did they know that she would gladly trade that warm bed and its unruly occupant for relative discomfort and peace!
In the morning Gwen returned to the bedchamber, intending to leave the blanket and rug and go straight out to her duties, only to walk into a storm. And at the center of that storm was Little Gwen.
Cataruna stood with her arms crossed and her lips pressed tightly together as Little Gwen tore through the two packs she had carefully made up, hissing angrily that Cataruna had stolen _her_ things. "Where is my comb?" she demanded, her voice getting louder with each moment. "You took it! And my ribbons! And my top!"
Quietly, Gwen edged into the room and dropped her burdens in the corner. She would have liked to edge out again, but by this point, Little Gwen's tantrum was turning into a full blown tirade when she didn't find any of the things she was claiming were "stolen." Cataruna's belongings were scattered all over the floor as if tossed by a whirlwind, and Bronwyn, awakened by the fuss, appeared at the door curtain—
But at that same moment, someone far more important than Bronwyn appeared at the door to the solar.
It was the king.
Without a word, he strode into the room, picked up Little Gwen by the scruff of her neck, and shook her until her teeth rattled. Shocked into silence, her eyes gone round as river stones, when he let go of her, she fell in an unmoving heap on the floor.
"How _dare_ you disturb the queen's rest?" he snarled, staring down at Little Gwen. "How dare you trouble the mother of my son? How _dare_ you, miserable changeling? Enough! More than enough!" He turned to Bronwyn. "See to it that _she_ repacks all of Cataruna's things with care, while my good Cataruna breaks her fast. Then see to it that when the top and the ribbons are found, they are given to some child of the village who deserves a reward."
He turned his gaze down on Little Gwen again. "I would have thought you had learned your lesson by now, but I see that you have not. Perhaps your hands are too idle. Perhaps you need more work to do."
Little Gwen stared up at the king, her face blank.
Bronwyn compressed her lips tight. "That may be so, my Lord King," she said. "Perhaps some kitchen work?"
Little Gwen made a faint sound of protest. The king ignored her. "Perhaps," he said. "Perhaps she will learn that churlish manners lead to being set among the churls."
Gwen winced. She knew that above all things, Little Gwen was proud. Being put with the lowest servants to do the most menial of tasks would be an agony to her.
The king turned to Cataruna and put gentle hands on her shoulders. "As for you, my daughter, go and break your fast well. We are pleased and proud that you are going to the Ladies; master your Blessing, become wise and true, and return to take your place at the queen's right hand, first among your sisters. I shall be with you anon to bid you farewell."
Cataruna's lower lip trembled a trifle with emotion. "Thank you Father," she said. "I will not fail you—"
The king chuckled slightly, and chucked her under the chin. "Now come, it is no more than a matter of lessons and learning, which we both know you excel at! You are not going off to battle but to something I think you will find a pleasure!" He gave her a gentle push in the direction of the hall. "Now go, for I am sure Bronwyn has managed something special from the cooks for you."
Cataruna ducked her head in a quick curtsy and turned, whisking her skirts as she slipped under the door curtain. Gwen took the opportunity to follow her.
"What was that about?" she asked, as one of the maidservants intercepted Cataruna with a platter heaped with good things, obviously being saved for her.
"I knew there would be a pother last night," Cataruna replied, as Gwen got a wooden platter and took bread and butter, cheese and carved cold meat from last night's dinner. "You know how Little Brat hates it when a fuss is made over anyone but herself, and there was a double fuss after dinner. Mother asked me to sit beside her, and when they weren't all talking about what I could expect to be learning from the Ladies, they were all talking about the baby. I could just see Little Gwen starting to get that look she gets when you know she's going to do something."
Gwen nodded; she knew that look all too well.
Cataruna shrugged. "I expected trouble from her last night, and I think perhaps Bronwyn did too. And maybe Mother. When we went to bed, Bronwyn gave us all possets to drink, and Little Gwen went straight to sleep. Bronwyn and I were able to pack my things in peace."
"If I'd known that, I wouldn't have slept outside," Gwen said ruefully. "I wanted to think a while, and I didn't want the brat poking and prodding at me."
"Well, I wish Bronwyn hadn't done that, because she was awake _far_ too early, and the first thing she did was to tear into my packs." Cataruna made a face. "Poor Gynath. You're off with the squires all the time. Pretty soon you'll all be made into a real warband, and you'll all be doing everything together. It could even be that you'll be out in the Great Hall with them, to sleep, and she'll be the one left to deal with the Brat." The eldest of the king's daughters sighed and ate some bread dipped in honey. "I am not going to miss that."
"Are you going to miss any of this?" Gwen asked curiously.
"Truthfully?" Cataruna nibbled pensively on her bread. "I don't think so. I don't make friends the way Gynath does, none of the boys here make me want to kiss them, I _truly_ will be glad to see the last of the Brat, and until now there was nothing really special about me except I was the eldest."
Gwen blinked, wondering obscurely if she ought to feel hurt by such a revelation. But she and Cataruna were too far apart in age to have been close—
"Until now, I never really had anything for myself," Cataruna was continuing. "Oh, I had the Blessing, but from what I heard it was never as strong as yours. I'm not pretty, like Gynath and Little Gwen, and I would never want to be a warrior. Up until you got singled out by Braith, I was just—really, nothing special. _You_ were the one that was going to the Ladies as soon as you ever could, and if I went, it would be only after you came back. And since everyone expected great things of you, I'd still be coming in your shadow."
Something about Cataruna's tone made Gwen feel obscurely guilty. And even gladder that she'd had Braith to send her in another direction.
"But now—" Cataruna finished the bread with a lift of her head and an air of satisfaction. "Now it's _me_ that's going to the Ladies, and it'll be me that will be the Maiden in the Circle when I get back. And the Ladies won't know, or won't care, what great things were expected of you. You've gone the path of Iron, and you'll never be as strong in magic as me now. So when I come back, I'll be me, Cataruna, with my own place and my own path, just as you'll have your own place and your own path." She turned her head to look at Gwen. "I'm really grateful to you, Gwen. That's why I don't think I'll miss home too much. It's not as if I won't be coming back, but when I do, it will be as the Blessed Daughter. You'll be the Warrior Daughter by then, and Gynath—" she chuckled a little "—Gynath will have half the war chiefs wanting her for a bride, and she'll make Father some good alliance, and then she'll make him a grandfather, if she hasn't already by the time I get back. Who knows? Maybe she'll even get a prince."
She didn't say anything about Little Gwen, and Gwen was not inclined to prompt her on that head.
"Did you really want to go to the Ladies that much?" she asked instead.
"As much as you wanted to be a warrior," Cataruna said fiercely.
"Then I'm _glad_ you're going." Gwen surprised her sister, and to an extent herself, by fiercely embracing her.
Cataruna returned the embrace. "And I'm glad you're happy where you are." She nodded. "We're lucky."
"We are."
At that moment, Bronwyn made her way across the Great Hall, trailed by a servant with Cataruna's two packs. Cataruna eyed them curiously.
"The king your father thought of several more things you should take with you," Bronwyn said, with a glint in her eye, but her lips set in a severe line. "Little Gwen will be making do with made-over gowns for a time; I trust you will find moments to spare to make yourself suitable garments with the lengths in the bottom of the packs."
Cataruna could not repress a gasp of pleasure; all the girls knew about the lengths of lambs' wool and linen that had been reserved for Little Gwen. Gwen had been indifferent, since gowns were the last thing on her mind at the moment, but she suspected Cataruna and Gynath had suffered a pang or two of envy. "I shall find the time, somewhere," she promised fervently. "Father is most gracious."
Bronwyn looked as if she might say more, but in the end, she only nodded. "Come, it is time. Your escort is waiting."
But it seemed that more than just the escort was waiting. The king himself came to see his daughter off, something else Cataruna had clearly not expected. He lifted her onto the horse himself, after kissing her on both cheeks. "We send nothing but our best to the Ladies," he boomed, in a voice intended to carry. "And we know you will make us all proud."
With her head high, her cheeks glowing, and her eyes shining, Cataruna bowed deeply to her father; then at a word from the king, she and the escort rode off at a brisk walk and were soon over the hill and out of sight.
Bronwyn remained staring after them long after everyone else had gone to their duties, one hand on Gwen's shoulder, preventing her from leaving. When there was no one else within earshot, Bronwyn looked somberly down at her.
"I would not say this in Cataruna's hearing, but it was a spiteful splash of venom from that unnatural child that caused the king to rethink her leave-taking. _Why such a pother over the second best,_ she said. And in the next moment, she turned her eyes on the servant and had _him_ doing the packing for her!" Bronwyn's lips tightened. "I confess that I am sorely tried by that child. If I had not been the midwife myself, I would suspect her of being a changeling. I think it may be she has some different magic of her own, not out of her mother, of charm or glamorie, that she is only yet vaguely aware of. And this is why I decided to speak to you."
"To me?" Gwen was astonished. "But—"
"If that child does have such a thing, the queen has armored the king against it, as she has armored him against any ill magics—which is why she could not sway his anger. But there are others that will have no such armoring, and they may be those with whom you must deal." Bronwyn shook her graying head. "I wish to tell you to be wary of rousing the child's envy. Try not to come between her and something she wants, at least until I have devised a means to deal with her, or discovered what it is that she has." She looked up again, down the road that Cataruna was traveling. "I am very glad that Cataruna is well away. And Gynath, I think, is safe enough for now. But you have ever had her enmity, and it is best you stay out of her gaze."
Well, that was easy enough to promise. "I will," she said, and Bronwyn let her go.
But it was troubling. This was the second time that someone she trusted had warned her against Little Gwen, and in terms that suggested she was more than just a spiteful little girl.
**Chapter Seven**
**"Gwen'" hissed Madoc.** _"Gwen!"_
She ignored him, working hard on her horse's harness with a polishing cloth, a little oil, and talc, trying to get the brass bits to look like gold. The leather was already cleaned and oiled and as supple as a snake. Adara and Dai were groomed within an inch of their lives every day, their hooves oiled, their manes and tails braided and clubbed up to keep them from tangling. Midsummer was barely a week away now, and, as usual, many of her father's war chiefs would be arriving for the festival and the rites. Braith was coming. There would be some abbreviated races—nothing like the ones in the autumn, since some of the mares had foals at heel and you wouldn't race one of those, but there would be a maiden race for the pages and squires, since all of them had horses past breeding age or geldings. Gwen was riding and driving both, and she desperately wanted Braith to be proud of how far she had come. She wasn't really concerned about winning the races—some of the others had horses much younger than hers, three of the boys about her age were, frankly, more skilled. But she _did_ want Braith to see that her backing hadn't been misplaced.
So she had gone over her gear twice now, cleaning and polishing, mending not only popped stitches, but stitches that only looked a little weak. The saddle, the harness, all looked new. But the brass bits still weren't _shiny_ enough.
_"Gwen!"_
They weren't supposed to be talking. They were supposed to be tending to their gear. "What?" she growled out of the side of her mouth.
"Is he coming? Here? Is he really coming?" Madoc sounded breathless and nervous. Probably at least as nervous as she was about Braith coming.
"Is _who_ coming?" she responded, her irritation growing. Peder glanced over in their direction; he'd clearly heard the hissing, though he hadn't picked out who was talking yet. She bent her head down to her task. With luck, he wouldn't notice. Maybe she had permission to end her chores of women's work, but that didn't mean an end to toil. If he felt she wasn't paying sufficient attention to repairing her harness, he would probably set her to wood chopping, water carrying, paddock building, or even carrying stones for the many hearths abuilding.
"The Merlin!" Madoc asked excitedly. "Is the Merlin really coming?"
The Merlin! Whatever gave him that idea? The Merlin was the High King's man. There was no reason for him to come here, of all places.
It was a title of course, not a name; the Merlin was the chief of all the Druids, as the Wren was chief of all the Bards. And his place was at the side of the High King, advising, working Men's Magic. Not journeying weeks away. Especially not at Midsummer.
"How should I know?" she hissed back, making sure her head was ducked down over her work so Peder couldn't see her mouth moving.
"You're the king's daughter! Don't you hear everything?" Madoc might well have said more, except that Peder had picked out _him_ as the chatterer.
"Madoc!" the older warrior snapped.
Madoc leaped to his feet. Gwen kept her head down. "Yes, lord!" he said, faintly.
"It's rare for you to have any thought in your mind at all, much less one so burning a hole in it that you can't leave it until later. Have you something you wish to share with us, Madoc?" Gwen kept her eyes on her work, furiously polishing, but she could hear the mockery in Peder's voice. She also heard his footsteps coming up beside her. He was just behind her, out of her peripheral vision, but she could feel his presence, looming.
"I only wanted to know if the Merlin is coming to the Midsummer feast, my lord!" Madoc replied, his voice breaking a little on the last word.
"Did you now?" There was a long pause. "Well, as it happens, the Merlin _is_ going to be one of the king's honored guests. So don't you think you should pay a little more attention to what you are _supposed_ to be doing so you don't shame yourself before him?"
"Yes, my lord!" Madoc squeaked.
"Then get back _to_ it, boy!"
Madoc dropped back down to his work and began polishing the brass of his horse's harness as furiously as Gwen was polishing hers. She heard Peder's footsteps again and saw his two hairy feet in their old sandals stop beside her. His left big toenail was black, where his horse had stepped on it. She held her breath and continued to polish.
"Acceptable job, squire," was all Peder said. Then he moved on.
Gwen breathed again.
But she could feel how the lot of them had come alive with the news of such an important visitor. Some of it was excitement, but more of it was fear. There had been fantastic tales told about the Merlin. That he had narrowly escaped being sacrificed by King Vortigern as a young boy, because he'd Seen the dragon coiled hidden beneath the base of Vortigern's tower—a dragon that subsequently was released to battle another high in the sky above that tower. Some said that he was responsible for the great Stone Circle out on the plain—though that was unlikely for it had been there long before the Romans had come. But certainly, _a_ Merlin had built it, which only showed the power that the Merlins held.
It was more likely true that when Arthur's father Uther lusted for Queen Ygraine, he cast illusions over Uther to make Ygraine and her entire household believe that it was King Gorlois returned from war. That, so they said, was how Arthur was conceived in the first place.
Now Ygraine was—or had been—one of the Ladies. And the Blessing was strong in her line, since both Anna Morgause and Morgana were her daughters, and both were noted for their skill at magic. Some even said Ygraine was a generation or two out of Fae blood, which would not have been completely unlikely. There were Sea Fae of great Power who often chose to wed mortal men, and Tintagel was on a coastal cliff, high above the sea. So to deceive her would have taken a great deal of Power—and a great deal of courage as well. The Ladies were not prone to appreciate men, even Druids, even the chief Druid, meddling in the affairs of one of their own.
Of course, Gorlois had been killed that very night. And Uther did not personally have the Orkney king's blood on his hands, since he'd been rather busy with Ygraine. And Ygraine had turned about and wedded him, so no one said much about the wrong or the right of it. Or at least not around Eleri's hearth fire, where, although Anna Morgause was the subject of much headshaking, Queen Ygraine came in for no such censure. Gwen knew better than to ask; she would have been told that the affairs of the very great were of no concern to a mere squire.
But since the Merlin was coming here, it behooved her dig as much as she could manage up out of her memory. The Merlin, it was said, had known that Uther's life was in danger, and he was the one that had spirited infant Arthur away and kept him safe until he could come into his own. Considering the number of rivals there were for the position of High King, that could not have been easy.
And it was certainly the Merlin, this Merlin, Uther's Merlin, that put Arthur in the position to take back the throne that was his, first Uther's own lands, then convincing all the other kings to make him the High King—or beating their armies so they were forced to accept him. There were a lot of stories about how the Merlin had a hand in that, too. Magic swords, mists that sprang up to hide Arthur's movements, and Arthur and his men being in two places at once, two battles on the same day. The Merlin had done the almost unthinkable: he'd turned an unknown stripling, a mere squire, into the High King in three years. And that meant Power. However you looked at it, whether all of the stories were true or not, there was no doubt that the Merlin was a formidable man. And an ancient one, since he must have been a man when Arthur was born, and now Arthur himself was full grown.
Which begged the question: Why was he coming here?
"Gwen."
Gwen's head snapped up, for it was Peder who had spoken her name. She jumped to her feet and bowed. "My lord."
When she looked up, Peder was eyeing her with speculation. "You'll be serving the Merlin."
Her jaw dropped. "M-m-my lord? Me?"
"You're discreet, you're well trained. But most of all, you are the king's daughter. We can't honor the Merlin too highly. The king your father has said this himself; we will show the Merlin that there is only the best for him. You'll be serving him."
She felt her head swimming. "Yes, m-m-my lord," she managed, and then she sat down heavily.
Serve _the Merlin?_ Surely not . . . there must be some mistake.
_There must be some mistake. . . ._
Gwen was still thinking that, as she nervously stroked the front of her tunic, waiting to be presented to the Merlin as his squire. All the squires had been lined up to greet the Merlin; he was too important to just be allowed to turn up and let his servants pitch his pavilion. He'd been watched for over the course of the last few days by outriders from the King's Band, and as soon as he and his entourage were in sight, everyone had lined up to greet him, not just the squires.
Now, however, all of the important people had properly greeted him, and only the squires remained in their stiff rank. The Merlin was talking quietly to the king, while Eleri and her women waited attentively. Like the other two girls among the squires, she was dressed as the boys were, in tunic and trousers, rather than a gown. Not that she looked all that different from a boy—except for her hair, which had grown out again and had been braided up and wrapped around her head, rather than just cut off at her shoulders or shoulder-blades.
At first glance, the Merlin did not look particularly imposing. He was quite an old man, in the usual white Druidic robes, but he had none of the usual talismans or other items of power about his person. Not even a single necklace or torque. His long gray hair had been braided and clubbed like a horse's tail, his beard trimmed short.
But his eyes gave it all away. They didn't look at you, they looked _through_ you, as if he were seeing something else entirely even while he took in what you looked like on the outside. They were very pale, those eyes, the same pale gray as his hair.
He had all his teeth too, a rarity in someone that old. It gave him a very fierce look. He had a curiously sharp, clean smell to him, like juniper. And he was lean, but not emaciated. Altogether, he put Gwen in mind of an old gray owl; you trifled with him at your peril, for he still had talons and knew how to use them.
Finally the Merlin's manservant came to tell him that his pavilion was ready. That was the signal for her to be presented.
The king crooked his finger; with her mouth gone dry, she came forward. "My lord," the king said, with the slightest of bows, "This is your squire for as long as you are among us. My daughter, Gwenhwyfar."
"Braith's girl." The Merlin nodded, and Gwen suppressed a start of surprise that he would use that term. "You honor me by sending your blood to serve me." He turned his attention to Gwen, and the force of his regard landed on her like a blow. "Well, by your leave, I shall take mine. I am an old man, and I need my rest."
The king laughed politely but in a way that said without words that he believed none of that. "Then your squire shall show you to your encampment. We look forward to your presence at our right hand at supper."
Gwen thought the Merlin would turn his attention to other things as she guided him to the spot where his encampment had been set up—against the east castle wall, sheltered from wind, shaded from the worst of the heat of the day, but warmed by the rising sun in the morning. And so he did, but not for long. Time and time again, she felt his eyes burning on the back of her neck, and when they reached where his pavilion had been pitched, he stopped her before she could go.
"I have some business I must carry out, and a message I need taken, squire," he told her. "Come." And he motioned for her to step inside the flap his servant held aside for them.
She didn't want to, but what could she do? Reluctantly, she obeyed. He sat down on the stool that had been set ready for him and gestured for her to stand before him. She kept her eyes fastened to her toes. She studied her own feet, studied the wrapped leather shoes she wore, with great care.
"Look at me, squire," the Merlin ordered, sounding impatient.
"Look up at me, look me in the eyes."
With even greater reluctance, she raised her eyes to his. The moment their gazes locked, his piercing gray eyes filled her vision, and she could not have looked away if she'd wanted to. She felt dizzy, and yet her knees locked, and she stood as rigid as a statue. As if from far away, she heard him speaking.
"Eleri. The queen, your mother. Was she at Arthur's wedding?" he asked sharply.
What kind of a foolish question was that? "No," she heard herself replying. "She was here, she was the Mother in the rites that night. Everyone saw her there and at the feast before and the fire after. Not even eagle's wings could have got her there and back in that time. Besides, she wanted to be the Mother in the rites, to share the power all the Circles were raising for the High King." She wanted to hesitate, not to say anything more, but the words kept tumbling out. "She wanted to give Father a son, after so many daughters. So she wanted to be sure she could share in that Power."
She heard him mutter to himself. It made no more sense than his question. "Could it be that? The sharing of _that_ power and not—the portent said it was his son, but could it have meant the child of his _Power_ and not of his blood?"
Gwen strained against the invisible bonds that held her but to no avail. "The child she bears—boy or girl?"
She didn't want to answer, but the answer slipped from her. "A son, as she wanted, the queen says, and so do the signs and all the women."
And again, the Merlin muttered. "—I dare not risk it. I dare not. Better a hundred innocent perish to remove _that_ one—"
She felt like a bird in a net. No matter how hard she struggled, she only entangled herself further. The cold hand of fear clutched at her throat. It was impossible to move even a finger.
"Your sister, Cataruna—did she ask to leave because of the new child?" he asked, as her head swam and she found it hard to breathe.
"No, my lord Merlin," she replied truthfully, and she found herself relating word-for-word that last conversation she'd had with her eldest sister.
"And you? Are you jealous of this prince-to-come?" he asked, his eyes burning into hers.
"No!" she gasped, caught unawares by the question. "No! I am going to be his guardian, his protector! And when he grows up, I will be among his war chiefs, like Braith is. I will be his bodyguard and maybe even his advisor! Father is proud of me! He said I would be chief among my brother's warriors! It's all I could want!"
He mumbled something inaudible, then sighed. "Well enough. I will find another means. You will forget all this, Gwenhwyfar. I asked you nothing, I said nothing to you." His eyes grew dark, and she heard a distant roaring in her ears. "You stood beside my seat, I gave you a trifling message to take to my servant who is with my horses, you delivered it and brought back the answer. That is all."
She felt as if she were drowning, felt her lips parting, heard herself whisper, "Aye, sir."
"Very good."
Abruptly she felt herself released from his gaze. She stumbled back a little, disoriented for a moment. Why was she here? Oh, of course. She'd delivered a message for him.
"Do you need anything more from me, my lord?" she asked, diffidently.
He looked up from the wax tablet he was scribing something on. His eyes were distant, unfocused, giving his whole face an absent-minded cast. "Hmm?" he said, then shook his head, smiling. "No, squire, you can go. Oh—but tell the king I will be very interested to meet the rest of his brood at dinner."
She bowed. "Aye, my lord," she replied and quickly left the tent. But she had two strange sensations as she did so. The first, was relief, as if she had somehow escaped from something very dangerous.
And the other—a sense of unfocused unease—because he wanted to meet her sisters. It made no sense, this unease, but there it was. She wanted of all things to prevent such a meeting, but that was impossible, of course. They would both be there at dinner.
And there was nothing she could do to prevent it.
The smell of baked meats and stewed vegetables, of beer and mead, of the herbs mixed with the rushes, and under that, just a hint that the dogs were not as good about going outside as they could have been, rose about them. So too did the smell of sweat and leather and wool, and over it all, woodsmoke, the eternal scent of the Great Hall with its central hearth. Soon all the meals would be taken outside, for there simply would be no room in the Great Hall for the swarm of guests, but tonight there were few enough that supper was indoors. Gwen stood attentively at the Merlin's left hand, making sure that his cup was never empty, he never wanted for anything his eyes lighted upon. He was the least demanding person she had ever had squire's duty for. He chose plain small beer, not mead nor stronger ale nor cider, and his drinking was moderate. He merely sipped, and throughout the meal she had occasion to refill his cup no more than twice. As for food, once served with his choice of a little rabbit, some greens, boiled turnip and bread, he ate slowly and never indicated he wanted anything else. Every time he moved, that juniper scent wafted from his robes, his hair. It was as if he were always part of the forest somehow. He was . . . strange. A distant thing, like a legend come to sit at the table. Maybe it was the Power about him, more than Eleri had, more than any except the Ladies at Cauldron Well.
While he discussed matters of the High King with her father, his eyes were, for a very long time, on Gynath. With the tables and benches set around the hearth fire, there was plenty of light for him to see whomever he chose to look at very clearly.
Completely unaware of this regard, Gynath exchanged clumsily flirtatious looks with some of the other squires, much to the open amusement of the king and queen. Seeing that the Merlin was watching the girl, the king leaned over to his guest and said in an undertone, "She'll make me a fine alliance one day, there's no doubt."
"Oh?" The Merlin smiled with his lips but not his eyes, which kept their sharp gaze on Gynath. "Her ambition rises no higher than that?"
The king chuckled. "Gynath, Goddess bless her, is a maid meant for a man. Oh, she's a bit clumsy now, but wait a year or two while she learns; the young bucks will be prancing and pawing for her attention."
And with that, the Merlin seemed to completely lose interest in Gynath. He turned his full attention back to the king. With nothing to do, Gwen found herself watching her youngest sister out of the corner of her eye and was glad to be in the shadows, for she blushed at Little Gwen's behavior.
The child was utterly shameless. She filched tasty bits off the plates of others when she was sure they weren't looking and slipped the tell-tale remains to the dogs under the table; and once, she smuggled a cake with a bite taken out of it onto the plate of the little boy next to her, so that when his father looked for the treat and found it missing, the poor lad got a cuffing and sent off to his bed, whimpering that he hadn't done anything. And Little Gwen watched him go with a smirk. Even when she was full, she continued to steal, hiding nuts and cakes in her pockets.
When she tired of that, she began doing something under the table; what it was, Gwen could not tell, until a dogfight erupted there, and the poor hounds were sent off with kicks by the men. No one else seemed to notice her antics, though, except for the Merlin. Any time anyone cast a glance at her, she was all dimples and sideways glances and got an indulgent smile in return.
It was a relief when the queen rose, signaling the men that it was time to pull the benches together for more serious drinking, while she and the women dealt with the clearing away. Or rather, the women did it under her direction. Little Gwen's smirks turned to scowls as she was set to doing tasks like anyone else, under the sharp eye of her mother. As for Gwen and the other squires, their duty until dismissed was to keep the cups and horns of their appointed guests full, and with that to be done, she had no more time to watch her sisters. Shortly, the women were gone, and the men were left to themselves.
Again, the Merlin was abstemious, paying close attention now to all the men as well as the king. He said little, and when he did speak, he asked intelligent and pointed questions. Gwen was relatively certain that he was probing for weak points in the king's loyalty to the High King and looking for signs of wavering or treachery.
If that was true, he found none of it. Lleudd Ogrfan Gawr was a blunt man, not simpleminded but open in his ways. His loyalty was first to his people, second to his personal allies, and third to the High King.
"It's a good thing to have a strong High King again, and a better to have one who knows his way about a battle," the king said, to the nods of satisfaction of those around him. "Goddess bring blessings to him! For all that he's young, he knows when to fight, and when to talk, and when to send sly men to buy him time."
"And if he calls on you for your levies?" the Merlin probed. "It's a hard thing to have to travel across the width of the land to fight some other man's battles."
"Hard aye, but they won't be some other man's battles, will they?" the king responded. "He's beaten off the Saxons once and the Northerners twice since he was made High King. If we'd had a proper High King when the Romans came, there'd have been no separate peaces, no tearing apart of tribe from tribe. We'd have fought the carlin knaves on the beach, and that'd have been an end to it! Nay, three years he's been High King, and only once has he called for levies, when the cursed Northern men came in force in those dragon ships of theirs. And what happened? We came, and we beat 'em, and they haven't come again!" The men slapped their knees or pounded their feet on the floor in agreement. "If he calls for levies, 'twill be because there's need. And as for other things, 'tis why he has you, Merlin. You're the Merlin. Whatever you tell him, you have to think of the whole land. That's your duty. Aye, men?"
The men pounded their feet again in approval or responded with "aye" in varying tones of enthusiasm and satisfaction.
"So. What Arthur wants from us, by the gods, Arthur will get, unstinting." With a nod, the king dismissed the entire question and moved on to the subject of the tribes in the North and whether or not they were likely to be a trouble this year.
Gwen saw the Merlin's lips curl ever so slightly in a smile. And then he bent his formidable mind to just that question. Gwen let out a little sigh of relief.
The talk turned to lighter subjects when that thorny problem had been dealt with as best it could be. "You have a fine brood of daughters, my host," the Merlin said, with a casualness that immediately set Gwen's senses to alert again.
"Four. My eldest has gone to the Ladies, and a fine Maiden for the Circle she'll return to us. My second you saw—a good girl, a sound girl. But my pride is at your left hand, my lord Merlin." The king cast a glance back at Gwen with a warmth in it that made her stand taller even as she blushed for the praise. "The queen always held that she was strong in the Blessing and should be the one to go in Cataruna's place—but the Goddess clearly had other plans. The Blessing she may have, but it seems it was Epona's, and she was born for the Path of Iron. She takes to weapons as if she were born with a spear in her hand, and as for the horses! Epona herself surely must have smiled on her birth!" The king laughed. "Well, you'll see. Her horses are old veterans, and if she doesn't win, it won't be for lack of skill or heart, and she'll make a good accounting of herself."
"You have great faith in her," the Merlin said, in a neutral tone.
"Oh, she has the heart of a Bouadicca but more good sense. If she can keep her head, as her model Braith does, she'll do well." The king seemed to realize that he was tempting fate with such praise and coughed. "Of course, that's in the hands of the gods. But it's clear enough, for all of that, her place is in the ranks of the warriors, and her love is for horseflesh and the sword."
"And your fourth?" The Merlin's eyes had taken on that hawklike brightness again.
"Oh, Gwenhwyfach." The King shrugged. "A mere chit of a child, given to childish ways and tempers. As unformed as an unlicked bear cub. Too soon to say what she'll be, and it may be we spoiled her a bit too much. But with the new son coming, she'll get over that quick enough or have it beaten out of her. My guess is, the way she queens it among the other children, she'll be another like Gynath, a maid for a man, and make me another alliance. Maybe to Arthur's son, eh? Now, my lord Merlin, on that head, what of the High King's coming son? What birth gift would be best to send? I've a mind to send him my best yearling foal that boy and horse may grow up together."
By the time Gwen was dismissed with the other squires, she was glad enough to crawl into bed with Gynath and Little Gwen. But Little Gwen was still awake, and strangely, for once, she didn't _torment_ her sister. Instead, she was as full of questions about the Merlin as any of the boys.
"What did he have you do all day?" Little Gwen demanded.
"Run errands and messages mostly," Gwen replied wearily. "Nothing exciting. I didn't see him work any magic, if that's what you want to know."
"And what did he talk about, with the men at the fire?" The child seemed crazed to know about the old man. "Did he talk about what he's done? What about his magic? Did he tell how he did some of it? How he hid Arthur? How he made Arthur High King? How he helped win battles?"
"Mostly he asked questions." Gwen yawned. "He wanted to know how Father and the men felt about Arthur, I suppose. He didn't talk much about himself, or about Arthur, or the new queen, or anything really. He asked about us, about Mother, as you do for politeness."
"What did Father say about me?" came the sharp reply.
"That you're too young for anyone to tell what you're going to make of yourself. But if you don't go to sleep, you'll look like a thrall that's been beaten, and no one will give you a thought." And with that, Gwen turned her back to her sister.
She half expected a sharp elbow to her ribs, but none came. Instead, there was a pregnant silence, and in that silence, Gwen gratefully fell asleep.
**Chapter Eight**
**The Merlin's own** servant was tending to his master's needs, while any errands that needed running would be addressed by one of the king's personal servants. Gwen had leave from her duties for this race, and that was all she was thinking about. Not that there was much attending the honored guest would need during the race; he was with the king, the queen, and both Gynath _and_ the king's own squire. He wouldn't be able to lift a finger without someone asking him if he needed something. The king was sparing no effort to make his guest feel just how honored they were to have him here.
Gwen herself was far more concerned with another person among the guests. Braith was here, and Gwen was very anxious that her idol be satisfied with her protégé's progress. She didn't want Braith to think that her trust had been misplaced.
So, in these moments before the race, now that she had gone over every bit of the harness and chariot five times over, she was standing between her two charges, as she had seen Braith do, breathing in their breath and letting them breathe in hers, scratching gently along their jaw lines, whispering nonsense to them. They were old hands at this game, of course, and were far less nervous than she was. They were properly warmed up, and she could sense the readiness of their muscles under her hands when she slid her palms down along their chests. They eyed the other teams nearest them, as if they were measuring their opponents, and then turned their attention back to her.
The starter was an old, scarred fighter from one of the guest contingents; he stopped chatting to a group on the sidelines and stepped up to the starting line. "Drivers!" he barked. "Take your places!"
With a final pat and a whispered word, Gwen left her horses and hopped up into her chariot, taking up the reins. The leather reins felt alive in her hands, as if the horses were speaking to her along them. She saw their haunches bunch as they prepared to leap forward on her command. "Get ready!" the old man shouted, and she flexed her knees, and braced herself for the start.
_"Go!"_
The horses didn't wait for the reins to slap their backs. They were off as soon as they felt her lift them—or maybe they had responded to the starting shout. No matter—they were off. The chariot lurched forward, Gwen bounced a little against the curved back of her vehicle and habit took over as she regained her balance and crouched down even with the rumps of her horses.
She glanced quickly to either side and saw that she was dead even with the chariots on either side of her. Farther than that, she could not see, and she turned her attention back to the course. Beneath her feet, her chariot bounced and rattled; in front of her, the firm haunches of her horses rose and fell, their heads bobbing as they ran, their hooves flashing within a foot of her head. All around her was the thunder of hooves on the hard-packed earth, and the turf flew past in a blur just beyond her feet. Clods thrown off by the horses' hooves pelted the bottom of the chariot.
And for a single moment, there was nothing but sheer terror.
Then, as always, _everything_ settled into place. She didn't really have the words to describe it. Calm descended, and she felt as if the reins, the chariot, even the horses were part of her. That she was wheel-to-wheel with the other chariots didn't matter. She _knew_ that things were going to happen an instant before they actually did, just enough time to avoid trouble. And she didn't have to think about it, her body reacted before her mind actually registered what was about to happen—
Suddenly she knew that, as they wheeled for the turn, the team on her right was going to veer toward her a little too far and that the only two ways to avoid a collision were to pull back a little or try and get her team to shoot ahead.
And she knew that, as game as the team was, their strength was in endurance, not bursts of speed. They were too old for that sort of burst of speed. So she held them back. They fought her a moment, then yielded and dropped behind the other chariot.
The other team blundered into the space where her horses _would_ have been; the driver shot her a look of alarm that blurred into relief, and then they had both made the turn and were on the return leg.
Through the reins, her hands told the team _fast but steady._ Through the reins, the team told her they would give what she asked for. She glanced to either side; the team that had almost collided with hers was ahead by more than a full length, but she recognized them with some satisfaction, for the driver was older than she by several years, and the team younger than hers, about two years into their prime. She was running second; in third, a length behind her, was another team driven by a boy with more experience and younger horses. His horses were laboring; hers were good for much more than just the run to the finish. If this had been a battlefield and not a race, he would be no good after this run.
She could hear the cheers; so could her horses. Their ears pricked forward. _Steady,_ her hands told them. _We are,_ they told her back. They stretched out their necks, though, determined to make the leader win his prize
And then they were across, and she was pulling them up, as the spectators swarmed the winner. But as she jumped out of the chariot and went to the horses' heads to take their halters and begin walking them to cool them, a smaller group was heading for her in a more leisurely fashion. Braith, Braith's lord, her father, and three of the warriors that were her teachers.
"I told you not to bet against her," Braith was admonishing her lord, as that worthy handed over to the king a fine silver bracelet.
"And you said she wouldn't even place, with horses that old, and young as she is," the king crowed. He pulled Gwen into a hard embrace, laughing. "Well done, daughter! Second place, and your team still ready for another charge! First place isn't everything."
"Not when you bring your team to the finish line heaving and winded, King," said Braith, a broad grin on her brown face. "Someone had better teach that boy in third that he's training for battles, not for sprints."
Gwen said nothing, but she felt as if she were glowing. She'd done it; she'd made Braith _and_ her father proud.
"What are the prizes, my lord King?" someone called from the crowd around the winner.
"For first place, a silver brooch!" the king called back. "For third, a fine, fat duck and a flagon of wine from the king's table! And for second—" He looked down at Gwen, his eyes twinkling. "—For second, a tun of ale and the boar meant for the king's table!"
"Then let my prize be served among all the drivers!" she called out, her high voice ringing clearly out before the cheering could start again. "For surely all have earned a share!"
Any grumbling that might have started among the others that the king's daughter had surely had some secret aid was erased in that moment, as the cheering started all over again.
Gwen looked up again at her father, and saw him mouth the words "well done" before he turned back to his guests to escort them to dinner.
But better even than the accolade from her father was the one from Braith, who winked, and mouthed the same.
The tables and benches had been set up outside, around the three hearths where all the cooking had been done. There were so many guests at a Midsummer gathering that the Great Hall would have been stifling hot, and you'd scarcely be able to cram them all in there anyway. There was great rejoicing at the table set aside for the squires who had driven in the race as they squabbled good-naturedly over the best parts of the boar, stuffing themselves with both hands, their faces shiny with the rich fat. Gwen, however, was just as happy back at her place behind the Merlin, serving him. For one thing, she already had the acclaim of the two who mattered to her; for another, her gesture—and her insistence on returning to duty—had favorably impressed her father's guests, the Merlin included. The old man gazed on her for a very long moment as she took her place, and it wasn't the sort of look he gave Gynath, but the sort of measuring he was bestowing on her father's chiefs. It was a look that said _I underestimated you, and you are worth keeping an eye on._
And anyway, although she liked a slice of good boar as much as the next person, she had overheard her mother telling the chief cook to set aside a quarter of a goose and keep it warm for "our brave Gwen." So she wasn't losing by her generosity.
Once the feast was well underway, however, the Merlin was his usual abstemious self.
But this time he paid special attention to Gwenhwyfach. She was up to her usual tricks, utterly unaware that she was being studied. _First me, then Gynath, now Little Gwen . . ._ She wondered what he was thinking.
Then it dawned on her; the High King was about to be the father of an heir. Such a boy was going to need a wife, and as soon as possible. An alliance with her father would give Arthur a near neighbor to the troublesome Orkney crew. And hadn't her father suggested it himself?
Cataruna had gone to the Ladies, and once she came back, the king would not want to give up one with both the Gift and the training. Gynath was, perhaps, a little too old—oh, you could betroth babies in the cradle, but usually they were closer in age than this, and when the boy was old enough to sire a child, Gynath would be twice his age. Besides, if Eleri did not, after all, have a boy, then the king would want to pick a good husband for Gynath, in order to have a male to pass the crown to.
Gwen herself? Possible, but probably still too old. And as long as she was a warrior, she would not only be valuable to her father for those skills but would be much in the company of the men—and without the pressure of being first- or second-born, she might make a match of her own. Or not. Braith never had.
But Little Gwen, now . . . that was different. She was young enough to be reasonably close in age to the High King's son, she was pretty and would likely grow to be even prettier, and she had immense charm. She'd make a good candidate for such an alliance. The king himself had said that there was no telling what she would grow into, so out of his own mouth the Merlin had it that she was not yet seen as a valuable asset. And she was fourth-born. Her father would have every reason to welcome such a betrothal.
So now the Merlin might well be watching her to see if she was trainable. If she _was_ betrothed to the High King's heir, they'd want her sent to them. They'd want to be sure she was raised _their_ way, with schooling in what _they_ thought needful.
_And wouldn't that be interesting._ Gwen schooled her more malicious thoughts. With the Merlin there, Little Gwen wouldn't be able to use her glamorie, if indeed she had one, to charm people into doing what she wanted. She'd actually have to learn how to behave. Probably how to work, too. The life of a queen was not all fine clothes and goose every day. The queen had charge over the household, and in the king's absence, could be expected even to command the warriors.
It would probably be the best thing that could happen to her.
_And Gynath and I would have the bed all to ourselves,_ she couldn't help but think, wistfully. And then she sighed. The way that Little Gwen was carrying on, the Merlin would probably think she was far too much trouble, even for such a good alliance as with her father. Especially since her father was already clearly loyal.
She lifted the hair from the back of her neck for a moment to let a breeze cool it. She was very glad they weren't stuck in the Great Hall. It was much more pleasant, eating outside, but the king, though he would have scoffed at such a notion, followed the Roman custom of having the family and retainers dining in the Great Hall most times. Sometimes Gwen wondered why, especially on an afternoon like this. It was easier to clean up after everyone was done eating, the sound of talking didn't get bounced about by hard stone walls so that you had to concentrate even to hear a near neighbor, and it didn't smell. As fastidious as Queen Eleri was, there was only so much you could do in a room where cats and dogs did as they willed, rats and mice came out at night, and people dropped food and spilled drink on the floor.
Maybe it was only because in the Great Hall the smoke rose straight up to the roof, and there was no "bad side" for the tables, where wind sent the smoke into your eyes. The people on that side of the hearth fires were looking uncomfortable.
Gwen checked on her charge again. The Merlin was still watching Little Gwen. _Oh, it would be so good if he picked her,_ Gwen thought fervently.
Finally, when the last of the food was gone, and the men had settled down to serious drinking and talking, the Merlin's manservant came and tapped Gwen on the shoulder and indicated with a jerk of his thumb that she should go eat.
She went straight to the head cook who had, indeed, saved her a good meal and, wonder of wonders, had carefully put the goose in a clay pot and left it basting in its own juice by the fire so that it didn't congeal in its own fat. Gwen enjoyed every bite, but she felt the need to hurry back, lest she be thought laggard.
By now, the sun had almost set, and the embers of the fire matched the color of the western sky. She took the jar of beer from the Merlin's manservant and quietly replaced him without a fuss. The conversation was about children—the children of the chiefs as well as of the king—betrothals that might be made, daughters gone to the Ladies, second or third sons that might be sent for harder training away from the family. No man would send his heir away of course, but it was thought that other boys would benefit from being away from the shadow of the eldest and the protection of the family. And, of course, _they_ might catch the eye of a daughter, and there would be an alliance-marriage out of it.
The Merlin cleared his throat. "I have some interest in your youngest," he said, with great care. "I would like to speak with her at some length over the next day or two."
"Little Gwen?" The King's voice betrayed a touch of confusion. "Why Little Gwen? The conversation of such a child is not like to be entertaining."
"I believe I may have detected another sort of Blessing on her than the one the Ladies look for," the Merlin replied. "Such a thing is elusive, as difficult to follow as a minnow among the reeds, but it is the sort of thing that is useful to the Druids. It may be that as the Ladies have called your Cataruna, the Druids, although we do not usually call females, might be able to train your youngest. We have on occasion great need for maidens. Pure maidens, with special kinds of power to them . . ."
"Aha!" Comprehension dawned on the king. "Virgin foot-holders, as the good Goddess Arianrhod was to Math ap Mathonwy, Lleu's liege lord. Has our High King the need of such, think you?"
"He might. Or I might. If the magic calls for it. There are other Druidic callings for pure maidens, though these rites be more secret than those of the Ladies." The Merlin smiled. "I can assure you that if she is indeed endowed with such a Blessing, she and you will be greatly honored for it, protected and guarded—rather better than Arianrhod was. And if she is not, well no harm will come of a little talk with an old man. Hmm? Besides, your trusted Gwenhwyfar will be there." He chuckled deeply. "I assure you, my lord King, I am not such that finds great interest in little girls except as they may grow to power or further the needs of the High King."
"Oh, I had no suspicion of that." The king's ears had turned a little red. "And who am I to deny the Druids what they may need, especially as it may be in the interest of the High King? I shall tell the nursemaid that you are to have custody of the little wench for as long as you require. Or—" he amended with a chuckle "—for as long as you can stand her prattle."
When the manservant again took Gwen's place and she picked her way through the snoring bodies bedded down among the rushes in the Great Hall to the bedchamber, she discovered that once again Little Gwen was wide awake.
She heard the child sit straight up in bed as she lifted the door-curtain. As warm as it was, the bed curtains had been taken down altogether and put away until winter. "Gynath is asleep and said she would beat me with a slipper if I woke her," Little Gwen hissed urgently. "What did they say around the fire? What did the Merlin say? Did he talk about magic?"
"Actually, he talked about you." Gwen figured _that_ would shut the little nuisance up, and it did. "He wants to talk to you. He thinks you might have some kind of magic that the Druids can use, and if they can, when you're old enough, they'll want you to come to them like Cataruna went to the Ladies."
"I _knew_ it!" Little Gwen squeaked with excitement and gloating.
Gynath rolled over and swatted at her, then rolled back without saying a word. Little Gwen squeaked again, this time with indignation.
"Well, magic or no magic, you had better be on your best behavior, because I am to be there too," Gwen whispered crossly, "You may be sure that Father will ask me about this, and if you act badly, I will tell him."
"I won't—!" Little Gwen began indignantly. Gwen cut her off.
"And if you act like a pigkeeper's brat, or try to lord it over me, the Merlin will take it ill. He holds good manners high, does the Merlin. He treats me like a full warrior, so you had best do the same." Gwen pulled off her sandals and tunic and crawled into the bed. "And you had better let me get some sleep, too, or I'll let the Merlin know that _you_ are the reason his squire is clumsy in the morning."
That threat was enough to still the questions—and the gloating—in the child's throat. She laid herself back down, and Gwen curled herself into a ball.
_Could_ Little Gwen have a magic that would be useful to someone besides herself? That glamorie, for instance? Well it might be useful enough if she tamed it and used it wisely. She could lead other children around easily enough; the High King might find it useful if a maid in his court could do the same with adult men.
If the little ferret could be tamed . . .
Thinking that, Gwen fell asleep.
She was up before dawn again and was attending to the Merlin's wants before the old man was even awake. Now well acquainted with his habits, she brought fruit and bread and clear spring water instead of the small beer and meat that the king's other guests would expect. She didn't actually expect Little Gwen to turn up until the sun was high, but to her shock, as soon as the Merlin had broken his fast, she and Bronwyn turned up to wait on the Merlin's pleasure. Gwen's eyes nearly jumped out of her head with shock. Little Gwen had never been up this early on her own, ever!
After Bronwyn had been dismissed, the Merlin also sent away his manservant and sat Little Gwen down on a stool at his feet. Then he looked at Gwen.
And once again, she found herself held prisoner by his eyes. It happened even faster this time, and when the Merlin told her that she would hear and see _nothing_ that went on, she nodded vaguely, though her mind battered itself against the fetters he placed around it like a wild thing in a trap.
Then he turned to Little Gwen. And try as she might, Gwen could only make out scraps of what passed between them.
Some things did manage to penetrate the fog that the Merlin had put around Gwen's thoughts. The Merlin asked about the coming heir, and Little Gwen replied with such venom, such hatred, that even Gwen was a bit shocked. And then—
Then the Merlin turned back to her and looked deeply into her eyes. "You fight me, girl," he said with a little admiration and some regret. "But this is not for the honest ears of one such as you. Sleep. And remember nothing."
And that was all she knew—
She came to herself with a start. _I must have been more tired than I thought!_ With a touch of alarm, she looked covertly about the tent, but the Merlin did not seem to have noticed her lapse. He was giving Little Gwen a small carved box and smiling with satisfaction. "So, use that as I told you, and your future will be clear," he said.
"But the Druids will call for me?" Little Gwen pleaded, with something like urgency in her tone.
"I pledge you that _someone_ will. You have Power, you will have more, and teachers seek such students out." He passed a hand over his eyes, as if he were suddenly weary, then looked up at Gwen. "Escort your sister back to her nurse, then tell your father that this child is indeed Blessed with Power but that the time is not right for her to leave her family."
"Aye, my lord," Gwen replied, feeling disappointed that Little Gwen was not going to be taken off far, far away—at least not for some time. Little Gwen looked even more disappointed, but she allowed herself to be led off, clutching her little box.
"What is that?" Gwen asked, as soon as they had left the tent.
"Something secret," her sister said, a sly look coming over her.
"I'm not to tell."
Gwen shrugged. "Then I won't ask any more." Her sister looked disappointed at that response; half of the value she placed in a secret was that she could torment her older siblings with it.
But she didn't have any time to come up with a new tactic, for Bronwyn was waiting for them at the edge of the encampment and looked with curiosity at the box.
"Tis a secret thing between her and the Merlin," Gwen said shortly. "So let her do what he wishes her to do with it."
Bronwyn nodded and took Little Gwen in charge, while Gwen went off to find her father and fulfill the second half of her duty.
Her father seemed a little disappointed as well but said only, "At least we know she _has_ a Blessing. But it must not be something the High King needs. Ah, well." He waved Gwen off. "We'll let her age, like mead. Mayhap she'll turn out as sweet with the help of whatever it is the Merlin gave her."
Privately Gwen rather doubted any such miracle could occur, but this was a case when the squire served best by keeping her lips sealed. "Aye, my lord King," she said carefully, bowed, and went back to her duty.
**Chapter Nine**
**The guests** were all gone, the Merlin with them, without his making a display of any kind of magic—much to the bitter disappointment of most of the young squires. This time Gwen had not had the slightest wish to spy on the Midsummer Rites. She spent that evening as usual in attendance on the Merlin, and when he retired to join the Rites, she sat quietly with the other squires, on her best behavior. They were all rewarded by a share of mead each, which warmed her belly and made her sleepy. When the Merlin and the women returned, she was surprised, for she had not thought that much time had passed. She was glad when he dismissed her, and she was happy enough to go to bed, even while the young women and men were still leaping the fire, dancing, or making sheep's eyes at each other. Of course, not all of them were confining themselves to that, for it was Midsummer after all, but they were out in the hayfields or the meadows or little bowers under the bushes, and not tumbling and panting in the Great Hall, so she didn't even think of them, but of the soft mattress and how good it would be to get there.
The truth of the matter was, that between serving the Merlin and seeing that her horses were tended perfectly, her gear in good order, and the gear of the older warriors attended to, she fell into the bed and slept like a stone every night, and she simply didn't have the will to sneak out for a clandestine look. Besides, her curiosity the last time had resulted in a vision that, while exciting, was also somewhat frightening. She'd spied upon the gods that night, and she rather hoped that she was below their attention. At least, until she was old enough to start earning some glory in battle.
Little Gwen had finally found something to occupy her besides tormenting her sisters, and for that, Gwen was so profoundly grateful to the Merlin that she would have run twice the number of errands he asked of her. Whatever it was that he had told the child, and given her, kept her captive and quiet in her own thoughts. And meanwhile, now that he was sure of her, the Merlin sent his assigned squire out into the fields and woods to acquire any number of herbs and bits. Mushrooms both poisonous and tasty, baskets of bark, roots, leaves, owl pellets, bones and teeth . . . there seemed no end to the odd things he wanted her to find. It wasn't capricious either; part of the reason he was sending her for these things was that he was graciously sharing his lore of curative things and homely spells with the queen and her women, showing them how he compounded remedies for all manner of injuries, curses, and diseases. The women loved him for this, but of course, this was not the conjuring of dragons or the summoning of demons that the squires hoped to see, so it was all terribly boring to them. In this, Gwen didn't agree; some of the things that the Merlin could cure were downright miraculous.
But at last, everyone was gone, and Gwen was back to duties that seemed light in comparison with the double burden she had carried while the guests were about. Now she knew why the squires had always looked so harried and haggard during festivals and had never had time for games or gamboling. In a time of feasting and leisure, they got none of the latter and only the leftover ends of the former.
It was about a week after the last guest had left that a traveling bard arrived, having spent Midsummer at the festival King Lot of Orkney held. Like all bards, he was as full of news as he was of music, and the women swarmed him to hear his largest burden, that Anna Morgause had been brought to bed of yet another son, her fifth. Four more she had, two older than Arthur—Gwalchmai, Gwalchafed, Gwynfor, and Agrwn. Gwalchmai and Gwalchafed were said to be as alike as she and Little Gwen, and the younger served the elder as a squire. She only hoped Gwalchmai's younger brother had a better temper than her younger sister.
"Thin, small, and sickly looking this one is," the bard said, with a little smirk that made Gwen frown. This man was angling for rewards from Queen Eleri, she thought. But she kept her head down over her task and held her peace. She was not allowed to completely escape the training of a maiden amid all the work of a squire; she still had to mend, if not make, her own clothing.
The king counted on his fingers, and chuckled. "So old Lot made sure of his wife by quickening her _before_ he took her to Arthur's wedding. Very wise of him."
"Well, if a man knows he's like to wear the horns," said one of the men with a leer, "That's the best way of knowing he won't be raising another man's brat."
Ribald laughter spread around the benches. Anna Morgause had a reputation that was none too savory. It was said she had even bedded a Northman once, and it was whispered that she did not confine her couplings to humans. And here, far from the reach of her magic, it was safe enough to gossip about it.
"I've half suspected old Lot of being her pander, a'times," said another with a snort. "And she, his."
Queen Eleri was shaking her head as she cradled her belly with one hand. "Four living sons, and what does she need with a fifth?" she wondered aloud. "Well, what's the poor wee thing's name? No matter what kind of mother he has, I'll ask the Lady's blessing on him that he shall thrive. It is hardly his fault what he was born to. And he is the High King's nephew, as she is the High King's half-sister."
"Medraut, gracious Queen," the bard said with a bow. "She calls him Medraut. Her little sister Morgana is much enamored of him."
"Little and sickly, and with the Orkney lot! He'll need Morgana to look after him," old Bronwyn predicted sadly. "If they don't bully him a-purpose, they'll still worry him like a lot of unwhipped pups with a rag they tug between each other."
"Little and sickly, perhaps Anna Morgause will tend to him as she did not her healthy boys. We will hope." Eleri raised her chin, signaling that the subject was concluded. "Did the Merlin come to visit them, as he did us?"
The bard shook his head and went on to other things. Gwen had felt an odd and uneasy interest in the subject of this unknown boy child, but maybe that was only because her mother had taken on an odd expression when she spoke of him. After more gossip concerning Lot, his wife, and their followers, Eleri asked the bard to give them some music, preferably a war song, for there were rumors the Northerners were moving again. Old Bronwyn made a face of disappointment at this; she took a particular delight in the bad behavior of Anna Morgause, to the point where Gwen found herself wondering what the queen of the Orkneys could ever have done to Bronwyn to make her so sour against her.
Little Gwen had been surprisingly good, although she looked as disappointed as Bronwyn when the queen changed the subject away from the Orkney clan. Gwen was relieved. Perhaps all the attention she had gotten from the Merlin had done her good. She certainly had been on excellent behavior this evening, fetching the queen anything she asked for and not even trying her coy little tricks on the bard. It was rather too bad in a way that Eleri _had_ changed the subject; the bard was not very good, and Gwen found her interest straying away from the war song that was less _song_ and more toneless chanting, mostly in praise of a nebulous leader who, she supposed, was intended to resemble her father. That was often the way with these bards; trying to flatter their hosts in hopes of a rich present, rather than earning the rich present by honestly performing to the best of their ability. Sadly, her father didn't seem to see the ploy for what it was; he nodded to the monotonous strumming and looked as if he were going to interject an approving grunt on the chorus, when suddenly Eleri clutched her swollen belly and screamed out in pain.
It was not just a "cry"—this was a sound that Gwen had never heard from her mother, and from the look of it, neither had any of the other women, not even Bronwyn, who had been with her through all of the births of her children. The look of startled alarm on Bronwyn's face, made a stab of fear go right through Gwen. Swiftly, Eleri's women surrounded her and half-carried her into the royal chamber, as the king tried to make light of the situation.
"You see, Bard, your song has roused my son, and now he wants to come forth and do battle!" He stripped off a bracelet—only bronze, to the bard's swiftly covered disappointment—and tossed it to the man, looking distractedly at the entrance to the chambers, now covered by the curtain. "Let us drink to him and to the safe delivery of the queen! And let us take our drinking outside, so that we do not disturb the women at their work!"
The rest of the men were nothing loath to do so, taking up their cups and moving with unseemly haste to the fire outside. And Gwen had to go with them, in her capacity as a page.
And of course, even though they were all outside and the cries were muffled, when the screaming began, everyone knew that something was going horribly wrong. It was bad enough that this was far too early for the baby to be coming. Two weeks more, better still, a month—not now. But the awful sounds that Eleri was making—she didn't sound human anymore, she sounded like an animal in pain. The men all raised their voices and gabbled about nothing at all to try to cover it, but the king was pale and sweating, and Gwen wanted nothing more than to run away, far away, and curl up in a ball with her hands over her ears.
It was worse when the terrible screaming stopped, and a cold silence took its place.
They came to get her, two of Eleri's women, sobbing. Gwen didn't want to go with them, but they took her hands and pulled her along into the room that smelled of stale sweat, and blood, and something else, something sweetly sickening. _Poison,_ she would have said, if they had asked, but no one actually asked her anything. Gynath was already there, sobbing as she wrapped something small in long bands of white cloth. They made her go to the side of the bed, but the thing in the bed with the twisted, agonized face was not her mother, could not have been her mother. Eleri had never looked like that.
But, like Gynath, she cried as she did what she was told to do. Eleri's women did most of the work, washing, dressing, and laying out the body, trying to smooth that tortured face, carrying her and the wrapped infant that had never breathed to the bier in the Great Hall. Gwen and Gynath gathered flowers, herbs, boughs of sacred oak and ash to make the bier. Once, Peder stopped her as she was gathering meadowsweet and made her look up into his face. "You are a warrior," he said. "You must grow used to death."
That only made her burst into tears again, and he awkwardly patted her head. "You must," he said, then, after a moment, his own voice choked. "But you never do."
After that, Peder kept her with him except when she was fetched by one of the women. He gave her hard things to do, things that forced her to concentrate, like splitting a wand with an arrow, or braiding a horsehair halter in an intricate pattern for a foal. Then he would give her things that exhausted her body, like carrying water and chopping wood. For the most part, though, she seemed to exist in a haze of disbelief, interrupted by the same anguish that caused Gynath and Bronwyn and some of the other women to kneel beside the bier and howl.
That was not for her, though. She couldn't let herself do that.
But it made her feel torn into a thousand pieces to see her father sitting there beside the bier, eyes dull, hands dangling, face almost gray.
It seemed a hundred years. It seemed no time at all. It seemed as if she had thrown herself down, exhausted with weeping and work and woke to find herself at the side of a barrow. The king's barrow, of course. She knew it; she visited it dutifully and left offerings of fruit and flowers and thought no more about it. Now there was a hole in the earth beside it, and at the bottom of the hole was Eleri. She had been draped with a linen cloth so fine that her features could be seen through it, and in her arms was the son she had died trying to give the king.
Gwen stared down at her, numb. There was no Lady here now, and they could not wait for one, so Bronwyn said the words for the women, and the bard, who had stayed, shaken, but there was some bravery in him to have stayed, said the words for the men.
Gwen wanted to run away as they all began, handful by handful, to throw dirt and flowers into the grave. She wanted to scream, to throw herself down there and beg her mother to return, to do anything but what she was doing—tossing in the meadowsweet and angelica she had picked, watching Gynath crumple to the ground, seeing her father look as if he were going to collapse at any moment.
All her anguish centered, at last, on that tiny bundle in Eleri's arms. The cause of all this grief. The brother she had intended to serve.
She didn't hate him. How could she? She had loved him for months. It wasn't his fault this had happened.
But with a stab of grief so deep it felt as if her heart had been ripped from her body, she swore a silent vow to Epona.
_I will never, never, never have a baby just to please a man._
Even when they were putting Eleri in the ground, Gwen couldn't believe she was dead. And now that the wake was long past, and there were even little pinpricks of green poking through the brown earth mounded over the queen's grave, Gwen still couldn't make herself believe it.
She felt numb, and her thoughts were muffled by a thick fog of grief and disbelief. She kept thinking that it was all some sort of nightmare, and she would wake up, and everything would be normal again. But she didn't, and it wasn't. Nothing would ever be normal and right again.
The rest of the family was no help. Gynath was utterly inconsolable; she and Bronwyn spent most of their time collapsed in each others' arms.
The king looked . . . shrunken. And old. He'd aged a dozen years in a night, it seemed. He still went through his day, doing all the things that a king had to do, but there was neither life nor light in what he did. He was a king, and he acted as a king, because it was his duty to be a king, although the man in the king wanted only to mourn.
Little Gwen was as mute as a stone; her face had a closed look about it, and she hadn't shed a single tear. She just went about, doing what people told her to do without saying three words in the entire day, like a little ghost girl.
The night it had happened, Gwen had stumbled over the box that the Merlin had given her little sister, open, cast aside, and empty. Gwen had numbly picked it up and put it on Little Gwen's chest; when she looked again, it was gone. For the first time ever, she felt sorry for Gwenhwyfach. Whatever charm the Merlin had given her, Little Gwen must have tried to use to bring their mother back, and it had failed. Not even the strongest magic could bring back the dead, of course, but Little Gwen wouldn't have believed that until she tried it for herself. Probably her faith in the Merlin and his promise had been discarded in the moment, like the box.
Gwen herself spoke only when she was spoken to, and she spent as much time as she could in the company of Dai and Adara, weeping into their manes.
Nor was the king allowed to grieve in relative peace. No, first the lords and the chieftains, then the messengers had descended. And now, here were come the Queen of the Orkneys and her brood. Supposedly to tender condolences and help, but . . . something in Gwen roused angrily at the look in Anna Morgause's eyes. There was a satisfaction there, a kind of gloating, that was ugly.
She came with an entourage, but without King Lot or any of her older boys. Gwen had to admit, the only word for her was "enchanting." Her lush figure would have been the pride of a much younger woman, her raven hair must have stretched out on the ground when it was unbraided, for the single plait that stretched down her back brushed her heels, and was as thick as a strong man's wrist. Her little face reminded Gwen of a fox. Her clothing would have aroused immediate envy in every woman there, if they had not all been so wrapped in grief.
When she was handed from her cart as she first arrived to be greeted by the king, she looked as if she had just stepped out of her own chamber rather than been traveling for a fortnight. And every man's gaze was riveted on her. Eleri had always looked far, far younger than she was. Anna Morgause looked ageless.
She had brought with her a wet nurse and Medraut, her new son, and Gwen hated him at first sight. He was long, thin, and pale, with a strange head of thick, black hair, and he didn't act as a baby should. He never uttered a sound, not even when he was hungry, and he stared at people out of round, black eyes like shiny pebbles, not the blue eyes of most babies. She hated having his eyes follow her, she hated that he looked like a changeling, and she hated most of all that this _thing_ was alive when her own brother, and her mother, were both dead. Vaguely, she felt that this was wrong; she was ten years older than this infant, she shouldn't feel so threatened by a baby. But she did.
With the queen had come her younger sister, Morgana. Gwen hated her, too. She was poised and controlled, and although she did not have the level of enchantment Anna Morgause had, she still made the young men's eyes follow her. Her hair was the same raven black, but her face was more catlike than foxlike, and her green eyes glittered with secrets.
When they were presented to the king, Anna Morgause said all the right things, but Gwen heard what was under the words. Silken, soft murmurs of condolence covered piercing blue eyes that looked everywhere for signs of weakness. And when she presented Morgana, there was more calculation. Gwen was proud of her father, though; he might be bleeding inside, but he gave no sign; instead he was gracious, hospitable, and offered his and his daughters' own bedchambers to the visitors.
"I would not like it that you should take your rest in a rude pavilion," the king said. "My chamber for you, your son, and his nurse, and Morgana can sleep in the chamber beyond."
"You are most gracious, my lord. Morgana can share it with your daughters," Anna Morgause replied, smoothly. Gwen immediately decided that it was time she began sleeping with the squires. Or out of doors. Anything other than sleeping next to the cat and waiting to see if she scratched you in the night. She made the best excuse she could think of, that she came to bed early, smelling of horse, and arose before dawn and would not for the world think of inflicting her coarse and boyish ways on a lady like Morgana. Her excuse seemed to pass muster with the guests, for they exchanged an amused look, but they said nothing at all when she took a rug and a blanket and went to sleep elsewhere.
For the first two days, Gwen did her best not to leave her father's side, and it was the purest of good fortune that it was her turn to act as his squire and page. She had an idea that Anna Morgause had brought her sister with the idea of getting her wedded to the king. She remembered what had been told her, of how Eleri had armored him against enchantments, and from almost the moment she set eyes on the pair, she was horribly afraid of what might happen.
And Morgana? As the queen? Lording it over Gynath, and her? The thought made her sick.
It appeared, however, that the same thought had occurred to some of the other women—and was just as revolting to them as it was to Gwen. After the first night, Bronwyn, under the excuse (inspired no doubt by Gwen) of keeping Morgana from being disturbed when Gynath arose for her morning work, took Gynath to sleep with her among Eleri's women.
By the third night, when Gwen was lying wakeful, restless under the double burdens of a bright full moon and a heart full of anxiety and mourning, she heard the sounds of several people slipping away from the castle. She left her rug and blanket, pulled on her shoes, and followed the shadowy figures as far as the Stones.
And that was when she was seized from behind by a pair of strong hands. A third hand was clapped over her mouth, smothering her yelp.
"Go back to sleep, Gwen," Bronwyn hissed in her ear. "We are armoring the king against the enchantments of that trollop and her sister. This is a women's war, and not magic for you. Keep yourself and your power as Epona would have you."
In the moonlight, one of the figures huddled about the altar stone turned her face toward Gwen. It was Gynath, and it seemed to Gwen that it was more than the moonlight that made her seem pale. The other woman let Gwen go as Bronwyn took her hand away, and with a shiver, Gwen crept back to her rug and a restless sort of sleep.
Whatever they did, it left Gynath listless and dull the next day, but it seemed to have worked. The king was courteous but distant, and Anna Morgause's eyes held an annoyance and bafflement that heartened Gwen.
Then it was Anna Morgause's turn to make some sort of trial.
Now, in all this time, both the queen and her sister had made a great pet out of Little Gwen, begging the king to release her from her ordinary work to play page for them, complimenting her, even praising her "charming manners" at meals. Gwen truly thought that they would use Little Gwen as their next means to get at the king, pointing out that she needed a mother, and how much she and Morgana doted on each other. That was a fearful thought, for Gwen couldn't see how Bronwyn and the others could armor her father against that.
But instead, Gwen woke with a start on the first night of the waning moon. At first, she couldn't think what would have woken her—especially not feeling as if a terrible storm were about to break. The sky was utterly cloudless, there was no hint of disturbance, and yet the longer she lay there, staring at nothing at all, the more certain she became that there was a disaster building, some horrific deed about to happen. She had made her bed, as usual, near the wall of the castle, and without thinking much about it, not far from the window of the solar where the king and queen had slept. But it was when she heard whisperings that sent chills up her back coming from that slit of a window, she knew _that_ must have been what awakened her. It sounded like two women whispering to each other. The queen and her sister, surely.
Those whispers were—not right. Not clean. She couldn't make out the words at all, but the very tone made her feel ill.
And when she heard the scream of a rabbit from _inside_ that room, her blood froze in her veins.
The whole castle seemed frozen, plunged into an unhealthy sleep. And there were no normal night sounds at all: no insects, no owls, not even a bat overhead. There were night noises in the far, far distance, but nothing _near._
The whispering grew more urgent, and there were definitely two voices in it. Then one made a wordless cry of triumph, which was mingled by the squall of a cat, swiftly cut off in a gurgle—
And suddenly, Gwen found she could move.
She snatched up her blanket and rug and ran, without thinking, blindly, and in pure panic. She didn't know where she was going, and she didn't even know how she got there when she came to herself again in Dai's stall, with the stallion sleepily whuffling her hair.
She cast her rug and blanket down and huddled in them, still shaking with fear, and remained there until morning. At some point she must have fallen asleep, for after a timeless age of mindless terror, she found herself awakened by the sound of ordinary voices.
She was roused by the other squires coming to feed their charges; no one commented on her sleeping in Dai's stall, but it was not unusual for squires to do so, if a horse was restless or acting a little "off." So she shook the straw out of her clothing, attended to Adara and Dai, and then shuffled back to the castle, still feeling horribly ill. Bronwyn immediately intercepted her at the door.
To her shock, _Bronwyn_ looked just as ill as she felt—but there was an air of triumph about her. "Drink this," the old woman commanded, shoving a beaker at her. It was something pungently herbal and very nasty, but it immediately made her feel better. When she gave the beaker back to Bronwyn, the old woman grasped her chin and made her look up, into her eyes.
"Aye, you felt it," she declared grimly. "There was dark magic last night, and this morn, there's a black cock missing from the hen roost, a black rabbit from the hutch, and a black kitten from the stable. But look yon—" she jerked her chin at the high table, where Gwen saw with astonishment that Anna Morgause and Morgana were picking at breakfast. Astonishment because they looked—common. There was nothing of the enchanting queen and her bewitching sister about them this morning.
The Queen of the Orkneys was wan, her cheeks sallow and waxen, her hair and eyes dull. Morgana was _plain,_ and she could hardly even manage to nibble at a bit of bread and honey.
"It was them, for nought else would have rebounded on our protections on the king. What they did came back on them," Bronwyn said with angry triumph. "Let this be a lesson in magic to you—what you try can be cast back on you, and you'll suffer for it if it does."
Gwen nodded and rubbed her head. It still ached a bit, but it looked as if the Orkney pair had heads that ached much worse.
"I've told your masters that you're ill and got you leave to sleep off what I gave you," Bronwyn continued, and gave her a little push toward the huddle on the women's side of the hall, where she could see Gynath's blonde hair among the sleeping women, several others, at rough count.
"Why—" Gwen began. She meant to ask, _why did you know I would be ill?_ But she never got that far.
"I reckoned, given all in all, you'd be sick too." Bronwyn did not explain herself, and after another moment, Gwen felt a heavy lassitude creep over her that smothered all curiosity. She stumbled toward a pallet, pulled a corner of blanket over her head, and slept till nightfall.
And when she woke, she learned that the queen and her sister had taken to their beds to be nursed, struck down by the "mysterious" illness that seemed to have struck so many of the women. The men did not ask about it—but then, that was hardly surprising.
". . . we will be grieved to see you go, my lady," the king said politely, but in tones of indifference that brought that flash of annoyance into Anna Morgause's eyes before she swiftly covered it. She and Morgana were long back to their enchanting selves, and whatever safer ploys they had tried to bewitch the king had also failed so much that he was not even sorry to hear that they intended to be gone.
"And I shall be grieved to part from you," she replied with false sorrow. "Your company, and that of your family, is so wonderful to me. I wish that I could take some part of you with me when I return to my home. My home is so lonely and remote, my husband so often gone, and my boys—are boys, and of little companionship to a poor woman and her sister—" She sighed theatrically, then snapped her fingers. "But I have it! I can help you and ease my own loneliness at the same time, my lord!"
The king looked at her as if she was mad. "Of course, my lady, but—"
She bestowed a dazzling smile on him as Little Gwen looked up with a sharp and avid alertness that made Gwen wary. Whatever was going on, Gwenhwyfach was in it up to her chin. "Oh, King, let me take your youngest to foster with me. A child that young needs a mother, and I so long for a pretty little daughter." The emphasis she put on the word _pretty_ made Little Gwen preen and Gynath flush and frown. "Only think! Coming to live with us, the child will grow up with my boys, and there are five of them—surely one of them will come to like her, and from liking cleave to her, and then we shall have an alliance of blood as well as borders! And even if that great good does not come to pass, I can teach her as her mother would have, in the maidenly, womanly things she must learn to be a King's daughter. She will not run wild with me, as she might if she is left to grow without a woman's hand to guide her. What say you?"
Now there was subtle insult in that, for Gwen, for Bronwyn, for Gynath—but it wasn't something that a man would note, and it was nothing they could take exception to, though Gwen felt her cheeks growing hot, and Bronwyn looked like thunder. The king looked bewildered, and Little Gwen took advantage of his hesitation. She flung herself down on her knees beside him and clasped her hands around his wrist. "Please, Father! Please!"
This was all leaving Gwen speechless with astonishment, and it seemed the king was just as surprised and unable to think, for the first thing from his mouth were the words, "Well, I suppose—"
Little Gwen flung herself on his neck. "Oh, _thank you_ , Father!" she squealed.
And at that point, of course, there was nothing to do but agree.
**Chapter Ten**
**It had been** two full moons since Queen Eleri died and one since Little Gwen had gone off to foster with Queen Morgause. In some ways, nothing had changed. The farmers still toiled in the fields, the herds still needed tending, all the work of the kingdom went on as it had no matter who the king and queen were. Gwen continued to toil at her lessons and chores: the cutting of wood and hauling of water to build strength, practice with bow and wooden sword and blunted spear, with staff and bare hands to make her a warrior, on horseback and in chariot to make her one of the fighting elite, a knight. She added new lessons: tracking and scouting—how to read signs, how to slip undetected across the face of the land, how to spy and not be seen. She was especially good at this last.
And in many ways, everything had changed. The king had emerged from his stupor of grief, but he seldom smiled and never laughed. It was Gynath who supposedly was "The Lady" of the kingdom, though in reality it was Bronwyn who made all the decisions and advised Gynath what orders to give. The evenings in the castle were quiet times, with the king withdrawing immediately after dinner to discuss whatever needed to be discussed with his chiefs and then going to bed. There were no more long evenings of drinking and tale spinning at the king's hearth. Gwen knew, of course, that such things were still going on, but it was at an improvised hearth, between the stables and the practice grounds. She had not been set to serve there at first; her teachers had let others take her place, but she supposed that now they thought enough time had passed, and it was time for her to do her duties again. And it wasn't as if there were anything happening there in the evenings that the king needed to be concerned about. Even the carefully "spiced" mead and ale would continue to be the same; it wasn't as if the secret of the brewing died with Eleri, for Bronwyn was well aware of the recipe and the same "spices" were going into the batches being made now.
No, it was nothing more than the same sort of talk and laughter that she had heard all her life; in a way, it gave her both comfort and melancholy. Comfort because it was so familiar. Melancholy because . . . she felt guilty. It seemed wrong not to go on mourning all the time, somehow disloyal.
And then, as the summer turned heavy and the first of the harvests began . . . the messenger from the High King arrived.
He brought with him news that the queen who shared Gwen's name had given the High King not one, but _two_ sons. Fortunately for his own safety, he had heard on his journey of Queen Eleri's death, so the first words from him were not of Arthur's good fortune but of condolence. Only after he had delivered a long—and to Gwen's mind, suspiciously fulsome—speech on Arthur's sorrow at hearing of this, did he deliver himself of his real purpose.
The king merely shook his head after a long moment of silence. "I wish the High King and his new sons well," he said at last, not troubling to hide his bitterness. "All health and long life to them. I do not have rejoicing in me—but I wish them all well." Then he dismissed the messenger with a small gift.
Bronwyn came and took him away to the women to be fed, and it was from Bronwyn that Gwen heard the thing that was both shocking and scandalous and almost not to be believed.
Bronwyn had made a habit since Eleri's death and the departure of Little Gwen of making sops-in-wine for Gynath and Gwen before they went to bed. This was especially welcome to both of them, because both of them were laboring far longer than they had used to. Gwen found herself pouring for her father and then being summoned to the men's fire to pour for one or another of her father's chiefs until the last of them went to their beds. And Gynath was taking on the task of being the chief of the women far earlier than anyone had reckoned she would need to. Of course, it was Bronwyn that actually made most of the decisions, but Bronwyn was very careful to make it seem as if Gynath were the one doing so. Under Bronwyn's eye and unobtrusive coaching, Gynath was doing almost everything that Eleri had.
Which meant both Gwen and Gynath were up at dawn and working long, long past sundown. They needed those sops-in-wine.
They also needed to hear what Bronwyn gleaned over the course of the day, carefully winnowing news and important details from mere gossip and speculation. Gwen had had no idea that Bronwyn had performed this service for Eleri until Bronwyn herself told them, over that first bowl of toasted bread covered with sweetened, spiced wine.
And she looked grim this night as she handed them the thick pottery bowls. "This is for no ears but yours," she said quietly, as they settled down on their bed—a bed luxurious to the point of decadence now that only two of them shared it. "I would not have the king your father hear of this, or his loyalty to the High King might well be tested to breaking. But you should know."
The bite Gwen was swallowing all but lodged in her throat; she swallowed it down with difficulty. Her stomach knotted with anxiety.
"This messenger was sent to spy on us," Bronwyn continued, her jaw tight. "He sidled about and put his questions mingled in with other things a-plenty but I could tell what was important to him, and it was about babies. Who'd given birth of late, who had sons, and when? Strange thing for a King's Messenger to be asking, I thought. And I liked it not at all. So I made sure to keep his cup full, and nothing loath was he to drink it. And that was when I heard the tale—"
She shook her head. Gwen waited, spoon resting in the bowl, no longer with any appetite.
"I don't have the gift the queen had, the knowing, that she could say when a man was telling true, telling false, or telling nothing more than wild rumor. But . . . well here it is." Bronwyn looked them both in the eyes, each in turn. "He said that once his sons were born, on the Merlin's advice, every boy child born in those parts within a week on either side of their birthing date was taken from his mother and smothered."
_"What?"_ gasped Gynath.
Gwen could only sit there, half frozen, as memories she didn't think she was _supposed_ to have came flooding back. Of the Merlin's questions. Of what he had mumbled.
"There were not, thank the good Goddess, many of them," she continued. "But . . ." She shook her head again. "The way he said it, made me think it must be true. And so cold-blooded—"
"Perhaps . . ." Gynath began, in a whisper, her face gone pale.
"Perhaps it was meant as . . . a sacrifice."
They all three exchanged sober glances. Even as young as she was, Gwen knew that there were sacrifices. From time to time one of her father's treasured white horses went off and never came back.
There were sacrifices at all the Great Rites. Mostly fruit and flowers and grain, of course; among other things, you didn't waste the life of an animal that could breed more of its kind unless you needed something really badly from the gods. But animals were sacrificed and—sometimes people as well.
That was mostly in the hands of the Druids. Mostly. Though sometimes there had to be a Year King . . . only in dark times though.
But the Merlin was the Chief Druid. And he was the one who had advised Arthur to do this terrible thing. Was he playing the Substitute King with the High King's new twins, sacrificing other boy children like them so that they would be spared? If he was, well, that was just wrong. Even Gwen knew it didn't work like that. The Year King had to go to the sacrifice willingly, had to know what he was doing, and do it for the Land and the people, and how could a baby do that?
But if they were sacrifices, what were the sacrifices _for?_
It was baffling, and somehow, that made it even more horrifying.
"This is something I thought you should know," Bronwyn concluded. "And it will go no further than the three of us. But you, Gynath, may well be queen here one day. And you, Gwen, will likely serve her as you would have served your brother, had he lived. And you must both know about things like this and keep a sharp watch on the High King's doings." She bit her lip, and the flickering flame from their rushlight made her look even older and more drawn. "It may be he has done this for the Land and the Folk. Unless the Ladies bring the word to us, we cannot know. But on the face of it, these are dark doings, and the High King is besmirched by their foulness. If these are dark doings, there is one thing you may be sure of."
"What's that, Bronwyn?" asked Gynath in a whisper.
"That they will come back at him when he least expects and be his ruin," the old woman said, grimly. "Blood will have blood, and innocent blood calls more strongly than any other."
The messenger went on his way. The season turned, summer to harvest, and the rites and the festival. Poor Gynath was at her wits end trying to arrange all, even with the help of Bronwyn and all the women, but out of respect for the king, few guests replied that they would come, and only the king's closest friends arrived. For the villagers, it was no different from any other Harvest festival. There was food and music, dancing and gaming, drinking and more drinking, coupling and handfasting, and all the usual doings in their season. And if the gathering at the king's hearth was a subdued one, if there were no races this year, well, at least there was, at last, a gathering at the king's hearth, and when the guests were gone again, there was no more going out to another hearth and leaving the king to mourn alone over the ashes. In part that was just plain sense, for there was no other place big enough to hold them all when the winter winds began to blow, but in part it was because the king was taking an interest in life again.
A few women made attempts to draw him out, but by Midwinter it was clear that there would be no queen taking Eleri's place.
As for Gwen . . . her instructors were keeping her too occupied to brood and had been for moons, so that when Midwinter arrived, it came to her one night as she served as her father's page that the terrible ache of grief, the chasm that had been inside her, was—not gone, never that, but—changed to something that was somewhat easier to bear. And looking at her father's face, it seemed he felt the same. He took an interest in things that he had not even at Harvest. Still not in women, but much the same, if somewhat grimmer, interest in the small affairs of his people and his kingdom and the greater affairs of what was going on outside that kingdom.
Perhaps it helped that there was, without a doubt, going to be fighting in the spring. The High King had sent out his messengers again, just before the snow flew, to warn that the seafaring chiefs, the Northerners, too disorganized to be called "kings," were uniting for what Arthur thought was another push to oust him and overrun them all.
It gave her father something to think about besides his own pain.
So at Midwinter, the talk was all of war and the preparations for war.
Gwen paid great attention to all this talk, for this was to be her business. There might not be a brother to guard now, but there were two sisters, one of whom would surely wed someone that their father would name as his heir. Whoever that was would need someone he could trust.
When the guests were all gone, Gwen and the rest found their hands being turned to those preparations that had been discussed. The nasty, barbed war arrows that would tear a man's flesh on being pulled out needed to be made. That was a matter of several steps, some of which could be entrusted to the squires. War chariots, spears, armor, bows, harness . . . all needed to be checked and put in good order. Much could be put in the squires' hands, and much was.
Gwen worked feverishly, and the work did much to help her set aside her troubled thoughts. There were no further ill tales, though more messengers came from the High King, traveling with great difficulty across the winter landscape, bringing with them the questions of levies and what could be supplied in lieu of or in addition to the levies. Now Gwen was glad that her father had not heard the tales, that Bronwyn had kept them to herself, for he threw himself into this work with a whole heart.
As might have been expected, there were other rumors coming out of the west, that King Lot had demurred, saying that mere rumors were no cause for raising levies, and that in any case, the Northerners might well lose interest before spring. "He intends to send nothing, or as little as possible," Gwen's father spat one night in disgust.
"There would be no loot in it for him," pointed out one of the chiefs. "Even if we drive them far back into their own lands and seize what we drive them off of, it is not on Lot's border, and he would get no share of it. If we only drive them back, well, what will we win? Arms and horses, both the worse for war." He shook his head. "And Lot is far enough from Celliwig that there is little the High King can do at this stage to enforce his will. Lot will find some excuse, a plague of flux or weather washing out the roads, and if he arrives, it will be too late to be of service."
"All the more reason for us to act with honor." The king set his chin firmly, and Gwen silently cheered. She felt better for seeing him so alive again and more like his old self.
The talk around the hearth was lively enough to satisfy anyone, and Gwen wished with all her heart that she would be allowed to go along with the levies. But she wouldn't be; none of the squires her age were going. Only the seasoned warriors, neither too old nor too young, would be sent. Even the king himself would remain behind, and that was on the orders of the High King himself. Her father grumbled at that, but he agreed that it was a sound decision, once he heard the reasoning.
"The High King is concerned that this might be a trick." The messenger that brought them this news was no mere mouthpiece; it was one of Arthur's handpicked warriors, part of his personal band. "He fears that either the Northerners themselves, or someone who has been scheming with them, is arranging for it to look as if they are preparing for a war when in fact they have no intention of facing us in the field. Instead, once the levies are committed, it is possible that the Northerners will retreat, drawing us after them—and then the real attack will happen somewhere else."
No need to ask where else. "The Saxons," her father spat in disgust. The messenger nodded. "So we need you, ready with a second force, to hold them back if they do push forward."
With Gwen watching and listening, committing everything to memory even though she didn't understand more than half of what she heard, the messenger outlined the possible strategies. Rough maps were sketched out in charcoal on the stones; the best of those were transferred with great labor onto tanned hide with a quill and walnut-hull ink. By the time the messenger left, Gwen's father had nothing but praise for the wisdom of the young Arthur.
There did not seem to be enough hours of daylight for all the preparations, and the warmer the weather became and the longer the days, the more the sense of urgency increased. Now it was Gwen who was up at dawn and hard at it until she almost fell asleep with her work in her hands; Gynath had a great deal to do, yes, but not nearly as much. Eleri had always kept ample supplies of healing herbs and so forth on hand, and there had not been much call for such things in the last year. "Always be prepared for warfare," had been her admonition to her women, and so they always were.
It was about lambing time, when it was possible to move freely about the countryside, and the storms of winter were past and boats could sail, that messengers again galloped among the High King's allies. The High King had been brought word from his spies. The Northerners were indeed massing ships, as if to make a great raid. The levies were called up and marched off to join the High King. King Lleudd made a great show of sending them off and advised the men he sent to make double fires at night, and drag brushes behind them to make it seem that their numbers were larger. Then he told those he had kept in reserve to be ready and to keep their weapons to hand, as Arthur had warned him.
And Arthur was right.
Near sunset, very near Beltane, a messenger on a winded horse rode across the southern border of Lleudd's kingdom of Pwyll, having already come through Pengwen, Calchfynelld, and Caer Celemion. The Saxons of the south were, indeed, massing for war and marching. And Lot of Orkney was about to have a rude surprise, for the Northerners were making straight for the shores of Lothian, not further south. Perhaps it was just as well he had delayed in sending his levies, for they would not have far to march to meet the enemy. Doubtless, he would claim that his wife and Morgana had had some manner of magical warning this was to be so. And doubtless, for the sake of peace, Arthur would accept this, whether he believed it or not.
So said Bronwyn as she and the women methodically passed the readied saddlebags to the squires, who put them on the horses they had already harnessed. The king had planned this to a nicety, so that the warriors could move out on a moment's warning, and the moment there was light, every man, woman, and child was up and putting his preparations into action. The cavalry would go first, followed by the chariots. There would be no men afoot; Arthur would supply the foot soldiers, for Lleudd's levies that had gone north consisted primarily of foot. Arthur had begged him to reserve the troops that could move faster for the Saxons.
The king himself would lead them. And this alone showed how grave the threat was. If he fell, that would leave Pwyll in the hands of three girls, none of them wed.
But he would not fall. Gwen willed it, fiercely. Besides, he would be in his chariot, and his chariot driver was second only to Braith in skill. He would be guarded by his sworn band, who also were well aware of what would happen if he fell.
By the time the sun was three fingers above the horizon, they were ready to depart. Gwen, to her sorrow but not her surprise, was not going. She was not being slighted; no one her age was being allowed to go.
She stood by the king's chariot, looking up at him. Around them, horses stirred restively. Gynath held her hand tightly, but of the two of them, it was Gwen who was the calmer.
"I rely on you, my daughters," the king said, his voice stronger and firmer than it had been since Eleri's death. Gwen could only marvel at how war had made him come alive again. For that, she could actually feel _glad_ about it. "I do not know how long we will be in the field, but come what may, the lands have to be tilled, the flocks tended, the harvest brought in, and the rites celebrated. You must see to it that these things are done, and done well."
Gynath looked up at the king, her eyes bright with tears, so it was Gwen who answered. "We will, my lord."
He nodded. "Now hear me well. I expect to return, in triumph. I _plan_ to return. I have every intention of coming back loaded with Saxon wealth, carried on good Saxon horses. But the gods mayhap have other plans. Should the very worst befall, I have left certain orders. Gynath, and you, Gwen, and those who choose to flee are to take shelter with the King of Gwynedd. He is my oldest friend, for we fostered together and swore an oath of brotherhood. I will make no orders other than that. If affairs have gone that badly, let each man act on his own conscience."
He had spoken loudly enough that his voice carried over the crowd, and though there were some murmurs, there was much nodding. Gynath sobbed. Gwen had a terrible lump in her throat . . . but also a strange certainty. King Lleudd would return. There would be others who would not, and she somehow knew there would be great grief for her, but her father would return and, as he hoped, in triumph.
Gynath had no such feeling of certainty; that much was clear from her look of despair. But she had courage. She swallowed back her tears, stood up straight, and despite red eyes and trembling voice, replied, "Yes, my lord Father."
He bent down and embraced them both, kissing the tops of their heads, then released them. As soon as he had, Gwen could tell that his spirit was elsewhere, already down the road, eager to face battle. Fiercely she wished she could go too—
But her fate was already written, and she had to step back and watch as her father took the reins from his chariot driver, and the horses, already impatient, lurched out at a trot.
And then they were gone.
Then came the worst part: the waiting. Gwen was too young to remember much about the last time the levies of Pwyll went to war, but Gynath was not, and Bronwyn certainly was not. Gynath collapsed in an orgy of grief and despair; Bronwyn allowed her two days to wallow in it, then roused her roughly, took her down to the brook, stripped her bare and ducked her in the freezing cold water. Gwen had no idea this was going to happen and only happened to look up from the bowstring she was plaiting to see Bronwyn hauling the weakly protesting girl in that direction.
There is such a thing as curiosity that can't be suppressed. Gwen pinned the string down and followed, just in time to see Bronwyn strip Gynath to the skin and shove her into the spring-fed pond.
The water was ice cold, and Gynath shrieked and flailed her arms wildly trying to keep from falling in.
She failed, of course.
The water was only waist deep, but she came up gasping and spluttering, only to be hauled onto the bank just as roughly, rubbed down with a drying cloth, and have her clothing shoved at her.
"Wh-wh-what d-d-did you d-d-do that for?" Gynath cried indignantly, between the chattering of her teeth. Gwen ran the last few steps to help her get into her shift and gown.
"You've had your wallow. Two days of baaing like a lamb taken from its mum is enough," Bronwyn said, her jaw set. "Your father is very much alive, and you have an example to set. What if every woman in this kingdom went bawling and blethering as if her man was already dead? Straighten your back, go to your duty, and remember that from the time you leave your bed to the time you take to it, you are being watched."
Gynath looked furious—but furious was probably better than weeping. Certainly Bronwyn seemed to think so. She nodded and pointed back toward the castle. With her head erect and her eyes practically flashing, Gynath stormed off. She didn't look back.
Bronwyn simply followed, without acknowledging Gwen's presence. After a moment, Gwen went back to her bowstring.
It was not that long after that Gynath went briskly past, followed by one of the servants, both of them with their arms full of bundles of something. Clearly, Bronwyn's ploy had worked, though it might take Gynath a while to forgive her.
Gynath was present at dinner, very much present, and sitting in their father's place. It actually made Gwen proud of her, to see her sitting there, dry-eyed and talking as their mother had talked when the king was not in the high seat. And when dinner was over, she invited the remaining men to stay at the hearth, picked the most senior of the warriors to take the king's seat, and directed Gwen to tend his cup, before taking the women aside.
"That was well done, tonight, sister," Gwen whispered when she came to bed. She didn't know if Gynath was still awake, but as it happened, she was.
"It was hard," Gynath replied, with a little break in her voice. "And Bronwyn was horrid."
Gwen debated a moment before saying anything. "Bronwyn was right," she ventured.
"Which made her all the more horrid." There was silence on the other side of the bed for a moment, then a sigh. "I wish one of us could See what was happening with Father. At least then I would know."
Gwen pondered this for a moment. "Why don't _you_ try?" she asked.
"Because I—" Gynath began. And stopped.
"What would the worst be?" Gwen continued. "That you don't See anything. You would be no worse off than now, and you'd know you tried."
"I'll . . . have to ask Bronwyn. For help. I've never tried scrying." Gynath plucked at the blanket covering both of them nervously.
"Cataruna went to the Ladies. I'm on the Warrior Path. That leaves you," Gwen pointed out. "You might as well try. You might be stronger in the Blessings than you think. Mother's blood runs strong in all of us." _Even in the brat, Little Gwen._
She wasn't sure where those words were coming from, but they seemed to do Gynath a lot of good. "I might as well," Gynath replied, and the tight sound in her voice was gone.
Gwen, somewhat to her own bemusement, had a real talent for braiding bowstrings and working with the fletcher, so that was what Peder set her to do. The work was exacting enough that it took her mind off her worries and fears, without being so demanding that she felt as if she were being pulled in too many directions at once. The men had taken almost every arrow and spare string with them, for there would be no time to make more on the march, nor when they closed on the Saxons; but that meant that just to have the means to hunt, a lot of work was ahead of those with the skill.
And now that she had rudimentary abilities in fighting—and now that all the older boys were gone—Peder had turned all his concentration on her and the rest of the young squires. This was not a bad thing at all. Such individualized attention meant that instead of being trained as a herd in the same things, Peder was taking the time to assess them, and decide what they might be best suited for. He might not have had that time until they were a year or more older, if it were not for the war. And if they were going to be the last line of defense against the Saxons, or a rear guard on an escape to Gwynnedd, they had better be doing what they were best at.
For some, the choice was obvious. Tall, meaty boys with a lot of sheer brute strength already were clearly made for fighting afoot. To them, Peder now assigned training with the staff, the cudgel, the hammer, the ax. Those with the best eye—Gwen among them—got extra training with bow and spear. Those who clearly were not doing well with their horses either had their difficulties sorted out or were (to their profound relief) dismissed from the chariot and cavalry altogether. Peder spent all of a day studying them, measuring them, looking at their parents, and consulting with the oldest folk in the village about their grandparents, in order to try to determine what they might grow to be like.
And that was when Gwen's own abilities became apparent. "Ye'll never be a giant," was Peder's shrewd assessment. "They tell me for size ye be the spit image of yer grammar and granther on king's side. Except the hair. Otherwise, small and fast and sleekit, not tall, like the queen. Braith was right. Epona put her stamp on ye. And the best place for ye, bodyguard to yer kin and scout. Cavalry or chariot an' ye _must,_ but I'd sooner see ye scoutin'. Ye've got the way of movin' quiet and not being seen that it bain't possible to teach. That's not be from the king's blood."
Now this was a revelation to Gwen, but it occurred to her immediately that this was true: She _did_ have a knack for getting around without people noticing her when she didn't want to be noticed. It had worried her that she was so little and would have to go up against much larger and stronger men. But Peder had found the right place for her, and it was something no one else would have been as well suited to, and she felt suddenly as if everything was _right._
Meanwhile, Gynath had made up with Bronwyn, and part of her day was spent in learning more of Women's Magic, so that she could try scrying as soon as Bronwyn thought she had the strength for it. In fact, Bronwyn heartily approved of the planned attempt. None of the other women had so much magic in them, and the mere fact that Gynath was going to at least try to see what was happening with their men made them all encourage her and look to her.
On the afternoon when Gynath was going to make her first attempt, Gwen found herself at a variation of her old chore taking goose feathers that she herself must have cleaned and carefully stripping the vanes, so that the fletcher could use them to feather his arrows. Of all of those who were left, she was the best at it, perhaps because she had cleaned so many and knew how to handle them. She spoiled very few; most were so perfect that the fletcher had very little to do but trim them to fit and glue them in place.
Her thoughts drifted to Gynath, wondering if she had begun . . . wondering what it felt like to be the center of a circle of Power . . . and that was when the feathers vanished from her hands, and she found herself . . . elsewhere.
On the top of a mountain? It seemed so, but this was not like standing on any real mountain, for she could see everything below her as clearly as if she stood within arm's length. A battle was about to begin.
A battle not between men but between two armies of animals.
On the one side, boars, an army of boars. Huge, brutish creatures, with greedy eyes and long, vicious tusks, with ravens circling above them. Leading them, a white dragon.
On the other side, another army, of mixed beasts: hounds, stags, keen-eyed wolves, with falcons on-watch above, and a great bear leading. Beside the bear, a noble white stallion.
She had only time enough to take this all in before the two forces leaped at each others' throats.
She had no experience of human wars, to know if this was more or less bloody, noisy, confusing, and chaotic. She wanted to look away, sickened by the slaughter, but she could not.
It seemed to go on forever. And then, at last, the boars began to lose. The mixed army drove them back over a field slick with blood and thick with fallen bodies. The white dragon turned tail and ran, leaving the boars alone.
Then it happened; pressing eagerly ahead, the white stallion stumbled over the corpse of a boar. Another, its tusks dripping with the blood of its victims, saw the chance, and leaped for him. Other animals saw what was happening but were too far away; they would never reach him in time to save him—
All but one.
With a high, thin cry, a falcon dove out of the sky, talons slashing at the boar's eyes. The boar roared with pain, reared, and snapped, catching the falcon before she could escape, killing her instantly. But that was enough time for the stallion to scramble to his feet and rejoin the army, which rushed on the boar and slew it before it could even drop the poor, mangled corpse in its mouth.
And then—she was back, dazed, feathers still in her hands. But this time, this time she knew what she had seen. The boars were the Saxon army, for boars were sacred to them. The bear must have been the High King Arthur, the stallion, her own father. And the falcon—the falcon could only have been Braith.
And she had just seen how Braith had died . . .
Heedless of the feathers, she buried her face in her hands, and wept.
**PART TWO**
**WARRIOR**
**Chapter Eleven**
**Gwen's breath steamed** in the frozen air as she looked down on the encampment of Saxon raiders, settling in for the night. She was in a tree at the edge of a natural meadow; they were camped just inside the trees, where the smoke from their fire would be broken up by the branches so that it wouldn't betray them. It was an orderly camp; that argued for a group that fought together regularly, with one man commander over the rest. They traveled lightly, no animals, one pack each, and their weapons. They camped properly, arranged around the fire, pine boughs and bracken over the boughs laid out to keep them off the snow. The fire had been well made in a scrape, so that melting snow didn't overwhelm it and put it out. They thought they were alone in the wilderness, roasting their stolen sheep, counting over their loot. Which was, all things considered, not much; they'd managed to find one poor peddler and had raided a single farmstead. It scarcely seemed worth the effort. They were bold, or desperate, to be making raids on her father's lands this deep in winter.
Unless, of course, they were scouts for a larger force. And if that was the case, they were looking to see what defenses were here once the snow fell and hoping to drive well into enemy territory before any organized defense could move in. The more she considered them, the likelier that seemed. Probably they were counting on the fact that her father was known, still, for his skilled charioteers, and chariots did not travel in snow at all.
But Gwen was not her father, she was her father's guard and right hand, and she had been schooled in a generation that was coming to rely on horsemen. More and more, the king was listening to her recommendations. And at her urging, he had gradually increased the strength of his cavalry over the past several years. His own near-escape in the battle where Braith had fallen had shown him that chariots were of limited use and even an actual hazard on broken ground. Now his chariots were mostly used for massed charges and rescues over good flat land. This year, for the first time, horsemen in his ranks had outnumbered chariot drivers by two to one. Even the High King was taking notice of his tactics.
She had a good idea what the Saxon leader was probably thinking, if that was a scouting force below her. Even if someone saw them and reported their presence back to King Lleudd, the winter would keep him and his warriors bound to their holdings. Meanwhile, the Saxon scouts could roam with impunity and bring back intelligence to the army in time for them to drive deep into this kingdom. Once there, it would be costly to dislodge them. This land was less populous than the area to the east; easier to take, easier to hold, and the Saxons actually tended to be decent to farmers who didn't resist them. If you could stay hidden until the worst of the fighting and looting was over, you'd likely survive. Saxon fighters didn't till the land, and they needed to eat; there was no point in killing the hands that would feed them, so farmers were generally safe. If they could take this country, they might have a better chance of holding it than the lands the High King was pushing them out of.
Ah, but horsemen could go anywhere, regardless of the weather, so long as food for the horses could be found. And all villages within her father's lands were required to put in hay and keep it for the use of the cavalry in winter. That had been another of Gwen's suggestions, and she was unreasonably proud of it. It meant that the cavalry could get anywhere quickly, even in winter, unburdened by the need to bring fodder with them.
The villages were not doing badly by the policy. King Lleudd permitted the unused hay to be fed to local animals as soon as the snows melted, and until this year, that was what had generally happened. Gwen wondered, as she crouched on her tree branch, if the pressure that High King Arthur was putting on the Saxons in the east was making them concentrate on him, and they were not even taking her father's reputation into consideration. Perhaps in concentrating on Arthur, they underestimated a "lesser" king, one who was old enough to be a grandfather to boot.
The tree Gwen was in, though leafless, hid her perfectly. Not that they ever looked up. But she, in her white furs and gray clothing, merely blended into the snow-covered branches and the haze of leafless twigs. She had mastered the art of holding absolutely still for as long as she needed to. And there was, of course, that subtle magic that was all her own, the ability to will herself unseen.
The ironic thing was that Arthur, by all accounts, would have been perfectly ready to accept the Saxon surrender and alliance, would honor their rulers and their customs as he honored those of his other allies, like Gwen's father, and Lot of Orkney and Lothian, and the King of Gwynnedd. But they would have none of this. And so they fought him, lost, slunk back behind their shrinking borders, recovered, and fought him again. In more than fifteen years since her father had sent out his levies, they still had not learned that lesson.
This tree was not in the familiar hills that she had trained in and run over in her first years as a warrior. Over the last several years, Pengwen, Calchfynelld, and Caer Celemion had come into her father's hands, and all peacefully.
First had been Pengwen; when those levies of so long ago had come home amid mingled rejoicing and grief, the young—very young—ruler of Pengwen had come with them, had seen Gynath, and within a day even a fool would have known that the lad had lost his heart. From that moment, the conclusion had been forgone. And because he was so young, his father fallen in that last battle, with the agreement of his own chiefs, he had given over governorship of his land to King Lleudd.
He could have taken his throne by now, but he was not the least interested in having it back. Quarrels among the chiefs bewildered and upset him as a youngling, and as an adult, they bewildered and exasperated him. He hated fighting, he hated having to judge men, and above all, he hated being _looked_ to for answers. He was happier by far doing the work of a steward; he deeply understood the land and the farmers and herdsmen. He had an instinct for what would be a good year, and what would be a poor one; those who followed his advice prospered. And so, instead of ruling, he served as steward and seneschal for what had once been four kingdoms, adored his wife and his children, and was a blessing on King Lleudd's house.
As for Calchfynelld, and Caer Celemion, the entire ruling household of the former had been taken by a rheumy plague one winter, and the latter's king died within an hour of his son on yet another battlefield against the Saxons. Seeing how well and justly her father had dealt with Pengwen, the assembled chiefs of both lands had come to him and begged him to accept their fealty. From the time of Gwen's second year in warrior training to now, the little Kingdom of Pywll had quadrupled in size.
Which was why Gwen was perched in a tree in the winter, just inside the border of what had been Caer Celemion, looking down on the evening camp of a band of Saxon raiders. She had no mind to move just yet; not until it got darker. She was as at home up a tree as under it, as cozy under a snow covered bush as any rabbit, and so quiet and near-invisible in her ghostings about that the men of her troop all said she truly was a "white spirit."
In fact . . . that was what the Saxons called her as well, except that they were sure she was a spirit in truth.
_I should think about that,_ she reflected, as the odor of burned mutton came to her nose. _That could be very useful. There must be some way to encourage them to believe I really am some vengeful phantom._
Peder had been right. And so had Braith. She was Epona-touched; there wasn't a horse in all her father's herds that she couldn't ride. She took to weapons work with the same ease that Gynath danced or Cataruna sang. Clearly, she had been born to walk this path, and Peder's careful weighing of her talents and physical abilities, his selective training, had made her the best scout in King Lleudd's entire army.
Her father was not just indulging her; she was of great value to him doing what she was. And it was not as if he lacked for heirs, for Gynath and her beloved Caradoc had already given him five living grandchildren. If that were not enough, Cataruna had graced him with two more. Four years ago she had returned from the Ladies of the Well not only a Lady full trained but with a bard husband who just happened to be one of the King of Gwynnedd's younger sons and well schooled to be Forest Lord to her Lady of the Fields in all the rites.
Which left Gwen free to do as she pleased, and what she pleased was to serve in peace as her father's right hand, and in war as his eyes and ears, and the eyes and ears of his army.
She bent her ear to the rough talk about the fire; she had schooled herself in the Saxon tongue this past year and more, reckoning it would be useful both in questioning prisoners and in understanding things she was not meant to overhear. It was an ugly speech, harsh and guttural, having none of the lilting beauty of her own, the song of that used down in Cornwall, the poetry of the Gaels, the measured grace of the languages of the east, or even the logic and cadence of the Latin it was said that the High King spoke. Cataruna's husband, Ifan, was the one who taught her all these tongues, and perhaps he had worked some special magic to put them into her head, for surely they came to her as easily as breathing.
An overcast sky meant no sunset; the darkness thickened as the Saxons huddled closer to their fire, hacking chunks of mutton from the carcass spitted over the fire with their knives. They were going short for drink, it seemed, melting snow in a battered pot rather than seeking out a stream. And they were not happy about this thin drink, either; there were muttered complaints and unhappy looks cast at the man Gwen judged to be their leader. He was probably what passed for a lord among the Saxons, and one's lord was expected to furnish good food and plenty of it, along with presents and loot.
There was not much to distinguish him from the rest save for the wolfskin cloak he sported. He might be a little older, but all of them had much the same in the way of arms and armor. Shield, spear, long knife, and a heavy leather jerkin; two had bows, the rest, slings. But the leader had a sword; in fact, from the look of it, Gwen judged it was a Roman sword, probably looted and possibly passed through several generations of owners. She liked the look of it; it was a proper Roman blade, so it was short by the standards of those her father's smiths made. That made it the perfect length for her.
_I should not mind being that sword's next owner._
Then she chided herself. She must keep her mind on those men below, not on their possessions.
The conversation around the fire was remarkably uninformative. The men seemed to be taciturn by nature, conversed mostly in grunts, and were uninterested in discussing the reason why they were here. The best solution would be to take one or more of them alive and beat the answers out of them. She'd learned all she could from them at this point.
She needed to time when she ghosted out of the tree very carefully. There had to be enough light to see her way through this part of the forest and back to her troop, but not so much that the Saxons would see movement.
_"You think King Bear has aught men about?"_ one of them asked suddenly, looking around, as if he had sensed her eyes on him. She froze.
The leader laughed. _"Nay. He be a-casting himself on grave of the she-bear and her cubs and weeping senseless. Mayhap he'll find his man-parts again come spring, but he's throwin' of his apron o'er his head now."_
The others laughed as well, and the first speaker shook his shaggy blond head and went back to gnawing his mutton.
_So that was why they chose now._ It made perfect sense—though she was more than a bit put out that these Saxons had better intelligence of what was going on at the High King's seat than she did. Word _had_ come, just before they'd heard rumors of skulkers on the border, that Arthur's twin sons had died, and his queen had perished of grief for them. The details had been confused and muddied; some said they'd been killed in a boar hunt, some that they had been murdered, and one grisly tale swore it was the High King's own foster brother, now his seneschal, Kai, who had murdered them out of jealousy and in secret, That is, the tale ran, it was meant to be secret, but the head of the fairest had been sent in a box that only the murderer could open, and Kai, all unknowing, had opened it before the whole court.
A boar hunt, well, that made some sense. They were _just_ of an age to participate in such a dangerous pastime. And murder, well that was possible, though less likely. But Arthur had a temper, and if it had been Kai, foster brother or no, there would have been a fourth grave and a new seneschal. On the whole, she was inclined to think it was a boar hunt after all, since one of the few details of that version said that Arthur's favorite hound, Cabal, had died defending them.
But there had been nothing more before Gwen and her troop had gone south and east as fast as their horses could take them. This was fresher news than she had, and she was heartily annoyed.
But . . . there was a certain feeling of grim satisfaction in hearing it, too. So the High King was prostrate with grief was he? Well, perhaps the carrion crows he had set to fly when he'd had all those tiny babies killed had come home to roost in the royal bower. Now he tasted the grief he had given to so many. And if it was the Merlin that had given him that evil advice, well, it was too bad the Merlin couldn't sip from that same cup of gall.
She could not help but think of her father, and her mother, and the little brother who never got a chance to draw a breath . . .
But that thought softened her bitterness. It had been said for many years now that this between Arthur and his Queen was not only a marriage of state but a love match. And she thought of her father sitting hollow-eyed in his hall and thought of the High King doing the same, and her heart turned to pity him.
But only for a moment; more movement below in the thickening dusk alerted her. All the men (except the leader) were settling onto their beds of bracken, their cloaks wrapped tightly about them. The leader had taken a seat with his back to the fire, scanning the open meadow. And, as if the gods of the place had decided to favor her entirely, thick snowflakes began to drift down out of the blue-gray sky.
She began to flex and stretch all of her muscles, from fingers to toes, warming them and getting ready to move. And when she judged she was ready, she moved as slowly and deliberately as a tortoise, backing her way down the branch and then the trunk, making absolutely sure of every hand- and foothold before committing her weight to it. It was the sort of climb that took great patience and a lot more strength than most might think. But she got quietly to the ground without the Saxon leader having even the faintest idea of her presence.
She blessed the snowfall; she had been planning to pull off her gray wolfskin cloak and drag it fur-side down on the ground behind her for a while to muddy her tracks. Now she would not have to. There would still _be_ tracks leading away from the tree, but it would not be possible to tell what had made them. And if she had more luck, at least one of the men would blunder about in there, looking for wood, and further churn up the snow.
At this point, however, night was all but upon her. Now she had to turn to her other trick to find her way. With her left hand, she reached for the trunk of the next tree just at shoulder-height; even though she had good night-vision, she could barely make it out, dark against the white snow. She ran her fingers along the bark, and found the little cut she had put there, pointing the way she should go.
Step by slow and careful step, making sure to make as little noise as possible, she made her way from tree to tree, following her marks. She counted each tree that she passed, and when she had gone far enough, she took a deep breath and called like an owl, three times.
The answer came back. Three calls, then a count to five, then four calls. She followed the sound, pausing now and again, to repeat her call and follow the reply.
She had done this so many times in the past that she had schooled herself to patience. It only _seemed_ as if it took forever to make her way through the snow-filled darkness.
But, at last, she did. She hooted and heard the answer right beside her, and she felt Aeron grip her elbow with one hand. She reached around and clapped him on the back, and the two of them made their way to the carefully concealed camp.
She didn't speak until she squatted down beside the fire and accepted a fire-warmed stone to cradle in her hands. "Small raiding party of six," she began, and made a succinct summary of everything she had seen and heard. "I think we're going to have to take them," she finished. "And get one alive to tell us what they're up to."
The others nodded. "Try to ambush them in the morning?" asked Aeron. "Or see if we can find a better place to bring them down?"
"Morning would be best. They don't think there're any fighters out here, just the odd farmer. They're good enough not to let their guard down, but they're also not as alert as they could be." She let the heat from the stone soak into her. "I want to hit them before they have any inkling we could be here." She looked around her troop; four, counting herself, but that should be enough. Aeron and Meical were the best of the archers. So they would be best put as first and last watch, so they had solid, unbroken sleep. "Aeron, first watch, I'll take second, Owain, third, Meical, last. Meical, wake us all at first light. We'll take them from the forest, and I only need one living."
The other three nodded. Aeron wrapped his cloak tightly around himself and ghosted off into the night. They set a proper watch, regardless of conditions, with the sentry making irregular rounds outside the camp. She smiled to herself. She could not have asked for better men.
The rest of them took heated stones from beside the fire and curled up around them to sleep. Like the Saxons, they had made beds of bracken to keep them off the snow. Tolerably comfortable, actually, especially situated as they were in the heart of a thicket, screened from wind and most of the falling snowflakes.
_Sleep when you can. Eat when you can._ Reminded of that second of the warrior's rules of the field, she rummaged out a lump of cheese and some cold rabbit from the common food pack. That was the one good thing about a winter campaign. Food didn't go bad; you didn't have to subsist on rock-hard journey bread and dried meat. If you had it in camp, you could take it with you for a good wholesome meal. She ate quickly and neatly, licked her fingers clean, then ate a handful of clean snow for a "drink," curled up around her own rock, and went straight to sleep.
Luck was with them. When the troop eased up toward the Saxon camp, five of the men were still asleep, and the sixth was nodding over his ax, his back warming at the fire. Gwen signaled all of them to leave the rightmost man alive. They nodded and spread out a bit, to get a better field of fire. Her shot would be the signal to the other three.
She lined up six arrows point-down into the snow, then put a seventh on the string. Seven. Always her lucky number. She pulled back her arrow, sighted carefully on the lookout, and let fly.
The first missed, lodging in his shoulder. But before he could shout, her second took him in the throat. Her third and fourth went into one of the sleepers, as two more arrows hit the sentry before he could slump to the ground, her fifth and sixth went into the next sleeper, and her seventh into a third. By that time, all of the men but the one she had designated as the one to save were feathered with four to six shafts, all without any of them uttering a sound. The last one woke by being kicked over by Aeron, to find three swords pointed at his throat.
He tried to get up and fight anyway. That didn't last long. He was lying down, and although his ax was at his hand, there wasn't much he could do before a vicious slash to his arm opened it up from wrist to elbow. Aeron was the best of them at sword work; he managed to keep from cutting the man open so badly he would bleed to death before they got any information from him.
Gwen had stayed well out of his line of sight, letting the men disarm him and tie him up. She had an idea; she didn't much like the results she had been getting from beating information out of prisoners—it tended to be wrong as often as right, and there was no way of knowing which. She'd talked this over with the troop this morning; they had agreed with her on that point and decided to let her try something different.
One of the things in her kit was powdered chalk; she dusted her hands with it when she was going to attempt a difficult climb or when she was unsure of her grip on a weapon. While the other two kept the prisoner busy, Aeron came over and helped her dust it all over her face. She held her breath to keep from inhaling any of it, then did the same with her bare hands. Then she took off her cloak, and unbound her hair, and approached the prisoner from behind, naked sword in her white hands.
Owain wrenched him around when she was in place and forced him to his knees so that he gaped up at the white-faced, white-haired, gray-clad virago glaring down at him.
His eyes registered his shock. She smiled.
"Do you know what I am?" she whispered in Saxon. She had reckoned that whispering would be more impressive than speaking.
His mouth worked for some time before any words came out. "Th-th-th-the White Ghost!" he stammered, sweat starting all over his greasy brow.
She leaned down slightly. "Yes," she breathed. "And I eat men's souls. The bodies I leave for my black chickens."
As if on cue, several ravens, attracted by the red blood soaking into the white snow and made bold by winter hunger, alighted in the tree branches above her, calling. She did not bother to keep the glee from her face. This could not have been timed better if she had planned it.
His face had been white with pain and fear, but now every vestige of blood drained from it. She leaned forward a little more. "I have feasted upon the spirits of your companions," she said, narrowing her eyes and smiling as if sated. "And I am inclined to let you live—if you tell me what I wish to know."
She straightened, and allowed the smile to slip from her face. "You might as well," she added. "I will have it from you anyway."
By the time the man fainted, he had told her everything he knew. Not a great deal, but it was enough. Indeed, this group had been advance scouts to test the borders of Pywll, moving ahead of the Saxon army. As she had suspected, they were making a push here, but not only because of the pressure that High King Arthur was putting on the Saxon kingdoms in the east; they hoped to flank him by spring, and when his army rode out again, to cut it off from his lands and supplies.
As her men looted the bodies—and she made a good trade with Owain, to whom the short sword had fallen, her longer blade for the Roman gladius—they discussed this. She glanced over at the unconscious prisoner, belting on the new blade.
"I have an idea in mind," she said, finally, as the other three debated the merits of trying to haul him back with them or killing him outright. The men broke off the discussion, which was getting a little heated, and gave her silence. "I'm thinking we should take off his thumb so he's spoiled as a warrior and turn him loose to make his way back to his lines."
They stared at her in utter astonishment. "But—why?" Aeron asked, finally.
But Meical had the answer already. "He thinks you be a thing uncanny, lady," the eldest of them said, slowly. "And you be wanting him to take that back with him. That King Lleudd has some terrible spirit bound to his service. Ghost, fae, witch, any or all. It doesn't matter, the tale will grow in the telling."
She nodded, and looked to the other two. "What say you?"
Aeron grinned broadly and spread his hands. "Peder'll be proud, girl. He'll wreak more havoc on his own with his tales than we could with a hundred men."
Owain finally chuckled. "Aye. Aye. I'm for it."
She wiped the chalk off her face with the fur of her cloak. "Right then. Take the thumb so he can't use an ax or any other weapon. I'll not send another fighter back to them. Cauterize the stump and that wound in his arm, and leave him with food and water enough to get back to his lines. He'll leave a trail a blind man could follow. Aeron, you and Owain ghost after him, make sure he actually _gets_ there, and come back to our lines when you see the Saxon army so we know where they are. Meical and I will get back to our people and report."
Aeron gave the old Roman fist-to-shoulder salute some of the men, particularly those that had served with the High King, still used. It was the first time, however, that anyone had ever given it to _her,_ and she felt warm inside. "As you will it, lady. 'Tis a privilege to serve you."
That warmth stayed with her for the long miles back to the main camp, better far than any heated stone.
**Chapter Twelve**
**"Medraut is here."**
Those were the first words to greet Gwen as she and her troop rode into the camp of the small force her father had sent with her. Aeron and Owain had caught up with her easily enough; she and Meical had been taking their time, and Aeron and Owain had made sure to harry their Saxon along by making uncanny noises at night. The wound to his arm and the loss of his thumb were both painful of course, but in the winter after being cauterized, they were unlikely to fester and were not going to slow down a seasoned fighter significantly. These Saxons were tough, and a seasoned fighter would have survived other, more serious wounds than that.
According to the men, he hadn't even stopped to make camps; he'd make himself a warm nest with whatever he could find when it was too dark to keep going, sleep till dawn, and move on as if demons were after him. _"Or as if you were,"_ the men had joked. He had stumbled into his own army within three days, and that was when Aeron and Owain turned back and put on all speed. The weather had remained good, and the snow was not too deep; her father's sturdy horses made good time in it.
So they knew now where the Saxon army was and that it was waiting for word from the scouting parties—for the ones they had come across were surely not the only ones. And Gwen had done something that, she hoped, would make the night a hell of fear for any more small groups the Saxons would send out. The White Phantom was hunting them, the Fair Apparition knew them, and being unsure if she was mortal magician or fae or even some bloody-handed goddess, they would be looking for her in every shadow. It gave her great satisfaction to imagine them so. And she knew men on campaign; they were greater gossips than any girls. The tales would only grow in the telling. If the commanders were foolish enough to forbid their men to speak of the White Phantom, it would only inflame them further.
Gwen and her men rode in to the camp on a bright, crisp, sunny afternoon having made all speed with their news, and she knew thanks to her work that a messenger sent to her father would have a substantial force here in plenty of time to give the Saxons second thoughts about invading. Her spirits were high, and with good luck she would see some fighting.
Above them was a sky of cloudless perfection. Before them was the camp, laid out in ordered rows. "Roman style," was what Peder said, though he would never, ever have used those words to her father. But Gwen now knew exactly what he meant. The Romans had perfected the art of making a defensible camp, and High King Arthur was not above using that art. King Lleudd's war chiefs and captains had learned it from him, found it good, and adopted it.
Such a camp could be made in much less than half a day in summer; in winter, it was oddly much easier. Square in shape, and surrounded by a ditch and wall system, it was possible to make snow walls higher and faster than dirt or brush walls, and in place of a ditch, simply making a fast fire of brush, allowing the snow to melt and freeze into ice served the same purpose. There was an entrance to the camp in the middle of each of the four walls, guarded night and day; the tents and pavilions inside were arranged in orderly rows, every tent was always in the same place in every camp, and if those tents were not as uniform as the ones that the Roman army had once had, at least it was possible to know exactly where everyone was in the camp. In the event of an attack, that was vital.
This wasn't a huge force or a huge encampment, not like the big Roman ones, which had held tens of thousands. Only a couple of hundred—just enough to for hit-and-run delaying tactics in case there _had_ been a Saxon army actually marching across the border. It looked very peaceful, with the horses picketed neatly, the stacks of hay brought from the nearby village, each man with his cook fire going. Almost like a village in itself. But peace was not what they were here for, and she knew the others were chafing for some fighting just as much as she was. Strange thing about winter—some people nearly went mad with inactivity, and some just contentedly drowsed the dark days away. She, it seemed, was one of the former. The ambush of the scouting party had only whetted her appetite for more.
But her good humor came plummeting down when the first person she met—aside from the sentry who challenged them—was Peder, who greeted her with those warning words.
Medraut. Son of Lot of Orkney, now eighteen years old. The only person she wanted to see less than Medraut was the woman he had married, her sister Gwenhwyfach.
Which, of course, utterly ruined her mood. She pulled her horse up; he was not happy about being halted so close to his picket and that lovely, lovely hay, and he curveted restlessly despite his weariness. Peder stepped back from him; this was her warhorse, Rhys, one of her father's famed grays; it was not safe to be too near those hooves and teeth if a mood was on him. "What is _he_ doing here?" she demanded sharply. There was no need to mince words with Peder; her old mentor knew exactly how she felt about the little pest. She had good reason for her dislike.
It had all begun five years after Anna Morgause had taken Little Gwen off to foster. The Queen of Lothian and the Orkneys had been making a state visit to the High King, which was a politic thing to do every so often, and had made sure to include in the journey a long pause at Castell y Cnwclas so that Little Gwen "could be with her family." And it had been unpleasant enough to have Gwenhwyfach swanning about, trying to lord it over Gynath, doing not a bit of work but making plenty. But that was not the end of the unpleasantness, for Anna Morgause had brought Medraut with her.
Now, when this planned visit had been announced, Gwen had thought that her worst difficulty was going to be with the queen herself again and attempts to work magic on King Lleudd. After all, this visit might just have been another excuse to lure her father into marrying Morgana again. Morgana was five years older now and still unwed; Pywll was four times the size it had been. King Lleudd had been a tempting prize before; now he was a brilliant one.
But she made no attempt to work magic, and old Bronwyn was watching her like a cat at a mousehole. Not only Bronwyn but also Gynath and just about every other woman that had been involved in thwarting the queen the last time.
It was not Anna Morgause that caused any difficulty; it was Gwenhwyfach, and that was merely petty. Gwen managed to avoid everything but feelings of irritation, and if had only been that, the visit might have been inconsequential enough.
Except for Medraut. It was absurd that a five-year-old child should trouble Gwen—yet trouble her he did.
Gwen had disliked him as an infant, and in her opinion, five years had not improved him. He was simply nothing like a normal child. He was thin, preternaturally agile; he looked more like an adult who had somehow been shrunk to a miniature size than like a child. He didn't play with other children. He didn't play at all. He was either somewhere doing secret things or . . . well, not underfoot exactly, but always there, nonetheless. His mother seemed to allow him to go where he wished and do as he pleased without supervision. And for some reason, he decided that what he wanted was to attach himself to Gwen.
He followed her about as much as he could, always watching her; he'd have followed her _everywhere_ if she hadn't figured out that there were places he wasn't welcome, like the stable and the practice grounds. Horses disliked him, as did dogs, and a small child was forbidden from being on the practice grounds; it was too dangerous. There, at least, she could escape him.
She could not account for how he made her feel, since no one else seemed to have that strong a reaction to him. She couldn't help herself. With his smooth cap of black hair, his thin little face, and those flat gray eyes that seemed to be looking for secrets, he made her skin crawl.
She couldn't escape him at meals, though, nor any other place where he knew she was supposed to be serving as page or squire. He never said anything to her, never interrupted her. He would simply be there, tucked into a corner, staying out of the way. And he just kept staring at her.
That is, that was what he did right up to the point where the queen's party was due to leave. That night, as she was serving the men and had gone to refill her ale jug, she felt a grip on her elbow and looked down into his flat gray eyes.
"I am going to marry you," he announced. A command. A princely command, from a prince to a servant. It was not the way a normal child would have said such a thing, with the silly baby-love some little boys got with a pretty woman, or in the manner of a joke, or even as if it were something he had overheard his mother discussing and was parroting. It was . . . imperious. It sounded as if it was something he had decided for himself without any coaching from Anna Morgause. And he spoke the words as if he, and they, were very, very certain. It made her skin crawl.
She stared at him, then laughed uneasily. She decided that the best way to deal with him was to treat him as . . . well . . . a child. Even if he wasn't acting like one. "Go away, infant," she replied, with a lift of her lip. "Or I will tell your mama that you have gotten into the mead, and you are making up lies and silly tales. You are too young to think of marriage, and even if you were not, I am not for your marrying."
She pushed past him and went back to her serving . . . but she could not help the strange chill that went up her back. The relief she felt when they were all gone on their way was so intense it seemed to brighten everything around her for days.
The next time she saw him, he was ten, and the years had not changed him, except to make him taller and even more uncanny. At ten, he was a full two heads taller than any other child his age—and he seemed more like a miniature man than a boy. He was Gwenhwyfach's great pet and Anna Morgause's pride. By this time, Cataruna was back, established as the Lady of Lleudd's lands, and the queen sought her out on all possible occasions in order to discuss matters of magic. For the most part, Gwen had very little to do with that, but it was impossible to avoid some of it. Anna Morgause expected great things from her youngest child, and she went on at great length about how powerful, magically, the boy was.
"If I have no daughters, the gods have chosen to give me a son as gifted as any girl," she asserted. And Cataruna (somewhat reluctantly, Gwen thought) agreed. At the time, Gwen wondered if that was what made her so uneasy around him. Men's Magic was that of the Druids, who did have to do with the warriors . . . maybe it was that unpredictable vision of hers that was trying to tell her that the child was strong in such things.
But after only a day, she knew it was not that. It was that Medraut was obsessed, unnaturally obsessed, with her.
At least this time he did not follow her about, but every time she was near him, she was acutely conscious of his eyes on her. More than once, she suspected he was trying to work some sort of magic on her—as mad as it would have been in anyone else, she had more than a suspicion that he had not given up his idea of marrying her. But if he was trying to bespell her in anyway, it didn't work.
Horses still disliked him, and she had every reason to be with her horses now. She was training her new warhorses, two of the best grays from her father's herd—Rhys and Pryderi. They were her sole care at the moment, for she was about to join the ranks of the real fighters and would need her warhorses.
Anna Morgause was there for more than just a familial visit. This time, however, her designs were not on King Lleudd, and Morgana had not come with her. No, she had other plans entirely, although they did involve marriage within the king's family. By the time she left, Gwenhwyfach had been handfasted to the repellent boy; they would be formally betrothed in a year and married when he was fourteen, and Gwen had strong hopes she would never have to see him again. After all, Orkney was far from Pywll, the boy was anything but a warrior, and he was to be married to her sister, which _should_ put an end to his uncomfortable obsession with her.
No such luck, it seemed.
And once she reported in, it seemed her luck was out even further. "Prince Medraut wishes to have speech of you," she was told by the war chief, in a tone of voice that said _and you had best go see him now._ Evidently, Prince Medraut was considered a Personage of Importance now. Reluctantly, she made her bow to her commander, and went to find him.
It wasn't hard. All she had to do was look for the showiest pavilion. It stood out in the encampment, with its decorations of red and black leather, its banners, and its utter new perfection. No one else had such things. The tents here had weathered many campaigns in all conditions and seasons, and they showed it.
And, of course, there he was. He was wearing all black: black cloak, black trews, black boots, black tunic. The only relief to the black was the silver penannular brooch holding the cloak closed at his throat. It was expensive, all that black. Black faded and needed to be redyed often. His was perfect. He was making sure he would be noticed. He invited her in, as his bodyguards stood one on either side of the tent entrance. The very idea of going into his tent made her want to turn and find her horse and ride as far away from him as she could. She demurred, politely, though. He was a Prince of Lothian and the Orkney Isles, and she was a Princess of Pywll. "I would not inflict my person on you at this moment. I'm straight from the field, and I stink of horse, Prince Medraut. And blood," she added, though she was rather sure that it wasn't the blood that would bother him.
Sure enough. "You do smell of horse, a bit," he said, wrinkling his nose. "I wanted to tell you of the news from my court in a more private surrounding, but . . ." His flat gray eyes did not warm with humor, or with anything else. "Well, everyone will learn this soon enough, from my servants if nothing else, so no harm if we're overheard, I suppose. First of all, my mother is dead."
He announced this in the same matter-of-fact tone that she would have associated with "I've killed a deer," or "one of the watchdogs died," so for a moment, she was so utterly taken aback that it took her a while to stammer out, "My condolences, Prince—"
"Oh, don't bother, the cow got what she deserved," he said, his eyes finally glinting with cruelty, which took her so by surprise that she actually lost her breath. "Two of my brothers, Gwalchmai and Agrwn, found her with a lover. Somehow, they were all too thick to realize she's had more lovers than a queen bee, but this time they caught her in the middle of making the two-backed beast. They killed her and him." He shrugged. "He was the son of one of the High King's allies, so there will be trouble over it, I expect. But it was the price of stupidity, and she was getting more stupid every year. Eventually someone was going to catch her, and if it had not been my brothers, it would have been someone else that King Lot could not ignore. Even if it was him that was her pander more than half the time. She had the appetite of a cat in season. My Aunt Morgana has more sense than the lot of them put together."
Gwen was so shocked, all she could do was stare at him.
"But that's not why I'm here," he continued. "I'm going to my father's court to present myself to him now that she's gone, and you should hear that from me."
She blinked, unable to understand. "Haven't you just come from there?"
He curled his lip again, and gave her a look of disgust. "Not Lot's court. My father's court. My blood father." When she failed to understand, he heaved an exaggerated sigh. "Arthur."
Her jaw dropped. "Arthur?" she repeated, stupidly.
He nodded with some satisfaction at her shock. "And now that there're no little princes in the way, I expect my dear blood father will be pleased to see me. He has no obvious heir, after all. His other sons also seem to have had tragically short lives. So I need you to promise me some things. Morgana gave me some good advice, and I am going to take it. First, I don't want Arthur to know I'm wedded to your sister. At least, not just yet."
Not that she was going to get anywhere near the High King to tell him, but—"Why not?" she managed.
"I'm trying to replace his sons. I'd rather he thought of me as a helpless little lad whose mother has just been rent from him. Someone in need of pity, comfort, and guidance from someone other than King Lot." Somehow, in that moment, Medraut . . . changed. In an instant, his face seemed to grow rounder and softer, his eyes larger and brighter and infinitely sad. His lower lip quivered ever so slightly.
In the next moment, he was back to his normal self, as always, looking like a man far older than his years, with eyes that belonged in the hardened face of someone like Peder. If Peder had no conscience at all.
"You can see how being married would interfere with that," he pointed out.
She nodded, finding herself agreeing with him, although she really did not want to.
"Second, don't tell anyone I have the Gifts." His eyes bored into hers. "That's something no one at the court needs to know. Ever. I don't want the Merlin to know, nor the Ladies. I've had good training at Morgana's hands, she has promised me more as I need it, and I don't feel as if I need to undergo it all over again."
Again, she nodded.
"Good. Thank you, fair sister." He smirked. "Fair indeed. I hear they have taken to calling you 'White Ghost.' That you frighten the Saxons. That they think you are some uncanny creature out of the spirit world or the realms of the elves."
She had felt so proud of that, but it felt so . . . foolish when she heard him say it. "There's no accounting for what soldiers will say," she replied harshly. "The Saxons don't believe that a woman can be a warrior, so they have to have some foolish explanation about why and how I can best them. It doesn't matter to me what they think I am. I do my job, and I am good at it."
"So you are," he replied, somehow making it sound as if he meant the opposite. "And, of course, there is nothing magical about you at all. Now remember. Keep my secrets."
"I will," she replied, and he turned and went rudely back into his pavilion, dismissing her as if she had been a churl and he—
Well, he was a prince. Rather more than just any prince, if he hadn't been lying. Arthur's son . . .
She didn't put it past him to lie . . . but somehow she didn't think he had this time. She turned _her_ back on his tent and went off to her own tent and the single camp servant she shared with her troop, intending to get something to eat. Most of the men did their own cooking over their own fires; she had always found it better to forego some of the duties her servant would have done in order to make sure that everyone under her command was properly fed. And it was only as she was sitting with her troop, alternating bites of hard camp bread soaked in the gravy of the ever-present stew with bites of the stew itself, that many things she had already known suddenly fell together into a pattern.
That Medraut, as a baby, had looked as if he had been born before his time because he _was_ born before his time. That he should have been born at the same time as the High King's twin sons.
_At the same time as Eleri's son . . ._ she thought, and hastily shoved the thought away.
But . . . that meant he had been conceived at the time of the Great Rite. At the very wedding, the celebration that Lot and Anna Morgause had traveled to in order to pledge their fealty.
And that was when the world went to white about her, as it had not for many, many years. The bowl and bread fell from her nerveless fingers, and she heard, as if from a great distance, Owain and Aeron shouting, and felt hands catching her. But that was of no matter, because of what she was seeing . . .
Anna Morgause, alone in a luxurious tent, lit by a dozen candles, and much younger than when Gwen had last seen her, working . . . well, magic.
Some sort of magic.
Impossible to mistake it when the whole tent glowed with power, when there was a knife of white bone in her left hand and one of black flint in her right. When there was a tiny cauldron steaming over a charcoal brazier at her feet, and when there was a litter of small objects around that cauldron. Most of what she was doing was hidden by the woman's body. The woman's nude body. But when she turned, Gwen could see that she was written all over with signs and symbols in what could only be the blood of the black cat that lay dead on the floor of the tent beside her. And she had turned because a man had come into her tent.
He was tall, handsome, with a warrior's body. He was somewhere between dark and fair, with a young man's beard. He moved as if he was walking in his sleep. Anna Morgause smiled and drew him to her. The High King. It must be he, though Gwen had never seen him.
Then there was a moment of darkness. When it cleared, it was Anna Morgause surrounded by women, now in a stone-walled room, another brazier burning brightly, crying out in the throes of giving birth. And at the same time, overlaid onto Anna Morgause, Gwen saw another woman, a second woman, in another stone-walled room, fair-haired as Gwen herself, and even in the middle of her travail, beautiful, also giving birth . . .
Darkness passed across her eyes again. Again it cleared.
And then . . . she saw a new scene, a single bright space in the midst of the darkness. In the center of that, the same enormous serpent she had seen fighting the bear, striking at two handsome young man-boys, who must have been Medraut's age. They fell dead without a cry.
And then she found herself lying on the snow with men around her, anxiously looking her over for some sign of sickness or a hidden wound, patting her face, putting snow to her forehead. It was Aeron who saw the sense in her eyes.
"Thank the gods, you're back with us!" he exclaimed. And before he could say anything else or try to prevent it, she struggled herself into a sitting position.
"I won't say I'm all right, but I'm not ill, and I'm not injured," she assured them. "This is just—it's part of Epona's touch on me, I think. I See things. Not often, this is the first time in—in years. It's harmless enough—" She let Peder chaff her hands in his, because she was cold from lying in the snow. And she considered what she might say. "It was something Prince Medraut said to me, the bloody news he brings to the High King. His mother's been kin-slain by his brothers. Anna Morgause is dead. I Saw it happen; I suppose Epona wished me to act as a sort of witness to such a terrible deed, in case a witness was needed."
That was enough to shock them all into silence and take their minds off her for long enough for her to get to her feet. "Let me get some drink and food into me, since I've managed to drop what I had."
Peder came out of his shock first. "Aye, lady, and I'll have someone put a hot stone in your bedroll, and when you've done with the food, you'll be going there. I know a little about these matters; when your sister does a Seeing, she needs rest after. You're no different, and you should do the same. Your father would have all our heads if summat was to happen to you. Do I need to find a Lady?" He looked so worried over her, she wanted to pat his head and tell him kindly not to be such an old hen. But she didn't. For one thing, she knew that, like her sisters, like Queen Eleri, she looked absurdly young, a fact that caused her much irritation when those who did not know her treated her as if she was merely Medraut's age and barely more than a squire. For another, her head really was still swimming, and for once, it was nice to be cosseted.
She shook her head. "This will be something they already know, I think," she said truthfully. The Ladies had ways of seeing these things that were more reliable than her own unpredictable visions. "And I'll be fine. I just need to sleep."
"Sleep you'll have. I'll make it right with our commander," Peder promised. And then, when she had eaten what she could, he escorted her to her little tent himself and saw to it she was rolled up in the now-warmed furs and blankets. As she settled in, another unpleasant thought occurred to her. Those infants that Arthur—or the Merlin, through Arthur—had ordered murdered. What if the reason he had done such a terrible thing was that he had been trying to be rid of Medraut?
She could almost . . . almost . . . forgive him, if that was the case. Medraut as a child made her want to shove him down a well. Medraut as a boy-man made her want to run to some land where he could never, ever go. Or . . . shove him down a well and fill the well in after him. What would he be like as a man grown?
As the High King's son?
Well, it wouldn't matter. He was married to Little Gwen. He wouldn't bother her any more.
She honestly could not remember what she had felt like the first two times this had happened to her, but she had a killing headache now. It made it hard to think. She reached for the skin of mead that Gynath had insisted she take, not to drink for pleasure, but as medicine at need; it was her mother's special recipe, and Gwen reckoned that if it calmed anger, it might just calm a headache too.
She gulped down a good tankard full, and after a while the headache did ease, and she felt muzzy-headed and sleepy, and then, she slept, dreamlessly.
**Chapter Thirteen**
**T** **he scouts' Gwen's** troop among them, had been ghosting about the Saxon army camp for a week. "Ghosting" was the right word, too, because it had soon become clear that Gwen's trick with the Saxon they'd let go was bearing fruit past all expectations. No one ventured outside the bounds of the camp at night. Even by day, no one went alone. Three spies had been sent in under the guise of selling the Saxons grain; they came back out again with a cart full of loot that had been traded for the food and a much richer store of camp rumors.
As a consequence, all the scouts had taken to doing what they could to add to the rumors of the White Phantom. Cries and screams in the middle of the night, for instance—not too often, or the Saxons would get used to them. And nothing that was obviously masculine either. But there were a couple of lads whose voices hadn't broken yet who could manage a very convincing female laugh or sob, and young as they were, they were carefully shepherded to the edge of the Saxon lines to give their little serenades.
When Gwen herself got involved, the nights got even more interesting. Since she knew Saxon—and seemed to have exceptionally keen ears—she would linger around a particular section until she had picked up on someone's name. Then, in the middle of the night, she would utter a blood-curdling wail, ending in the words, "Horsa"—or Ordulf, or Sidric, or whoever's name she had picked up—"Tomorrow I come for _you."_
She tried to pick very common names, the better to give Fate a hand in giving her a victim. And more often than not, Fate gave her one. Where there were armed and edgy men, there were always accidents and quarrels. Where there were armed, edgy, men convinced that a supernatural agency was after them, the accidents and fights were fatal or near-fatal as often as not. A man who is sure he is going to die will do so even from a minor wound. By the time the king's full force arrived, it was a full moon again, and Gwen had been emboldened enough to show herself.
Never for long. There was no point in risking a lucky bowshot. But by now she and her scouts knew every inch of land around the Saxon camp, and they could, in the shifting clouds and moonlight, make miraculous appearances and disappearances. So at one moment, a hilltop would be empty of all but moonlight, then suddenly a sentry would shout in fear, for the White Phantom was there, silver rider on silver horse, staring down at the camp. Then a cloud would obscure the moon, and when the Saxons looked again, she was gone.
It was very effective.
And by now there were desertions, not many, but enough to make the commanders angry, and angry commanders faced with desertions often make poor decisions regarding the treatment of their men. When you added to that the fact that those same men were not eating as well as they expected, had not had much loot, and their lords were running out of presents . . .
So it was that once King Lleudd's men were rested and ready to deal with the Saxons, the Saxons were not nearly in as good a condition to deal with them.
The night had been an active one for Gwen and her troop; with a good moon and intermittent clouds, they had taken full advantage of the circumstances to bedevil the Saxons almost until dawn. There had been little sleep in that camp, and the lot of them had take to their bedrolls with weary satisfaction. A few more nights like this one, and the Saxons would be falling asleep on the battlefield.
She woke to hear a great commotion in the camp, and she was on her feet with her sword in her hand and her blankets cast aside before she realized that this was not the sound of an attack. Men shouted orders, but not in the tone of voice that indicated trouble; horses were clearly being brought in and picketed. It sounded as if a substantial addition to King Lleudd's troops had arrived.
_Well, any additions are welcome._ She couldn't for the moment think who would have been able to muster out winter fighters, but it didn't matter. She would find out soon enough, since she had best pull on a good tunic and present herself to welcome them. She might not be a general, and her actual rank was low among the officers, but she _was_ King Lleudd's daughter, and as such, it would be an insult not to greet and thank the new arrivals.
Her servant was of the same mind, for even before she had started to shiver, he came diffidently into the small tent, prepared to wake her if need be, with her best leather trews and embroidered wool tunic in his hands. She laughed at his relief—she was not known for waking gracefully—and pulled the clothing out of his grip. "Go wake the others," she ordered, "I'll be ready quickly."
She normally kept her hair tightly braided and clubbed like a horse's tail, so it was tidy enough not to need combing out and rebraiding. She cast aside what she had been wearing, smelling of horse and sweat as it probably was. The gray wool trews and leather tunic could use a good beating and cleaning in snow, and the linen shirt could stand a boiling. She hopped from one foot to the other, shivering as the cold air bit at her, dressed again from the skin out in good clean linen and woolen hose, then pulled on the trews and wriggled into the tunic. She reflected wryly as she did so that among the captains, war chiefs and generals she was going to stand out as much as that pest Medraut had; the trews were white doeskin, and the tunic, unlike the festal garb of most of her father's folk, was _not_ a checkerboard of bright colors, with contrasting bands of embroidery at hems and neck. Her best tunic was light gray, with silver and white bands. Somehow, she realized, she had come to have most of her clothing made in these colors, as if she were trying to live up to her name. And, thank the gods, it was so stark as to give her too-youthful face a more serious cast. There was nothing she could do about the fact that her cheeks were not scarred, browned by the sun, weathered by the wind. Nor could she change that she had not so much as a sign that she was more than old enough to be a mother six times over by now—twenty-five, and she looked sixteen at best! But at least she could look as serious and remote as a vengeful spirit.
_Bah, it is more that I am trying to look as unlike Gwenhwyfach as possible,_ she thought, a little crossly. Her sister, the last time she had seen the chit, was as profligate in her love of opulent, showy dress as Medraut was—except she did so in colors rather than stark black.
Well, no matter. All things went to serve a purpose, and she would stand out, which was good, but not in an ostentatious way or as if she were trying to, which was also good. And the clothing had been laid up in lavender and meadowsweet, so she would smell less of horse than usual. She opened the small chest that held her few jewels, bound the silver fillet around her brow, got out her silver torque with the horsehead finials, and put it on and fastened her cloak, not with her old bronze brooch, but with the silver Epona brooch that had been the latest gift from her father. Stamping her feet to settle them in her soft boots, she pushed aside the tent-flap and headed in the direction of the tent of War Chief Urien, who was the chief of all her father's generals. That was where newcomers of importance would be taken.
It was the largest tent in the encampment, and that was needful, since outside the hours of sleep, it had to house the table where the maps were laid and strategy made, and in the hours of sleep had to hold Urien's entire personal band of companions, some twenty men in all. Companions of this sort were men who did nothing other than hold themselves ready to fight; they held no lands, and they got all their substance from their chief. This was a Saxon custom not often found among Lleudd's folk or the other tribes north of where the Saxons held sway. But Arthur had adopted the practice, making the sons of his underkings into his band of companions and setting them, it was said, about a round table that had neither head nor foot, as a sign that there were no "greater" or "lesser" men among them, that all were equal. Shrewd, that was. Supposedly he had got the curious table, which must have been enormous, as part of his queen's dower.
His now-dead queen . . .
_To think I envied her as a child._
At any rate, Urien followed the High King's example, and Lleudd saw no harm in his doing so, though he himself did nothing of the sort. Having to haul around so large an expanse of canvas and hide was a nuisance, but Gwen was glad of the shelter and relative warmth in this winter campaign.
Outside the tent was all astir with men coming and going with purposeful looks and brisk paces. She winced a little at the bright light; being out so much at night . . . she smiled to herself, thinking she was as sensitive to the sun as the spirits she was imitating, now. She did not have to push her way through the crowd, even though she was a good head shorter than most of them. Those that did not personally know her made way for her anyway. After all, there were not that many woman warriors in this camp, the fact that Lleudd's daughter was the head of the scouts was widely known, and dressed as she was, there was no mistaking who she was. She pulled aside the tent-flap and entered unannounced.
Inside the great table had been set up and the hide maps that she and her scouts had drawn up laid over it. All of the war chiefs and generals had gathered about this table, and all of them were listening with rapt attention to a young man not much older than she.
He had plainly come straight off his horse and into this meeting; there was horsehair no servant had yet brushed off clinging to his cloak, and his dark hair was all sweaty and askew from the helmet he had taken off and set aside. He was still in armor too, chestnut-colored leather breast- and back-plate over softly gleaming chain mail that she immediately craved in a way that she had never craved fine gowns. He was not handsome, his face being too craggy for beauty, but it was full of intelligence and character, and his voice was as worth listening to as that of any bard.
". . . and obviously, as I am sure you have already seen, we want to find a way to force them up this slope," he was saying, as he arrayed handfuls of wooden counters representing the Saxons onto the map. "It's not so steep they'll even think twice about charging it, but every time we force them to charge, they'll be laboring against not only the snow but also the slope. We'll tire them further."
"The trick will be to get our men to hold and not answer their taunts," Urien replied with a frown. He was a big man, looming over the newcomer, and yet his posture bespoke willing subservience. Whoever the young man was, Urien was giving him pride of place without in the least resenting it. As dark as Urien was, and as bearded, he looked like a great bear in his fur cloak. "The good gods know I favor Roman tactics, but our men are not Roman soldiers . . ." He looked up, spotted Gwen standing diffidently in the door, and motioned to her to come forward. "Lancelin, this is Princess Gwenhwyfar, daughter of King Lleudd."
The young man looked up, and Gwen found herself the focus of a pair of the bluest eyes she had ever seen in her life. He had the direct gaze of a hawk, with a challenge in it that melted away when he smiled.
"My lady." He came from around the table, and bowed to her. "Your reputation precedes you."
She flushed, but she did not look down as a "maidenly" girl would; no point in giving him any reason at all to discount her. "Your courtesy seems equaled by your grasp of strategy, sir," she replied, with an enquiring look at Urien. "If you can hold War Chief Urien's full attention, you must be cunning indeed."
"Gwen, this is Lancelin, the High King's _best_ strategist," Urien replied in immediate answer to that look. He beamed. Gwen blinked a bit in surprise. Urien must feel that the young man's mere presence was a kind of honor.
"Arthur sent me, in place of himself," Lancelin added. A shadow of something—disapproval? Uncertainty? Passed over his face. "And as many of his cavalry as could be mounted and sent in haste. This is an unprecedented push, and the High King wants a decisive blow struck against the Saxons, one that they will not forget soon. Arthur himself . . ." he trailed off. It was Urien who laughed coarsely and completed what Lancelin would not say.
"Arthur is trying to replace his heirs, having already replaced his queen," Urien said with just the hint of a leer. "Another Gwenhwyfar, can you believe it? Gwenhwyfar, daughter of Gwythyr son of Greidiawl. I suppose having had such luck as to get twins with one Fair Apparition, he decided to try another."
The rest of the men chuckled as well, and Gwen made an amused and wry face. They had long since ceased to treat her as anything other than a fellow warrior, and as such, she shared in their jibes and bawdy jests—and again, an unmaidenly reaction merely helped to reinforce a position she had to fight to hold in their eyes. Only Lancelin seemed abashed. "There are many rites that the priests of the White Christ are demanding," he said, looking uncomfortable. "Arthur must conform to them before they will let him have his new queen. Greidiawl, King Gwythyr's father, was a great patron of those priests, and all his household was brought up in that service. Greidiawl brought to the last battle with the Saxons a banner that was said to be holy, and it is true that the Saxons broke and ran when it was brought on the field. When the queen died of grief, Gwenhwyfar the Golden, who was one of her ladies, strove to comfort the High King—"
"Oh, aye, _comfort,"_ Urien chuckled, and the other men roared with laughter. Lancelin squirmed.
"There's fine comfort to be had between a pair of white legs," someone said loud enough to be heard, and even Gwen had to chuckle at that, shaking her head.
When the laughter faded, Urien came around to where Lancelin stood and slapped him on the back, staggering him a little. "We mean no harm, lad, and no disrespect to the High King either. The old queen followed her boys to the Summer Country, and alas for that, but she was a follower of the Good Goddess and knew as well as any that Arthur could not mourn her forever. Better he find himself a new queen quickly, before the thaw, in time for the seedling time. As the king, so goes the land. He was mateless for too long, and the land suffered for it. There is not a man here that begrudges him a new queen, nor looks through his fingers at the notion that you are here instead of he."
Lancelin coughed a little. "I make no excuses—"
"Nor need you. Look you, he sent with you full eighty of the best of the best of his cavalry." Urien nodded his shaggy head. "And I've been on the Saxon campaigns; I'd as lief have you here as Arthur. The companions may be all equals, but in strategy you have no peer."
Now Lancelin flushed, but he held his head high, as a warrior should. "By your leave then, sir, lady? Since the lady has seen and scouted the ground herself with her men, I've need of her counsel and memory."
She hid her relief. The battle had been won again. He took her seriously. Now they all gathered around the map table, while Lancelin examined the maps, asked Gwen highly intelligent and detailed questions about the terrain, asked the others equally intelligent and detailed questions about the temper and skills of their men, and he and Urien moved counters about.
And now Gwen saw exactly why Urien valued him so highly. There were two reasons. The first was that while this was Roman strategy indeed, it was Roman strategy adapted to the much more volatile men of the tribes. If a war chief or general said that he did not believe his men could do such-and-so, Lancelin immediately changed the strategy to something they _could_ do. Some could, and would, hold the "Roman Square." They had fought under Arthur, they understood how the thing worked, and they would overcome their own battle spirit to stand and not respond to the Saxon taunts. Some would not. Those, Lancelin appointed to places in the lines where it would do no harm, and much good, for them to follow the standard battle practice of running up by ones and twos, casting their spears at Saxons who had done the same, and perhaps engage in single combat.
And as for the cavalry . . .
"I know what my men will do," he said with confidence. "They will be here, and here, and at my signal, they will close in around the rear of the Saxons and harry them onto the spears and javelins and archers of the Square."
In his hand were the few counters that represented Gwen and her scouts. He juggled them, looking from the map to her and back again. She answered the unspoken, and very awkward, question.
"My men are like me, small, light of limb. We are horse archers, mainly. But we have King Lleudd's finest and fastest warhorses; I would reckon they could be at the finish of a race while your men were halfway down the course—and be ready to take you all over again," she said with pride.
He brightened. "Fast, agile, and deadly. Good! There are two tasks for you and yours, lady. The first is to sting the Saxon boar, but precisely; I want you here, beside the Square, to run out in relays, find a leader, try to take him and no other, and race back to our lines."
She sucked on her lower lip. "Not likely we can hit more than once in a dozen shots," she replied honestly. "When we fight, we generally shoot at the mass of men, and try to arc over the shields. Generally we hit something because they are so close-packed."
He nodded. "But deliberately choosing a leader—that will goad them, even if you do not hit. His companions will have had their honor touched, and they must defend him. _That_ is what I want; I want them enraged, I want them charging up that hill and onto the Square without a second thought. And the second task is this: After they charge, you all retreat behind the Square, and when they break, and they will, you come out again to sting them a second time." He smiled. "This terrain, this weather, can all play in our favor. We can wear them down, saving ourselves, in case they have more than one force out there."
Now that had not occurred to her, and from their faces, it also had not occurred to Urien and his men. Lancelin shrugged. "The Saxons fight like maddened boars," he said. "That does not mean they cannot be cunning. We must be more cunning."
"And fight like _men!"_ Urien roared, slapping Lancelin's back again. The others shouted their approval.
Lancelin was still looking at her, and she realized belatedly that he was waiting for her assent, as he had for the other chiefs. "That we can do," she replied, nodding. "We all have changes of horses too; we can keep both at the lines and make sure we always have fresh mounts."
He didn't smile as she had half expected, but his look of satisfaction was the same he had given to the other chiefs and generals. "Then by your leave, my lords, I will take these plans back to my men, and you take them to yours. One day for my men and horses to rest, and then we will show these Saxon pigs that it is ill done to covet the acorns beneath the High King's oaks."
She took her leave while Urien was still speaking to the young man and returned to her troop. They had been awakened and were sleepily devouring their stew and bread. Over food, she laid out what was to be expected of them, while they listened thoughtfully. Although this seemed a fine battle plan to her, she half expected that there would be some discussion, if not objection, but there was nothing of the sort.
"Clever," said Owain after a long silence.
"Aye, but not too clever." Peder came to sit down to join them. Gwen made space for him beside her on a log. He accepted a bowl of stew from her servant. "If the High King and the Merlin have a fault, it's the making of plans that are a bit too clever, so no one understands what's to happen but them. I like this Lancelin."
"Come to steal our food again, old man?" asked Meical with a laugh.
"Aye." Peder cuffed him; or rather, cuffed at him. Meical ducked out of the way. "I'll not poison myself before a battle with my own cooking."
"Arthur's Companions do the same," said Aeron suddenly.
"What, poison themselves?" The others laughed, and Aeron wrinkled up his nose.
"No fools, have a common store and a common cook pot. Like we do. No man starves because he didn't want to burden himself, no man carries too much. Food is always waiting, and they never go into a battle or to bed hungry."
"Another Roman thing?" Owain asked, curiously.
Aeron shook his dark head. "Nay. This was Arthur's idea."
Gwen ate another bite of stew. Someone must have been hunting, for there was rabbit and maybe some duck in this along with the usual dried mutton, turnips, parsnips, and pease. "The Romans did as we do, except that there was a grain wagon a man got his bread ration from," she offered. "I can see the advantage, but what happens when the enemy fires your provision wagon or carries it off? And it would slow you down."
"No slower than foot soldiers," Peder pointed out.
"True." She savored the smoky taste of the broth, but she wished for a little thyme. "Something to think about."
When the men had finished, and Peder had wandered back to his own tent, she sat beside the fire, thinking. There was enough afternoon sun on her back to warm her; between the fire and the sunlight, she was, for once, nicely warm. So Arthur was not so grief-stricken that he had not filled his bed again . . . that was interesting. She could not imagine her father doing the same . . . . . . unless . . .
She scratched the back of her head, absently, staring into the fire. There might have been more to this than just a man not wanting a cold bed, and a woman willing to sleep her way to a crown. Anna Morgause was not the only woman in the world to employ the magics of _glamorie._
_But this Gwenhwyfar is a follower of the White Christ! Don't they shun magic?_
Maybe. But Anna Morgause had—supposedly—been one of the Ladies. And the Ladies would not have approved of what Gwen had seen in her vision. You did not use Gift of the Goddess to lure a man that was not yours to your bed. You did not steal the magic meant for the High King and his Queen to put a babe in your own loins so you could use him later as a tool to manipulate the High King himself.
She had no doubt that was what Anna Morgause had intended for Medraut.
She brooded into the flames, listening with half her attention to the buzz of the camp life about her, and tried to think this through, as the daughter of a king should do.
The priests of the White Christ had been angling at the High King for a very long time. His father, Uther, had toyed with them, although he had not actually committed to their faith; but he had given them shelter and leave to build their churches. Even one very near to the Isle of Glass, where the Ladies taught.
It was hard to imagine these men and what they were trying to do. She had never actually met one. The notion of converting a man to another spiritual path was foreign, even a little alien to Gwen, but it was one of the chief pursuits of these people, it seemed. So much so that it appeared they would do almost anything to bring a man into their ranks.
_So maybe they allow—or forgive—magic, if it brings them another man. And if that man were the High King?_
Probably anything short of murder would be forgiven.
Well, the High King was far away. And he would never repudiate the Merlin, nor would he do anything to drive away his allies, who were not Christ-men. _Glamorie_ could do only so much; it would not turn a man against a friend or make a friend out of an enemy. The most that this Gwenhwyfar could accomplish would be to grant the Christ priests more tolerance, to put their rites on equal footing, at least at court, with the Old Ways. Probably.
Gwen considered what others had said about these men, these priests, how they pushed themselves and their god forward. Was it possible that Arthur would neglect the Old Ways in favor of the ones his queen followed, if he were infatuated enough?
_Well. Yes. Anything is possible._ After all, the gods had done nothing to preserve his sons. He might even be persuaded that his sons had died _because_ he did not favor this new god.
She made a face at the fire.
Well, the High King was not here. And by his own decree, the customs of a kingdom held of him were to continue. She was certain that he would not dare to offend his allies by demanding that they give over their rites and gods and take up with this new one. If he did, he would soon find himself without allies altogether.
_Fine. Let the Christ-men have him. The Romans brought their emperor and their Mithras, and look where they are now! Tumbled in the dust._
Then something else occurred to her. Medraut was still on his way to the court, fully expecting to find a distraught Arthur who would welcome this unlooked-for, undreamed of son—
—this son of his own half-sister—
_Oh, that will put the cat among the pigeons._
Even among the followers of the Old Ways, people would look a little askance at that. They would accept it, if Arthur did, and find excuses for him. Tell themselves he could not have known Anna Morgause was his half-sister. Or that he was under her spell so deeply that he did not know who she was. Those things might even be true. But still . . . there would be some looks askance, and if harvests were bad, or winters long, people would ask themselves if this was the fault of the High King's dalliance.
But Medraut would not find a father in mourning and an empty throne. He would find a father infatuated with a new love, a queen who looked to supply him with more heirs, and one who followed the Christ to boot, whose priests most certainly would _not_ look kindly on the love child not only conceived out of wedding bonds, not only sired on a Lady-trained sorceress and a follower of the Goddess, not only begotten on someone else's wife, but the love child of a man and his half-sister.
She almost laughed aloud to think of it.
Arthur certainly could not acknowledge Medraut now, even if he was not beglamored, even if he was not inclining to these new priests. How could he? He had a queen with whom he expected to produce true heirs. The last thing he wanted was to set up a rival to them.
The new queen was hardly going to welcome him, either. He would always be a rival to her own children. And if this same queen actually was given Gifts and the use of magic . . .
_I think they will eat each other alive._
She went to her bed, chuckling at the thought.
**Chapter Fourteen**
**I** **f Lancelin had** not been so modest and self-effacing away from the war table, Gwen would have been hard put to restrain her jealousy of his instant prominence among the war chiefs. He had overleaped her and the position she had spent seasons, _years,_ achieving, and he had done so overnight.
But he was, in fact, a quiet and astonishingly modest man outside of the tent, and when she was honest with herself, she had to acknowledge that _he_ must have spent just as long a period among Arthur's Companions to get that same position. So jealousy was not what she was really feeling. It was envy. And she had to admit that he was a genius at strategy.
Every man in the oddly assorted army fielded by her father was perfectly placed to take advantage of his strengths—or, at the very least, to take advantage of what he _would_ do no matter what had been planned.
Those who were going to charge no matter the orders had been put in the front lines of the flanks, so at least when they charged, it would be across the hill rather than down it. After that initial planning session, Lancelin had made a round of the fires, using charm, honesty, or, occasionally, a skin of strong mead to find out what each commander knew of his mens' behavior in battle and what he thought the others would do. Then he had revised his plans to account for what he learned.
When he spoke to Gwen, it had been with respect and honesty. She and her scouts—for the scouts had seen much more of how the others fought—answered him with the same frank candor. The result was that their disposition remained the same: to sting the Saxons until they charged, then hold back and harry the outliers, watching for an effort to flank.
She sat her horse easily, looking down the shallow slope to the Saxon army spread out in their rough battle line at the bottom.
There was a great deal of noise: challenges being shouted on both sides, weapons beaten on shields, insults, catcalls. It didn't matter that most of them didn't understand each other's language; the tone made the content clear enough. And if they had been fighting with traditional tactics, eventually one man or another would break from the lines, run forward, and throw a spear into the enemy nearest him. Unless he was extraordinarily strong or lucky, the spear would glance off the shield, fall short, break, or bury itself in the wooden shield. Then the man attacked would wrench it out, pick it up or take his own spear, run forward, and return the favor. Then the two would fight, one on one, while the rest of the armies cheered them on. The victor would taunt the enemy, return to his own lines, or remain for someone else to challenge him. Perhaps another fighter from his own side would join him. This would continue, with the number of single combats increasing until the tension broke and one side or the other would charge.
Of course, that was not going to happen here. Gwen would have thought that by this time the Saxons would have realized, the moment they saw forces forming the Square, that they were facing another force using the High King's Roman tactics.
_Perhaps they think it is a ruse. Or perhaps they are confident that_ this _time they can induce us to fight their sort of battle._
The noise was making her horse dance and fidget in place; if this had been summer, she would have soothed him to keep him from wearing himself out. But it was winter, not summer, and all the prancing and stamping was keeping his muscles warm. This was all to the good.
She watched her men out of the corner of her eye. Their horses were as restive as hers, and they sat them as easily. They looked calm. She hoped she did. This would be her first major battle, the first where the armies of more than her father had joined together to face the foe.
There had only been one point of conflict between her and Lancelin. She had wanted to lead the scouts on their stinging attacks on the Saxon line. He had insisted that she ride somewhere in the middle of the skein. "You are almost the only woman in the army, lady," he had pointed out. "It will not be hard to identify you as the White Phantom. This will make you a tempting target for all archers if you ride first. But if you are in the middle, the confusion you and your men will cause will ensure they do not even realize you are a woman."
She didn't like it, not at all, but she had to admit he was right. What was the point of creating the legend of the White Phantom if the feared creature went down under the first volley of arrows? Still. She didn't have to like it, that he was right.
She watched the front line of the Square. It was Urien, not Lancelin, who would give the signal for her group to begin their assault. At least they would be _doing_ something, not standing there chafing against the inactivity like the steady fellows who had formed the Square.
The noise rose and fell like the sound of waves on the rocks at Tintagel. The sun burned down on the white hillside, soon to be churned into an expanse of blood and mud. Things always grew well on a battlefield . . . as if the gods were saying, "Out of death comes life." If the local farmers were not eager to plow and plant this expanse come spring, they would surely not hesitate to scythe down the lush grass that would spring from the blood that watered this land. It would only last a season, but that season would be a good one.
From the center of the Square, a pennon on the tip of a lance shot up. Urien's forces released their pent impatience in a roar as Peder spurred his horse, leading the scouts in their gadfly charge.
She was third and had forsaken her usual gray clothing for ordinary leather armor with metal plates riveted inside, protecting breast and back. It obscured her shape, and her sex was further concealed by a half-helmet. All of the scouts looked reasonably alike, except for Gwen's long braid of white-blonde flailing her back. She had tried coiling it up under the helm, but it wouldn't stay. She needed a new and better helm.
Peder's horse labored a little, galloping through the snow. This pass would be the hardest; as the horses tired, at least the snow would be easier to get through. The others pounded in his wake, snow clots flung up by their hooves. The Saxons watched them in astonishment. Evidently, they had not expected this.
It was not easy firing a bow from the back of a moving horse, and even Gwen's men, who had practiced this with her against the day when they might be surprised and have to flee pursuit, were not what anyone would call _good_ at it. But then, when the idea was to discourage pursuit, you didn't need to be accurate. You only needed the appearance of accuracy.
Gwen, however, was good. After all, she had reasoned, if Braith and some of the warriors she led could hit a man from a moving chariot with a spear, enough practice and a horse you could guide with your knees should make such a thing possible for a rider with a bow. Peder and the man following him more or less marked their target, a big Saxon with a russet shield. It was fairly obvious who they were shooting at, as two men near him screamed or went down. Gwen shoved her reins in her mouth, guided the horse in daringly close to the line, aimed quickly, and fired.
It was all luck, of course. She was aiming for the broader target of his chest, since he'd dropped his shield to gawp. She got him in the eye.
She kneed her horse, heeling him over to follow in Peder's wake, taking control of the reins again. A shout of rage followed her from the Saxon lines.
She didn't look back.
They gathered again at their first position, and only then did she wheel her horse to see the results of the attack.
"Well, they are not charging yet," Peder observed.
"Aye. But they aren't happy."
In truth, that was an understatement. The Saxons were outraged. Gwen smirked as she made out some of what they were saying. "They are calling us dogs without honor," she said. Peder laughed.
"They're welcome to chase us," he suggested. Gwen's smile turned into a smirk. The scouts were not mutton-headed bull-men whose idea of "honor" overrode the need to win battles. They couldn't be. All of them were small and wiry, and to stand and bash at one of those Saxon boars would have been suicide, and from the time they had gotten their full growth, it was very clear that they would never be the sort of fighters that won champions' battles and got songs written about them. While this turned some away from the warrior's path, this lot had become pragmatic. Let other men worry about gaining honor and glory. They would become clever and invaluable. And if no one sang about them, well, the war chiefs knew their value, and they were well rewarded with gifts and loot.
"Well, the cursed Saxons can throw whatever names about they care to. We might get a song out of this from our side," Gwen observed.
But Peder was already setting his horse for another part of the line, and a moment later, the second run began.
It took four before the Saxons' temper broke. Gwen was never again lucky enough to take her man down, but she forced the leaders to duck behind shields like nervous maidens, and that infuriated them. Finally one of Gwen's targets had enough. His face purple with anger, he waved his sword over his head and charged after her, roaring.
That was her signal to send her tiring horse not for the side, but uphill, straight for the Square.
The front line of the Square opened up to let her and the men behind her through, then closed behind them. She pulled up her horse to a trot and joined Peder, waiting for the rest. She didn't look back; the clash of arms and the shouts and screams from the front of the Square said everything that needed to be said.
With every nerve afire now with excitement, once the rest were gathered up, she made a chopping motion with her hand and pointed to either side of the Square. They split into two groups, one led by her, and one by Peder, trotting off to either side, first to scout for any hidden reinforcements, then to harry the Saxon flanks and rear.
They already knew the likeliest places to look, and on horseback, even in the snow, Gwen and her group moved swiftly across the landscape, finding nothing. She could see from their faces that they were as impatient to return to the battle as she was. It was with relief that she sent her horse homing for the noise in the middle distance. As they pushed over the last hill, the smoke from a dozen fires rose blackly to their left. Gwen laughed when she saw it. Peder's men had fired the Saxon camp. Victorious or defeated, there would be nothing for them to come back to. No food, no shelter, no carts, no oxen or mules to pull them.
Not the time to think about it, however. They were coming up fast on stragglers, either left behind or fleeing the battle. Gwen drew her Roman sword, a fine piece of steel that she'd put a good edge on. Reins in her left, blade in her right, she charged down on the man in her path.
The Roman sword was meant for thrusting, but she used it to slash instead, cutting viciously at the man's face as he looked up at her in shock. He gurgled out a kind of scream, there was blood, and then she was on to the next, her heart pounding, shrieking herself, afire with excitement, full of sick nausea, driven with a cold anger and a hatred of these men who had dared try to invade _her_ land, enthrall _her_ people.
She slashed at men in her path until the edge of her blade grew dull and she used it like a club. At one point there was a spear sticking up out of the bloody snow in front of her; she snatched it up in passing and ran it through the next man to be in her path. It was only when her horse stumbled with weariness that she reined in her emotions and nudged the poor fellow over to the side, off the field, and under the trees where her servant, Gavin, waited, with their remounts, hidden. She was the first in.
She dismounted, handed the gelding's reins to Gavin, and mounted the mare, noting absently that her sword arm was blood-soaked.
That was when the nausea hit her like a club.
She doubled over in the saddle. It was always like this. When battle fever wore off, sickness would overwhelm her for a moment. Her stomach knotted, cramped, and heaved; she swallowed bile that burned in her throat and fought it down. Gavin handed her a water-skin; she took it and gulped down several mouthfuls, pushing them past the lump of sickness in her gullet. Then it passed; she straightened and handed the skin back to Gavin as one of the others rode in, spattered from head to toe with blood and mud.
When they were all gathered— _all,_ which anxiety had been part of her sickness, worry for them—she led them at a trot for a good place to get a quick reconnoiter.
The battle had degenerated into knots of combat. One was centered around Urien; one around Lancelin. These were not Gwen's concern, although she wasted a moment admiring Lancelin's fighting. He was ahorse—all of Arthur's chosen Companions were horsemen and fought mounted—and though there were a dozen men around him trying to pull him down, he and his stallion fought like a single lethal entity.
Mentally she scolded herself for losing even a moment and turned to her men. There was still no way of knowing how this battle would turn, "Scout again," she ordered. "Then it's bow work."
They nodded. Once again the group divided, and they pounded off to make sure there were no reinforcements coming in.
The Saxons had committed everything. Gwen led her group as far as was reasonable and then scattered them. They came back to her to report—nothing. _If_ there were reinforcements, provided that Urien won this battle, it would be too late for them to do anything.
They galloped back to the battle lines. They were all riding mares; less speed, but more stamina.
They saw the deserters before they heard the battle. As one they pulled out their bows and strung them.
Shooting from the back of a running horse was hard. Shooting from the back of a standing horse wasn't.
It was over.
That is, it was over for _most_ of the army.
There was loot to be had, of course, and here the mounted had an advantage over those on foot, although those on foot would be where the chieftains and war chiefs had fallen, in the thick of the battle. Still, not all of those chieftains had fought to the last, and Gwen's scouts had taken down enough of them that all of her men wore weary, satisfied smiles as they packed their takings on their horses.
And once they'd all mustered back at camp, eaten some food, and made at least an attempt at cleaning themselves and their gear, Urien called them to inspection, sent out the least exhausted to patrol, and ordered the rest to their beds. Neither Urien nor Lancelin were taking chances.
Gwen herself reported to the commanders with tally sticks of everything (well, mostly, you couldn't prevent the men from cheating a little) her scouts had taken. In theory, half of that should have gone to Urien and her father. In practice, there had been so much that Urien simply waved the tallies off. "Your men fought bravely and deserve what they took." In the corner of the tent, Lancelin was winding a bandage around his wrist—not because he had been struck but because, unbelievably, he had sprained it, he had cut down so many of the enemy.
Some stragglers might have escaped, but Gwen didn't think there were many of them. The snow had hampered escape and had made it easy to see escapees. And for those who _had_ gotten away, without food, without shelter, with no real knowledge of the land, possibly injured . . . the night was going to be very cruel. And if a storm came, which it very well might . . .
So far as the Saxons were concerned, their army would have vanished utterly into the winter.
Lancelin looked up and caught her eyes. "I think enough messages got back to the Saxon leaders of the dread White Spirit that they will probably blame this defeat on her," he said, with a wry smile.
She blinked at him in surprise. "I wasn't even thinking of that," she replied.
"I was." He finished winding the bandage and tucked the end in, then flexed his hand experimentally.
She flushed. "I'm sorry to have spoiled your victory for you then."
"No, you aren't." His smile remained.
"I'm not what?"
"Sorry." He stood up. "And you shouldn't be. That was very clever. I will advise the High King to make use of what you began."
Urien laughed. "Your High King's new queen cannot be half as clever as our princess," he said with unconcealed satisfaction.
"Not in the same way, nor at the same things, no." Lancelin lost his smile. "Queen Gwenhwyfar turns her mind to a different path than the princess."
_And it is one you don't approve of,_ Gwen thought with some surprise. That was when she wondered if she should warn Lancelin about Medraut. She had sworn to tell no one but . . .
The moment passed. He bowed to her and left. She spoke a little more with Urien about the disposition of her men, but weariness had begun to fog her thinking, and it showed. The war chief sent her off with a laugh.
Still, it nagged at her. Someone should know about Medraut. Was there any way she could tell Lancelin without actually _saying_ anything?
She decided to wait until morning. Sometimes things came clearer in the night.
In the morning nothing was clearer, but by midafternoon the last patrol reported that there was still no sign of any reinforcements. And ravens, both two-legged and winged, had come to scavenge on the bodies.
When pickings on a battlefield were lean, the winners generally stripped the bodies of the dead bare before burning them. But from all appearances, either the Saxon war chiefs had anticipated trouble from their men because of the difficulty of a winter campaign and had come laden with many gifts to keep them contented, or they had been forced to send back to their holdings for rich gifts in order to retain them after Gwen began her "haunting." In any case, the bodies beginning to freeze in the churned-up bloody snow were still mostly, or at least partly, clothed, though good fur cloaks, fine shirts and trews had gone into packs and on backs.
Out of nowhere, the last of the battlefield gleaners had arrived; the local villagers and hunters who had hidden during the battle and hoped that the conquerors were not the Saxons. Urien sent out men to meet each little group as it arrived and struck a bargain. Now they were cleaning up the battlefield, stripping the corpses of the least rags, piling them up for burning. This, of course, would disappoint the ravens, who were gorging themselves and berating the humans for stealing their food from under their beaks. If it had not been that they were Saxons, the bodies would have been given at least a modicum of dignity. It had not been so long ago that the tribes here, the little kingdoms had been constantly skirmishing with one another, for the death of Uther, the High King's father, had had them all vying for ascendancy.
"I pity them," said Lancelin, as he walked up to stand beside her. "I do. It seems so unfair, to have followed their chieftains so far in the dead of winter, on the promise of land and more, to end like this."
She shrugged. "I don't think about it. I think about our people, who had to hide in the forest, who would have suffered greatly had the Saxons gotten this far, who did nothing to deserve an army come to make them thralls. If they did not think about ending like this, these Saxons, then they were fools. And if they did and came anyway, then they were doubly fools." She turned to look at him, a strand of hair blowing across her eyes until she moved it impatiently out of the way. "They will not come here again, I think, or at least not for a long time. And since they know that the High King himself is not here, they will know that it does not require the High King's presence on the field of battle to be defeated."
"True enough," Lancelin replied. They had all managed to clean themselves of the filth of battle by now, and she noticed that his hair had a touch of gold in it. A little Saxon blood? That might account for the pity. "That is a good thing, but I do not think it will keep them quiet for long. They are growing desperate. Arthur is pressing them hard."
"Was, you mean." She shrugged. "He has a new bride. That will keep him home a season or two. The Saxons said as much around their fires. They may be less desperate if they are left alone. I think the queen is like to wish to keep him at her side, and he is like to stay there until he has himself an heir again, at least."
Lancelin made a sour face. "And the new bride may keep me from court for longer than that. She does not like me, nor does she like my faith. I cannot say I care for her, nor hers."
Gwen did not ask why there should be dislike, and he did not offer. She only replied, "The High King, I have heard, is accustomed to keeping his Companions close. A man might abide by the crochets of a lady for a time, but he grows impatient for his old comrades. I do not think that any woman will change that for long."
Again, he made a wry face. "Perhaps. This one also has the Christ priests hiding behind her skirts. Thus, it is difficult to predict. Arthur wishes these men to support him; their followers grow more numerous with every year."
She wanted to ask why, but she refrained. Instead, she shrugged, because this gave her an opening to drop some hints about Medraut without actually telling what she had pledged to stay silent about. "Then Prince Medraut will find himself unwelcome, I think. He is the son of a sorceress, and the Druids are more welcome at Lot's court than the Christ-men. The High King may find himself poised between pleasing the queen's priests and pleasing the prince, and I think that he will choose in her favor in that."
"I had heard the prince had come and gone before my arrival." Lancelin eyed her with speculation. "Why did he not remain to fight?"
A hundred answers danced on the tip of her tongue; she chose the most polite. "Business more urgent sent him to the court." She explained about the murder of Anna Morgause by her own sons. Lancelin stared at her in horrified fascination.
"I know Gwalchmai well. His temper has often been his bane, but this . . . it seems impossible. Is this widely known?" he asked after a moment.
"I think not," was her reply. "I think Medraut intends to tell the King only that she is dead and not at whose hands. After all, the ones who murdered her are Arthur's Companions. This would put him in a difficult position."
Lancelin looked pained. "He should always choose justice over . . ." "Convenience?" she suggested. "Friendship? Expediency?" She snorted. "And I think King Lot would not be pleased to have his sons haled up to answer for their mother's murder, since he has not pursued this himself."
"Walk with me, warrior?" Lancelin replied, looking about for a moment to see if there was anyone near.
_Warrior? And not lady . . ._ There was a brief tinge of regret in her, that he had named her the former and not the latter. This was not the first time that a young man had regarded her so. It seemed that she could be one or the other . . . but not both. Like women's magic, the more she took up the sword, the farther she went from the path her sisters had taken. The twinge went deeper for a moment, almost a stab of pain, as if something had been cut from her. Then she squared her shoulders and accepted it. So be it. This must have been the same choice Braith had made, and it was not a bad one. And at least he treated her as the seasoned warrior she was and not as the stripling she resembled. She was listened to with attention and respect by the war chiefs. Her ruse in this latest campaign had brought her praise. It was very likely that when her father went to the Summer Country and Cataruna's husband took the throne, she would be his favored war chief and advisor. She did not want a throne, but she did want respect. And freedom.
Perhaps giving up the notion of a lover, and womanly things, was not so great a thing to sacrifice for freedom.
"Surely, Companion," she replied, and the two of them walked slowly away from the charnel field, facing away from the piles of naked bodies and the feasting ravens, moving slowly and obliquely in the direction of the camp.
"You seem more familiar than most with Lot of Orkney and his brood."
She nodded, being careful where she stepped, both literally and metaphorically. "My youngest sister went to foster with Anna Morgause when my mother died. That was about the time of the birth of the High King's sons."
She turned her head slightly and saw him make a calculation. "There is often a handfasting in such cases," he said cautiously.
"And there is in this one." She said nothing more. He was intelligent. She would see how intelligent.
"Ah." He waited some time for her to elaborate, and when she did not, he nodded thoughtfully. "You are fond of her, this sister?"
"There is no love between us," she said, the words coming from her mouth before she could stop them. _Curse it. Ah, well. I shall never make a courtier._
He nodded again. "In that case . . . I would be in your debt if you can tell me what you _can_ of the Orkney brood. For while I hold Gwalchmai my friend, and there is no sweeter-natured man than Gwynfor, I have never met Medraut, Gwalchafed is as hot-tempered as Gwalchmai with none of his brother's virtues, and as for Agrwn, the less said the better."
Gwen pondered this for a moment. "Well," she said carefully, "I had very little to do with any of the brothers but Medraut. He is crafty, cunning, and exceedingly intelligent. He can convincingly feign whatever he thinks will bring him the most advantage. He is much like his mother in that he will use any craft or guile to get what he wants. And there is only one person I have ever seen him exert himself to benefit."
"That would be Medraut himself, I think?" Lancelin's face was quiet, and thoughtful. "I think he will find himself very much at odds with the queen." He nodded decisively. "Thank you, warrior. You have given me a great deal to consider."
With that, they reached the camp and separated. She did not envy Lancelin, returning to a court that evidently contained a queen with an uncertain temper, and Medraut, as well as whatever other factions were simmering.
Not in the least.
**Chapter Fifteen**
**G** **wen returned to** a life of work and solitude.
There was absolutely no doubt in her mind that she was _needed._ There was no doubt in her mind that she was, as she had always wanted to be, respected. Her father's men were accustomed to her now, and they took no more thought of her being female and looking strangely young than they did of her father's gray hairs. It was only when they were among strangers that they seemed to realize it again; now that they were home again, everything went back to normal
Which meant that Gwen sent her scouts out to patrol the borders, keeping their skills sharp. Any that had good reasons to bide, she found other work for and replaced them. And she herself served as Caradoc's personal bodyguard when he went out to look over the lands or stood behind her father when he welcomed strangers. When she was not doing that, she was hunting, and when she was not hunting, she was training.
On the whole, she preferred to wake early, work to exhaustion, and fall into bed at night. So long as she did that, she did not think too much about how narrow and solitary that bed was, nor how she had no fast friend among the men or the women either in whom she could confide.
Rarely, very rarely, she would watch Cataruna and Gynath with their heads together over something and wonder what it would have been like if Little Gwen had been her friend instead of her enemy . . . after all, there was really no reason why they should have been rivals. They didn't want the same things and really never had. But then she would shake that off and go on about her business; she had neither the time nor the energy to waste on fantasies. And the more she could put Little Gwen out of her mind, the happier she was. Presumably she was queening it at Lot's table, since rumor put Morgana somewhere about Celliwig, and she would be the only woman of rank there now. With luck, that would be enough for her.
Spring came and went with no sign of the Saxons making any more trouble, which was just as well since there was more than enough trouble in the South to make eyebrows rise.
King March of Kerrow . . .
It seemed that the Saxons were not the only ones who were interested in the High King's obsession with his new wife (one could scarcely call her a "bride" at this point). Now, Lot was a sly snake and not to be trusted, but March was an entirely different cut altogether. If you were the sort—like King Lleudd—who held that fidelity to one's oaths was of the highest importance, then March was as treacherous as they came. Not only did he seem to regard his oaths to the High King as of importance only so long as they were of benefit to him, he seemed to regard all oaths in the same light.
Add to that, so far as Gwen could tell from the reports of others, the man was mad.
He had a temper that he did not even try to govern. Not only had he slain messengers and even the High King's Companions when a rage was on him, he had killed dozens of his own warriors.
And now, for reasons best known only to him—or out of sheer insane spite—he had raised an army and was marching on Arthur. The fact that he was going to have to cross either lands holding fealty to Lleudd (who was not going to allow it) or Saxon holdings did not seem to matter to him.
Gwen studied the maps alongside her father and his war chiefs. "I had rather that March wore himself out against the Saxons," Lleudd growled. "A pox on the man! And a pox on whatever demon sired him! No sane man would act as he does."
Much to Gwen's pleasure, on the other side of the table was Arthur's Companion Lancelin. True to his prediction, he was staying far from the High King's court at Celliwig to escape the jealous regard of the queen. Lleudd had welcomed him with his knowledge of warfare with pleasure, and his self-effacing nature ensured that the other war chiefs were not made to feel that they had been put aside. She regarded him with pleasure not only because she enjoyed his company but also because his respect for her reinforced her own position among even those who knew her. Perhaps she was finally overcoming those too youthful looks.
Though without a doubt, wherever she was, Little Gwen was taking every advantage of the apparent youth they shared.
"If that is truly what you want, my lord King," Lancelin ventured, "I do not think that March can win against your men and especially not against your chariots. There are plenty of places along the way where the ground would be ideal for them."
"But the loss of a single man to that fool is one man too many," Lleudd replied. "Be sure the Saxons are watching this with greedy pig eyes, still smarting from the last defeat we handed them. If we engage March, they will be on us when the battle is past and we are spent and exhausted." He looked around the table, and his other war chiefs nodded.
"He probably will not fight the Saxons," Lancelin said, after staring at the maps a while longer. "He will probably bribe them to let him pass. It is what I would do."
Gwen smirked. She couldn't help herself. "Perhaps we can find a way to trigger that famous temper," she suggested. "Even if the Saxons accepted reparation rather than killing him themselves, they might ruin him with weregild."
The idea of March finding himself forced to pay a heavy weregild in addition to a bribe made the other war chiefs chuckle a little. But Gwen had more to say at this point.
"I have a thought about keeping him from trying to cross our lands," she continued. "Look here—" she pointed at the map. "This is where he will have to make the decision whether to bring his army through our land or to treat with the Saxons. We need to make the choice easier for him, but by not opposing him at all."
Lancelin looked at her quizzically. "Why would you say that?" he asked.
She smirked. "Because March is—" She _almost_ said "a man" but quickly modified it to "—like to a bull. Wave a red rag at it in the form of armed opposition, and he _will_ rush at it. We have a choice ourselves; we can send him across Saxon lands, save _our_ men and join _our_ force with the High King's, and the two will crush him. Or we can take the chance that he will defeat us, pillage our lands, then attack Arthur. So we do not present him with visible opposition but rather make it unprofitable for him to try to cross our land."
"Unprofitable?" Lleudd looked at his daughter in puzzlement.
"See here?" She pointed at an area of flat land. "My dear brother-by-marriage is a bard and a Priest, and Cataruna is a trained Lady. I think that between them they can persuade the waters to rise here and make that a marsh for as long as we need it to be so. Faced with a swamp, I think March will take the Saxon road."
They all stared at the map. "It seems the coward's way . . ." Peder said, doubtfully.
"Not if, when we are sure of him, _our_ army joins that of Arthur," her father replied, decisively. "It is merely postponing the fight and choosing our ground. Only a fool fights a battle going up a hill."
Gwen nodded, grateful that he had thrown his support behind her.
Lancelin studied the map, rubbing his chin, but he said nothing, neither for nor against the plan. That disappointed her a little, but in the end it was King Lleudd's decision and no one else's.
Which meant, since this was her idea, she needed to have speech with Cataruna.
Ifan and Cataruna had their own room, as did Gynath and Caradoc; two new rooms had been made by the simple expedient of partitioning off two spaces side by side at the end of the Great Hall where the entrance to the king's solar and the room they had all shared as girls was. Now you passed through Gynath's room to get to the door that led to what had been the girls' room, which now belonged to Cataruna. Gwen had the smaller space, not much bigger than the bed, but she didn't need much space. Cataruna often sought privacy in that sanctuary while Bronwyn watched her children. But it was in the Great Hall that Gwen found her sister and brother-by-marriage .
Cataruna was sewing, and when Gwen explained what she had in mind, her sister pinched the bridge of her nose between thumb and forefinger and made a face. "I mislike meddling with the land—"
"I mislike having King March's men come across it, love," said Ifan, as he put aside the tuning pegs he was carving. "I mislike seeing herds slaughtered and farms laid waste. March is unpredictable and not entirely sane. There is no telling what the King of Kerrow is like to do."
Cataruna's brows furrowed for a moment, then her face cleared. "As Lady of the Fields, if I hear the Lord of the Forest urging protection for our people, I think it would be wise of me to heed his words." They beamed at one another, and Gwen felt a twinge of envy as well as of relief.
"But can you do this?" Gwen wanted to know. She hesitated. "The place is often marshy and soft. But—"
"Alone, no, but with Ifan, Bronwyn, and Gynath, yes." Cataruna smiled at her. "Well, find us some swift horses, and I'll find Bronwyn. We will need them to get there before March's army does."
Gwen grinned at Ifan. "I thought bards lived for epic battles to make songs about."
Ifan snorted but did not comment. Gwen left them making preparations and headed for the paddock.
She would not be using Rhys or Pryderi. Both of them were ideal for scouting, with great endurance, agility, and intelligence, but not much speed. To get to the right place before King March and his army did, they needed only speed and endurance.
They needed five horses out of the king's herd used by his messengers. They were ugly as mongrel dogs, stupid as stones, and uncomfortable to ride; you would _never_ dare to leave one unattended or it would run or wander off, and no few of them were as skittish as ferrets, but they had a ground-eating lope that they could hold from dawn to dusk with minimal rest.
She picked out five with relatively even tempers and ordered them saddled and bridled, speeding things up by taking care of the fifth one herself.
Ifan shook his head in dismay as he brought a small pack and traveling harp to the paddock where the five horses were tied up to the fence. "My back will curse you for this, Gwenhwyfar."
"Your back isn't the part of you that I am worried about," Gwen replied without thinking and then blushed as he roared out a laugh. "I meant your _hands,_ brother!"
"I'm sure you did." He was still snickering when Cataruna and Bronwyn arrived, both looking resigned when they saw the horses awaiting them. Then he sobered. "However my back will complain, I will endure it."
It was not only Ifan's back—and rump—that were complaining when they reached their goal. It was worth it, though. March's army was not in sight. After a few hours of rest, Gwen took it on herself, while Ifan, Cataruna, and Bronwyn made their preparations, to ride out as fast and hard as she could to the west, taking two of their mounts with her in order to change them out and keep them all relatively fresh. March's army was not within a day's hard ride, which meant they were not within three to four days' of the border yet.
She and the horses were weary when she rode back to the campsite. She had carefully chosen a spot hidden away from casual view, like her old favorite nutting spot, in a copse tangled with nettles and raspberry bushes, and she had instructed Ifan on how to further conceal the camp. He had done a fairly good job—not nearly as good as she would shortly but not at all bad for someone who had only made hunting camps before this. If she had not known they were there, she probably would not have spotted them.
There was just enough room in there for the horses, but since she now knew that March's army was quite far off, it would be safe to move them and hobble them where they could browse. Her three were tired enough that they would probably not cause any trouble, at least, not for a while.
She whistled the signal that they had all agreed on and was rewarded with the sight of Ifan popping out into the clear and waving at her.
"How far?" he asked, when she was in hearing distance.
"Far enough that we can finish the work and be gone," she replied, dismounting with a wince. How the messengers weren't crippled, riding these boneracks, she could not imagine. "How near are you three to being ready?"
Ifan grinned and ran his hand over the top of his head. Gwen was struck, once again, by what an odd sort of fellow he was. He looked as if he had been put together from the gods' leftovers. His hands seemed to be too long for the rest of him, and they were very graceful, which was at odds with the rest of his body, which was gangly and awkward, like an adolescent's. His chin stuck out like the prow of a boat, his brow was almost too broad, his hair was so coarse and perpetually tangled it could have come from the mane of a wild pony, and even his eyes were strange, one blue, one brown. Yet those hands could charm the most amazing music from any instrument he picked up, and as for his ability to tell a tale or create a song, well, it left his listeners spellbound.
"Cataruna can do anything if she puts her mind to it," he said with admiration. "Of course, you chose the right place, she tells me." He waggled his eyebrows at her. "Mind you, we're going to be right miserable before she is finished."
Gwen was not certain she wanted to hear the rest, but Ifan told her anyway.
"She's calling the rains. They should be here soon. And now that you are here," he added with a smirk, "We can call the waters."
Cataruna had spent the time while Gwen was gone in preparing her ground, creating a ritual circle by cutting into the turf and peeling it up, setting in a stone for an altar, and four more at cardinal points.
As directed, Gwen took her place at the southernmost stone; Ifan and Cataruna took west and east respectively, leaving Bronwyn with the north. And from that moment on, once Cataruna cast the boundaries of the circle itself to seal the power in, it was unlike any ceremony Gwen had ever taken part in before.
While Ifan played a small hand-drum, he and Cataruna chanted in a language that was nothing like anything that Gwen knew. The words sounded as if she _ought_ to recognize them, but she didn't; she did, however, get the sense that she knew the gist of what they were chanting without knowing the words.
It was vaguely disconcerting. After a while, she decided that they must be using one of the secret languages of the Druids, a tongue much older than the one Gwen knew.
As for the sense of what they were chanting—
They were begging the waters to rise to the surface and cover the land here. Begging the gods to allow this to take place, and asking the waters to remain this way for two fortnights.
This was not an exercise of power as such. This was more like going to an ally and asking for help.
At least that was how it felt to Gwen.
She began to lose herself in the chanting, and although it was broad daylight, she began to feel as if she were walking in a dream. A silvery mist crept over the valley, seeming to form from nothing and, in defiance of the bright sunlight, growing thicker by the moment. Soon it had closed in around them and rose to obscure the sky and the sun. Tiny sparks of glittering color hung suspended in it, winking gold and green. Each time she blinked, she got glimpses of . . . something else scuttling through the mist, just out of view. Something, or rather multiple things, just out of the corner of her eye, that vanished when she turned to look fully at them. She didn't get enough of a look at any of these things to have said successfully what they were, but she did know that they weren't, and had never been, human.
And she started to feel things from them; not all of them were particularly friendly. They weren't inimical to the four of _them,_ but as Gwen listened to the chanting, she understood that Ifan and Cataruna were striking a bargain with these creatures: For as long as the waters stood above the ground here, they were being given leave to do what they willed with any human (save the four of them) who tried to cross that they could catch and hold.
She shuddered a little; at first there was no acknowledgment from the creatures, but then, between one moment and the next, the circle was surrounded by them.
Their shapes faded in and out, ghostly and transparent at one moment, solid in the next. Nearest were the Gwragedd Annwn, the Ladies of the Lake, golden-haired and so fair of face that Gwen felt utterly coltish and rough hewn in their presence. Small wonder that they came; they were the guards and guardians of the Ladies at the Cauldron Well and were surely on speaking terms with Cataruna. They were tall, as tall as Ifan, and looking on them, Gwen suddenly wondered if the white-gold hair she shared with her sisters and Eleri had come not from Saxon blood but from these creatures. There were more of the Ladies than there were men of their kind, and bards were full of tales of love and marriages between their race and that of mortal men. They were said to live in their own villages at the bottoms of lakes and ponds, guarding some of the entrance points between the world of mortals and Annwn, the Otherworld. One of the High King's two famous swords was said to have been given to him by them . . . though Eleri had always said, no, it was not the sword that had been given but the sheath, which was by far the more important of the two. The sword Caliburn signified only because it had been Uther's, and been driven into a stone by the Merlin—only the lawful heir to Uther could pull it out. But the sheath—Caliburn's sheath—was said to be able to heal any wound. And it would make a great deal of sense for such a thing to have come from the hand of one of the Gwragedd Annwn.
Their faces were solemn, a little stern, and all their attention was on Cataruna and Ifan. Gwen was just as pleased. She did not want the attention of the Folk of any kind. Yet she could not help it, feeling an odd kinship with these creatures that only grew the more she was in their presence. If they felt it as well—
One of them cast a sidelong glance at Gwen, who felt warmed and chilled at the same time. Then she returned her gaze to Cataruna. Cataruna, who shared Eleri's blood. Blood that, Gwen was now sure, was shared also with these ladies of the Fae. It was to this blood, it must be, that she, her mother, and Little Gwen, owed their curiously youthful looks . . .
And it was Cataruna's blood they had answered to, not whatever she and Ifan had chanted.
Equally lovely were the Swan Maids and Men, who flocked close beside them. Again, there were a half dozen of the Maids and only two of the Men; among the Folk of Annwn, there were often such disproportionate numbers. They were silent and stayed farther back in the mist, their golden eyes glittering and betraying their difference from humanity.
But near to Gwen were a pair of the Ceffyl Dwr, the Water Horses, who were more mischievous than nasty. Initially appearing as a pair of tangle-maned black stallions, they caught her looking at them, and in a blink she found herself staring at youths who initially seemed very handsome and who both winked at her as if they knew her. Looking closer at them, she noted their water-weed-entangled hair and hooves instead of feet.
They grinned at her, and one of them made slight, but suggestive movements with his hips. She flushed a little, and looked away, and heard them laugh.
Deeper in the mist, she also got glimpses of what might have been Nykers, although it was hard to tell. There was something out there, dark and ugly and hunched over, with a hunger about it and a malevolence. It might have been Nykers or it might have been Groac'h, the females of the same sort: ugly, evil creatures who made a habit of snatching folks and drowning them. Some said they were the spirits of the drowned themselves, others that they were the dark cousins of the Gwragedd Annwn.
Even the Gwragedd Annwn, for all their beauty, were known for being chancy to bargain with. But they would at least stop to bargain with you; the others would pull you under before you even knew they were there.
And so they came, flocking thicker and thicker about, as Ifan and Cataruna chanted, only staring, never answering, until at last one of the Lake Ladies _did_ step forward and reply in the same tongue, in a voice like a nightingale.
Ifan and Cataruna stopped chanting, listened, and then Cataruna replied.
The Lady spread her arms wide and sang again. Ifan looked startled. Cataruna, speculative.
The Lady repeated herself. Gwen concentrated as hard as she could, trying to pull sense from the words. When the Lady was done, she stared across the circle at Cataruna. "She wants to make a marsh of this place _permanently?"_ Gwen spoke in hushed tones, as the cold mist collected around them, chilling her.
Cataruna nodded, but it was Ifan who replied. "She says that we mortals have pressed the water peoples hard. She wants a grant of this land and the right for the water folk to do as they will here for as long as Eleri's blood flows in our people." Cataruna took a deep breath. "I told her that I have not the right to make such a bargain, for I am not a war chief, only the Lady of our land. But I told her that you can."
Gwen considered that, as all of them, mortal and fae, watched her expectantly. "I'm not likely to give land away, for all that Father's given me the right to. I'll be having a bargain of this." Inside, she shook at her own temerity, daring to bargain with the Other Folk. But they didn't respect anyone who didn't bargain, at least, not in the tales. Cataruna repeated her words in the language of Annwn. The Lady nodded, as if she had expected this.
Gwen considered every possible way in which she could phrase her bargain. The good part was that this area hadn't been claimed for farming, and any herders who were using it could come to King Lleudd for other grazing lands. But the point was, if she closed this—treaty, she supposed it must be—she'd be opening this place to who knew what sorts of dangerous creatures. And even if, as some claimed, the beings of Annwn were not fae at all, but just mortals with a great deal of the Gift and the Power and some ugly odd shapes . . . well, that made them all the more dangerous.
"Tell the Lady . . ." She faced the speaker squarely and looked into her cold eyes, the color of lake water before a storm, and she did not, not for a single moment, doubt that the Folk of Annwn were not of the world she knew. "Lady, this is the bargain I will be having. By the right my father, King Lleudd, gave to me as a war chief and able to make grant of land, I give you and yours this valley, to be covered with water and made your own. In return I will be having this: No creature that lives here is ever to _take_ a child, a youngling, a maiden, or a woman. No creature that lives here is ever to _take_ a man that comes in peace, with no ill will toward my people or those of Annwn, nor those that pledge to the High King."
There was muttering behind her, discontent from those dark shapes that would not let themselves be seen. Anger, even, of a sort that put the hair up on the back of her neck. Nevertheless, she continued. "But for those that would trouble my people, and those that will not pledge to the High King, or those that are oathbreakers of that pledge, whether they are an army bringing upon them war and sorrow or merely thieves and rogues who would bring them loss and grief, should they put so much as one toe in your waters, they are yours. Take them, drown them in deep waters, harry them across the marsh, drive them mad with fear and despair. That is my bargain. Take it, or not."
Cataruna repeated all she had said, but the Lady had already nodded as if she understood it all, and turned back to the others.
Gwen waited patiently, feeling colder by the moment, as the otherworldly creatures conferred. The mist roiled darkly around all of them now, and the sounds of their voices rose and fell. Both Cataruna and Ifan looked a little bewildered, as if they had not truly expected this to happen.
_Well, and I cannot blame them. Who would?_ She had never seen these beings even once in her life before—though both of them surely would have, the Ladies, at least. But the others? Who did she know had ever confessed to seeing a Swan Maid or a Water Horse? And to see so many of them . . .
And then to have the temerity to bargain with them?
She reminded herself of who she was doing this for. And why.
Finally, the muttering stopped. The Lady turned back to them and sang. Gwen did not need Cataruna's translation. It was a bargain.
She stooped, seized a handful of the soil at her feet, and took a little knife from a sheath in her boot—not iron or steel, which was anathema to these folk, but a flint knife she used for skinning game, for it was easier to keep at a razor edge. She cut her thumb across and bled onto the handful of dirt, squeezing it tight. "My blood upon it," she said, binding the bargain.
The Lady stepped to the edge of the circle, cut her own thumb with a knife very like Gwen's, and added her blood to the handful of soil. Gwen noted absently that her blood was as red as any mortal's, and not blue, or green, or starshine.
Gwen stooped down again and patted the handful of soil into place, opening the circle. The Lady clapped her hands, the mist swirled around them so thickly that for a moment Gwen could not see anything at all—
And then they were gone.
And her boots were beginning to get very damp. She looked down, and saw that water was rising around them.
Fast.
"Back to camp!" Ifan said, as the mist thinned, but only in the direction of their campsite. Gwen had no wish to argue with him, for the water was already at her instep and rapidly rising to her ankle. All four of them ran up the way that had opened in the mist and did not stop until they were well out of it.
Only then did they pause and look back down at the valley.
For as far as the eye could see, it was covered in that thick mist, which the setting sun was now turning to gold. There were things moving in it. She shivered. She pitied March's men if they did try to cross here.
Cataruna and Ifan looked at each other, numbly. Bronwyn shook her head. "There's more moving here than we reckoned on," the old woman said.
That night, the storm Ifan and Cataruna had called broke, and Gwen had cause to regret that she had not put some form of provision against _that_ in her bargain.
Not that there was any way of knowing whether a bargain with water spirits would have any effect on a storm.
They had done their best to prepare the camp for the onslaught, but there was only so much shelter that branches and stacked bracken could give against the sort of storm that eventually arrived. This was not a country for caves, and they had been traveling too light even for a bit of canvas.
When the storm hit, it did so as a full tempest. Torrential rain, lightning, thunder, wind . . . it would have been impressive within the walls of Castell y Cnwclas. It was a nightmare out in the open.
They had gotten the four horses into the little clearing, and because Cataruna had a foreboding, they had tied and hobbled them so that they could scarcely move, then made crude blinders and tied them over the horses' heads. It was a good thing they had done so, or they would have been kicked to bits, trampled, and, had they survived that, found themselves without mounts the next day. As it was, the poor beasts whimpered and moaned and fought the hobbles until they were exhausted. Based on Cataruna's foreboding, Gwen had opted for "sturdy" over "space" when it came to the shelter. It was a lean-to made of branches and many layers of bracken, and the four of them could barely squeeze into it.
They had been sitting around their fire, gnawing the last of the meat off the bones of the rabbits Gwen had shot, when they heard the storm coming. As it approached from the southwest, the steady growling of thunder was like a great beast in the distance. The closer it came, the more the horizon lit up with so many lightning strikes it looked as if it were crawling on dozens of legs toward them.
Down in the valley, the mist still had not lifted, and there were strange, dim lights moving in it. Those lights actually brightened in response to the coming storm. And strangest of all, as a wind sprang up, strengthening until their cloaks were blowing straight away from their bodies, the mist remained, unchanged, and unmoving.
At that point, with the branches of the trees tossing wildly, the horses fighting their bonds, the fire actually blew out. That was when they all scrambled into the tiny shelter and wrapped their cloaks tightly around themselves. Gwen and Ifan put themselves on the outside corners and grabbed the branches, determined to hold onto the thing no matter what.
Then the storm hit.
Rain pounded down onto them quite as if someone had emptied a river on their heads. The wind was terrible, and it was a good thing that Ifan and Gwen were holding to the shelter, or it would have blown away. There was so much thunder, and the wind was roaring so, it would not have been possible to hear a shout in your ear. All Gwen could do was duck her head, keep a good grip on the pitiful lean-to, and hope they would not all be struck by lightning.
The gods themselves must have concocted such a storm. Surely she heard the Wild Hunt out there, the hooves of their monster steeds pounding anything that got in the way as flat as cloth. They were all soaked within moments even with the shelter. All it accomplished was to keep the worst of the rain and wind off.
Before long, the pounding and howling and cold numbed her into a state of unthinking endurance. She couldn't manage to put a single coherent thought together, and all that mattered was the slightly warmer place where all their bodies met. How long that went on, she could not have even guessed.
Then, at some point, the storm passed. The wind dropped. And although they could not have managed to separate their tangled limbs to attempt a fire, the warmth of their combined bodies finally dried out their cloaks enough that they began to doze.
Gwen woke with the birdsong of false dawn. Trying not to wake the others, she got herself loose to check on the horses. She was too tired to really think clearly, but she would not have been in the least surprised to have found them dead.
The poor things were in a sad state, but they were not dead. The crude head coverings had been blown away, and they had all fought their bonds so hard that they were now in a state of head-hanging exhaustion. She released some of their hobbles, gave them each a couple of handfuls of grain from the saddlebags, which they lipped up dispiritedly, and felt their legs to see if they had damaged themselves.
She could feel that the muscles had been strained, enough that it would be a good idea to give them a couple days of rest, but there were no sprains. With a sigh of disbelief at their luck, she crawled out of the open center of the brush-tangled copse to see what the rest of the world looked like.
And gaped at what she found.
Where there had been a flat valley, there was now a marsh. Not just _water;_ she had expected water. No, this was a marsh, one that looked as if it had been there for generations.
Huge reed beds separated by stretches of open water spread out before her, out to the horizon. Here and there a was a hummock where a few trees and bushes hung on; the reeds and marsh plants in most places were as high or higher than a man's head. Mist threaded its way along the water, hung in banks in other places. Ten feet in, and you would be lost and disoriented. If fog closed in so you couldn't see the stars or the sun, you would never even know what direction you were going. It was a place that warned you, just by the look of it, that it would be full of sucking mires and unexpected sinkholes. You'd never find a secure, dry place for more than a couple of men to sleep. You'd never find the wood to make fires, or a place to make them. And that was all aside from the supernatural dangers hiding in those mists. It would be insane to take an army across that.
Of course, King March _was_ insane, and he might try.
He wouldn't get far, though. The border here was safe from him.
Gwen set about finding deadfall for a fire, then when she had piled up enough at the entrance to their little copse that the others could remake the camp while she was gone, she went hunting for some breakfast.
There was a great advantage to suddenly being on the edge of a marsh. There were fish in it, and they all seemed hungry. She fashioned a fish spear from an arrow, scattered some crumbs over the surface, and set to work. By the time the sun was a thumb's breadth above the horizon, she had enough to satisfy the most ravenous of appetites. And she had the shrewd idea that she had been "helped" in this, for she thought she had caught a glimpse of amused eyes among the reeds.
She wasn't going to argue about it. Given the size of this marsh, the water spirits were going to have plenty of room for some time to come. It was a good thing that Ifan was a bard, though. He would know to be careful of coming down here, even avoid it altogether. The Lake Ladies were a mixed sort, and there were those who would not hesitate to steal a bard from his lawful wife and take him down to their dwelling beneath the waters.
She brought the fish back up to a camp of people already packing to leave, though a fire had been started and twigs prepared to spit whatever she brought. She raised an eyebrow.
"I had thought to stay and rest the horses," she offered.
Ifan took the fish from her, and he and Bronwyn began cleaning and gutting them, as Cataruna shook her head. "We can walk them if we need to, and make our way slowly back home, but I think we should put some distance between us and—that," she said, thoughtfully. "Yes, they are feeling well-inclined towards us now, but—"
"Besides, we have raised a great deal more power than either of us expected to," added Ifan, with a frown, as he set a fish to cook over the fire. "One could liken it to setting down a chest of gold and silver and spilling it open in the village square. Some will come to admire, but word will spread."
She blinked. She had not considered that. "And what comes to look will not be bound by the bargain I made with the water spirits," she said, slowly. "Which could be equally bad for March _and_ for us." She straightened her back. "On the whole . . . I think a slow walk back for a day or two would be of great benefit to all of us."
"Healthier than remaining here," said Bronwyn.
**Chapter Sixteen**
**L** **leudd's war chiefs** and captains sat around his hearth fire in varying states of relaxation. Gwen had already recounted what she had done to Peder and her father privately and had gotten praise for her quick thinking. Now she had been asked to tell the tale at the hearth for the rest, who were all relaxing because there was no longer an immediate threat from March. Relaxing because of what she had done.
Supper was over, the mead was being poured out by the young squires, and Gwen had to hide a smile when she realized from the taste that Eleri's special recipe had survived intact. The fire smoked just enough to drive the insects away and imparted just enough warmth to be comfortable. This was an occasion for a more . . . bardic retelling.
So she obliged, as best she could. At the end, King Lleudd roared with laughter. "Well, my war chief daughter, I hope that you are content with _your_ lands being the ones under water!"
That elicited laughter from the rest. "Will you be farming eels and frogs?" one of the others asked, straight faced. "I hear the Romans thought frogs right tasty, and I am partial to an eel pie."
"When you plant eels, do you plant 'em head first or tail first?" asked another.
Gwen smiled ruefully. War chiefs were expected to offer gifts, of course. And up until now she had mostly given things like ornaments, horses, or weapons. But land was always an option, and as Lleudd's daughter, she was entitled to a certain amount to hold for herself or give as rewards as long as it had not been granted to another.
"I am content with awarding the new guardians of that border with the land they are guarding, my lord King," she replied dryly. "If they prefer it being under water, well so do I."
The king laughed again, as did the rest of his chiefs. "Well said. And, yes, I approve, most heartily, of your decision." He looked around the fire at the men on his benches. They were all nodding too, even if one or two of them were doing so reluctantly.
"Also . . . if I were to give advice on this," she added cautiously, "I would say it were best to simply stay away from that marsh. While Cataruna thinks they are bound, and well bound, by the oaths they gave . . . the less traffic with the Folk of Annwn the better." _With the Folk of Annwn. With my mother's people? Does Father guess? "I_ certainly have no plans to return there. Not even to see what March makes of the situation. He cannot pass there, that is all we need to know. That will force him through Saxon lands."
Now no one nodded reluctantly.
She realized, and not for the first time, that she was, always had been, and always would be one apart from the rest. Even those who had come up with her as pages and squires; she shared a level of camaraderie with them that never went farther than the battlefield and the camp. Though Lleudd had never shown any favoritism to her, she had still always been the king's daughter. Some had been jealous of that, some had been resentful, and even when she proved herself over and over, there had still been that distance of rank between them.
Even the handful of girls that had begun training with her had kept a wary distance, a distance that had only increased as most of them had decided to give up and try some other path. The only two who were left were chariot drivers, and she saw nothing of them.
Well, it was what it was.
The remainder of the talk centered on what to do when March moved toward the Saxon-held lands. Gwen listened but did not comment; this was not where she had any level of expertise. Everyone was agreed that he would at least try to buy his way to free passage. Some thought he might well try to ally with them.
"He would be very foolish not to try," Lancelin said, his big hands absently rubbing the silver band on his drinking horn. "And they would be equally foolish to fight him or reject such an alliance. Neither of them can afford a battle on two fronts, and the Saxons are somewhat weakened from the losses they took this winter." Lancelin's suggestions were very astute, however, and she found herself admiring his knowledge and skill all over again.
And . . . truth to tell . . . admiring him for himself. He was not a beautiful man, but she had never cared that much for beauty in a man. A quick mind, however, a good and even temper, a sense of humor—those were things she cherished and admired.
She was not the only female to find him attractive; he, however, did not seem to notice any of the women casting glances at him. Or if he did, he was feigning not to notice. She wondered if he had a love elsewhere.
If he did, she could not imagine that it would be at Arthur's court. No one she knew would be kept from the side of a lover just because the queen misliked his presence.
She regarded him across the hearth fire, and decided that he was probably heart whole. He didn't act as if he were pining for a love. If anything, he seemed relatively content with being here as Lleudd's advisor and liaison. The only time she had heard him voice any discontent, it was because he was missing the fighting at Arthur's side.
_As for that fighting—pay attention. You are in charge of the scouts, now._ That was the reward her father had given her. She, and no one else, would be the one commanding all of the scouts, the saboteurs, and outliers for whatever force was sent to aid the High King.
As she listened, she began to formulate some ideas. A few were based around her ruse of "The White Apparition," but she had plenty of others. March might very well know that "Gwenhwyfar" was a very real, mortal human creature; she would have to determine that, first, before she tried such tricks on his forces. But he would be fresh from dealing with her "allies" of the Folk of Annwn; there were other ways she could invoke "supernatural" terror among his men. The Saxons, of course, knew about the White Lady; she would find herself a few more of the woman warriors and recruit them to impersonate her. If one White Phantom was terrifying, what if there were many haunting the dark?
And spies, of course. She needed spies. People in March's camp, people in the Saxon camp.
_I wonder how much it would take to buy the ears of washerwomen and camp whores?_ If she could succeed in convincing them that when this was over, they'd have a place, protectors, on the High King's side . . .
More than that, she'd have to find places. And each one would probably be different. There would be women who had gone to the life because they had no other options, women who were captives or near captives, women who liked the life, or at least, liked the sex when they weren't afraid of being abused or beaten . . .
_I should talk to Bronwyn. Maybe Cataruna, too. Don't the Ladies need servants, helpers?_ It couldn't be impossible. _Bah. If I have to, I'll make them my own retainers. And if they're the sort that are hot as cats in heat, I'll get them money enough to go to a town and set themselves up as courtesans._
It would also enrage the Christ priests, she suspected, if they found out about it. Well, that was not her problem, and she would not make it the problem of the women. If she dealt with this properly, no one would ever know who her spies were. But she really liked the idea of the women as spies; women had the potential to go anywhere and listen to anything in the camp. She was probably not the first person to think of doing this, but it was a new idea to _her,_ which meant it was likely to be a new idea to their enemies as well.
As for sabotage . . . well, she would think on that, as well.
Meanwhile, as the other war chiefs continued to talk, she was making mental notes. Nothing was decided tonight, of course. They would have to discover what March was doing. The High King would have to decide what _he_ was going to do. Then he would have to ask for levies through Lancelin.
Would he ask Lot? Probably. And Lot would say "yes" and actually do nothing. But now all four of Lot's sons were with the High King; whatever Medraut had told Arthur about how Anna Morgause had been murdered, all of it had been smoothed over somehow, for Lancelin had several times said that Gwalchmai, Agrwn, and Gwynfor were still Arthur's Companions, and Gwalchafed was absent only because he had wedded recently and taken up life in his lady's lands.
_And Medraut is still at court as well._ Gwen pondered that, as she pondered how the firelight made shadows on Lancelin's face. From all that Lancelin had said, Medraut had made himself welcome there—although, like Lancelin himself, Medraut was no favorite of Arthur's queen. _Hardly surprising. She would be no favorite of Medraut's either._ Lancelin had said nothing about Medraut being Arthur's son . . . perhaps Medraut himself had not made that openly known. But Arthur had made him one of the Companions, and from the little Lancelin said, he was giving a good account of himself among them.
Was it possible he could have . . . reformed, somehow?
_A nice dream. A viper does not cease to be a viper because it smiles._
In the absence of concrete information, the talk had devolved to mere man-gossip. The mead had made them mellow and sleepy; even Lancelin, who had drunk but sparingly of it, looked heavy lidded. She slipped away.
Only to have her arm seized once she was away from the benches.
It was Bronwyn.
"You are not thinking of using the Folk of Annwn—" she whispered urgently, drawing Gwen into the shadows. Gwen was startled.
"No!" She shook her head. "No, I had rather stay well clear of them. They are unchancy. And unreliable as well, if you listen to the tales that Ifan sings. Too often those in stories call upon them only to be unanswered or not answered in time. Too often they flit off elsewhere or turn on you because you gave them some unintended slight. No. Let them dwell in the new marsh and leave us be, and I will be content."
Bronwyn let out a deep sigh of relief. "I saw that you had that thinking look and—what were you thinking, then, that you did not tell the other chiefs?"
She was glad that the shadows hid her blushes, for she did not want to say that at least half the time she had been thinking about Lancelin. Instead, she explained her idea of using the camp followers among the Saxons and March's army as spies. Bronwyn heard her out.
"It could work," she said at last, "But better that we find some women among our people willing to go."
Gwen blinked. That had not occurred to her. "But—would—I thought—"
"Leave that to me," the old woman told her. "There are those we took from the Saxons who would dearly love a taste of revenge. There are those of the western lands who are shamed that March is rebelling against the High King. The Ladies favor the High King; there would be some among them, mayhap. And . . ." She chuckled. "I can think of one or two who would gladly do this for the sake of the means to set themselves up in luxury in a city. Not everyone thinks the height of all good things is a sheepcot, a flock, and a shepherd who cannot put two words together without 'baa' in them."
Gwen giggled a little. "I leave it in your hands, then," she said and was about to go to the room she now shared with no one when Bronwyn tugged again on her arm. "My girl, that Companion—I would give you good, sound advice."
She froze.
"There are men, a very few, who could look on a warrior, see the woman within, and remember the warrior. He is not one." Bronwyn's voice was steady. "He will see you as a warrior and a comrade or as a woman. Never both. It will be up to you to choose which he sees. And when you make that choice, remember, he will treat you as you have chosen."
Gwen went cold inside for a moment. Bronwyn was right. She knew that Bronwyn was right. It made her angry—at herself and at him. It made her sad with disappointment. It made her embarrassed. But that did not make it any less true.
She could go to her chest and dig out one of her gowns, let her hair loose, and go and act as Gynath had, back when they were younger. Make big eyes at him, hang on his words—yes, she could do all of that. And, yes, he would see her as a woman, and he might even find her attractive. And so he would treat her as a woman.
Even in her armor with her hair clubbed up, he would treat her as a woman.
And so would the other war chiefs.
All that she had worked for, all that she had built, would be gone. Her father would lose the war chief that she was becoming. Her sister would lose the steady guard and guardian for her own children. Caradoc would lose the captain she would be for him. And for what? So that she could play the fool over a man.
Or she could keep things as they were, and she would have the friendship and high regard of a man whose company she enjoyed. They would speak and act as equals. He would listen to her ideas with respect, criticize them if it was needed, teach her more of the ways of war.
It was only years of schooling herself, training herself, controlling herself, that kept her from raging, weeping or both. She knew that outside the tiny group of her family and Bronwyn, she was thought to be cold, unfeeling, and in no small part that was because she meant them to think of her in that way. In that first year of her training, when some of the older boys had bullied or snubbed her, and even some of the younger had sometimes tried to sabotage her with dirty tricks and things meant to put blame on her, she had pretended that there was no hurt, no loneliness, that nothing would mar the armor of her control. Now that was habit.
"I see," she was able to say, slowly. "Thank you for the warning, Bronwyn. You are . . . entirely right."
"I have lived a very long time, my dear," Bronwyn said, a little sadly. "I have seen many a girl throw over what she held dear for the sake of a trifle."
She patted Bronwyn's arm, glad that the old woman could not see the expression on her face. "This one will not," she said.
Then she went to her bed. She lay, staring into the darkness, angry at fate for making her female, angry at herself for being so foolish, grateful to Bronwyn for seeing what she had been blind to, yet angry with her too. There were bitter tears in the back of her throat that she would not shed. Not now. Not ever. After all, what was she weeping for? Nothing more important than that poppet that Gwenhwyfach had torn to bits all those years ago.
Gwenhwyfach—and what would _she_ have done?
_Put on the gown of, course, and thrown herself at Lancelin—_
But she was not Gwenhwyfach, nor did she ever want to be. She was herself. And even if that was a cold and lonely thing, it was what she had wanted to be. Not "someone's wife." Not "someone's mother." Herself, with her own honor, her own place, and her own path. She owed nothing to anyone, save duty to her father.
It was comfort, if cold comfort.
She turned on her side and stared at the wall, sternly telling her eyes that they must dry. Or rather, she stared at where the wall should have been.
For at that moment, she felt that dizziness come upon her once again, and where the wall was, there was dim light instead, light that grew, and warmed, until she found herself staring into a fire-lit room, and at the backs of two women.
One had white-blonde hair that streamed down her back to her ankles. The other had raven locks that pooled on the floor. Both were wearing nothing more than their hair.
They bent over what at first she took for a table; then she realized that it was an altar, not a table. What there was upon it, she never got a chance to see, for the blonde suddenly raised her head.
"Morgana," said Gwenhwyfach, in a voice so like her own that Gwenhwyfar felt her breath catch. "we are overlooked."
The second also raised her head and turned slightly, staring straight into Gwen's eyes. And now Gwen felt her breath freezing in her throat.
"Well," Morgana said, her tone even and measured. "Blood will tell. Even untrained and on the Path of Iron, look who has found her way to our working."
Now Little Gwen turned. Her naked body was astonishingly beautiful, even overwritten as it was with runes painted in blood. And her face was Gwen's own, but contorted with a sneer.
"Spying, sister?" The sneer turned into a snarl. "Well, that will never happen again. And you will forget what you have seen,"
And something hot and red flashed between them, struck Gwen like a thunderbolt, and sent her tumbling down into darkness, her memories slipping between her fingers and running away like water.
Despite a near-crippling headache the next day, Gwen went grimly to work on her plans. Bronwyn found women as she had promised, and they were a varied lot. One had been a Saxon thrall and had lost her family to them and wanted nothing more than revenge. Two were very poor indeed and honest about their wish to be amply rewarded. "As well be swived by a mort'o lads an' come to a saft bed after as be swived by one an' come to a mud hut," was the calm and logical response of one. One was sent by the Ladies and remained silent about her reasons; since Cataruna vouched for her, Gwen accepted her without comment. What all of them had in common was that they were attractive, under no illusions as to what would happen to them as camp followers, and were as fierce in their desire that March and the Saxons be beaten as any of Arthur's Companions.
They did not need to remain in the camps long, much to Gwen's relief. She felt enough guilt about sending them in there in the first place.
"And you have no guilt about sending your scouts out to spy?" was Bronwyn's dry question, when she fretted aloud one day.
"Of course I do!" Gwen snapped. "But . . . this is different!"
Bronwyn raised an eyebrow. "So you see them as women and not as warriors."
Gwen opened her mouth to protest and shut it again. Because, yes, she did. And she felt great irritation that she did so. And yet—they were women. They were not warriors. They had not been trained as warriors.
But she was glad enough when they got what she needed and made their way back to her—the sure information that March had allied with the Saxons, rather than buying his way across their lands, and the combined forces intended to attack Arthur together.
Now she could concentrate on her real duties with a whole heart—or so she thought.
Gwen had not chopped wood like this since she had been a mere squire, but she needed to take out her temper on _something,_ and splitting wood was less damaging than hurling pots against a wall and more satisfying than perforating a target with arrows. She swung the ax against her hapless targets with accuracy and fury. Every blow split a log. At this rate, the squires would not need to chop wood for a week.
The squires who had been assigned to this task had all taken one look at her face and fled. Everyone else had already heard the news and wisely were avoiding anywhere she was even rumored to be. The pile of neatly split logs grew, and her temper was eased not in the least. She was in a self-imposed circle of silence in which there was only the wood, the ax, herself, and her anger.
Finally the king himself came down to the yard, and sat on a stump, and waited. She could not remember him _ever_ coming here before. But she knew herself well enough not to trust herself to speak right now, so she pretended that she had not noticed him there.
The ax handle was a comfort in her hand, and the steady _chunk_ as it cleft each log was just as much of a comfort. This, at least, she could control. She had chosen to do this. No one had said "you must," or "you must not." No one had come to say "So-and-so would do this better, go tend to your horses." Yet it took her quite some time before she was able to get anything like words past the tightness in her chest and throat.
"It's not _fair,"_ she managed at last, the final word punctuated by the blow of the ax. She tried not to wail. She tried not to sound as if she was accusing Lleudd, whom she did not in the least blame.
"Indeed, it is not," King Lleudd agreed. "Very unfair. You have spent long days training your scouts. You work as an effective group, and without you, they will be less effective. They trust you; they will not trust another leader so much. You have proven yourself in battle. You should have been the one to lead and command them."
The ax thudded into another log. The two halves fell to either side of the chopping block. "Whoever this 'Kai' is, he cannot possibly know what they can do! I am not even sure he knows how to properly use scouts, much less my men!"
"He is the High King's foster brother, and no, he cannot know what they can do, nor do I think from what I have heard of him that he is a particularly good war chief." Lleudd sighed. "He is usually in charge of the squires and the court. He is not terrible . . . but he is not particularly good, either. At least they will not be misused. The High King fights with Roman tactics, and your men do not charge into battle like Saxons with no strategy. They will be just one more scouting troop among another dozen."
"But they will get no chance to use all the things we have worked out together," she said angrily. "They will get no chance to harry the Saxons as we did this winter."
"No, because Kai will think such things unnecessary. But at least, because you trained them, they will know to be clever. They will know how to fight with the Roman style that the High King uses." Lleudd sighed again, heavily. "I am sorry, my daughter. I am sorry that their command has been taken from you. But the High King prefers to use his own commanders."
"And the High King does not trust a female warrior," she said, bitterly. "He does not think such a one as I can command anything. Younger _men_ than me have been put in command. Younger _men_ than me are his warleaders." _Thunk._ The ax split another log. "He thinks that I am only a chief because I am your daughter, and he does not trust my ability."
"Probably not," King Lleudd agreed.
"And Lancelin did not see fit to argue for me." _Thunk._ That was another sore point. He spoke with her as if they were equals. He seemed to consider her a friend. He knew she was intelligent. And he had not spoken up for her.
"Possibly not. I cannot say. Possibly he did. Possibly he did not try because he did not want to remind the queen of his presence." Lleudd shifted his weight on the stump. "I do not know, because I was not there. It is hard for a young man when he is caught between a man and his wife."
She finally stopped and turned to face her father.
"Which makes him a coward?" she asked, angrily. "I had not thought him a coward."
"It makes him . . ." The King sighed. "It makes him a man torn. On the one hand, he knows what you can do, even if he did not consider himself your friend. Which, I believe, he does. He knows you are not only a good leader, he knows that you know your men as no one else, and you are always thinking of the best way to use them with the best outcome. And as your friend, he would desire to advance you. On the other hand, the one thing he desires above all else is to serve his lord, his king, and his friend. Someone he has known far longer than you. You have seen that with your own eyes."
Reluctantly, she nodded. She could tell; every moment he had been here, his heart had been with his king. She had been wrong in thinking him heart whole. He was a man driven by duty, and protective of his friends. He mistrusted the queen. There was nothing else that would have so great a part in his life. Not even, maybe, a lover.
"Perhaps, perhaps, there is also a touch of wariness there," Lleudd continued. "You bargained with the Folk of Annwn. You are being served by them, in a sense. You are known to be subject to the Sight at times. Most warriors are uneasy in the presence of magic. And, yes, the Merlin has served the High King for longer than Lancelin, but the Merlin has ever been secretive about his magic. Few have ever seen him actually use it."
Slowly, slowly, the king's calm reason overcame her fury. Tears started into her eyes, and she dashed them angrily away. "You are not uneasy in the presence of magic!"
"I was wedded to Eleri," he pointed out dryly. "I have a Lady for a daughter, a bard for a son-by-marriage. Even so, _I_ have never seen the Folk of Annwn. No one I know has, until now. This is more than mere magic, my daughter. This is meddling with the Spirit Realms."
And this was her fault, how? "I didn't know they would come! I only wanted to make a swamp to last for a fortnight or two!" Her eyes burned, her stomach tightened. "They wanted to treat with _me,_ not the other way around!"
"I know that." The king pointedly ignored her reddening eyes. "But . . . you are like your mother. You look much younger than your years. You are fair, and most of them are dark. And now this; it makes people wonder if you have the blood of Annwn in your veins yourself. Now, this is unfair. It is unjust. But it could have been predicted, I think."
She stared in unhappy outrage—and some guilt, for had she not thought these very things herself? "What can I do?" she asked, controlling herself with an effort. Again, she tried not to wail.
"First, we do not speak of the Folk of Annwn in your swamp. Your bargain means that they will not harry our people; likely will not show themselves."
She nodded. That was good sense. "You think maybe people will forget?"
He shook his head. "But we can put it about that it was Ifan they treated with, and I will say I granted _him_ the lands you gave them. Only my war chiefs know the truth. Ifan is a bard. Everyone knows that the Folk of Annwn favor bards."
Again she nodded. "And—"
"And as for the rest, this will be hard, but you have done harder things." He smiled at her. "The High King has never had a female among his warriors. And if you are to break past that, you must remember that you are a warrior first, last, and always. That you are a woman is merely . . . an inconvenience. Do you understand?"
She was very glad that the other war chiefs were not here to see her fighting to hold back tears. The last thing she needed at this moment was to seem weak. Womanly. Her father was right, very right, and he was only reminding her of what she had known herself.
"Yes, my King," she replied, straightening her back.
"Good." He smiled. "Now, any warrior thus supplanted could be expected to be angry. I have seen many of my own chiefs in a rage over such an insult. Chopping wood is a good way to relieve that anger. Is your anger relieved?"
She took several deep breaths and blinked her eyes dry. "Yes, my King."
"And since the High King has seen fit to leave one of my _ablest_ strategists behind, I expect War Chief Captain Gwenhwyfar to take command of all of my men that have been left to me." He waited a moment for the meaning of what he had just said to come home to her. And the moment it did, her eyes widened in shock.
"But—I—"
"My remaining chiefs do not think as quickly as you do. For that matter, your king and father does not think as quickly as you do." He gave her a look of warm approval. "You have a knack for solutions where others see only that there must be fighting. You dealt with March on our border in a way that cost us only a little land and no men. Should March double back, or the Saxons desert him to attack here, we will have to defend our lands with less than half the men we _should_ have. All of my chiefs agree that you are the fittest to lead in that case. Now. Make me a defensive strategy." He stood up. "In fact, make me several. Think like that madman. Think like a Saxon. Find a way to make ten men fight like forty."
She gave him the fist-to-shoulder salute of the Romans. "Yes, my King."
"That is my war chief." He patted her shoulder with approval.
"That is Eleri's daughter. You fight with your head. My chiefs only know how to fight with their swords. Now come." He beckoned to her. "Let us go back to the maps. Arthur is my High King and possibly the greatest leader I have ever seen, but no one has ever said he was incapable of being a fool. Though in this case . . . _I_ am not the loser by his foolishness." He laid one hand on her shoulder. "In fact, he has done me a great favor, in leaving me the finest sword still in my armory."
And that was enough to take most of the sting out of the insult.
**Chapter Seventeen**
**N** **o one ever** _said Arthur was incapable of being a fool._
Never had Gwen thought that those words would come back to haunt all of them. But they had. Arthur's current actions had brought them all to a stalemate.
A chill mist hung knee-high above the ground around a lake and billowed higher above it. It was very quiet; a little splashing somewhere out there in the mist and an occasional call of a loon or some other water bird only made the silence deeper. For some reason, even the frogs were quiet. Gwen glanced uneasily at the great tor that loomed over them all in the predawn light. There was Yniswitrin, the Isle of Glass, rising above that mist that always hung over the lake that surrounded it. At the top, if you knew what to look for, you could see a squat stone tower. That was the abode—or at least, the visible part of the abode—of Gwyn ap Nudd, one of the Kings of the Folk of Annwn, so it was said. Either there beneath that tower, or beneath the waters of the lake, or both, were entrances to Annwn, the Otherworld, itself. On the shores of the lake were two more poles of power. On the one side, a church and abbey of the priests of the White Christ that was over three hundred years old. And on the other, the Cauldron Well, hidden, secret, guarded by the Ladies who had their school here, where it had stood for far, far longer than the church. The three formed a triad of balancing powers, and managed a sort of uneasy truce.
But that was not why they were all here, this army of the High King's allies. Before them, also on the island, was _that_ reason. Built into the side of the tor, its top barely visible above the mist, was a stronghold made of stone. The fortress of Melwas of the Summer Country, a man who had once been one of Arthur's Companions, whose blood was at least as old as Arthur's, and who _might_ have a touch of the Folk of Annwn about him.
A man, and a king. A man and a king who had taken Queen Gwenhwyfar when Arthur was off skirmishing with the Saxons, carried her off to this fortress and was using her as his claim to supplant Arthur as High King. He had every intention of wedding her, according to all the sources, and using the claim of his old blood and hers to take the throne.
And there was rumor about the camp that Gwenhwyfar might not have gone unwillingly.
Gwen rubbed her aching head; this was all a hideous tangle, and it was only getting worse. Arthur had tried to get across the lake any number of times and had not even landed more than a handful of his men at the base of the stronghold. The mist would come up and bewilder them all, the boats would land anywhere but where they should, once a storm nearly drowned them all by all accounts, and the one time he did get some men at the foot of the castle, they'd been successfully repulsed.
She had not actually seen the High King in person, but she could well imagine the tone of his temper.
And what had happened to the Merlin did not help matters at all.
Oh, the Merlin . . . if there was anyone who might have been able to find a way to get Arthur's men onto the island, it was he. He had purportedly worked greater feats of magic in the past. He could probably have disguised Arthur as Melwas and gotten him into the fortress that way, or somehow built a bridge to the island out of the mist itself. There was only one small problem.
The Merlin was no longer in a position to conjure anything.
Though rumors were flying throughout the camp about just what, exactly, had happened to him—the wildest of which featured him being locked inside a cave, a rock, or most improbably, an oak tree, by the Lady Nineve—one of Ladies had come to Gwen as soon as she had made camp and told her precisely what had befallen the Merlin.
"He was elf-shot," the woman had said. "Though whether it was a curse, or some cruel weapon bought of the fae by Melwas, we cannot say. But as Melwas was fleeing, with Queen Gwenhwyfar as his captive, the Merlin was looked for in vain. He was found at last on the floor of his room, taken with a fit. And now he lies as one made of oak, with Nineve tending him. He cannot speak, and only his eyes seem alive."
She could not help but wonder, although she did not say, if this was the punishment for all those innocent infants he had ordered killed so long ago. Certainly now he was as helpless as an infant, as trapped within an unworking body as if he had in truth been encased in a tree.
So much for the Merlin. The Ladies, of course, did not have any sort of magic that could be used to solve Arthur's problem. And if Gwyn ap Nudd was inclined to help, well, he had not even so much as showed a light in his tower.
Gwen had turned up at the head of King Lleudd's contribution to the army; she shortly thereafter discovered that in some ways, her arrival had made things even more complicated. To begin with, there was her name. It had caused rumors to fly through the camp when she first arrived, that Arthur's queen had escaped, that she had arrived at the head of her own warriors, that she was, in fact, the ghost of Arthur's _first_ queen come from beyond the grave to help him. It seemed that everyone and his dog needed to come look at her to be sure that she was only herself, Lleudd Ogrfan Gawr's daughter. It had gotten to the point by sunset that she simply left her own encampment and with a small escort made a tour of Arthur's entire forces, introducing herself to all the war chiefs and making sure that everyone got a good long look at her.
That solved one problem, anyway, though now scarcely anyone called her by name. "The Giant's Daughter," they mostly called her. That was maddening, but understandable. What else were they going to do? Two Gwenhwyfars was one too many in this situation. And it wasn't as if she had yet earned one of those clever descriptive names some warriors got.
More vexing was the unspoken assumption that Gwyn ap Nudd was simply going to appear and declare himself for Arthur just because _she_ had turned up.
And oh . . . what a mixed set of expectations _that_ was. Because not everyone here wanted a King of Annwn to turn up and make himself an ally. First and foremost of those that would object were the Christ priests.
With the abbey so near at hand, it was not surprising that there were monks wandering about the camp; and since the abducted queen was a follower of the White Christ . . .
Well, she supposed they were finding it necessary to make it clear that they favored Arthur. If the queen had, indeed, turned her coat, then they certainly would want to show by their presence that they still favored Arthur. Although, of course, there was a further complication because Melwas himself was Christian.
Gwen felt, rather cynically, that it was possible these priests were trying to play both sides; although they were praying ostentatiously for the return of the queen, if Melwas won out, they would also be right here to be the first to proclaim him the new High King.
Whatever was on their minds, they did _not_ approve of anyone who consorted with "demons" as she was said to do—and evidently, a "demon," in their eyes, was any creature that was not mortal and not an "angel."
The monks, therefore, did not like her, and the rumors that Queen Gwenhwyfar was not an unwilling captive were making them uneasy. And that made them even more unhappy with _her_ presence. She was a living reminder of everything the queen wasn't—including, it seemed, loyal to the High King.
Then there were the followers of the Old Ways, who evidently expected her to conjure up Gwyn ap Nudd, who would then divide the waters of the lake, or build a bridge of rainbows across it, or fly the entire army through the air to take it to the fortress where the queen was. And then, of course, more magic would breech the walls, and in the conquering army would go, stopping only for enough combat to make them all heroes.
After all, hadn't she won allies of the Folk of Annwn already?
Oh, it was irritating; here she had foregone the credit for striking that bargain in her marsh, only to have everyone turn right round about and decide that of course she _had_ done it after all.
It made her head hurt. And she wanted to swat them all for being so foolish.
Well, she had gotten another summons, this time from Lancelin, to meet with him, some of the Companions, and some other, unspecified, leaders. And where once she would have been excited to meet with these warriors who were famed from the Channel to the Western Sea, now—
Well, she just hoped they weren't expecting any magic out of her.
She nearly jumped out of her skin when the first person she saw as she entered the fire-circle was Medraut. She restrained herself however, and by the time he turned away from the person he was talking to, a huge, broad-shouldered man who looked just about as angry as if he had strapped on a helmet full of hornets, she had composed herself.
Lancelin had spotted her by then and welcomed her, giving her a seat between himself and the angry man, who turned out to be Gwalchmai. Gwalchmai actually _was_ as angry as if he had strapped on a helmet full of hornets, and with good cause. He had been out in a boat trying to find a place to land; Melwas mocked him from the battlements.
And so did Gwenhwyfar.
Now, according to Lancelin, at best Gwalchmai had what might, at the kindest, be charitably described as a prejudice against women.
_Of course, given his relationship with Anna Morgause . . ._
But this was a great deal more insult than a warrior and one of Arthur's Companions could be expected to bear with an unruffled temper, even if that warrior was the next thing to a statue. Gwalchmai had, by all accounts, a nature so hot that he got into quarrels merely because he thought someone had looked at him oddly.
He glared at her as she sat down. She gave him the most sympathetic look she could muster.
His glare turned to suspicion. She shrugged and put on a rueful expression, trying to convey that she not only sympathized with him, she had no sympathy whatsoever for the queen. She caught Medraut watching them with veiled amusement.
This meeting turned out to be mostly Arthur's chief Companions. Lancelin, of course. Gwalchmai, Kai, Bors, Peredur, Geraint, Bedwyr, Trystan, Medraut, Caradoc, Dinadan. The firelight made moving shadows on their faces, these famous men, Arthur's closest comrades. Square and narrow, bearded and beardless, dark-haired, most of them, a few lighter. She supposed she should have felt intimidated by them, but they looked no different, really, from the men she had fought with and beside for all these many years. Experienced, yes, but so was she. Kai looked petulant, as if he forever labored under a grievance. Bors seemed weary, as did Bedwyr. Trystan, the nephew of March—oh, now that one gave her a chill. There was a look of doom about him, and a melancholy, as if he felt it too. Dinadan was impatient: clearly a man of action and few words. Caradoc was sardonic, and Geraint looked as if he considered everything something of a joke.
They were men, like any others. No matter that she had spent years listening to tales of their deeds. Braith had been just as courageous and deserved just as many tales. The only two that gave her pause, really, were Trystan and . . . Medraut. Of course. It was always Medraut.
There were three of the allied war chiefs she had not met yet, the chief men of three of the allied kings, sent, as Gwen herself had been sent, at the head of their forces. There was a Druid, Aled ap Meical, who seemed to be taking the Merlin's place, although he did not have the title and looked ill-at-ease in the position. And there was a Christian priest, Gildas, who glared at the Druid and Gwen with equal impartiality; clearly he hated them both.
"I asked you all here," said Lancelin, carefully, "Because of something that happened to Gwalchmai today. I do not believe this should be bandied about the camp yet, but we need, I think, to discuss this. Old friend?"
Gwalchmai got heavily to his feet. "This afternoon, I took a squire and a boat and went to look at that bastard's walls," he rumbled. His shaggy red brows furrowed together. He was a bear of a man, and he gave the impression he could easily snap an ordinary man in half with his bare hands. "I bethought the mist would keep me hidden, but I should have known my cursed luck would make sure that whatever I wanted, the opposite would happen. The mist blew off, and there I was, and there was Melwas on the tower, and if I'd had but a knife or even a stone to throw, we'd not be sitting together having this meeting, because I'd have killed him on the spot."
The last was growled with an air of frustration, and Gwen didn't blame him.
"At any rate, he commenced to flinging insults instead, and I did the same. And then, after a bit of this pleasantry, someone comes to join him. Gwenhwyfar."
Those who were not yet aware of this news exchanged uneasy looks and murmured to one another.
"If his tongue's sour, hers is like a whip," Gwalchmai continued, flushing a deep red with anger. "I'll not repeat what she said to me, though there wasn't much of it before she ended it with, 'Let us leave the loons to paddle back to their nests,' and drew Melwas away. But she looked nor sounded not like any captive."
And with that, he cast a glare at Gildas, who was plainly taken much aback.
"I came and told this straightaway to the High King and to Lancelin, and Lancelin called you here." Gwalchmai sat down again.
"This is ill hearing," Kai muttered, staring at his clasped hands. "But I cannot think what we are to do about it."
"Well, I will tell you what you are to do about it."
All their heads came up as a voice like the sound of a hunting horn cut across the silence. And one strode into their fire-circle as if he owned it and immediately caused all the hair on the back of Gwen's head to stand straight up.
He was beautiful and gold and white, with golden hair, pale skin, gold-embroidered white tunic, trews and boots. He could easily have been the brother to one of the Lake Maidens, and he was as beautiful as they were. Inhumanly so.
"Inhuman" was a very good word for him. Having seen one of the Folk of Annwn once, Gwen was not likely to forget their look again.
This one wore a thin gold circlet about his brow and a torque of gold with orm-headed finals, so there was only one person that he was likely to be.
And she was the first of them to recover her wits and realize it. She leaped to her feet and bowed deeply; she made sure that they saw her offer the ultimate respect before the others, who might not have the eyes to see what and who he was, offered him an insult.
"Greetings to the noble and generous Gwyn ap Nudd, King of the Folk of Annwn," she said, as she straightened again. "Welcome to our Council. I know that the High King counts you as a friend and one of his Companions, as well as ally."
Those who had recognized him, had also gotten to their feet and likewise bowed, a bit later than she had. Those who had not, looked stunned for a moment.
Then one by one they recovered their wits and their manners and, as Gwyn ap Nudd looked them over with amusement, scrambled to follow their example.
"Greetings, my fair cousin, fair of speech as you are of face," he replied genially. "I regret that I did not seek out the High King before this, but I had hoped that this situation would sort itself out without my intervention." He lifted one long brow at Gildas. "My meddling is not always considered welcome."
Gildas looked uneasy.
"And I have a solution to this knotty problem. If—" now he turned an ironic expression on Gildas "—if the honored and holy Abbot Gildas is prepared to follow up on the— _assertion,_ for of course no priest would boast!—that I know that he made to his fellow monks."
Gildas went red, then white, then red again, and back to white. He was caught, and he knew it. Whatever it was he had boasted that he could do, or at least attempt, he had done so in the hearing of Gwyn. And now he had two choices. Either try it, whatever it was, with Gwyn's help—the help of a pagan thing, perhaps a demon, certainly a creature with whom the good Christians were not supposed to consort. Or back out of whatever he had said, and be held up to ridicule by, yes, that pagan thing, that possible demon, who would no doubt find a way to mock the religion as well as the man.
The latter, clearly, was not a choice for him. He straightened, still white. "I said that I would try to bargain a settlement between Melwas and Arthur if only I could get into the fortress," Gildas said bravely. "And so I shall."
"And I shall get you in. I weary of this Melwas, who calls himself King of the Summer Country, which is one of _my_ titles that he usurps." The blue-green eyes turned nearly black, although that was the only sign of the King of the Annwn's anger. "I weary of him setting himself up on my island. I weary even more of the presence on my island of Arthur's queen. This quarrel stirs up my people, your iron and steel bring them discomfort, and the peace of my island has been disrupted. I want them gone from my shore. But he is—supposedly—a follower of your Christ. So, man of Christ, as I and mine have not troubled you in all the years of your presence, perhaps you can repay that peace by making him come to see reason."
Gildas swallowed. "I hope I may. And if you can take me to him—"
Gwyn ap Nudd laughed softly. "Nothing easier." Before Gildas could move, or even flinch, the king had seized him by the arm.
Even Gwen could not rightly have told what happened then. To her, it looked as if Gwyn had stepped through a door, drawing Gildas after him. But there was no door there. They were there . . . and then two steps later, they were gone.
Gwen blinked and rubbed her eyes.
"Well," said Medraut into the silence. "That was curiously satisfying. I was wondering if there was anything that could silence that pompous prig."
There was clearly nothing more to be done that night, so the council broke up, with Lancelin and Kai volunteering to tell the High King what had just transpired. The awkwardness was palpable, as no one really knew what to say or do. Gwen wondered, though, just what sort of magic they had seen before—after all, the Merlin had been an integral part of the High King's entourage since the beginning. Had he simply never done anything in their presence?
Or maybe the awkwardness was partly due to the queen's defection and partly due to the fact that Gwyn ap Nudd had just appeared and trumped them all. Whatever plans they'd had in mind would have involved more siege, more fighting. Gwyn had aborted all of those, carrying off Gildas to try and end this thing without further warfare. At the moment, they were all so taken aback that they couldn't think.
Well, if they couldn't think, they could certainly _talk,_ but she realized immediately that as she was not one of the inner circle, they were not going to do any frank talking around her. Wryly, she decided that sleep was her best option, so she bid them all farewell and started back to her encampment.
She had gotten just out of the reach of the firelight when she realized that she was not alone. And the figure that was keeping pace with her was not one that she welcomed.
" 'Fair cousin,' is it?" said Medraut, in a tone that sounded perfectly pleasant if you didn't know him and realize there was certainly some other motivation behind his question than the wish to be conversational. "Are there folk of Annwn in your bloodline, then?"
"Not that I know of," she replied, throttling down her revulsion and replying with the same surface pleasantry. There it was again. And he was married to her sister; wouldn't he _know_ by now if there was fae blood in them? Or—maybe he wasn't as strong in magic as he liked to believe. "I'm sure someone would have mentioned it before this if there were. I believe that the King of the Isle of Glass was merely acknowledging that technically I am the overlord to some of his people now. Of course, he could have had some other motive; it's impossible to tell with the Folk."
"Ah, yes. Your little bargain." Medraut stalked alongside her, and with his longer legs, there was no way she could outdistance him without running. Damn him. He was the last person she wanted to talk to. You had to be at your cleverest to exchange more than a few words with him, if you didn't want him to ferret more out of you than you wanted him to know. "That was cleverly done, by the way. I salute you. I had no idea you had enough power in you to call up the Folk."
"I don't." Actually, she didn't want Medraut to think she had any magic at all. "I gave all that up when I took the warrior's path. It wasn't me that summoned them, it was Cataruna and Ifan, and even then, I think it was entirely accidental that they did so. We only summoned the waters to make a swamp, so King March would have to take his forces across Saxon lands rather than ours. I actually think that the Folk came by themselves."
"Still clever. You saw an opportunity and took advantage of it. It was a good bargain; you lost nothing but a bit of land and got some formidable guards in exchange. Morgana was annoyed that it had not occurred to her to do the same. By the way, you may congratulate _me._ I have a son." There was a flash of teeth, catching the light of a camp-fire as they passed. "And before you ask, no, Arthur is still unaware that your sister and I are wed."
Which meant, of course, that he didn't want Arthur to know and was reminding her of her promise. "I see. Well, congratulations. You are now ahead of the High King in that game. And the queen remains childless." Unspoken was the depth of Medraut's ambition. Unspoken, too, that although Medraut was not only a bastard but the product of incest, when presented with a grown man, a proven warrior, with his own heirs, if Arthur died it was likely that the irregularities of Medraut's birth would be . . . overlooked. No one wanted to go through the chaos that had followed Uther's death.
"I know. I live in hope." There was another flash of teeth. "Meanwhile, I find that I quite enjoy being one of the Companions. It is a strange thing that I find get along better with my brothers now than I did at home. Gwalchmai has been a particular boon friend; he seems to appreciate my wisdom, and I certainly appreciate his muscles. Perhaps he wishes to make up for pummeling me so much as a child."
That was easy to read. Medraut was finally able to manipulate the rather dim eldest of the Orkney clan and possibly the others as well. "This is the first I have encountered any of them but you. Well, again, I give you congratulations on siring a son. Where are you keeping him and your wife?" she asked. "Surely not with Lot—"
"Oh, Morgana has her. They get along famously. " He waved a hand airily. "Like sisters, really. It's quite affecting, to see them together."
Now what did that mean? That Morgana and Gwenhwyfach hated each other as cordially as Little Gwen hated her real sisters? Or was this to mock her with; implying that Morgana and Little Gwen were alike? Surely if Morgana hated Little Gwen, she would not have her in her own castle, no matter how much she wanted to oblige Medraut. Gwen had heard stories about Morgana, who was supposedly an even more powerful sorceress than her sister, Anna Morgause. She seemed to spend half her time helping Arthur, and the other half being a thorn in his side.
But then—stories. They were only that. Men were uneasy enough around a woman with power of any sort. It would not be surprising that they made up tales about one who was powerful and refused to tie herself to any man to boot.
For just a moment, something too faint to be called a memory drifted past in her thoughts. An image, a glimpse, of Morgana and Little Gwen, side by side—but it was gone before she could grasp it.
She decided that she had better say something; she had been silent a little too long. "So long as I can assure Father she is content, that is all that matters," Gwen replied untruthfully. The reality was, somewhere down inside, she was sickened. Gwenhwyfach by herself was bad enough. Gwenhwyfach tutored by Anna Morgause was worse. And Gwenhwyfach working hand in hand with Morgana? Gwen pitied anyone foolish enough to cross them.
"Yes, well, you can tell King Lleudd anything you like," Medraut replied, stopping suddenly. That was when Gwen realized that they were at the edge of her encampment. "Just as long as you keep the oaths you swore. I have many plans in motion, and I would be very vexed if they were to be disrupted." His eyes glittered in the darkness. "Morgana and my wife would be even more disappointed than I."
That was easy to read, too. _Keep my secrets, or there will be a price to pay._ Morgana had always struck Gwen as the sort of person who liked being the hidden power and preferred to do nothing overtly.
Morgana was also, by all measures, someone who never staked all of her ambitions on one plan, or one candidate. If Medraut lost his bid for Arthur's seat, she would have a dozen more directions she could go. But Gwenhwyfach? Without a doubt, she was already, in her mind, measuring her brow for the High Queen's crown. Cataruna could probably handle Morgana and her magic if Gwen were to tell what she knew. But Gwenhwyfach, or the two of them together? Oh, no. Gwen was not minded to cross her little sister.
"And I have no plans except to serve my father and his heirs," she replied honestly. "I am a plain warrior, cousin. I have no head for grand schemes."
"Sometimes it is a good thing to have no ambition." The flash of teeth, the glitter of eyes in the dark, put her in mind of something feral. "And on that, I bid you good night. It has been a most fascinating evening, with great potential for amusement to come. We will see what the morning brings."
She was only too happy to leave him there and retreat to the safety of those she trusted.
She gave her own chiefs a brief explanation of what had happened, omitting only Gwalchmai's report of the behavior of the queen, the strange way in which Gwyn ap Nudd and Gildas had vanished—and that the King of Yniswitrin had called her "fair cousin." If the word of the queen's treachery was to be spread about the camps, she did not want it to come from _her_ people. And as for Gwyn ap Nudd, well, she intended to publicly distance herself from the Folk of Annwn and from magic as much as possible. Especially with Medraut snooping about. The less he thought about her, the better.
They accepted the news with astonishment. Then she left them to mull it over themselves. It was always better to let the men talk themselves out without her there to overhear them. It let them know that she trusted them; it also allowed them to air whatever foolishness came into their heads without the risk of looking foolish in front of _her._
_As mother once said; men are worse gossips than women ever were._
In the morning, nothing much had changed, except for the rumors flying about the camp. As she had expected, a garbled version of Gwalchmai's narrative was all over the encampment, and the stories of how Gwyn ap Nudd had made off with Abbot Gildas were even more incredible than what had actually happened. In some, he vanished in a flash of lightning, in others, he grew great wings and carried Gildas off, and in some . . . good lack, it was _Gildas_ who sprouted wings and flew to the Island.
At least she could, with great virtue, make the assertion that none of that had originated with _her_ men.
In the meantime, the orders from the High King were to wait. So, wait they did. Morning became midday, and still there was no sign of anything going on, either on the mainland or on the island. The mist did not lift; if anything, it thickened. An overcast day meant everything was shrouded in gloom, and it was easy to imagine strange shapes in the mist. Most men stuck close to camp, save for hers. King Lleudd's force, emboldened perhaps by her connection to the Folk of Annwn, went out hunting and fishing. Gwen thought about trying to pay a visit to the Ladies and the Cauldron Well, then thought better of it. With all these strangers here, they had probably hidden the entrance to their school and stronghold, as they often did when times were uneasy, and although they would probably let her in, it might take her a while to get their attention. Besides, she had little or no magic these days. She would not be there as a fellow Lady, but rather as one who comes to see the sights . . . not entirely welcome under the circumstances. No, they knew she was here. If they wanted to see her, they would send a messenger, and if they did not send one, it was because mere visitors were not, at the moment, welcome.
The High King had not summoned her though he had sent courteous, if overly formal, greetings and thanks to her and her father and further thanks for the gift of the two of her father's famous gray cavalry horses that she had brought. Until she was summoned, it was poor manners to intrude on him and his councils, and really, there was not much more she could add. Nothing about this situation answered to either Roman tactics or anything she was good at. Add to that—her name. It would not be easy, hearing the name of his runaway wife attached to someone else.
But there was not much more she could do here at the camp, except add to gossip. She saw to her gear, but she had been so thorough that there was nothing left that she needed to attend to; Rhys and Pryderi were not much inclined to go riding out in the mist and gloom and showed their reluctance clearly. She didn't blame them and couldn't think of a reason why she needed to risk their legs and necks to an accident. After a good long while of staring blankly at the fire, it occurred to her that there was one foot of the power triangle here she could visit after all. After mulling it over, deciding against it, then deciding she was being a coward, she went to have a look at the church and abbey of the Christ priests.
It was not very imposing; the abbey was about the size of the village at Castell y Cnwclas; it was not a single building but a bevy of little wattle huts inside an enclosure, with the church, a more substantial timber structure, at the center. The huts looked like chicks surrounding a hen, and the church was about half the size of her father's castle. But one thing struck her almost forcibly when she ventured inside the dark, incense-scented building; as small as it was, within those four walls she encountered a sense of deep peace the like of which she had not felt outside of a Sacred Circle. And that—was astonishing.
When she left the church, she was accosted by a swarm of the inhabitants. The monks that lived at the abbey were all in a state, not quite panic but certainly great anxiety about the well-being of Gildas. She got the sense that he was greatly admired, and even loved, here. And far from being made to feel unwelcome, when they made sure of who she was, she had a group of tonsured men in plain brown and black robes surrounding her, pressing fresh, hot bread and butter and a mug of small beer into her hands, asking her anxious questions. Was this Gwyn ap Nudd truly an evil creature? Was he honorable? Could he be trusted? Would he use some sort of magic on Gildas to corrupt him? Would the Abbot come back to them safely?
"Wait, wait," she said, as they clustered around her. "I will answer any question I can, but I must be able to hear them!" She got them to stop talking all at once, finally, and sat down on a stone bench in the abbey herb garden where they had gathered around her. "I'll tell you everything I know about the Folk of Annwn and Gwyn in particular," she said, calmly, reassuringly. "But first of all, Gwyn ap Nudd is a friend to the High King, and, so I was told this morning, counted among the King's Companions of the Round Table even if he seldom comes to court." She waited for them to take that in. "If he comes to the Round Table, he has already passed the many tests that the High King sets his men. Yes?"
They looked at each other, then nodded.
"Now, among the Folk of Annwn, vows are taken as seriously as—" she looked about her, and although she _did_ see a few faces showing suspicion or fear, she didn't see any she would have thought dishonest "—as seriously as among you. Vows are sacred. Gwyn will have taken the same vows to the High King that all the Companions have, and one of those is to protect those who do not bear arms."
"That is true," murmured the fellow who had insisted she have some of his beer. "Women, children, and men of the cloth . . ."
"Furthermore, among the Folk of Annwn, the person of an envoy is held in the highest esteem. Their lives are sacred. Their words are to be listened to with courtesy, and they are not to be threatened nor harmed just because one side does not like what they have to say. Abbot Gildas is an envoy. Gwyn will defend him to the death and would not allow harm to come to him even at the hand of his own lady or son. I would lay my _own_ life on that or that of my father, whom I hold dearer than myself."
There was a collective sigh of relief at that, and a little of the tension eased. "Now, as to the Folk of Annwn . . . no, they are not mortal as we are. But they are not demons, either. They are just . . . other." She shook her head. "It is hard to explain, but I think I can pledge to you that Gwyn of the Annwn would have no more difficulty in being within the walls of your church, there, than I did."
"A demon cannot abide within church walls," said someone else. "Nor stand on consecrated ground."
She had to smile a little. "I daresay that if you looked closely at some of those who have come once or twice to your rites, you would find that more than one of them are of the Folk, for they are a curious set of peoples, and you are their near neighbors. They dwell in the Other World, not here on the middle earth, nor heaven, nor hell, but as if it were _sideways_ to the lands we know. The doors to their lands are few; two are here, which is why Gwyn's stronghold is here."
"I heard a tale once," one of the fellows faltered. When the others made encouraging murmurs, he got up courage and went on. "It was said that when Lucifer revolted and made war in heaven, there were some spirits that would take neither God's side nor the Devil's. And so, when the battle was over, and Lucifer and his minions cast into Hell, these other spirits were also driven from Heaven. Because they had not taken God's side, they could not remain. But because they had not taken Lucifer's either, they were not sent to Hell. And so they came to live beside, but not among, mortals, in a state that was half of spirit and half of the world . . ." His voice trailed off, uncertainly.
She shrugged. "I had not heard that tale before, but it is as likely as any other explanation. They are as many and varied as mortals and all the mortal creatures. There are good, bad, and middling ones. Many are tricksters. Some are evil, but Gwyn will keep _those_ firmly under control here. They are quick to anger, slow to forget. A gift places a debt of obligation on them, and the freer and more genuine the gift, the greater the obligation. They will always hold by the letter of a bargain, but you must be careful, because if they feel they are being coerced into it in any way, they will try to find a way out of it. As I said, they hold the person of an envoy sacred. The best thing you can do if ever you see one is to offer it a gift, however small; by making a gift you will bind them not to harm you, and they will not rest until they feel they have discharged their obligation. Bread is always a good gift." She thought some. "Would you continue to live in peace with Gwyn's folk?"
"We had rather convert them and save their souls, if souls they have," said a dry voice from the rear of the group. "As our brothers in Eire saved the souls of the Daughters of Lyr. But yes, if we can buy peace of them—"
"Then make a gift of bread at the water's edge, once a week, say, if you have it to spare." She smiled. "Most of them live beneath the Lake, and it is a little difficult to bake bread at the bottom of a lake. Mark it with one of your crosses, so that they will know from whom it comes, and nothing evil will be able to touch it."
There were murmurs, but nods. She found herself smiling even more; she had not expected to like these men and certainly had not expected them to be asking advice of her.
They asked her a few more questions, which she answered as honestly as she could, and she left burdened with bread, butter, and honey for her men, for the abbey's cattle and bees were evidently famous. One of the monks came with her, there was so much to carry.
She returned to the encampment burdened as much by thought as by the gifts. She had expected acute disapproval, even hatred. While some of those men clearly disapproved of her, more simply accepted her as her own people accepted her. And there was no hatred. Mostly they seemed to be grateful that she was taking the time to explain things and reassure them. Even those who seemed to disapprove of her had listened to her words.
So she found again, when she had seen that the food was properly distributed. As the monk said farewell and began to leave, he suddenly turned back to her.
"You are a great and kind lady, to have spent so much time explaining matters," he said, shyly. "I hope you do not mind that I brought the brothers to speak with you."
She grinned a little. "So it was your doing?"
He flushed. "Aye. When I saw you in the chapel, as fair as Our Lady is said to be, and with such a look of peace upon you, I knew that you had a good heart, even though your soul is pagan. I knew that you would tell us the truth and not put us off, as lord Kai has done. And I knew that because you are a woman that knows the hearts of your men, you would see us as a kind of warrior too and serve us the truth, instead of seeing us as womanly, as the Companions do, and serve us empty assurances."
She was so taken aback that all she could do was blink and blush. He didn't seem to mind; he just took her hand and wrung it a little.
"I know that goodness and beauty do not always go hand in hand," he finished, simply, "But in you, White Spirit, I think they are united. God's blessing on you. I will pray for you."
He trotted off back to his duties and his brothers, leaving her staring dumbfounded after him.
**Chapter Eighteen**
**O** **n the third** day after Gwyn vanished with Gildas, a parley flag appeared on the tower of Melwas' stronghold. After much discussion, Arthur sent his foster-brother Kai out in a boat to hear what was to be said.
They watched as Kai was taken into the stronghold. And then there was more waiting. As the time passed, the tension grew greater, and it was with tremendous relief that they all saw Kai come back out again.
This time, he was not alone. Two more men were with him; in the shifting mists, it was hard to make out more than Kai's red tunic and the vague shapes of the other two, but—
"No, fair cousin, one of them is not me," said Gwyn right into her ear. She jumped, and he laughed as she spun to face him. She was standing a little apart from the rest of her men, and they didn't seem to have noticed that Gwyn had simply—well, probably, he had pulled the same trick as he had the last time, stepping out of nowhere to end up beside her.
"Gildas is a stiff-necked fellow, but honest and fair, and once I saw that he was going to make good on his boast, I left him to it," Gwyn told her. "Let him have all the fame, if fame comes from this, for reconciling Melwas with your High King." He chuckled a little. "In truth, cousin, I think that Melwas was getting mightily weary of the company of his prize, confined as he was to one small island, and not all of that."
"And will he still be calling himself 'King of the Summer Country'. . . cousin?" she asked.
His smile grew teeth. "I think not. He has seen that it is not wise to usurp what is another's, whether it be a wife or a title. And by the way, I thank you for calming his flock of little brown chicks." The smile softened. "That was courteously done."
She flushed a little. "That hadn't been my intention when I went to look over their hennery," she said, with a slight laugh. "But they clucked and fussed so, it moved me to pity. Besides, it was no great effort, I only had to tell them the truth."
"As fair-spoken as you are fair of face," he laughed. "It is as well that I have me a lady who holds my heart fast—and _you_ have your duties to your father. Elsewise I would steal you away as Melwas stole that fool of a Gwenhwyfar to the true Summer Country." He lifted an elegant brow and gave her a thoughtful look. "I think you have great things in you, cousin. I do not yet know what they are, but surely the hand of a goddess is on you."
She was a little flustered now, although she was determined not to show it. That was twice, now, that men had called her attractive. She was not at all sure what to make of this . . .
Then again . . . the two men who had found her lovely were the King of the Annwn and a monk. Neither were "men" in the ordinary sense. She ought not to place too much importance on this.
"Have you any notion of what Gildas brought about?" she asked instead.
"Some. He'll turn over the queen, of course. And for taking her, there will be some Christian punishment or other. I think he'll be giving over his stronghold to Gildas, though what the monks will do with it, I've no notion." He shrugged. "They do not trouble me, I do not trouble them. They will bring no weapons of iron and steel to my door, and that is all I care for."
She pondered this. "Well . . . if ever the Saxons overrun this place, the stronghold will make a safe place for them to go."
Gwyn nodded, his eyes on the nearing figures. "And this is no bad thing. Blood spilled so near my door would bring the sort of the Folk that I do not care for. The sort that only look for more blood, and finding it not, goes hunting for it. That is always bad. You mortals are not so discriminating when it comes to my kind and are like to punish all for the faults of a few."
She could find no reason to dispute that claim and sighed. "I wish it were not so. But if wishes were horses, my father would have no need for stallions."
"Well said." He bowed a little to her. "With that, fair cousin, I take my leave. The Folk still owe you something of a debt. You may feel free to claim it of me at your will."
And then, he stepped . . . away . . . again. A single pace to the side, and he was gone, just as the boat touched the shore.
And so there was more waiting.
Not with the tension that there had been, however. Her men, grateful for the fresh bread, something all too seldom seen by warriors in the field, went out hunting and fishing again, and they shared their catch with the monks, who in turn supplied another round of bread and honey. An interesting spirit of camaraderie sprang up between them; a spirit she encouraged. In the rest of the encampment, the sense of relief was palpable. It was one thing to go to war against the Saxons; they were the enemy. It was quite another to go to war against someone whose men you had recently fought beside.
There was no doubt that Gildas was going to do well out of this. He did not much care for Arthur, or so it was said by a few of the monks, but he cared even less for Christian to be fighting Christian. And he would likely exact some sort of price from Arthur as well as from Melwas for his services. Gwen could not fault him for any of this; actually, it only seemed fair. When he had agreed to negotiate, _he_ knew nothing of Gwyn ap Nudd, had no assurances that Melwas would not kill him out of hand, nor that Gwyn himself could be trusted. Gwen might not like Gildas, but she could admire his courage.
Finally, just before sunset, the word came at last.
And shortly after the word, the lady who was the cause of it all.
A breeze—no doubt engineered by Gwyn ap Nudd—blew the mists off the lake as she came, rowed over in another boat. The setting sun touched her golden hair and made of it a crown and gilded her linen gown. She sat upright and proud in the stern of the boat, with no sign that she felt any guilt.
Gwen was not sure what her feelings were. Mostly relief that all of this was over. Some contempt, perhaps. And puzzlement, that the woman would be so foolish as to desert a man who engendered such passionate loyalty. It should have been obvious that very few of his allies would desert him and that the ruse that she had been carried off against her will could not have held up for very long.
Lust? Love? Ambition?
Not that it mattered in the long run.
When she alighted, she was surrounded immediately; the bodies of Companions and monks hid her from view, so it was impossible to tell if she was led off, taken off as a prisoner, or went under her own power and will. But off she went, heading for the High King's tent, where Arthur and Gildas awaited. Melwas was gone. The queen would face her judgment alone.
Gwen shook her head and decided that today might be a good day to go hunting.
She returned, empty-handed, which didn't really surprise her; with so many men hunting the same fields, the game was probably hunted out by now. And perhaps because of that very thing, she returned to find many of the allies already packing up to leave.
"Have we been dismissed?" she asked Afon ap Macsen, her second in command.
"Not yet. But there is no real reason to hold us here," he pointed out, and looked uncomfortable. "A good fight, that's one thing. But this—it isn't the sort of thing a man likes to have witnesses to."
Well, she could see that. The High King had been made a cuckold of in front of his allies, and his queen hadn't looked in the least repentant. She wondered what Arthur would do.
It wouldn't have been a question if he had been a follower of the Old Ways, as her father was. King Lleudd would have had an easy choice, since a woman, particularly a queen and a Lady, _did_ have one irrefutable excuse for something like this.
_It was done for the Land._
Arthur was still childless and looked to remain so. And while he was still in fighting trim, his queen, if she had been a Lady, would have been bound to show herself fertile. And . . . well . . . this was his way to _prove_ he was still worthy to represent the Land. If the Old Stag could not drive off or slay the Young Stag, then it was more than time for the Young to supplant the Old.
Even time for the Old Stag to shed his blood to renew the Land. Now, that had not yet happened with her father, in no small part because neither Ifan nor Caradoc were minded to make the challenge to King Lleudd. Besides, Cataruna was firmly Pywll's Lady, and the vigorous and very, very virile Ifan was Lord to her Lady. There was no need for King Lleudd to be the Land King, for Cataruna had a consort, and all was well.
But Arthur—
Well, the Old Stag had conquered the Young, so no one would be pressing for him to be supplanted yet. And it was through no fault of his own that he had no heirs but Medraut.
Gwen sighed. "Tell the men to be ready to move out. You are right. I have no wish for the High King to have us present for this."
The queen was a follower of the Christ, and there were no excuses for her behavior in their creed. She would have no allies there. Not even Gildas would support her now.
Gwen tried to think of what options were open to Arthur. This was treason, of course. But would he put her to death? Could he put her away by Christian law? If he tried to put her away from him, she was still going to be a source of contention for his throne. She could still attract another like Melwas, maybe more. She could still be a source of trouble.
It was a situation fraught with ugliness and difficulty, and one she was deeply grateful that she was not involved in.
There was one thing she might do, though; it would remind Arthur that the followers of the Old Ways had not wavered in their loyalty, and it would reflect well on her father.
She had come here with a gift of horses for himself and his Companions, but in anticipation of fighting, all of King Lleudd's men had come with extra mounts. She herself had brought six—Rhys and Pryderi of course, but also four more, just in case something happened to her two main mounts. Now she pulled those four extras from the picket line, found a squire, and sent them off to the High King with the simple message that the horses were from King Lleudd Ogrfan Gawr.
The camp was uneasy that night and unsettled. This did not taste like victory, even though Arthur had won.
Talk around the fires was subdued, and no one had much appetite. Gwen was thinking very strongly of making use of that mead Cataruna had sent along to help her to sleep early, when she looked up to see one of Gildas' monks peering around the circle of warriors at her fire. He finally whispered to the one nearest him, and to Gwen's further surprise, the man stood up and conducted the monk courteously to her.
"If you would be so kind," the monk said, diffidently, once he had given her the bow of respect, "Abbot Gildas would like to speak with you."
She stood up immediately. "I would be honored," she said honestly. Whatever the abbot wanted her for, he was clearly an important man. He was also a beloved man; however disagreeable he had seemed to _her,_ he had to have earned that regard.
So, she would give him the courtesy that she hoped he would show her, and see what happened.
The monk conducted her quickly to the Abbey, and it was quite clear that the subdued mood in her camp was shared across the entire encampment.
Gildas was waiting for her at another fire, and he rose to greet her without the disagreeable expression he had worn before. She gave him the same bow of respect that she would have given the Merlin.
"Lady . . . I wish to thank you," Gildas said awkwardly. "You were very kind to reassure my people."
"Abbot Gildas, your people were extremely worried for you, and they deserved to have someone treat them with courtesy," she replied. "The High King's Companions would have done so if they themselves knew what I did about the Folk of Annwn. Since they did not, and what I knew could ease the hearts of your people and allow them to devote their attention to—to—"
"To prayer and their devotions," Gildas supplied, with a little smile. "Yes. And again, I thank you. I also wish to apologize to you. Without knowing anything of you, I harbored ill thoughts of you. You, in turn, rather than doing the same to me, have given me a lesson in what should have been _Christian_ charity. For this lesson, too, I thank you. I want you to know that despite our differences in belief, you may count me as a friend."
She was for a moment taken aback, but she quickly recovered. "I am honored, and I would be more honored if you will accept the same from me."
"I know that you are all curious as to what is to happen to the queen." He sighed. "I should prefer, as you seem to not be prone to exaggeration, if you were to make it known that the High King and the queen will remain here for a time while I strive to make peace between them."
She winced. "I do not envy you that task. This was . . . a sad and bitter thing."
"I wish that I had hope of success." A shadow passed over Gildas' face. "But that will be as God wills it. I shall do my best. Arthur is a great man. I would that he were more a man of peace and less of war . . . for one of my brothers rebelled against him, you know, and met his death at Arthur's hands."
_Well, that explains a great deal . . ._
"Still I have forgiven him. And I know him to be a great, and great-hearted, man. And a good leader, of the sort that this land needs. He has a vision of this part of the world being united and strong, as the old empire of the Romans was. I hope that this does not harden his heart and make something terrible out of a good man."
_Something terrible . . . like the sort of man who could order the deaths of infants?_ She said nothing, however, only nodded. She and Gildas exchanged a little more conversation, then he pleaded exhaustion, and she took her leave—making sure to stop with several war chiefs on the way back to her encampment to relate what Gildas had tacitly asked her to pass on.
And then she and her men followed the example of the rest, packed up, and returned, thankfully, to their homes.
Nevertheless, she was somehow not at all surprised to learn, about a month after their return, that Queen Gwenhwyfar had caught an unexpected chill, sickened, and died, and was buried on the grounds of the Abbey.
**PART THREE**
**QUEEN**
**Chapter Nineteen**
**I** **t was just** cool enough for a fire at the king's hearth, but the light it cast gave very little aid in reading facial features. Gwen could not believe what she had just heard, and stared at their visitor in total disbelief. "If this is a jest, it is in very poor taste," she finally managed.
But her father looked completely serious, as did the visitor, the Lady Aeronwen. "Lady" in the sense of "one of the Ladies." The Lady looked outwardly no different from any other woman, and Gwen was not Gifted enough to sense the Power in her; her clothing was unusual only in that it was of plain, undyed white linen and wool, and her hair was unbound, signifying she was not a married woman. There was nothing whatsoever to mark her as a person of any importance at all, but she had been sent directly here from the great School, and Cataruna, who bowed to almost no one, practically groveled to her.
She did have the most piercing dark eyes that Gwen had ever seen; eyes that definitely looked far beneath the surface of everything around her. Her speech was clipped, her manners rather severe. That, of course, was probably very effective against the young women sent to the School, but it cowed Gwen not at all.
And her proposal was . . . well, on the surface of it, sheer insanity. Why in the name of every god and goddess should _she_ become the High King's third wife? She had never even laid eyes on him to her certain knowledge, and she doubted he had ever seen her. And she was twenty-seven. Even if she did look eighteen. Surely he would want a younger bride.
_If he does, he'll reject this whole scheme out of hand._
"The High King _must_ have a queen. He dallied not at all after the death of his first, and there is no reason to wait this time, either. He drew up a pathetically short list of names that he indicated would be acceptable to himself and one or another of his advisors. The only other candidate that we will accept is Morgana," said Aeronwen flatly, her eyes hard. "And leaving aside the little problem that she is also the High King's half-sister, she is completely out of the question, because she is completely uncontrollable."
"Oh. And you can control me," Gwen replied dryly, raising one eyebrow. The tiny, dark woman flushed, disconcerted. Gwen sensed that she did not often find herself contradicted or her will thwarted.
"That is not what I mean, Gwenhwyfar." The Lady's glare could have put ice on a pond in summer. "I mean that you will work for the good of the land, for the good of the followers of the Old Ways, to protect the Folk of Annwn. You will think first of the good of others, not yourself. You have proven that, as a warrior. Morgana will work only on her own behalf, or Medraut's."
"And leaving aside whether or not Arthur will be remotely interested in a bride who has followed the warrior's path, just how do you propose to get the High King to accept a third wife with the name 'Gwenhwyfar'?" she asked. "I should think at this point he will regard that as very ill-omened."
"Or he will hold by the common notion that the third time pays for all," the Lady countered, and shrugged. "I confess, I am not in his confidence. I do not know what he will think, I only know that, like you, he considers first the good of his people. He needs an heir, the land needs a queen, and all else is secondary. He is getting no younger. He has no time to waste. We who have counseled him have made very, very sure that he understands this."
"There is another factor; the High King wants my horses," her father rumbled, nodding. "To get them, he will take you. It is a good bargain, as you know I do not part with them easily."
Her cheeks flamed with suppressed anger. "So _that_ is what this is about. I'm now the unwanted part of a horse trade!"
"Unwanted by the High King perhaps, but greatly desired by us!" the Lady snapped. "The King's second wife did us great damage with her adherence to the Christ priests. The High King grows old; in the back of his mind, I suspect, is the fact that the Young Stag supplants the Old, and Lleu slays Goronwy. The land is not suffering—yet—but if it does, his age may be blamed, and the followers of the Old Ways may look for a Young Stag. The Christ priests do not demand that the High King sacrifice himself—ever. Except metaphorically, of course."
"And do you?" she asked, pointedly.
The Lady shrugged. "It has been our experience that the gods take that in hand before we need to. The Merlin is useless to us now, and the King has decided to forget that his old mentor was a Druid before he was the King's man. Even though you have not the Gifts, Gwenhwyfar, you can undo some of that. You are called 'cousin' by Gwyn ap Nudd, and you are accepted by Abbot Gildas. You can turn some of the rancor of the Christ priests away from us. You can bring Arthur back to us. And perhaps you can supply an heir to the throne."
Gwen felt like a rabbit in a snare. All of this did make very good sense. She probably _was_ the best candidate to be the High King's new wife. And she _could_ do much. Unlike many of the followers of the Old Ways—the Ladies being prime examples of that—now that she had actually met with some of them, she didn't think all that badly of the followers of the White Christ.
But this was not what she wanted to do! This had nothing to do with _her_ dreams!
_But I am a king's daughter. And kings' daughters know that duty comes before desire. Kings' daughters know that they will be called upon to sacrifice much. I have had my dream for years. Now . . ._
Now it was time to pay for having had that dream in her hands. And it felt horrible. As if something she loved was dying before her eyes.
_It's me that's dying. It's the Gwen that is the war chief, the only Gwen I've been for all of my life. And something I don't recognize is going to take her place._
And . . . it wasn't Arthur she wanted to wed . . .
"Am I really the only one?" she asked, in a small voice.
"Would I be here if you were not?" Aeronwen shrugged. "At least the High King is not in love with you. He was in love with the last Gwenhwyfar, and that did not end well. His wedding to the first Gwenhwyfar was far more arranged than the tales would make it seem; he wanted her father as an ally in the days when he had far fewer. Trust me, he is no stranger to marrying for expedience. For his second wife, he pleased himself; deluded himself, perhaps, but he did not think first of his people, or the Land, and the result was almost a disaster."
Gwen wanted to ask how the second queen had really died, but—no. It was probably better not to have an answer to that question. Whatever had happened was in the hands and judgment of the gods. Whichever gods those were.
It was ironic, when she thought back to her childhood and how when she had heard that the first queen had her name, she had wished she too could be a queen and have goose every day and gowns that were not made-over. Now all she could think was how it meant the end of her freedom, that not all the fine food and handsome gowns in the world would make up for that loss. She had not been willing to give that up for one she truly wished for—and now she was being asked to give it up and for what?
Duty.
Finally she hung her head in defeat. "If I must . . ." she said reluctantly.
"The alternative is Medraut on the throne," replied the Lady, her voice showing that she very clearly cared no more for Medraut than Gwen did. "You know Medraut as well as any of us. You know your sister, who was trained by Anna Morgause, just as Morgana was. You know what will come of that."
That was no alternative at all.
"Very well. I accept," she sighed. _And I will find some way to have at least a part of my dream, too._
But first, as she had feared, she found that to be made into a queen, she must be unmade.
This was a strange world that she reentered. It was not that she had abandoned womanly things so much as that she had made a choice that left no room for them. But now, suddenly, there was a veritable flood of womanliness that had swept her up and was carrying her off, and she watched the banks of simple practicality rushing past, out of reach, as Cataruna and Gynath and all the women of Lleudd's court descended on her, determined to "make her over."
She understood that this was needful. She could not turn up at the High King's stronghold in her armor and tunic and trews. And if she did not _act_ like a queen she would have ridicule for her portion. If she did not _look_ like one, well . . . not only ridicule, but perhaps even scorn.
She hated it. But she threw herself into it with a will. There was no turning back now, and hard as this was, it had been far more difficult to become a warrior. She had discipline, and she applied it as firmly as she had ever applied herself to learning a weapon, or to ride.
The women began with her hair, which seemed a logical way to start.
She had not chopped hers off short, as Braith had, because it tended to behave itself if properly braided, and what was as important, it made a good padding under a helm. But now it was unbraided and brushed until her head was sore, and washed first in lime-water to make it even paler than it had been, then in rainwater. Then she had to lie with it spread out while it dried. They did all this several times over the course of a week. She got very tired of it by the second round.
With all this came several sorts of baths. Now, as a whole, she enjoyed baths. But she did not really enjoy _being_ bathed, then oiled, then bathed again, then oiled again, then bathed for a third time and rubbed down with perfumes while there was a woman on each hand and each foot, tsking and fussing over the toes and fingers.
When they were done with the bathing, and her hair was finally pale and silky enough to make them happy, it was time for the final step in the process. It was braided up, but no, not in her sensible single plait. Now it was braided in two, hanging down on either side of her face, braided with gold cord, which seemed a shocking waste of gold to her, then the bottom third of the braids were wrapped in a bit of fine cloth, and that, in turn, was held in place by a criss-cross of more gold cord. The braids hung heavily from her temples and made her head ache.
Why couldn't she just keep it loose, like every other maiden she'd seen?
Evidently because that wasn't what a king's daughter did.
She liked to keep her breasts bound—not flat, and not tight, but enough so that they didn't get in the way or move about and cause problems.
Well, that, it seemed, was completely out of the question. Her breasts were to be . . . prominent, and she found herself with braids _and_ breasts encumbering her and making it impossible to move quickly.
Then there was the new clothing to get used to.
Oh, she was not averse to wearing a gown now and again, provided it was one that was comfortable, easy to move in.
Well.
First, a whole new wardrobe had to be constructed. The women did this at breakneck speed, while her hair and body were being scrubbed like a fish being descaled. The new wardrobe began with the linen chemise, of which she had three. They were fine; they were quite comfortable and very soft and lovely on her almost-raw skin. She would have enjoyed them except that they gave no support to her breasts whatsoever. Then came the undergowns, with tight sleeves—so tight she could never have drawn a bow or swung a sword or an ax in the wretched things. That was not fine. It didn't at all matter that they were of a perfectly lovely linen and wool mixed, as soft as the chemise. It didn't matter that they had grand bands of embroidery of a sort she could never do herself. It didn't even matter that every woman who looked at them sighed with naked longing. Because they were an absolute horror to wear.
Nor was it fine that they dragged on the ground behind, making them exceedingly impractical anywhere outside. Still, she could kirtle them up . . .
But then there were the overgowns, with wider, shorter sleeves and more bands of heavy embroidery on them. They were just wide enough that she had to try to keep the edges of the sleeves from drooping into things and getting filthy.
And last of all came the wide, embroidered belt, that she was supposed to tie as tightly as possible to show off her small waist and push up her breasts (though it gave them no support at all), from which dangled keys, a knife for eating, pouches for this and that—
On top of all this there was the mantle, which was not a practical cloak, oh no, but a great awkward rectangle of fabric that she was supposed to drape becomingly about her waist, and arms, and sometimes over her head.
Finally, as a last insult, a fur-lined overmantle she was supposed to pin at the shoulders over this entire mess of cloth; it didn't even close properly at the front, so she would stew at the back and freeze at the front.
So there were all these swaths of cloth to manage, and the tight arms of the undergown, and the dangling bits on the belt, and it seemed as if she was catching some part of the outfit on something whenever she moved. She had never felt so sorry for other women in her life. She felt even sorrier for herself.
Nevertheless, she was a king's daughter and a war chief, and she was not going to allow herself to be defeated by mere fabric.
So she did what anyone with sense would do. She put it all on and practiced. Practiced walking, walking quickly, moving about indoors and out, maneuvering around furniture, eating, carrying things—she couldn't possibly do most of the household chores that other women did in this stuff, but, then, she wouldn't have to. Cooking, cleaning, all that would be done for her. The High King's queen did not even have the duties that Queen Eleri had had (and Queen Eleri had dressed much more simply, with one chemise, an overgown, and in the cold, a good heavy cloak). She even practiced some dancing, and riding—and with some teeth gritting, being carried pillion behind a rider. And the others, anxious for her success, helped her. They had some little time; although the High King wanted her father's horses a great deal, he was less anxious to leap into a third marriage, and so the negotiations and bargaining went on through the autumn, and only concluded when the first snow fell. So she would go to the High King as his new bride a bare four months after the death of his second.
And by then she was the master, or perhaps mistress, of her own clothing. She moved as gracefully in it as Cataruna, if not more so. She had managed to contrive a breast-binding that at least made her chest stop aching. It might not be the height of fashion, but she didn't care. It was one comfort she _would_ have.
By then, too, she had learned how to carry on a conversation that did not involve two or three ways to kill a man, nor how to track game, nor the three best remedies for horse colic. Her childhood skill with a needle had come back to her, though she was never going to be able to embroider with any level of competence. She had learned a great many songs that did not involve any marching cadences nor randy bed frolics. In one thing at least, her warrior training stood her in good stead: She could concoct a medicine and bind up a wound with greater skill than any of the others save Cataruna, who was Lady-trained.
And then, far too soon, it was time to be off to her fate. It was with mixed relief—for she was finally able to put on her warrior gear—and regret that she mounted Rhys; and with a guard of her own warriors, the escort sent by Arthur, and a half dozen horse keepers, she set off with the herd of grays for the stronghold of the High King at Celliwig.
The land lay barren before them, not yet covered with a sheltering blanket of snow, the trees bare, the grasses sere, the sky for the most part sad and gray. The only birds were rooks, crows, ravens, and now and again a wood dove. There was nothing festive about their group, either. They might as well have been riding to a parlay or a possible battle as to a wedding. Or perhaps to a funeral.
At night, she kept very quiet, quieter even than her usual habits, and listened to the men talking. That was how she learned that it was not only the Merlin who had been struck down, but that the senior Druids were dying, getting ill, or outright vanishing.
This was the first she had heard of such a thing, and it rather took her aback. But when she asked one of the escort, a fellow named Neirin, what he made of it, the man just shrugged.
"They're all old, lady," he pointed out. "There's nothing mysterious about old men dying."
She certainly couldn't refute his logic, although there was still something about it that bothered her. But surely if something was wrong, the Druids themselves would be falling all over themselves to get to the bottom of the matter . . .
They passed within a few miles of the Isle of Glass, and she was tempted to detour to pay a visit—but there was no guarantee that Gwyn would come out to see her, she had already had just about as much of the Ladies as she could stand, and Gildas was, in fact, waiting at Arthur's Castle to wed them by the Christian rites, along with Aeronwen to bind them by the Old Ways.
She was just as tempted to detour to the great Henge, but again, there was not much there to see. She did not have the Gift to see the Power in the Stones outside of the time of a major ceremony. There was no School or Convocation of Druids permanently in residence there as there was at the Cauldron Well. Other than marveling over the construction itself, there really was nothing to "see."
So in the end, she bypassed both places and kept on the straight road.
The nights were the hardest. Not because they were cold, though they were, but because she knew that every time she slept, she was that much closer to the end of her former life. But rather than feeling desperation, she felt only a deepening melancholy.
Until, finally, it was over. The road finally brought them within sight of Celliwig and the hill on which Arthur's castle stood.
At first, she was not at all impressed. There was a hill; on top of it, the walls of the more permanent version of the Roman-style fortification she was altogether familiar with, and just barely visible above that, roofs that appeared to be tiled. It was disappointing, actually. She had expected, from all the tales, to come upon some enormous artificial mountain of stonework, looming high above the plain below.
It did seem odd that there were no men patrolling the top of the walls, however.
It wasn't until she saw small dots moving atop the walls that she realized her mistake. It wasn't small. It was enormous—not in height, but in size. Probably the individual buildings were no taller than Castell y Cnwclas, but they were _each_ just as large, if not larger. And there were as many of them, at least, as there were huts in the village. Clustered at the foot of the hill were houses and huts, indeed, enough to make up twenty villages the size of the one she had known.
Now she was very glad that she had fought in so many big engagements; if she hadn't, the sheer number of people would have been daunting.
Before they even reached the city of Celliwig—for it was a city, not just a village—she caught sight of what looked like a cluster of tents and pavilions at the side of the road. As they drew near to them, she saw the High King's red dragon banner flying above them, and she thought for a moment that Arthur had come ahead to inspect his . . . bargain.
But no, as they reached the tents, the party split into two; the horses and their keepers went on, while her escort halted, and one of her chests was taken out of the cart that held all her belongings. That was when she knew, with a stab of pain, that this was truly where she was leaving her old life behind . . .
Without a word, she dismounted, and went straight for the most elaborate of the pavilions. Before she even reached it, the flaps were opened by a pair of servant girls; two more took her by the elbows, exclaiming with distaste over her travel-worn and "manly" garb. Numbly, she gave herself over to them.
They couldn't manage a bath out here, but they did strip her down, warm some water at a brazier, and scrub her down and perfume her. Stubbornly, she did _not_ allow them to take her comfortable breast bindings, but other than that, she submitted herself tamely to dressing, braiding, fussing, and bejeweling. And she submitted to being picked up and placed on a pillion pad behind the oldest of her escort. She hated it, and so did Rhys; he was tied to the saddle and following behind, and he eyed her with confusion and resentment. He didn't like being hauled along like a pack mule.
Well, she didn't like being baggage, either.
But she put a good, brave face on it. And when they reached the outskirts of the city, with people crowding around the road to the stronghold, cheering and peering, she continued to put a brave face on it, waving and smiling, nodding, and acting as if this was the culmination of her greatest dream.
Even though at that moment, if she'd been given an honorable way out of it, she'd have bolted like a rabbit.
Through the city, up the hill, through the gate in the wall, and then . . .
The entire cavalcade, which had, by now, acquired quite a long tail, stopped in front of the largest of the buildings. It was of stone and white-plastered timber, with roofs of red tile. Dead center was a grand entrance with tall white columns, and beneath the triangular pediment that surmounted them was a group of richly dressed men. She recognized Lancelin, Kai, Gwalchmai . . .
. . . Medraut . . . looking outwardly happy enough, although she very much doubted he was pleased with all of this.
And in the center of them, the man who could only be the High King.
Bearded, the red in his hair going to gray, he looked . . . worn and tired. His gold crown seemed to weigh him down. Over his fine red tunic he wore armor, breastplate and greaves in the Roman style; under it he wore sensible trews and boots. His red mantle was lined with ermine and was easily large enough to serve as a bedcovering. His expression was resigned.
As for his Companions, many of whom had met her already, their expressions were far more gratifying. Kai looked astonished; Gwalchmai grinned with great appreciation, as did many of the others. These were expressions she was not used to seeing on the faces of men when they looked at her, and at first, she had to stop herself from looking about to see what lovely woman they were staring at.
_Am I really . . . pretty?_ she wondered. Practicality asserted itself. It was only the contrast, of course. They had seen her streaked with soot and dirt, in clothing that made everyone look the same, equally sexless. They were just surprised that she _was_ a woman and that she had turned up looking like one.
But then she saw Lancelin's face.
He looked utterly stunned. And when his eyes met hers, her breath caught in her throat, and for a moment, her resignation turned to something else. A sorrow that stabbed her, as if he had pulled out his knife and driven it into her heart.
_If only he were the High King . . ._
The thought was repressed, instantly. It did not matter. The High King could be a bear in a crown and it still would not matter. It was her duty to wed him. So wed him she would.
A servant brought a tall stool with three steps and placed it beside the horse. Gracefully, as she had practiced, she gathered up her garments and alighted, one foot outstretched, as if she were a goddess slipping down from the sky. Gracefully she descended the three steps and waited for Arthur to come to her, dropping her garments to fall about her in the most becoming folds. He took her hand and bowed over it.
"Welcome, Lady Gwenhwyfar," he said, without any hesitation when he said her name. "We rejoice at your coming."
And that was when she felt it. The sheer force of his personality, which crashed over her like wave. It was not meant for her—not meant for anyone in particular—it was merely what he _was._ You felt that, the power in him—felt his wisdom, his care for his people, his strength—and all you could think was that it was not a duty to serve him but a privilege.
It was a glamorie, of course. But it was all the more powerful because beneath it, the strength, the wisdom, were real.
But when she felt it, she fought against it. She was here from duty. She would fulfill her obligations. But she was not going to be seduced into liking it by magic.
"And I to be here at last, my King," she replied, with a slight inclination of her head.
And he led her into his palace. Which felt, as the walls closed about her, altogether too much like a prison.
**Chapter Twenty**
**W** **ith a cloth** on her lap protecting a fine gown she would rather not have protected at all, Gwen carefully laid in the feathering on another arrow. Much to the horror of her ladies, who were all gathered about her with their fine sewing and bands of embroidery.
She was beyond caring how scandalized they were. She had already horrified them by laying aside the woolen mantle and tying back the sleeves of her overgown. They shivered in the occasional draft. She was too warm by far. These rooms were heated by means of something they called a hypocaust, a contained fire that sent warm air under the floor. It was as warm as spring in here, although these fragile flowers seemed to think there would be icicles hanging from their noses at any moment. This device was Roman, of course. Arthur was . . . extremely fond . . . of all things Roman.
She laid in another line of glue from the pot on the brazier beside her and quickly laid down the line of fletching.
She was working on arrows because these charming ladies had made it painfully obvious that there was nothing she could sew that they would not have to undo and resew again. She simply was not allowed in the still-room to make medicines. That was the job of a single servant. This exhausted her repertoire of "womanly" tasks. She wasn't going to sit there with her hands in her lap and listen to them giggle and gossip.
So she was, by the gods, doing something she _could_ do, and do well. She was making arrows.
With both sets of vanes in, she took fine thread and bound them at the nock and the end of the vanes, laid the arrow aside to dry, and picked up a new one.
Inwardly, she seethed. Another thing that Arthur seemed very fond of. Roman customs. Such as the custom that confined women to a single section of this villa and kept them, for the most part, from mingling too much with men. Kai was in charge of the household. Not her. He set the menu for the day's meals, he oversaw the chief servants, the housekeeper and the cook, and kept track of and dispensed the stores. She had never seen the cook. The housekeeper pretended not to understand her and went about ordering things in the way _she_ pleased. Gwen was expected to remain here, in the queen's chambers, until called for. Men were not supposed to come here unless they were servants or entertainers or came with Arthur. _She_ was not supposed to mingle with the Companions, except under very supervised conditions, like meals or celebrations.
She was only at those meals perhaps once every three days, and such meals were as structured as a magic rite. She and her ladies entered the hall after the men; she was seated beside Arthur. There was music, to which Arthur paid careful attention, so that she did not get much conversation from him—but she got contradictory glimpses of both the tired old man and the charismatic leader. She heard maddeningly brief bits that hinted at ideas that were truly visionary. Most of all, she saw how the Companions all virtually worshiped him, and they did so in a way that told her that he had earned that worship, that it was not the result of some trick of attraction. And then, when the meal was over, they all rose, and she and her ladies went back to the maddening confines of her "bower." The only man that was allowed to come and go as he pleased there was Arthur.
Which he did, precisely, every night. And then went away again to sleep somewhere else.
She knew very well what lovemaking was all about. She hadn't been afraid of it. But she certainly hadn't expected it to be like . . .
. . . like a household chore. Something tedious, to be gotten over with as quickly and efficiently as possible.
Not that he was unkind, and not that he hurt her, except for the first time, and then it was nothing near as bad as some of the milder injuries she'd gotten in training. And for a while she had tried to be at least _pleasant_ to him. Tried her best to look attractive where she waited for him, made sure that she smelled sweetly, that her breath was good. It was all to no purpose. She was nothing but a not-so-prize mare to him; he just wanted her breeding, so he need not visit her anymore. The Arthur that came to her room was neither the tired old man nor the vividly alive leader that she saw glimpses of at the table now and then. He was . . . like a horse trainer who had no vested interest in the horse he was training.
Making arrows was soothing. She felt in grave need of some soothing.
Was this why the other Gwenhwyfar had run off with Melwas? Because she was so bored she finally could not stand it any longer? At the moment, Gwen could not find it in her heart to blame her.
But that Gwenhwyfar should have been raised and trained to appreciate this life. She should have found the too warm rooms, the endless hours of sewing, the gossip, the idleness appealing. And Gwen had to admit that this villa was wildly luxurious by her standards.
There were no dirt floors anywhere, nor floors covered with rushes. Even the floors in the servants' quarters were tiled, and the ones here were covered with jewel-like mosaics. Her quarters included her own bedroom, her own dining room, rooms for her ladies, this room, which _they_ called a solar, just for receiving visitors and spending the day with her ladies, and hearing the reports of Kai, the housekeeper, and a few other important servants. Not that she was expected to _do_ anything about those reports . . .
There was even a bathing room just for her and her ladies. And all these rooms surrounded a colonnaded courtyard, in which, she presumed, she would be "allowed" to stroll on the perfectly manicured grass in fine weather. All she had to do was produce an heir and look, if not beautiful, at least queenly.
It was driving her mad.
The only relief she'd had from this cage was when Gildas had come to talk with her. Presumably, being a Christ priest, he had been "safe." He and Aeronwen had presided over a pair of marriage ceremonies with civility and calm, if not liking. Aeronwen had made her immediate departure. He, however, had stayed for another fortnight, for the weather had turned foul as soon as Aeronwen was gone. She wondered if he suspected the Lady had something to do with that; certainly Gwen did.
Gildas did not care for Arthur; that was hardly surprising, since Arthur had slain his rebellious brother. But for some reason he had taken to Gwen. He had spent many hours in this solar, asking her intense questions about her beliefs, inviting questions from her about his. Arguing cordially with each other. She came to see what it was that made his monks so intensely loyal to him. Under that dour expression was a remarkably sweet temper, and if he was stern, he was also able to forgive readily, even eagerly.
"I think that you will never convince me to leave my path," she told him, finally, "But I am becoming more certain after listening to you that our paths are so near one another as to be identical in many places."
He had looked at her with a raised eyebrow. Opened his mouth. Closed it again.
"There are things that the Ladies cleave to that I find . . . wrong," she admitted. "I will never believe that the gods and the land require blood be spilled so that both can prosper. Think of all the blood spilled in war—if it were merely blood that was required, the lands that were battlefields should forever be waist deep in lush grasses and yielding four times the corn of others for all eternity. Yet I have never seen that. The first year after a battle, yes, but that is just logic, since you could get as goodly a harvest spreading manure. But not after."
"And neither have I!" he began, eagerly.
"Wait," she had said, holding up a hand to forestall him from yet another attempt to persuade her to his way of belief. "Aside from that, now I must look to the followers of both our gods. Your own god has said that one knows the tree by the fruit it bears. Those people that heed the Druids and the Ladies, I see to be not much different from those that follow Christ. There are liars and thieves among both, kindly, honorable and wise among both, virtuous and vile in equal measure. Can you refute that?"
He had looked as if he would have liked to, but he admitted that he could not.
"So our peoples are not so very different. Their hearts are not so different. So—" she shrugged. "Since it is the gods that rule men's hearts, it follows that your gods and mine are not so different. It seems to me that the faces we put on them have more to do with ourselves than with them."
He had looked at her with such astonishment on his face that she'd had to laugh. Eventually so did he, and gracefully he had turned the talk to more questions about the Folk of Annwn, about whom he was as curious as an eager child.
But now he was gone, and there was nothing to make one day different from the next. She rose after sunrise. She ate. She heard what the cook would be making. She approved it. She came to the solar, to be surrounded by these fatuous women, and tried not to die of boredom. She ate. Then back to the solar. Or every other day, a bath.
And not the efficient sort of bath she was used to, no indeed. This was a bath that took up an entire afternoon. First, she was ushered into an even warmer room, a bath in the Roman style but reserved for her and her women. This was, she was told, almost atop the furnaces that put warmth beneath the floors, and it was full of steam. There she put up with being washed with soap and cloths—as if she could not even wash herself!—and rinsed with jugs of warm water, which ran away into a drain in the floor. Then her hair was pinned up on the top of her head, and she was led like a dotard into a second room, where there was a pool—a pool!—of steaming hot water. All the ladies soaked in it together, occasionally going to a tub of cooler water, only to return to the hot one. And there they would gossip, gossip, gossip and talk of nothing but trivialities. She heard nothing of what was going on in the greater world, only endless details of dresses and love affairs. The few times she actually heard anything that _did_ sound worth listening to, it turned out to be so distorted as to be incredible. Then, when she was sure she was going to fall asleep from boredom or the heat, came the drying, the massaging with lotions and scented oils, and at last, dressing and going to dinner. Dinner was generally in the company of the King and his Companions, but _they_ never discussed anything worth listening to either! Oh, no, it was all pretty compliments and talk of hunts and weather—not a word of the Saxons, or King March, or anything else actually worth hearing about.
The whole tedious business happened every other day. And she was certain that at least some of her ladies would do this _every_ day if they could.
This was not a bath day, so there would be no dinner with the King either. And finally fed up past bearing with the boredom, today she had ordered a servant to bring her the fletching materials from the armory. He hadn't wanted to, but there was no reason why he shouldn't, so at last she bullied him into it.
At least she was getting something constructive done. She had not seen one single arrow in Arthur's forces that was any better than hers. None of these women had ever seen fletching done, much less put feathers to arrows themselves, so there would be no undoing what she had done.
Arthur finally had something to say to her besides a curt greeting when he turned up that night and the doors closed behind him. He looked at her, as she was waiting patiently in the far-too-luxurious bed, and frowned slightly. The bedroom was—like everything else—in the Roman style. It was long and narrow, with the bed under a vaulted ceiling at the far end. The floors were warm enough to go barefooted on them, but the alcove with the bed was a little drafty, and she pulled the fur up around her shoulders. Every night her women put her naked into this bed; every night the King turned up to perform like a bored stallion and depart.
"I heard an odd thing from Kai, my lady," he said, carefully, making no move to disrobe, although she was already naked beneath the covers. "This afternoon, he said, you ordered certain materials brought to you. You were . . . fletching?"
She nodded and wondered how much of her expression he could read in the light from the single oil lamp at the bedside. "I was."
He paused. "I should like to know why. It seems . . . an odd occupation."
"Because—" she took a deep breath. "Because it was better to make arrows than to pick up small objects and begin flinging them at the heads of those vacuous, simpering, gossiping idiots that I am supposed to be polite to."
His mouth dropped open, and he looked at her in astonishment.
"Husband, I am _not_ one of these women!" she exclaimed passionately. "I was not made, nor trained, for idleness! I am a warrior, trained from childhood to be a warrior. I have not one thing in common with them. I do not believe that any of them has done a single piece of simple, practical work in all her life! They have no thoughts beyond dress and gossip. I do not find gossip to be entertaining! _I am a warrior!_ And being caged up in these rooms, hour after hour, day after day, doing nothing with any meaning to it, hearing nothing but trivialities discussed as if they were matters of the realm, is driving me mad!"
"I—see—" he said. Finally he walked heavily to the bedside and sat down on the foot of it.
"Husband, I am stifled. I cannot breathe here. My clothing weighs upon me, heavier than any armor; the rooms are too warm, the food so rich it makes me ill. I feel that if I do not see the sun and feel the wind, I will lose the few wits I have left to me." She looked at him with pleading. "Surely you can see now what is wrong."
And then she saw understanding dawn on him, and he smiled a little. "Yes, wife, I do see!" He picked up her hand and squeezed it. "I understand. I shall leave orders I think will please you, and I expect after such a stressful day, you will want some sleep. I shall leave you to your rest."
And with no other words than that, he left her. This time, _without_ the . . . the "servicing" that was so automatic that it felt like nothing more than a tedious chore for both of them.
Relief suffused her like the warmth from the floor. Finally, he realized what kind of a person he had taken to wife. And he was truly as good and kind a man as she had seen him be with others. She blew out the lamp and pulled the covers about her, thinking happily of the hunting she would do tomorrow and of being, at last, part of his councils.
She awoke to silence.
Her first thought was gleeful. He had sent those awful chattering women away! Or at least, told them to take their unwelcome company elsewhere. The servant that slept in the chamber attached to hers woke up as soon as she heard Gwen moving about and tried to put her into those maddening drapes, but Gwen sternly ordered her to find her old clothing, the tunic and trews and good sturdy boots, and though the servant protested, she obeyed. A glance while she was dressing at the light coming from the tiny window up near the top of the ceiling—after waving the servant away—told her that she had slept well past midmorning. Another sign that the gaggle of ninnies was elsewhere! She quickly tied on her boots with a happy heart.
Silently thanking the goddesses, Epona in particular, Gwen strode cheerfully into her solar and headed for the doorway to the outer corridor, intent on getting to the stables and finding Rhys. She hadn't seen either of her horses since she had arrived here, and of the two, Rhys was the one most inclined to be lazy when he got the chance. _Probably stuffing himself on hay and congratulating himself on escaping exercise, the slothful beast,_ she thought happily. _Time to wake him—_
She pushed open the door, and at once was stopped by a bar to her exit. "Halt!" the guard at the door said, "Boy! What are you—"
"Boy?" Gwen slapped at the spear that had been lowered to stop her from going any further. "Alun ap Grwn, are you blind? I'm no more a boy than you are. Now enough with your nonsense. I'm going to the stables."
The guard gaped at her, then snapped the spear back up. His usually stolid expression was gone, replaced with utter confusion. "Queen Gwenhwyfar, I—didn't recognize—"
She waved the apology off. "Never mind. I'm going for a ride, and I suppose I will need an escort. Send for whoever of the Companions isn't busy, will you, and direct him to the stable. Or better yet, go yourself."
"Ride?" the man replied, looking dazed. "Stable? But, Queen Gwenhwyfar, you can't—"
"I most certainly can," she said sharply. "and I am going to. Now get one of the Companions to—"
"But—there's no one here but Kai and Medraut," the man stammered. "And I'm under orders from the King himself. You're not to be disturbed, and on no account I am not to let you leave—"
The first part of his sentence was lost in the slap to the face that the second part was. She whirled on him. _"What?"_ she exclaimed in outrage.
"I'm not to—let you leave—your rooms?" he faltered, as she put one hand to her belt knife and stared at him, eyes blazing with rage.
"We'll see about that!" And with that, she headed off at an angry trot, outpacing him, as he tried to follow her, protesting every step of the way.
She was so angry that she just shut his words out. She headed straight for the King's privy chambers, since it wasn't yet time for the usual audiences, nor for the Companions to gather about that famous round table. Her blood boiled. He had _said_ that he understood! How could he—how dared he—
Her chambers were separated from his by the courtyard; she passed along one side of it, the first time she had actually seen the sun and the open sky in days. Her breath steamed in the cold air; it felt good and clean after all the heat and perfume.
She stormed past the startled guards on his doors, the protesting Alun right behind. The first room, where he would usually have been, sitting at a desk, was empty. There were no maps on the desk, no discarded cloak, and the mosaic floor that imitated the pool of the courtyard outside had been swept immaculately clean.
The second room, where he usually lounged with Kai or others he considered close as kin, was also empty. The cushions were placed neatly on the Roman-style couches. There were no cups and horns waiting on the side table to be collected, no litter of food from breaking fast. And the small council chamber, with the frescos of Hercules defeating a lion, was just as empty. And his bedroom, as small as hers, was not only empty, but cold. Very empty, even of servants.
She turned on the guards, who had followed her in. _"Where is he?"_ she shouted.
"G-g-gone, Queen Gw—l"
"I can see that! _Where?"_ If he and the Companions had gone off hunting and left before she was awake so he had an excuse to leave her behind—
"Roughly half a day from here, more or less southwards, dear sister."
That was not a voice she wished to hear.
She stiffened as Medraut strolled past the guards, a goblet held negligently in one hand. He took a sip of the contents as she stared at him, uncomprehending. Surely they were not hunting that far afield? And surely there was no need for Arthur to go visiting an ally in this weather—was there?
"Half a day—what does that mean?" she demanded, her stomach sinking with dread. Because there was _one_ reason why they would all have left . . .
"Just what I said. He left this morning to join most of the Companions and the warriors. And his allies, of course." Medraut smiled at her, evidently enjoying every moment of this.
"Warriors—allies—why?" No. Surely not. Surely Arthur would not have—
"The Saxons, of course. The moment they heard he'd married again, they decided to take advantage of it. Just like the last time, when they attacked in the winter. Evidently they did not learn the lesson. Or they heard that Arthur tamed the White Phantom, so now they believe it is safe to harass our border again." His grin widened. "You've been carefully sheltered from all this terrible news so that you wouldn't be upset by it. Arthur was only waiting until he was sure you were breeding to go take the field himself."
Her mouth dropped open. "Wh— _breeding?_ " Suddenly the conversation—or lack of it—they'd had last night all made sense. But not in the way that she'd assumed last night.
_He thought—_
"Of course, we were all sympathy when we learned of your outburst. And we agreed that it was safe enough to leave you now—not to mention that it's very unpleasant to be around a female when she is so . . . temperamental. Women do get so emotional and so irrational when they're breeding." Oh how she hated the snide smile on Medraut's face! She wanted to smash it off . . . her hands clenched and unclenched at her sides. How much of that nonsense he had just spouted had _he_ poured into Arthur's ear? Her jaw was clenched so hard that her teeth were actually beginning to hurt, and she forced herself to relax, but her fury at _both_ of them did not abate one bit. Of course he had taken the field himself. He hadn't wanted her in the first place. She was only now beginning to realize just how he thought of women in general—that he had never, even with the evidence in front of him, thought of her as a warrior. Certainly he had not thought of her as the equal of one of his Companions. Bronwyn was right; though he had first seen his first wife as a warrior, she had later shown herself to him as a woman, and he had buried the warrior beneath the woman in his mind. He was not a man who could see both. And in her case, he did not want to.
And Medraut? Medraut had encouraged him.
"Here. Drink this, dear sister," Medraut said, handing her the goblet. She almost dashed the contents in his face. But instead, she swallowed them in two gulps, not even tasting them, except to recognize them vaguely as mead. She thrust the cup back at him. "Your women protested that it was too early to tell, but he only smiled, and said, 'Well, whatever else would cause a lady to suddenly demand fletching supplies and sit in her solar to make arrows? I expect her next demands will be for pickled vegetables, and stewed dormice.' And then he laughed and appointed Kai and myself to be in charge of the realm while he was at war." Medraut chuckled. "Such a trusting man. I suppose he thinks he's tacitly grooming me to take Kai's place eventually. But then, he knows that Kai will take excellent care of his queen, given her condition. And I, of course, told him that I would be sure that you had my very particular attention."
"He— _what?"_ She was so enraged now that she was dizzy with it. "But I am the queen! I—" She groped blindly for the edge of the table to steady herself. _She_ should have been the one left in charge, not Kai, and certainly not Medraut! That she had not—it was an insult past bearing.
"Exactly, dear sister." He laughed. Oh, how she hated that laugh! "You are only the queen. Obviously he couldn't leave a mere woman in charge. That is hardly the Roman way—but you look ill, dear sister."
She held the table with both hands now, the room spinning around her.
"You see, you have exerted yourself entirely too much. Let me help you to your chambers—" He waved off the anxious guards. "No, no, it's quite all right. I can carry her easily."
And indeed, he bent a little and scooped her up as if she had been a child. He was much, much stronger than he looked. And by now, she couldn't even push him away. Her arms and legs didn't seem to want to work at all, and she was so dizzy that she couldn't even get her eyes to focus.
Her head lolled against his shoulder, and she hated, _hated,_ the foul, possessive way his arms tightened around her. She tried to speak, but nothing would come out.
Once more she crossed the end of the courtyard, but this time, even though she wanted to squirm out of Medraut's arms and run away, she had to close her eyes against the way the heavens swung wildly about.
The chill air didn't help, and the warmth that enveloped her once they got to her rooms only made things worse. She wanted to scream in protest as he invaded her very bedchamber, but her voice wouldn't work. "Go get her women," Medraut ordered the single servant, as he laid her down on her bed.
"That didn't take long at all."
That was a voice . . . a voice she should know. But it wasn't one of her women. Gwen stared up at Medraut, and at the woman who had come to join him. A woman wearing _her_ dress. A woman that was so like her, that Gwen seemed to be looking into a mirror. For a moment she thought, _magic._
And then her mind finally presented her with the right answer. "Hello, sister mine," Gwenhwyfach said, and giggled, looking down at her. "What? No words of greeting?"
Gwen's throat worked, but nothing came out.
"My potions have always been effective," Medraut replied. "Because I take more care with them than my sister does."
"But your sister has other talents." Gwenhwyfach reached up with a proprietary hand and smoothed Medraut's black hair, and for one moment, his eyes flashed annoyance. She was looking at Gwen, however, and didn't see it. "I have the cart all ready, my love. We only need to roll her up in the blankets and have your man carry her out."
"Good." Medraut reached down and tilted Gwen's chin so she was looking directly at him. "You see, dear sister, I could not take the chance that any woman the High King married actually _might_ manage to breed Arthur an heir. I must have put together a dozen plans, depending on how important the woman was. The worst would have been one of the Ladies . . ." He made a sour face.
Gwenhwyfach laughed. "There is no chance one of them would have given up her Power to come here!"
"True enough." Medraut looked down at Gwen, and she wanted to shudder at the expression in his eyes. "But when he decided to marry you, I knew I had the easiest and most elegant—and least risky—solution in my own two hands. _My_ Gwen becomes the queen she has always wanted to be and makes sure Arthur dies childless. _You_ will be taken away."
His wife interrupted him, glancing with some concern between herself and Gwenwhyfar. "Do you think that anyone will notice that she was wearing those—things—and I am wearing her gown?"
Medraut shook his head. "Only the guards and the servant saw her. Besides, she can always say that she changed her clothing after her spell of illness. I dismissed the servant that dressed her to the kitchens, and no man ever remembers what a woman is wearing."
"Only what she isn't." Gwenhwyfach said mockingly, and Gwen felt chilled to hear her own laugh coming from her sister's throat. "Oh, I am looking forward to this. You may be sure I will well bewitch the High King, my love. Arthur will have such a greeting when he returns as will make him never want to leave my bed again. I will use every wile your mother ever taught me."
"It would greatly please me if you managed to dispose of him there, my love," Medraut smiled. Incredibly, he was not the least bit disturbed at hearing his own wife describe how she intended to seduce another man! Then again . . .
. . . he was certainly Lot's son in spirit, if not in actuality.
"But if you do not, when the Saxons finally kill the old man, or the Ladies give up and let me spill his blood for the Land, the Old Stag will give way for the Young Stag, and I will be High King. Just as mother promised." His eyes glittered, and inside her, she grew cold with fear. How had she never seen this before? How had she never seen how ruthless he was, how he would do anything, use any tool, to take the High King's throne? Now, of course, it was far too late.
"I'm sure by now you are also wondering, 'But what about the Druids?' Since it was the Merlin who was so very eager to kill me in my cradle." He laughed. "And of course, the Merlin managed to imprint his desires on the entire Druidic Council. I thought about that, too, well in advance of putting my plans in motion. I have been working at this for years. All of the Merlin's cronies have tottered off to the Summer Lands, and I hold the young ones in the palm of my hand." He spread his hands wide. "And now it all comes together. You, the High King's queen, disposed of. The Druids, mine. The Ladies so concerned with fighting the encroachment of the Christ men that they ignore me. My wife in your place. All of it, building the stair that will take me to the highest place in the land."
She was fighting hard now to even stay conscious. Her vision narrowed, darkened. There was a roaring in her ears. She couldn't hear him anymore. Couldn't see him.
_So this is death,_ she thought bitterly.
And then she had no more thoughts at all.
She hadn't expected to wake, so when she did, it was with a shock as great as the blast of cold air that struck her in the face. She struggled to move, to open her eyes, and plunged into despair when she couldn't. Wave after wave of nauseating emotions washed over her. Panic. Terror. A deeper despair. She tried to force calm on herself, tried to get control, only to have fear wrest it away from her. Her ears were still full of a roaring sound, but under that, she heard the clopping of hooves, and her body was bouncing on a hard, flat surface, and rolling about a bit. So she was in that cart Gwenhwyfach had mentioned. She'd been incompletely poisoned. But she still couldn't move. She was being carted off, to be buried alive. The thought of the frozen clods falling on her face, the earth filling her throat, her lungs, choking her—
She thought she would be submersed in terror forever.
But even the terror wore itself out. It ebbed, slowly. And that was when she realized that she _could_ open her eyes again. And she could—barely—move her fingers and toes.
When she forced her eyes open, she couldn't see anything but light filtering through a coarse cloth that covered her face. And she was tied firmly hand and foot—tied, in fact, to a pole that ran past her head and feet, so she couldn't bend or kick. But she was awake, and she could move. That counted for something.
And that was when she realized that even if her hands and feet were bound, her mouth was not.
"Help," she croaked, weakly. Then, "Help!" she yelped, louder. _"Help! Help! He—"_
The cart stopped. The cloth covering her face was pulled back, roughly.
"Now, now," said Medraut, making no attempt to hide his gloating. "Surely you don't want to leave my company so soon, Gwen?" He gave her no time to do more than gasp at seeing him. He reached down and wrenched her head back by the hair, stuffing one end of a horn into her mouth. "You'll just need to go back to sleep for now. We have a way yet to go." He let go of her hair and pinched her nose shut, then poured more of that cloyingly sweet mead down the horn. "Drink or drown, my love."
She had no other choice. Choking, coughing, she drank. Some of it got into her lungs, where it burned terribly. As soon as he was sure the drugs were taking hold of her, he pulled the horn out of her mouth and smoothed her hair with a tender hand, wiping the tears of pain and rage from her eyes, and fastidiously cleaning some of the slopped mead from her mouth.
"There we are. That's better, isn't it." His eyes were alight with a strange look of pleasure. "What? You thought I was going to kill you? I told you years ago that you were going to be mine; why would I want to kill you? I only married your sister because she was so like you." He patted her cheek, while she shrank back inwardly in horror. "And now I have you all to myself. Your sister will be so concerned with keeping Arthur happy, she won't have time to worry about what I am doing. Besides, she thinks I am going to throw you in a river or bury you, not that I am taking you off to—well, it doesn't matter where. All that matters is that I prepared it for you years ago. Oh, you don't like me now, I know. But you'll learn to love me. I know you will. You won't be able to help yourself."
He laughed, and pulled the coverings over her head again. And mercifully, the roaring, and the blackness came back, and she was carried away by them and hid inside them.
**Chapter Twenty-One**
**G** **wen sat** cross-legged on her pallet on the floor, patiently braided her own hairs into a thread. A few threads and she could make a cord. If she had a cord, she might be able to strangle Medraut with it . . .
There was not much else to do. She lived in a small room with a high window in one wall and a mattress heaped with furs on the floor. The floors were stone, the walls were stone, and the timbers of the ceiling could not be reached by any means from the floor. Without a knife, it was not possible to cut up the furs or the canvas cover of the mattress. She was wearing heavy woolen gowns of material too tough to tear and too closely woven to pick apart, without any fastenings or cords. She was barefoot.
The latrine was a heavy stone basin in the corner with a hole much too small to stick anything down. The huge guard that brought her food sloshed a bucket of water down it when he came in.
Medraut had gone to great lengths to make sure that there was nothing in here she could use as a weapon. Her food was served in a grass basket, and she ate it with her fingers; her drink came in a blunted drinking horn that wouldn't serve as a weapon itself and wouldn't smash to give her something with a point or edge. Those were taken away when she was finished, and the guard stayed there until she finished.
This place, whatever it was, must have been built on the Roman style, for the floor was warm, though not nearly as warm as Arthur's palace.
She was not sure how long she had been here. Weeks, certainly. Months . . . probably. For most of the early part of this ordeal, she had been unconscious for long stretches thanks to Medraut's potions.
Medraut visited her from time to time; his visits were irregular, and the only way that she knew one was going to occur was when she began to feel dizzy after eating. He made sure that she couldn't move long before he unlocked her door. She had been completely unsuccessful in detecting whatever he was putting in her food; she'd tried not eating altogether, but eventually hunger drove her to eat. After all it wasn't as if she wanted to die—that was the last thing she wanted. She wanted to get free.
She was pretty certain that on the last several visits, Medraut hadn't touched her, although she knew very well he had done whatever he liked early on. Probably he had found that lying with someone as unresponsive as a corpse was rather unsatisfying. Instead, of late, he had a chair brought and sat in it, talking at her until she lost consciousness. That might actually have not been so bad if he had given her any real information. She knew far more than she wanted to know now about how he had gotten rid of Arthur's sons, how he had hoodwinked Arthur into trusting him, what most of his late childhood had been like—and far, far too much about how he had been certain she was destined for him from the moment he saw her.
But a very, very strange thing also happened when she was drugged—and sometimes, when she was asleep.
Visions—maybe. If visions they were, she could hardly credit them. But if they were not, why on earth would her mind have made such a thing up?
She got glimpses into the life Little Gwen was leading in her place, and at first, everything happened as she would have predicted. Little Gwen absolutely reveled in her place as queen, wallowing in the baths and the preening, gossiping viciously with her ladies and for mischief setting them against each other, ordering gown after sumptuous gown, and entertaining Arthur in her bed with a wanton abandon that made Gwen blush with shame.
But then something happened. A new Arthur began to appear in that bedchamber of nights. An Arthur that _she_ had never seen, a man who, despite his years, seemed more vibrant, more alive, than she had ever seen him. And under the charismatic spell of _that_ Arthur . . . Little Gwen softened. Gradually, she ceased tormenting her ladies. Gradually, her demeanor took on a cast that Gwen couldn't really identify at first.
And when she did . . . that was when she simply couldn't believe the dreams. Because—if she was right—Arthur was taming the untamable Little Gwen, winning her to him the way he won his men's hearts. And she simply could not believe that anyone as self-centered as Little Gwen could come to care for anyone other than herself.
She'd had another of those dreams last night. It seemed just as impossible as the ones before it. If she didn't know better, she would have thought that Little Gwen was having second thoughts about betraying Arthur.
Impossible.
As she braided, she began to feel the tingling in her lips that signified he had slipped a potion into her again. With a resigned sigh, she thrust the thread she was braiding with the others she had made under the mattress, then stretched out under the furs and waited for the paralysis—and Medraut—to arrive. She stared up at the ceiling and the tiny bit of sky that was all she could see through the window.
She was almost beginning to look forward to this. It made for a change in the endless sameness of her days. She had thought she was bored as Arthur's queen; here she had nothing whatsoever to do except exercise, comb her fingers through her hair, and braid what came out.
At least she was still fit. She did every exercise she could remember, practiced fighting moves even if she didn't have a weapon, stretched and flexed until she was more limber than she had ever been in her life except as a small child. She had learned how to run and tumble in these wretched gowns, even if she couldn't run very far in the tiny cell.
She even practiced that meditation that the Ladies did, though she wasn't very good at it. She prayed a great deal. She recited what she could remember of bardic ballads and epics.
She did that now, waiting for the potion to take effect, staring upward, because when she couldn't move, she really didn't want to be frozen in a position where she had to look at Medraut.
The room began to spin, even though she was lying down. Beneath the furs, she tried, experimentally, to move her arm, and couldn't. So . . . he should be entering at any moment.
This was when she heard the bar on the outside of the door slide aside, and the door scraped open. Footsteps on the stone followed as Medraut entered the room, followed by a servant with a comfortable chair; who placed the chair and washed out the basin with a bucket of water. She could just see Medraut out of the corner of her eye; he made a face, and waved a hand in front of his nose.
"Time for another bath and a new gown, my love," he said. "You'll like that, won't you?"
She felt a little sick inside. Yes, she liked being clean. No, she did not like the fact that it happened while she was unconscious. Not one bit. She would wake up with her hair washed and braided, completely scrubbed, and in a new clean gown. She had no idea who or what was doing this, nor what, if anything, happened besides the washing. What was the most disturbing, perhaps, was the level of detail; her fingers and toes were neatly manicured, the nails trimmed, and even buffed to a soft polish. There were none of the perfumed oils of Arthur's baths, but there was a faintly pleasant scent on her skin afterwards. Any tiny abrasions or bruises were anointed with a balm, and calluses were sanded.
"Well, now, where were we?" Medraut asked, rhetorically, since she couldn't answer. She turned her attention back to the ceiling. In a way, since she was forced to listen to these monologues, she was glad even her expression was frozen. At least he didn't know how revolted she was most of the time by his confidences. And why did he ever think that this would make her care for him?
_Maybe because Gwenhwyfach used to hang on his every word?_
"Ah, I don't believe I ever told you how Lot told me that I wasn't his." She heard him move a little as he settled himself in the chair. "It was one of those rare moments when he was sulking about being Mother's pander, rather than gloating about it. Possibly his temper was because she was lying with someone he hadn't picked himself, and she wasn't allowing him to watch. So when I interrupted him to show him the results of the sacrifice and blood spell I had done all by myself, he knocked me into a wall and called me 'Arthur's unnatural bastard.' "
At this point, likely, Gwenhwyfach had been cooing with sympathy to him. Oh, how she wished she could stop her ears. The images that his narrative called up made her feel even more ill. Her imagination—given what her visions had shown her of Anna Morgause and her past—created scenes of Medraut's mother disporting herself with a lover all too vividly. And it was hardly that she disapproved of lovemaking—though her own experiences were not inclined to make her crave it herself. It was how Anna Morgause had used it: as a tool, a weapon. Even with Arthur. _Especially_ with Arthur.
"I knew better than to move. Lot is entirely unpredictable, and there was no telling how he would react. He glared at me a moment, then stormed off. I went to ask Morgana what he meant." Gwen couldn't turn her head to see his expression, but his tone was casual, as if he were telling a tale about someone else. This had probably hurt him—yes, even him—if it was true. If. There was no telling, with Medraut. Perhaps the reason for his casual tone was that it actually had never happened at all.
"She told me that what Lot had said was entirely true. Even the 'unnatural' part." He chuckled. "She explained it all to me, that Mother was Arthur's half-sister, and that even though the gods themselves often mated with their siblings, or daughter with father and son with mother, small-minded mortals thought this was wrong. A very enlightened woman, is Morgana. None of that really mattered to me, either." His voice took on a faint tone of gloating. Now _this,_ this she could believe. Very little mattered to Medraut, so long as he got what he wanted. "All that did matter was that Lot, whom I hated and despised, even at so young an age, was not my father. My real father was the man who was King over Lot, who had the Folk of Annwn as his allies, and the Merlin as his servant. My real father was Arthur, the High King. What Lot intended to be the moment of my humiliation became the moment of my release and elevation. That was the moment that I knew that I was destined for great things. I would either create something unparalleled, or destroy it. Either way, my name would never be forgotten."
She would have shivered at his words if she had been able to move. She believed this, too, believed fervently that Medraut hated Lot and Lot hated him—and that Medraut craved fame or infamy and didn't care which he got, so long as he had it.
"Mother sensed that I had learned the truth and questioned me about it. I told her, but only in Morgana's presence, because I wanted Morgana to know I had told, and I wanted Mother to know that we were together on this." He let out his breath in a long sigh of reminiscence. "Mother was always a little afraid of Morgana, and I didn't know why at the time, but I felt that with Morgana there, she wouldn't dare punish either of us. I found out later, of course, just why Mother feared her. Morgana had pledged herself to the Morrigan when her woman's blood first began to flow."
That meant nothing to her—well, except that if Anna Morgause was wary about this Morrigan, it would be wise to be even more wary. He laughed softly, mockingly. "You're puzzled, of course. You wouldn't know of the Morrigan. She is the Dark of the Moon to Cerridwen's Full Moon. They know her well in Eire, though, and it was a wise woman of Eire that taught our Morgana of her. She is the chooser of the dead, the storm crow, the washer at the ford. She is power and chaos, and she suits our Morgana most perfectly. Even Mother was afraid of the Morrigan's power."
Gwen felt a cold that had nothing to do with the potions or her paralysis. It wasn't wise to mix with the gods, the dark ones in particular. "Lot himself has always left Morgana alone, even though he lusts for her to this day. I often wonder if that wasn't why Morgana pledged herself in the first place."
Well, Gwen couldn't fault Morgana for protecting herself from Lot, whose excesses rivaled those of his wife. But dealing with the dark side of the moon goddess—risky, risky business. Everyone knew there were always two sides to every Power, but dealing even with the bright side of the changeable Goddess of the Moon was a great deal like trying to bargain with the Folk of Annwn. Cerridwen was fickle enough; what was the Morrigan like?
It wasn't wise to put a name to the dark ones, nor to give your name to them, and it was even more foolish to bargain with them. Not unless you wanted them to come for you one day, asking a payment much too high for what you got.
It did rather sound as if that was exactly what Morgana wanted.
"So, Mother didn't argue with Morgana, she didn't even chide her. She just said 'Since you have told him, you might as well have the teaching of him.' And that was what she did." Gwen heard him get up from his chair and walk over to her pallet to peer down at her. The ceiling seemed to move in a slow circle, with his face as the center of it. "Ah, still with me. Good. It is really quite important that you hear this, my love. You need to understand just why it's futile to resist me and important to love me."
He sat back down in his chair, satisfied that she was still listening to him. "Naturally, Morgana told me everything then, not the least of which was how the Merlin had tried to have me killed when I was born. Morgana had seen just this thing in her scrying and had told Mother, so Mother had made certain I was safe by giving birth early. By that, Morgana was as much my mother as she was, if not more. Well! When she told me that, I was all for pledging to the Morrigan myself! Unfortunately, the Morrigan does not accept males." He sighed, theatrically. "Nevertheless, Morgana taught me and kept me safe from my brothers until I could defend myself. Shortly after that, Mother decided that it would be a fine idea to wed Morgana to your father. She had intended him for herself, but her magics were thwarted."
Oh, Gwen remembered that all too well.
"Now I would imagine at this point, you are wondering why Morgana didn't ensnare your father. She was more powerful than mother, and the moon goddesses, bright _and_ dark, are goddesses of passion and love. It's a logical question." The chair creaked as Medraut leaned back in it. "The answer is simple enough. She didn't want him. Why would she? He was an old man, more than old enough to be her father." After a pause, he began to laugh, harder and harder, the sound filling up the entire room, battering her ears. After what seemed like far too long, his laughter died down. "Oh, my. That was funny. You should be able to understand her feelings perfectly, my love. After all you _are_ married to an old man who is more than old enough to be _your_ father."
As Gwen teetered on the edge of unconsciousness, it came to her in a last moment of pure nausea that for once, Medraut was right; she _did_ understand Morgana's feelings in that, if in nothing else. She understood them perfectly.
Gwen awoke, as usual, slowly. But as she woke, she was aware almost immediately that she was not where she expected to be.
Scent came to her first, and the scent was of steam and soap, with a touch of rosemary. Then came the sense of hard pressure at her back, not the soft mattress. And there was no weight of furs on her, either.
It was warm, extremely warm. As sensation came back to her fingers, she flexed them, and ran them over the surface she was lying on.
Wood.
There was no wood in her cell except the beams of the ceiling.
She fought against the clinging hold of the potion, struggled to free herself of it, feeling hope begin to stir. She had to see where she was! Finally, she got her eyes open, and looked up at the ceiling above her. It was tiled in blue mosaic. And although it was not tiled in a pattern she recognized, she knew very well what this must be: a Roman bathhouse in a Roman or Roman-styled villa.
She was where she was always groomed while she was unconscious. Only this time, for some reason, she was alone. These rooms echoed dreadfully; if there had been anyone else here, she would have heard the breathing, even if they didn't stir.
So, alone, and somewhere other than her cell. Hope took on strength. By this time, she knew exactly how soon she could move as the potion wore off; she was nearly on fire with impatience, until at last, she was able to sit up.
She had been lying on a wooden bench very near a small soaking pool, smaller than the one she knew in Arthur's villa. This definitely was a Roman bathhouse, for the entire interior was paved in mosaic—blue with scenes of mermaids on the walls, brown with plants on the floor and in the pool. Her hair was still damp and a bit heavy but not soaking, so someone had been drying it before she had been abandoned. She was in a chemise, but not a gown, though there was a clean one nearby.
There were, in fact, a great many things nearby . . . including a knife that someone must have been using to clean and trim her nails. It wasn't a big knife, but it was more of a weapon than she had seen in far too long.
With her eyes fixed on it, she held her breath and listened. There was a lot of commotion going on in the far distance. Shouting. Fighting? Something urgent had interrupted the people grooming her, and kept them occupied long enough for the potion to wear off. If that was fighting, they might even have forgotten her.
At some point, though, someone would realize that they had been gone too long. She had to act, and act quickly.
The first thing she did was to don the gown, slit it up the middle, and use strips she cut from the towels she found to bind the result to her legs like a pair of trews. She followed that by making crude cloth shoes of the remains of the towels. Once, she would have been able to go barefoot in anything but snow. No more. And if she managed to escape, she couldn't afford damaged feet. She braided her hair roughly, tied the end with a bit of scrap, then hunted, quickly for what else might be useful.
She took what was left of the towels, the knife, and the pumice stone she found there, and a dipper, shoving everything but the knife into a small wooden bucket. She didn't have the time or the strength to break up the bench to get a club, but she could swing the bucket to bash someone with, and she had the knife.
The only entrance into this room probably led to the changing room. She eased toward the doorway and peered cautiously through it. The next room, also paved and walled in mosaic like the first, was empty, but unfortunately there was nothing useful there in the way of clothing or a weapon.
There were two more doors into the changing room. She could not afford to take the wrong one, lose time, possibly be trapped in the one with the cold bath in it. She listened again, going over how a bathhouse was laid out in her mind; there would be at least one room that had a cold bath in it, but any sound would be coming from the doorway that led to the rest of the building.
_That way._ What she wanted was the quickest way outside, one that didn't pass any more rooms. Granted, she didn't have much in the way of resources, but stopping to try to steal anything would only increase the risk of being caught. She moved quickly to the corridor. Here the mosaic continued only on the floor; the walls were plaster, painted with fading scenes of Roman gods and creatures of story.
The cloth wrapped around her feet muffled her footsteps and allowed her to move in complete silence. She listened intently as she moved and kept a sharp watch for places she might be able to hide if anyone came along this corridor. But no doors gave onto it except the one at the end, and the only light came from slit windows high up under the ceiling.
The noise was all coming, so far as she could tell, from the opposite side of the villa. And to her delirious joy, the corridor she was in opened not onto a courtyard but onto a bit of graveled yard surrounded by a laid stone wall. And in the center of the yard was a pile of wood, a chopping block, and an ax, left stuck in the block, as if the user had been interrupted. This was the yard that supplied the hypocaust with wood!
With that in her hand it would take more than two or three men to make her a captive again. She ran out into the yard, seeing the mouth of the furnace in the wall to her right as she did so.
She shoved the knife in the bucket, grabbed the ax, and yanked it out; the wall had been built to keep people out, not in; there was a rough way up it by way of the wood stacked against it, and she took it, flinging herself flat on the top of it to avoid being seen.
The wall was built at the top of a steep slope, with woods at the bottom. It was a long way down to the ground. But this height was nothing she hadn't managed before, so long as she remembered how to fall and tumble. The building she had just left loomed higher than the wall—there was no way to tell what all the ruckus was about. She just hoped it would continue.
Breathing a prayer to Epona, she tipped herself feet-first over the edge, ax in one hand, bucket in the other.
She hit hard enough to hurt but not hard enough to break or sprain her ankles, and she turned the fall into a barely controlled tumble and let the momentum hurtle her down the slope at a pace far faster than she could have run. This came at a cost, of course; stones hidden in the long, rank grasses bruised her ribs as she rolled over them, and she collided abruptly with a tree trunk at the bottom. But still—nothing broke, and she was able to scramble to her feet and duck into the woods.
She felt as if she was on fire with exultation. She was free!
_Free, yes. But the trick is to stay free._ She paused, panting, to take stock of her situation.
_All right, I have no idea of where I am. Or . . . when . . ._ It could be early spring or autumn. The trees were leafless—
But buds on the branches of the bushes that screened her were greening.
_Spring, then._ She had been Medraut's captive for most of the winter. She still didn't know where she was, and there was no way to find out quickly. Or slowly, for that matter. Assuming she got away, far away, and encountered farmers or a village, she didn't dare ask anyone, for as soon as it was known that she had escaped, Medraut would have his men out looking for her. _Think, girl._ East was dangerous. South was the Saxons. North was Lot's.
_All right. No matter where I am, if I go west, eventually I will come to our lands, or at least the lands of Father's allies._ All she had to do was figure out just which way was west.
But first she had to put as much distance between her and that villa as possible, and for that the best answer was to travel directly away from it, no matter _which_ direction that was.
Bucket in one hand, ax in the other, she made herself think calmly and gathered all of her scouting skills together.
Then she slipped into the forest like a phantom.
Those scouting skills returned with every step she took, until she was slipping through the woods as silently as any deer and leaving less trace. Perversely, the fact that her feet were wrapped in rags meant that she left almost no footprints, and the few she left were unrecognizable as human. Every time she came to a stream, she waded into it and walked along it for as long as her feet could take the cold. She never went in the same direction twice, either, going upstream on one and downstream on the next. So when she heard the hounds behind her and then heard their baying turn to bafflement, she knew she had bought herself at least a little more time.
But if they got downwind of her, they would find her without finding her trail, so she needed to either get downwind of them or get something between herself and them that could confuse the scent.
She was hoping for a nice swamp, or some other pungent way to break her trail, when she realized that there were some sort of animals in the woods ahead of her, for she heard slow footsteps and the occasionally breaking twigs. She froze as she heard snuffling, then relaxed as she recognized the sound as a herd of deer rather than the vastly more dangerous herd of swine. She altered her course to find them, pushing through more underbrush, until she surmounted the top of a little ridge, crouching to keep from making a "human" silhouette that would spook them.
When she did spy the herd, grazing on twig ends, she realized she had made a mistake, but a fortunate one. Not deer. Goats. This was much, much better than deer. Probably the fighting had driven them away from their usual pasture, and their pungent smell would surely cover her scent, and they should be used to human beings. There were about twenty of them, brown and gray, still shaggy with their winter coats.
Cautiously, she stood up. They looked at her calmly, the sure sign that they were not feral. With a grin, she walked toward them and clucked at them. "Come on," she whispered, making a little shooing motion. "We need to go, you and I. There are dogs coming, and you won't like them any better than I do." The lead goat looked at her with his strange goat eyes, snorted, and stamped his foot. The other goats all looked up at him and stopped eating. He bobbed his head, then led the herd off in the direction she wanted.
They let her get right in among them. She began to wonder after a few moments if this was something more than an ordinary goat herd . . . because not only were they going the way she wanted to, but very soon the leader was taking them at quite a brisk pace, and the rest were not protesting at all, nor trying to stop to graze. He took them to a track that was wide enough that she wasn't being slapped by underbrush and kept them on it. She was able to trot along in the middle of them quite as if they had accepted her as one of them.
Even as she thought that, the leader turned his head over his shoulder and looked at her. There was a green flash as his yellow eyes with their kidney-shaped pupils became laughing green eyes; there was a shiver of Power, and she almost stopped dead in her tracks at the shock. Then they became goat eyes again, and the he-goat continued shoving his way through the underbrush beside the path. She hurried to keep up with them.
_The Ceffyl Dwr,_ she thought to herself. The Water Horses sometimes took on the aspect of other hooved animals than the horse. The green eyes were a good clue as to what they were, and so was the fact that this path they were on was never very far from a stream. As they pressed on, he increased the pace again until they were trotting and she was really stretching her legs. It had be a long time since she'd walked this far. Her legs started to hurt. _Ah, gods, if only he would be a horse so I could ride!_
But she knew that was impossible, for he would be keeping his distance from her because of the iron ax and knife. And she dared not abandon the only weapons she had. But "Thank you!" she called softly. The he-goat bobbed his head but did not look back at her again.
Behind them, the sound of the dogs faded with distance, then died away. If they hadn't lost the trail before she joined the Water Horses, they surely had now.
Her side ached; she pressed her elbow into it and kept up.
_He could be taking me to the Otherworld . . ._
That was a risk she would have to take. Annwn was a dangerous place for mortals, and the Water Horses were not often known for having kindly natures. There was no telling what else she might meet there, either.
But she thought she could probably keep herself safe as long as she kept her wits about her. At this point—yes, Annwn was much to be preferred over being in Medraut's hands.
The goats pushed on, and she held her aching side and ran with them. Wherever they were going, one thing was sure. It was away from Medraut.
**Chapter Twenty-Two**
**T** **he goats finally** stopped in the last blue glow of twilight at the edge of a lake—stopped and then plunged in. They didn't stop, either—nor did they swim. They ducked beneath the still, cool surface with hardly a splash at all and didn't emerge again. Gwen found herself quite alone except for a fluttering in the reeds of birds, and the distant mutter of ducks.
Gwen was not at all surprised at their sudden abandonment. Exhausted, yes, but not surprised. The Ceffyl Dwr, like all the Folk of Annwn, were fickle and quite easily lost interest in the plight of mortals. It was wiser, when you got aid from them, not to count too much on it and never to expect anything further.
So here she was, on the edge of a lake with nothing more than the clothing on her back, the ax, and the contents of her bucket. In the dark, hungry, and with a raging thirst.
All right. Things were not so bad.
Though she was hungry, she had been eating well in captivity; a few days without food would do her no harm, and a single night was negligible. She had water right here at her feet. She could find some place to hide in order to sleep, even in the dark, and if the moon came up, well, all the better. The important thing was that she was free, and the Water Horses had made sure that Medraut would have a wretched time trying to track her. Even though he had hair of hers to do so magically, being so muddled up with the Water Horse magic might well be enough to throw him off the "scent" there, too, for a while.
While she could still see, she bundled the knife in the leftover strips of toweling, then got herself a bucket full of water. The dipper made a fine cup, and she drank until she was sated, then sat down and waited to see what sort of moon would rise.
To her great joy, it was full; the sight of the pale orb lifting slowly above the trees made her breathe a sigh of intense relief. She would easily be able to see now, to get into what was probably the single safest place to sleep unless she found an old den to hide in—tied into the crotch of a tree as far above the ground as she could manage.
The light painted a swath of silver across the lake, and touched the wisps of mist that were just beginning to rise from the waters. In the morning, well, there were a lot of things that she could do to find food. There were edible roots, and if she could manage to make a line, she could certainly fish. The ax was a comfort to have, but it was the sharp little knife that was going to make all the difference to her survival.
She gathered up her things and began to prowl the lake shore, and within moments she found exactly what she needed: an ancient tree, uprooted by a winter storm, lying half in, half out of the water. She explored the trunk, pulling brush that had piled up against it aside, and uncovered a hollow beneath it full of dead leaves blown in by the winds that was just big enough to hold her. She shoved her possessions in as far as they would go and crawled in after, pulling the brush back across the opening. The leaves crackled and gave off a slightly bitter smell, which should further serve to mask her scent.
It appeared that the Water Horses hadn't "abandoned" her after all, since this shelter was no more than fifty paces from where they had left her on the shore.
For the first time since she had stormed into Arthur's chambers, she smiled. Triumph tempered with caution made her spirits rise. She had done it; she had escaped, and although she'd had _some_ help in getting away and had certainly benefited by good luck, _she_ was the one that had rescued herself. That triumph eased the aches of over-used and too tired muscles, warmed her all over, and, finally, let her ease down into the first real sleep she had had since she left Castell y Cnwclas.
It was the sound of a small wren peeping inquisitively not a foot from her ear that woke her. She knew exactly where she was; a warrior got into that habit of waking with full knowledge fairly quickly, and it wasn't one that was easily lost. The sound of the bird was reassuring. If anyone or anything had been snooping about, that bird would not have been poking through the brush that hid her sleeping spot.
She stayed right where she was, though; she could not afford a single wrong step out here. Her resources were too thin to allow for mistakes, and even though she had a head start on those hunting her, they had the advantage of numbers and mobility. She had no time at all to waste. Everything must be carefully planned.
She needed food; it was too early for berries, finding a cache of nuts was chancy, and she didn't want to wait here to see if she could snare rabbits. Roots were possible, especially those of water plants, but the best idea was to fish. In the spring, fish were hungry. The best use of that toweling was to make a fishing line. She could carve a hook easily enough, and a bit of twig would serve as a bobber. She knew exactly where to dig for grubs and worms. So, unravel a long woof thread from the toweling, make a hook, get bait, fish. That was the first order of the day. Next, try to find a flint or other sparking stone; they were often enough found among the pebbles in streams and lakebeds. She had the ax, so she could make a fire if she could find a piece of flint.
Cautiously, she pushed the brush out of the way and took a careful look around before emerging into the dawn.
By the time the sun was overhead, she was full of fish, she had a hook and line, a flint, and had even found a way to sew the "shoes" together, padding the bottoms for a little more protection. They were only cloth, so they wouldn't last long, but she only needed them to last until she managed a better substitute, or found someone she could trust, or stole something.
With more cooked fish, cress, and some baked cattail and mallow roots in the bottom of her bucket, protected by a bit of cloth, she headed west.
She was very glad now that she had taken the bucket. It was proving as useful as the knife. It now held food, dry tinder, and the flint she had found among the stones at the lakeshore, as well as the rest of her meager belongings. The Water Horses had not made another appearance, and she assumed they had either forgotten her or had given her all the help they were inclined to. So before she left the lake, she had left three nicely cooked fish and some baked cattail roots on a rock beside the water by way of a thank you gift.
As she cautiously threaded her way through the forest, using streams as often as possible to keep her trail broken, she made a mental inventory of things she wanted. Real shoes and real trews were both high on the list, and so was a bow. She tried very hard not to think too much about the fact that she had no idea where she was. She was a scout, and an expert one at that. She knew all of the signs that showed where people were, and the farther she got from Medraut's villa, the more likely it was that it would be safe to approach them.
She also kept her eyes open for anything edible, and she gleaned some early mushrooms and a squirrel's cache of nuts that way.
It was not until she found another good place for a camp, this one a hollowed out but still standing, tree, had set several snares made with more raveled thread from her towels, had eaten and made herself comfortable for the night that she realized something.
Even though this was real hardship and was only going to get harder, she didn't care how long it took to find her way to friends.
For the first time in her life, she was free. There were no demands, no duties she was obliged to perform. She answered to no one out here, and her own skills and her own two hands were enough to keep her fed and safe.
As she restlessly shifted, finding a comfortable position in the hollow she had scooped dry in the rotted wood, the inescapable thought came to her. _What if I never went back?_
She immediately scolded herself for being impractical, if nothing else. She was well enough equipped to stay healthy and fed in the spring and summer, but winter would surely kill her. She did not have enough in the way of protection or hunting gear to survive even a mild winter.
But what if—what if she could find a way to live out here? Never go back to Arthur? And for just one heady moment, she entertained a daydream of complete freedom. Perhaps she could find an old hermit's hut—she wouldn't need much. If she were settled, she could spend her time hunting and tanning the hides of what she caught. She pictured herself making serviceable garments from rabbit hide, then, making a crude bow, bringing down deer . . . living out a life with no obligations to anyone but herself.
She sighed, the fantasy dissolving almost as quickly as she had conceived of it. _I'd go mad._ Although she liked her own company well enough, she knew she was not the sort for a hermit's life.
And aside from all that . . . Gwenhwyfach was masquerading as her, and that could have no good ending, not for Arthur and not for anyone else, either. She had to get back and expose the treacherous bitch. Medraut had had a very long time to plan whatever it was he was going to do, and he probably would not have kidnapped her if his plans weren't close to fruition. She owed Arthur that.
The weight of duty and responsibility descended on her again, as if someone had piled heavy stones on her heart. And she cried, just a little, as she settled in for sleep.
After two days of almost direct westward movement, Gwen relaxed a little, and began to look for signs of human beings. While it was true that Medraut's control extended this far, practically speaking, she didn't think he was all that interested in anything that went past the immediate boundaries of his villa. Medraut was, at heart, disinclined to trust anyone but himself. Governing land required a great deal of work—work he couldn't perform if he wasn't physically present. She had the feeling that the reason he had, as time passed, left her alone for so long, was that was still cultivating his place as one of the King's Companions. The work her father did day to day meant he was always dealing with his chiefs and nobles, sometimes over details as small as the harvest from an individual farm. Medraut couldn't possibly oversee extensive property himself, yet it was work he would never trust to anyone else.
So the villa was probably just a remote hideaway, and one with no village, no farms, nothing outside its walls. And while Medraut could probably force or bully cooperation from those living near the place, it was unlikely he even bothered to try to rule anyone living more than a day's ride away.
She began listening carefully for the distant sounds that would tell her there was human habitation—the crow of a rooster, the sound of a dog barking, the echo of an ax on wood.
But the faint sounds she heard first were nothing so peaceful. They were the metal-on-metal clash of swords, faint, far, but not all that far away . . .
And she didn't even think, she reacted. She ran toward the sounds, aided by the fact that the game trail she was on went in the same direction. Whoever was fighting, the odds were good that one side or the other would be friendly to _her._ The brief pang of regret that her strange idyll of freedom was over was lost in the fierce wash of glee that at last, at long last, she was going to be able to strike back at _someone._
But as she stopped just before the clearing where four men were being held off by a single, incredibly skillful fighter, she froze in shock for a moment. She _knew_ that fighter.
It was Lancelin, with his back up against the trunk of an enormous tree so that they couldn't ring him. And from the look of things, he was tiring. She didn't recognize the four men who were clearly trying to kill him, but they were well-clothed and well-armed, and the odds were good that they were Medraut's.
She assessed all this in no time at all, dropped her bucket, picked her target, and leaped to Lancelin's aid, ax held in both hands as she raced in for a killing stroke before they realized she was there. She aimed not for the body, which might be protected by riveted metal plates inside the jerkin, but for the back of the man's neck, where the helm ended. She couldn't see his neck beneath the hair, but she didn't need to. She knew there was no protection there.
She hit that spot with all her momentum and all her strength.
The ax struck home against bone; the handle shivered in her hands as the axhead severed the spine and went halfway into his neck; it lodged in there, but she had already let go of it and was reaching for the sword his powerless hand had dropped. As if she had practiced the move a hundred thousand times, she snatched it out of midair, and throwing herself into a half spin, slammed the flat of the blade into the belly of the man next to him. She hadn't enough time to hit him with the edge, but she didn't need to; she just needed to buy time for a better attack.
As she had expected, there was metal under the leather, but she knocked the breath out of him and drove him back a little. And the shock and surprise of her appearance had given Lancelin the opening to drive his own sword into the third man's throat. That man went down with a strangled gurgle.
Now the odds were two to two.
The two men left glanced at each other, shocked.
Lancelin and Gwen didn't pause even for a heartbeat. As if they were linked together, they both acted and grabbed the moment of that glance to attack.
And in the time it took to draw a quick breath, the second pair were down—Lancelin's from a thrust into his eye, Gwen's from a deadly and accurate swing at his legs, where he wasn't armored.
There were great advantages to being shorter than your enemy, sometimes; she spun again, this time able to aim, and took him across the back of his legs at the knee.
Her man went down, too shocked to scream, hamstrung. And in the next instant, Gwen stepped on his sword arm, keeping him pinned, while Lance put a foot on his chest and a sword point at his throat. She reached down and wrenched the sword out of his hand.
"Whose men are you?" the Companion panted. "What do you want?"
"Medraut's!" the man gasped. "He sent us to hunt for her—"
Lancelin looked at Gwen, his mouth a thin, grim line. She nodded. They had no way to keep this man prisoner without risking themselves. And to let him go would be suicide. Granted, he was hamstrung, but it was possible he would be found.
And if he wasn't found . . . they would be leaving him to die slowly and painfully. Lancelin thrust the sword home, removing the risk.
Then he collapsed back against the trunk of the tree, spent. Wordlessly, she went back for her precious bucket, emptied the contents out beside him, and went in search of water. He might as well eat the food that was in there; it wouldn't keep much longer.
Water was never very far away here—wherever "here" was. She found a stream quite soon and filled the bucket. When she returned with it, he was no longer alone.
But his company was not human. The horse had a familiar look to it, and she was fairly certain it was of her father's breeding, and it was clearly Lancelin's, since it was nuzzling him as he fed it bits of her baked mallow root. She put the bucket down beside him; he didn't bother with the dipper, just picked the whole thing up and poured the water down his throat. Only after he had drunk half the bucket and poured the rest over his head did he finally say something.
"You are the real Gwenhwyfar," he said, in a tone of weary satisfaction. "You could only be the real one."
"The false one can't fight," she said wryly, sitting on her heels beside him. "She prefers that unpleasant things are all taken care of for her, preferably where she can't see the unpleasantness and can pretend it is not happening. Are you injured?"
"Bruises aplenty. Maybe a cracked rib. Those churls might have had horses somewhere about, though they attacked me afoot when I stopped to let Idris graze for a bit." He tried to stand up and winced.
She got back to her feet. "Stay there. I'll have a look about for them, but don't hope too much. I don't think Medraut lets too many of his men have anything as costly as a horse."
A brief look didn't turn up any horses, nor any sign of them. She wasn't surprised. Even afoot, they'd had plenty of time to get ahead of her; _they_ hadn't needed to stop to fish and cook and try to make some makeshift equipment for themselves.
When she came back to him, he'd gotten his armor off, and he looked as if he'd been put in a barrel full of stones and rolled downhill in it. But he wasn't cut anywhere significant—a shallow gash across the ribs, a couple across the backs of his hands, and another over one eye. And careful probing proved that he hadn't actually cracked his ribs.
So now she asked the question that had been burning on her tongue. "Were you looking for me?"
He nodded. "When we came back from trouncing the Saxons with Arthur, the queen—the false one—didn't seem . . . right. She looked like you, but . . . there were too many things that weren't like you, at least, not to someone who'd fought beside you." He grimaced. "This will sound rude—"
"So be rude," she replied. "We've fought together, and more than once."
"She was too womanly." He glanced at her, apologetically. "I don't mean that you are not womanly, but she—she was like the king's second wife; she reveled in luxury. You were indifferent to it, at least it seemed that way to me. She spent hours in the bath, and when she wasn't in the bath, she was fussing over gowns and hair, and when she wasn't doing that, she was all over Arthur like a camp whore."
He said that last without thinking, then flushed a deep crimson, glancing at her. But she just nodded, grimly. "She's my sister," she replied, around clenched teeth. "Schooled by Anna Morgause and Morgana, and Anna Morgause was . . . insatiable. Those weren't just rumors you heard about her legion of lovers, they were facts. We called my sister Gwenhwyfach, 'Little Gwen.' She's married to Medraut."
He blinked at that, and blinked again. "But—"
She snorted. "Oh, Medraut is perfectly happy to have her where she is. He may think he's nothing like Lot, but he has no trouble playing his wife's pander. The only difference is that he does it for power, not pleasure. He has several plans afoot to be named Arthur's successor, and he's using Gwenhwyfach to open the door for him."
Lancelin's mouth made a shocked little "o," then he cleared his throat self-consciously and continued. "I couldn't get anywhere near her, of course. And Arthur . . . well, Arthur was . . . rather pleased . . ." He flushed again. "He said, now and then, that his wife must have missed him a—very great deal."
"Arthur is a man," she said dryly.
He coughed. "Yes, well . . . the thing is, Gildas turned up around Midwinter, and she acted as if she had never seen him before, and when he tried to converse with her, she just turned him away. Arthur wouldn't hear that there was anything wrong, of course . . ." He coughed again. "So Gildas talked to a few of us who knew you. Asked us to try to find out what was going on—if maybe the queen had been possessed or enchanted or—well, then he had another idea. Gwenhwyfar, this sounded mad to me at the time: He asked if maybe it wasn't you at all. He pointed out that the Merlin had enchanted Uther to appear as Ygraine's husband, and that was how Arthur was conceived in the first place. He thought that maybe someone had enchanted another woman to look like you."
She blinked at that, because it was so near the truth. Gildas was great deal more observant, and more clever, than she had thought. "And you thought—"
"I knew something was wrong. That queen wasn't the warrior I knew. Her hands were smooth and fair, and she was . . ." He groped for words. "She was _petty._ Instead of wanting to know about King March's schemes, or what the Saxons were about, or even peaceful things like the state of the harvest, she only seemed to care about gowns and gems and how to be amused. So I watched her, and I saw that she stole away now and again to speak privily with Medraut. I told that to Gildas, who suggested that the next time Medraut went on one of his excursions from court, I should follow him to find out where he went. So I did, and then I went to the Isle of Glass and told him about Medraut's villa. And the next thing I knew, Gildas had rounded up some of his monks and gone trotting off to see what Medraut was up to."
She stared at him for a moment, then began to laugh. Because she could, all too easily, imagine Gildas doing just that, trusting in his god to keep him safe. And then she laughed even harder, because she knew now what had caused the commotion that allowed her escape. It had to have been Gildas pounding on the gate, demanding hospitality, which Medraut would not at all have been willing to give him—but which, he would have known, he had to.
Lancelin looked at her as if he was afraid she had gone mad until she explained why she was laughing. "He must have been the one that distracted everyone so I could get away."
She sketched in something of what her captivity had been like, and her escape. She left out the part about being fairly sure Medraut had amused himself with her unconscious body until that palled on him. It would probably only make him angry, and in the long run . . .
_In the long run, there isn't much difference between how I feel about Arthur's using me and how I feel about Medraut doing the same . . ._ Horrible . . . but true. Which was something Lancelin, who adored Arthur, did not need to know.
"It must have been Gildas, the brave fool." He smiled a little. "I was a day or two behind him, he set off so suddenly, and I am ashamed to say, I stupidly assumed no one would attack someone as well armed and armored as I am." He shook his head ruefully, and a lock of hair fell into his eyes. He brushed it away. "And then you came to the rescue . . . this is a rather inglorious end to the story."
"I don't think—" she began, then abandoned what she was going to say. "We should get away from here. There will be more of those men out looking, and some might come this way too."
He nodded at her ruined gown. "Take what you need from them; I'll get into my armor again."
And there it was, exactly what she had wished for; her pick of trews, tunic, armor, sword, bow. Medraut was fastidious about his person and just as fastidious about the men that served him. The first man she'd downed had bled very little, for she hadn't cut the major blood vessels. She took his armor and shirt, the trews from the first man Lancelin had killed, since he hadn't voided himself when he died and they were unsoiled, and the boots from the last one, which were almost a fit. She made it all into a bundle rather than getting changed; when he looked at her askance, she raised an eyebrow. "I can ride in this, and it will take some time to cut myself out of it; I'd rather put more space between us and Medraut than stop to change."
Without a pause, he nodded, mounted his horse, and offered her a hand. She used it to pull herself up behind him, settled herself over the bare rump of his horse, then put her arms around his waist tightly, so that he wouldn't hesitate to get some speed from Idris. He nudged his horse into a canter, and they were off.
She became increasingly self-conscious as they rode—and conscious of him. The feel of his body under her hands, the smell of him—horse, and clean sweat, a little blood, and what smelled like rosemary in his hair. And she became aware that her body was responding to his in a way it had never responded to Arthur.
_It's the fighting,_ she scolded herself. _I've heard the men talking about it. I've seen them afterwards, they can't get to the camp whores quickly enough. It's the fighting and the fear of death and then the realization when it's all over, that you didn't die. That's all._
But it wasn't all, and she knew it. From the first time she'd seen Lancelin, she had wished, without admitting it to anyone but herself and Bronwyn, that he would look at her not as a fellow warrior but as a woman. That he would give her the kind of glances that men gave Gynath and Cataruna. That he would touch her not with friendly indifference but with pent-up passion.
Which was about as likely to happen as for this horse to sprout wings and fly them to Celliwig. She was a warrior.
And she was Arthur's.
**Chapter Twenty-Three**
**A** **s she was** already well aware, riding pillion on the bare rump of a cantering horse was not a comfortable way to ride. Especially not a horse of her father's breeding, which had wide hips and a muscular set of hindquarters.
And she hadn't ridden in—well, a very long time. Months. She'd done her best to stay limber, but by the time Lancelin slowed his mount to a walk, her legs were definitely sore. The horse wasn't any too pleased, either, and she didn't blame him.
"I don't suppose you have a place in mind to camp?" she asked as she tried to adjust her perch on Idris' rump; she hoped she didn't sound as if she were whining. This patch of forest was identical to the one they had been riding through, which still gave her no clue as to their location. "Where are we, anyway?"
"North of Celliwig," he said. "If I hadn't been following Gildas, I'd have come straight from there, and you would not likely have found me at all." He shook his head. "Gildas would say one of his good spirits was watching over you. If you had kept going and no one had stopped you, eventually you might even have reached your own father's lands."
"Well, I am very glad I did find you." She laughed. "It was a good thing for both of us. But now we are going south—"
"We are, and into lands I know. As for camping, yes, I do have a place in mind," he continued. "I've used it before. It's very well concealed. We'll be riding until twilight to get there, though."
"I would rather do that than take any chance of Medraut's men catching us." She said it, and she meant it, but she knew when she finally got off this horse, part of her would regret saying it.
But even as she thought that, he turned the horse's head and sent him down into a ditch or ravine with a tiny thread of a stream running in the bottom of it, a ditch that quickly deepened until the sides were higher than their heads. There he dismounted. "Off," he said. "All three of us need to stop for just a few moments."
The horse proved the truth of this by plunging his nose into the bit of a stream and noisily slurping up water. And as soon as her legs stopped hurting, the running water reminded her that there was something else she needed desperately to do. With a rueful glance at each other, they parted company until the brushwood hid them. She was still not willing to stop long enough to change clothing completely, but since she was going to have to retie everything anyway, she did cut the gown off at the hips and pull on the breeches and the boots. Immediately—and not just because she also relieved herself—she felt better. More like herself.
And there was the added benefit that she had two large pieces of heavy fabric that were likely to come in very useful.
She folded the fabric into a pad she could use under herself and trotted back to the horse and Lancelin. A little stretching left her feeling a lot happier about getting back on that horse. The leg of rabbit Lancelin fished out of a saddlebag and handed to her made her feel happier in general. She made short work of it, as he did the same with another leg.
"I'm going to stop one more time so we can hunt," he told her, as he swung himself up into the saddle, then offered her his hand and let her pull herself up behind him again. "We won't have a chance before dark otherwise, and that was the last of my provisions."
"I hope I can still remember how to use a bow," she said dryly. He laughed and put heels to his mount.
True to his word, in late afternoon, he did stop. Under any other circumstances, Gwen would never even have considered hunting, and not just because there might still be men out looking for them. This was springtime, and unless you were very careful, you'd shoot animals with young and leave orphaned babies to die, which was poor husbandry and land care. But there wasn't a choice.
But luck was with them. He tethered Idris in the brush near a pond, and both of them could hear the quiet quacking of ducks. She nodded him towards the pond, and she headed in the direction of a glare of sunlight through the trees that probably meant a clearing. As she stalked carefully along the edge of a meadow, she heard a tussle in the grass and saw two hares fighting. Now, hares fighting could only be male. And the male hares had no part in anything but the siring of the young ones; they went off and left the does to tend the babies alone. She froze as soon as she saw them, but they were so deep in combat they paid no attention to her. Carefully she stuck one arrow in the ground in front of her, moving as slowly as a leaf in a light breeze. Carefully, she put a second to the bow, and pulled it back to her ear.
She let fly. And without waiting to see if the first arrow hit, snatched up the second and put it to the string.
Hares were not very bright at best, and when fighting over females, they were single-minded as well. The second continued to attack the first for a critical moment after it fell over dead. By the time it realized that something was wrong, and its head came up as it froze with indecision as a few dim thoughts managed to escape from the sex fight-sex madness that spring brought on, it too was dead.
Feeling utterly triumphant, she collected them, gutted them then and there, cleaned her knife and the arrows with a handful of grass and brought back the cleaned carcasses to where Lancelin had tethered the horse. He was already there, tying a gutted drake to the saddle bow.
He looked up. "Two were fighting over a hen. I shot the loser."
She nodded and held up her prizes. He actually grinned as he tied the carcasses alongside his catch.
As the sun set, it turned everything the color of roses—the greening forest, the sky, the clearings they passed through—and she could not help a feeling of triumph as she thought about all the nights she had seen this same rosy light fill her tiny window. She would swear that somehow she would win herself free, and now she had.
"Are you disappointed?" she asked into Lancelin's back. "That you weren't the one to win me free, like some warrior in a tale?"
He was quiet for a while, although she did not feel his muscles tense, so as she was used to seeing, he must have been carefully considering his words. "While the glory of being your rescuer all alone was a heady fancy, it was never more than that," he said, slowly. "First, of course, I did not know if you were actually held captive by Medraut. Second, if you were, his men are many, and I am one. What I planned to do, I fear, is somewhat less glorious. I was going to skulk about to determine if there was a captive there, and if it was a female, and if so, where she was being held. Then to see how closely guarded she was. Then to see if it was you. After that . . ." He shook his head. "My plans were unformed. Pray remember, so far as anyone knows, _you_ are still in Celliwig. My first course of action would have been to free you if I could, but I assumed I would not be able to. And I would have to think who would believe me that I could count on to fight with me."
She began to chuckle. "It appears that Abbot Gildas and his monks were willing and able to put up some sort of fight."
His laughter was deep in his chest, and she felt it vibrate in his muscles. "I owe the Abbot a profound debt of gratitude. I hope no one came to any harm."
She didn't _know_. "I don't think Medraut would dare. Though he follows the Old Ways, still, a holy man is a holy man, and you harm one at your peril."
While they had been speaking, the sun descended below the trees; the sky to the east darkened and filled with stars, while the sky to the west faded into ashes-of-roses. Idris picked up his pace; it appeared the horse knew where they were going.
They had to duck under low-hanging branches, and even though the leaves were barely budding, the trees here were very old, enormous, and thick, enough that it was hard to see. The horse could barely get between them, and his hooves made scarcely a sound on ground with a padding of old leaves that gave off a bitter scent as he picked his way over them. The air was close and warmer than it should have been. Even though Gwen was not Gifted in that way, she felt the Power here, humming along her skin, like the warning before lightning is going to strike nearby.
And then, without any warning, the trees opened up. And before them was a ruin.
It was not, as she had more than half suspected it would be, a henge. It was a small house, a house and not a hut nor a cottage of the sort her people raised, yet it was not Roman nor of any other style that she could identify. The roof had long since vanished, and yet several trees and a litter of smaller branches and a thatch of leaves had somehow fallen across the stone walls to create a new one.
"I have no idea who built this here," Lancelin said quietly. "Some Druid? A Lady? Whoever it was, that person had great power. Even I can feel it, and I have no Gift for Power at all."
"It welcomes us." She felt that, as well. This place was pleased to have them there.
He nodded, then threw his leg over his horse's neck and jumped down, lifting her down before she could dismount herself. "I come here when I need to be away from Arthur and the Companions. I can think, here. I can find myself and know even what I am hiding from myself—"
He broke off what he was going to say and quickly took off Idris' tack. He handed her the saddlebags and took the bucket himself. "There's good dry wood in there, and a hearth, and if they have not broken, some pots. For sleeping, I fashioned a pallet, and, there is good, dry bracken and some old horse blankets. If you can get a fire going, I shall get water."
She was about to ask from where, but he was gone. With a shrug, she went into the one-room stone house and found it was just as he had said it would be. In the last light, she quickly made a fire, using his flint and steel, catching the sparks in a nest of leaf fragments, blowing them into a tiny flame and feeding it with twigs until it was strong enough to take the logs. The bracken was piled in one corner, well sheltered, with the blankets atop it and the pallet tossed atop that. Once the fire was going, she hauled the pallet, which was of more bracken stuffed inside a worn canvas cover, down beside it. As she worked, Lancelin came and went several times, filling some of the pots with water. She took the first of those, skinned and cut up the hares, and put the pot into the side of the fire to stew. He continued to bring in water and wood, and at last he left the full bucket outside with Idris.
With a sigh and a wince, he settled down onto the pallet beside her. Only then did she break the silence. "If I had such a place, I would open it to no one."
He did not look at her; he stared at the fire. The soft light did not touch his eyes, "Not even Arthur?"
The air hummed with Power. This was no place for lies. She touched his hand, and when he finally turned, she gazed into his eyes. "Especially not Arthur."
He caught his breath, and emotions chased across his face too quickly to read. "Then . . . there is no love between you?"
She tried not to feel bitterness as she shook her head. "This is the lot of princes. I knew that one day I might be needed for—some bargain. I was the unwanted part of a bargain for horses," she said, the bitterness coming through anyway. "The Ladies wanted a bride for him who was pledged to the Old Ways. He needed an heir. The land needed one. He gave way, but grudgingly. There is nothing about me, the real me, that Arthur wants. I honor him as the High King. But I do not love him, and he does not love me. He wants a dream of a compliant, complacent woman who will bend like a willow to his will, who will ornament his great hall, greet his guests graciously, bear him heirs, give him bed sport, and never seek to join him in council or battle. That is not me. And he does not want what I am." She could have wept to say it out loud at last. It felt as if she had dropped shackles from her wrists. Somewhere out in the darkness, an early frog sang. "If I had known this, I would never have consented. This is no marriage, it is bondage."
Something that she had never, ever expected to see, flared in his face. "Then the gods be thanked!" he cried, and clasped his hands about her face, and kissed her.
A fire leaped up between them, a fire that began at their lips and swiftly raced to her groin. She moaned and opened her mouth to his even as her own hands drew him to her. His mouth was that of a starving man, it devoured her, as hers devoured his. A hunger she had not known was inside her obliterated all other thoughts except of him. Her hands, with a life of their own, unbuckled his armor; he cast it aside. His hands caressed her breasts, thumbs rubbing her sensitive nipples through the thick cloth, and the fire leaped from her groin to her breasts. She moaned into his mouth and pushed him away just long enough to pull the remains of the gown over her head, discarding it into the darkness. His shirt followed it, and they fell back together onto the canvas pallet, touching, tasting, hands and mouths exploring one another.
His fingers traced the line of her side, and she ached, arching her back as his lips and tongue played with her nipples. Impatient, more than impatient, she pulled down his breeches; hers were already around her knees, and she kicked them off. She parted her legs for him, and he knelt between them, staring down at her, his face alight, his eyes shining.
"I love _you,_ Gwenhwyfar," was all he said. Then he was on her, inside her, and the two of them moved to a rhythm all their own, until the fire became a conflagration, and devoured them both.
With their discarded clothing for a pillow, they lay in each other's arms and fed each other bits of hare—which, by some miracle, had not been burned to blackness in the bottom of the pot. She listened to his heart pound and traced her fingers over his chin. He held her as if he would never let her go.
"I think I began to love you when you spoke to me after the battle in the winter," he said, quietly. "But I thought—I thought you were spoken for, maybe. And if you were not, well, you were a warrior, your father's eyes and soon to be his right hand. You were the White Phantom, the legend the Saxons had learned to fear. What could I offer you? I have no land, let alone a kingdom. I have only my status as a Companion. Not even my horse is my own."
_Cataruna's husband came to us with less,_ she wanted to say, but how could she? That was the past, and words would not change it. "So I put you from my mind, and when I thought of you, I told myself to think of you as another warrior. And so I did. Until I saw you as Arthur's bride, so beautiful, so regal, and—" His voice choked a little. "—and I knew what a fool I had been, and you were going to Arthur, and if you did not love him then, you would love him soon."
_As you love him?_ She did not say that either. "He did not want another wife, much less one with my name," she said quietly. "And he especially does not want one like me. He kept me as much a captive as Medraut, even if that captivity was in a cage of gold rather than stone."
There was more, much, much more, that she wanted to say. But these were not things that you said to a lover. _When we lay together, the only thing that kept it from being rape was my consent._ And _I cannot, and never will, welcome him into my bed. He may come there, but I cannot welcome him, for it is not_ me _he wants—any empty vessel would do._
Or _he thought I was breeding. He stayed only long enough to put a child in me and then could not leave me fast enough._
"I love _you,"_ she said, knowing it to be true.
"But—" he began, his voice rising a little in distress. And she knew what he was going to say. That she was still Arthur's—oh, not necessarily by the laws of _their_ gods, but certainly by the law of the land and of the Christian one. That Arthur would never give her up. That they had together betrayed Arthur, just as the second Gwenhwyfar had.
_But the second Gwenhwyfar's betrayal was because he loved her. He does not love me. He does not even want me._
And she was not going to lie here and try to counter all those things. Not though Arthur had "betrayed" her—because he surely could not have been so blinded by Gwenhwyfach that he didn't realize she wasn't his wife. Not that Arthur could be persuaded, she was sure, to give her up, so long as he could keep his precious horses.
Instead she stopped his protests with her lips and built the fire anew.
As dawn grayed the sky, she woke, and she knew they should move on, of course. They should leave this place in the first sun of the morning, and they should ride straight to Arthur's villa. She knew it as the thin light of dawn penetrated the trees and filtered gently in through the broken wall of the house. She knew it as she listened to the birds sing, as she lay with her head propped up on one hand, watching him sleep. If they left now, they could pretend to themselves that last night had been a moment's madness, the lust that came after battle. They could pretend to forget all the things that had been said, half said, and unsaid between them. If they left now, it would all be over, and she would go back to her joyless couplings, and he would slake his needs with whatever lady of the court or serving wench was willing.
And that . . . would be unbearable.
She considered her options, looked over what could be done as if she were planning a battle. A battle? No, a war. This would be a campaign. She would need to persuade so many people of so many things. First of all, the Ladies, that she would never, ever bear Arthur an heir because if it had not happened by now, it was never going to. For that matter . . . once she told them of her captivity, it would be obvious that for whatever reason, the fault was with her, for certainly, Medraut would have sired a child on her by now if it had been possible. She would have to open the whole sordid tale to the Ladies and show them what a threat Medraut was to the Old Ways. And maybe Morgana too, though that would be harder. Morgana had done nothing overtly, and even though she had pledged herself to Morrigan of the Dark Moon, that alone did not make her a traitor, either to Arthur, or to the Old Ways. The Goddess had both a Dark and a Shining face, and it was wise to never forget that.
And then . . . she had to expose Medraut and her sister for what they were and what they had done before Arthur himself and his entire court and Companions. Arthur's blood he might be, but he could not be Arthur's heir. She would have to find proof of what he had done. She couldn't do that without still being queen, so . . . persuading Arthur to put her aside would have to wait until Medraut was no longer a threat and Gwenhwyfach was properly dealt with and confined by the Ladies where she could no longer harm anyone.
Then, once that was all sorted out, she had to explain her situation to her sisters. And her father. And, finally, Arthur himself.
She almost groaned at the thought of what it was going to take. It could be a year—more—until she and Lancelin were free to be together. But she was a king's daughter and the wife of the High King, and the good of the land and the people came before her own desires. This land must be made safe from Medraut. A new bride for Arthur must be found—one who could be as compliant and complacent as he desired. Yes, even if she were a follower of the Christ priests. Unlike the Ladies, after knowing Gildas—and after having the Abbot himself come so gallantly to her rescue!—she was by no means convinced that their way was at odds with the Old Ways. Did they, too, not have a Lady that they served? Their god too had died and returned.
Oh, this could take months. A year. A year in which every moment of every day must be spent in cunning, in persuasion . . . And yes, she would do this. This would serve the greatest good for the land and for the King. Even her leaving and making way for another was not entirely selfish.
But she could not . . . she could not face that year, without having a little joy hoarded up for herself. She needed this; she needed this in ways she had not even been able to imagine before last night.
Besides . . . she looked at Lancelin, at the shadows under his eyes, at the deep bruises on his chest and stomach, at the half-healed wounds on arms, shoulders, and hands . . . he needed this too. Not just the love, he needed the rest. Arthur was hard on his Companions, but Lancelin was harder still on himself. How long had it been since he had actually taken the time to heal? Too long, by the look of things.
So they would not be leaving this morning. And not for several more mornings.
She put her head back down on his chest, let the morning light creep across their bodies and warm them, and drifted off to sleep again in its embrace.
She sat, drooping a little, on the pallet. "I can't," she said, quietly but firmly. "I cannot ride today and maybe not tomorrow. I haven't ridden in over a year. My hips feel as if they have been dislocated, and if I get back on Idris today, I am going to be half crippled." _That_ was not even a lie—and not much of an exaggeration. "And look at you—" She gestured at him as he stood half clothed in front of her. He was the very image of the Young God to her at that moment—haloed with sunlight, motes of dust drifting about him. She fought back desire that made her body ache and concentrated on winning him. "What if Medraut ambushes us? You are in no fit shape for a fight."
He opened his mouth to protest. She gave him a measuring look. "Be honest," she warned. This was Gwenhwyfar the warrior, speaking to Lancelin the warrior, and he recognized it as such.
He shut his mouth. Looked at her with longing that made her feel warm inside. He heard the warrior and wanted the warrior-woman. She seized on his hesitation and capitalized on it. "I need rest," she said, plaintively. "So do you. And who is being harmed if we take it?" She watched his hesitation fading.
"What about warning Arthur?" he asked, biting his lip.
"Medraut—"
"Medraut dares not make a move against Arthur until he knows where I am and whether I am alive or dead." She had thought about this long and hard; and truly, if there had been danger that Medraut would act, she would be on that wretched horse this moment. "Gwenhwyfach will probably flee when she knows I have escaped, and even if she does not, Medraut does not dare leave her there for fear of what will happen to her when I do appear. I do not think he trusts her because I do not think he trusts anyone. He won't risk her betraying him. Arthur is in no worse danger if we remain here long enough to heal."
"But how do we explain taking so long to return to Celliwig—"
She chuckled. "We were pursued. We were elf-led. We were just plain lost. You were wounded. I was ill or injured. It doesn't matter. There is no one to dispute what we say."
He sighed, and his expression turned wistful. "There is truly no danger to Arthur?"
She bit back a sharp retort. _Are you more in love with Arthur than with me?_ It was unfair, unkind . . . and yes, it was somewhat true. The bond that tied him to Arthur was complex. Worship of the office and the man, admiration, friendship, a kinship of spirit . . . yes, it was love. He had loved Arthur long before he had met her. He would love Arthur without regard to Arthur's flaws. And while she could not help but feel more than a little jealous, this was something that men did, felt. They needed this. Perhaps it was the way that they saw the reflection of the gods on earth in their earthly brothers.
Even Gildas' monks felt this same passion for their Abbot.
She had seen this many, many times in her men—mostly for her father, sometimes for their war chiefs, and occasionally for her.
So she could and would feel the pain of jealousy, but it was a foolish, stupid woman who thought to take this from the heart of her man. As well to cut off what made him a man.
"I have seen no visions," she said, patting the pallet, so that he finally sat beside her. "I cannot say for certain. But this is what I am sure of, based on what I know of Medraut and of my sister." The memory of Medraut sitting beside her as she struggled with the haze of his potions made her feel like vomiting. "Medraut talked a great deal to me. Talked _at_ me, that is—"
He interrupted her, cupping a hand to her cheek. "Don't think about it," he said urgently, and then kissed her. "As long as Arthur will be safe while we tarry a little—then tarry we will." He kissed her again, this time, lingering, his hand straying from her cheek to her breast. "Now . . . let me drive his shadows from your heart."
The fire rose between them again, and she lost herself in it.
**Chapter Twenty-Four**
**T** **hey lingered seven** days. Seven days that would have been utterly blissful had they not been overshadowed by the knowledge that these days _would_ come to an end, that they would have to return to Arthur and the Companions and pretend that nothing whatsoever had happened between them. If it were not for that, she would have been happier than she had ever been in her life.
Seven days, during which she was more completely herself than she had ever been since her childhood. Seven nights so full of love speech and lovemaking it seemed as if she were packing enough loving moments for a lifetime into those warm, honeyed nights. They confided secrets, revelations, history, and memories, and then between them, they made more.
She learned that he had been raised by one of the Ladies who said she was his guardian; he had no reason to doubt her, since there was not the slightest resemblance between her and him. She had him trained in all the arts of war, then sent him on his way with armor, sword, and horse, giving him directions to Celliwig, when he was twenty. There he became one of Arthur's Companions; not the first, but soon the closest, for of all of the Companions, Lancelin's education most closely matched Arthur's, and they spoke the same language. He had remained the closest until the second Gwenhwyfar; then the estrangement began. And she could tell it hurt—hurt then, and still hurt. She did her best to soothe that hurt, but there was no denying that what she and he had was going to drive another wedge into the widening breech between him and the High King.
The most ordinary act took on weight and meaning when they shared it. She laughed more than she had in ten years. But at the end of the seventh day, he began packing up their things, and although her throat ached with sudden sorrow to see him do so, she did not protest. All things had to end; there was even a tiny leavening of relief that now the dread of ending was over. By now, Medraut knew he could not recapture her. By now, Gwenhwyfach must know she had escaped. Gwen and Lancelin needed to find out what both of them were doing and then put their own campaign into motion. If they were to have a life together, it would have to begin by giving each other up for a time. Even though she ached so much she felt as if she were bleeding from every pore.
So, at dawn on the eighth day, Lancelin saddled Idris and loaded him with their scant property. Wearing the looted shirt, breeches, and boots, Gwen helped him. And when everything was ready and they had led Idris out into the meadow, they turned back for a last look at the place that neither of them wanted to leave.
She felt a heavy weight of grief settle over her, and a lump formed in her throat. She fought back tears with every particle of will and determination that she had mastered over the years, but her heart felt as if it were going to burst with sorrow. The time ahead, when she must never look at him, never touch him, never give a sign of her love, stretched out like a road of ashes that she would never see the end of. She wanted to throw herself down on the ground and wail, or grab him and beg him to come with her, far away, anywhere—
But if she did that, if _they_ did that . . . it would be the murder of part of themselves. Duty and responsibility had made them what they were. Could they still love each other when they both would have betrayed that? Would they be the same people? And even if they were, knowing that they had forsaken _that,_ there must then always be the doubt, the wonder, if they would forsake each other . . .
No, they must endure this. And she must endure it without weeping. She must have let a single sniff escape, though, for in the next moment, he had wrapped his arms around her. She turned her face into his chest and gave herself a single moment of weakness.
"This is the hardest thing I have ever done, to go back to him, after—" Her eyes burned with tears. She blinked them back.
"I know," he murmured into her hair. "And to see you, and not be able to touch you—it will be like death, a thousand times a day. But I will never leave you. Even if all I can do is look at you, I will never leave you. I love you, Gwen."
_"Oh, how very touching."_
The sarcastic voice, hatefully familiar, cut across the clearing.
She felt as if someone had dropped her into the heart of winter. Her pulse fluttered erratically, and she felt sick as she slowly turned her head.
Just where the path they were going to take began, Medraut stepped out from under the trees, sword held loosely in his hand, wearing a carelessly sardonic expression. Except for one thing. His eyes were furious. Gwen stared at him, mind going numb but her own hand reaching for her sword. With almost the same motion, she and Lancelin drew their weapons and stood side by side, prepared to defend each other.
"How charming," Medraut sneered. But as his eyes rested on Gwen, she clenched her hand on her sword hilt. He was never, ever going to forgive her this. "How delightful. You _love_ each other. And how long, I wonder, have you been so enamored? Months? Years? What a lovely couple you make. Don't they, my King?"
To Gwen's horror, Arthur stepped out of the shadows to stand beside him.
And so did an entire half-circle of warriors, all of Medraut's brothers among them. She felt choked; she could scarcely breathe.
Arthur's face was black with rage, but he said nothing. Perhaps he was too furious to speak. And all that Gwen could do was stare, helplessly, all of her plans in ruins at her feet.
There was only one thing she thought she could salvage from the wreckage. _He can't charge us with treason. We never conspired to take his throne. Not like the last wife—_
"So, when were you planning to take the High King's throne along with his wife, Lancelin?" Medraut asked, poisonously, as if he was reading her mind. He smiled at her, his eyes dancing with malice.
"Never." Her heart thrilled with pride at the steadiness of Lancelin's voice. "I never wanted a throne, not Arthur's nor that of any other king."
"Ah, but the wife?" Medraut grinned. But that grin goaded her as nothing else had until now. That hateful grin—she had been forced to suffer it for months, that grin that said _I won, you lost, and there is nothing you can do about it._
Her mind unfroze as a flash of rage fired it, and in a flash, she assessed the situation. They—well, Lancelin—had one chance to escape this. He was a superb horseman. She had seen him leap into the saddle and ride off at full gallop. If he did that now, no one would be able to stop him. The warriors around them were carrying bows, but they had swords in their hands, not the bows. They were also, some of them, still in a state of shock and disbelief; and many were his friends, and for the moment, they would hesitate to attack him. He could get away as long as _he_ didn't hesitate or pause for anything. If he stayed long enough to pull her up behind him, though—
"Lance," she whispered urgently, making sure not to move her lips too much. "Get on Idris and get out of here."
Shock at her words made him glance down at her, though he did not move his head. "But—"
_"Leave me."_ She made it a command. "He's not thinking, and he won't, Old Stag that he is, while the Young Stag stands before him. He'll never listen to anything as long as you stand here. He'll challenge you, and you'll either let him kill you or kill him yourself. There's no other outcome for this."
_If he kills Arthur, he'll never be able to look at me again without thinking of that. And if Arthur kills him, I will follow._ She heard the breath catch in his throat. He loved Arthur; still loved Arthur. _"Go!"_ she hissed. "He won't harm me. He'll lose the Ladies and my father if he does."
Though Arthur might not be able to think at this moment, Lancelin certainly could, and her logic was inescapable. With an inarticulate cry of grief that wrung her heart and made a sob catch in her throat, he leaped into the saddle with a single jump. Idris, well used to what this meant, reared a little and plunged toward an opening in the line. The warriors, caught off guard, or perhaps not really wanting to try to stop him, did not react in time. He flashed between them and was gone.
With a look of contempt at Medraut that should have blasted him on the spot, Gwen tossed down her sword.
And waited for them to take her prisoner.
She paced the tiny, dark hut that they had locked her into. Ironic that they had brought her here, to Glastonbury Abbey. But Abbot Gildas had interceded again, so she'd heard; she didn't know first hand, of course, since she hadn't been allowed to see anyone but her guards, but that explained why she was here rather than at Arthur's stronghold. That good old man was still honoring their friendship; she hoped he wouldn't lose by it.
The hut walls were not that thick, and the guards gossiped; she heard practically every word they said. Arthur was incoherent with anger. There was no word of Medraut. There was no word of Lancelin either, which she took as a good sign. The guards didn't know what Arthur planned to do with her—
Well, he could _plan_ all he wanted to, but that did not alter the law. It was not yet treason for a woman, even a queen, to take a lover. She could, if she chose, even make the argument that she had only done so to give him an heir . . . and between bouts of weeping, she toyed with that idea. But it would be a lie, and she decided against it. She was done with lying to Arthur to save his pride.
They'd brought her a gown. She'd refused to change into it. She had no intention of surrendering her identity as a warrior a second time. She did behave herself honorably, otherwise. She did not rush the guards that brought her food and water and took away the bucket. She did not insult them, nor shout at them, nor demand anything of them. She stood quietly in a corner, let them come and do what they needed to do at dawn and dusk, and spoke only when she was spoken to. And yes, she wept, she had cried until her eyes were sore and dry and her cheeks sore and her nose sore and red with weeping, but she had done so silently. If— _when_ —Arthur finally confronted her, she was going to force him to acknowledge what she was. In no small part because that was what Gwenhwyfach was not.
It had been three days. That was a cold sort of comfort. The more time that passed, the more chance there was for her friends to rally to her side. The more time that passed, the farther away Lancelin would get and the more likely that Arthur's anger with him would cool a little. The only thing that worried her was—time was also on Medraut's side.
She had to fight with herself constantly, every waking moment, not to break down completely; this was like the conflict with Medraut in a way, and she dared not show any weakness, not if she was going to be taken seriously. It was worst on waking, for her dreams were full of Lancelin; in her dreams she was back in their sanctuary, held joyfully in his arms, and when she woke to find herself curled in the heap of straw in the mud-walled hut, the pain of disappointment was so bitter she could hardly keep herself from crying out with it.
Lying in the darkness, waiting for sleep, was almost as bad; that was when the doubt and the fear plagued her, dogged her every heartbeat and warned her that, no matter what, _this_ had forever poisoned what lay between them. That nothing would ever be the same again. That forced to choose between her and Arthur, Lance would always choose Arthur.
Those thoughts were like knives in her gut. And although those thoughts were worst at night, when she fought for sleep, they were never far away.
So she paced, counting the paces, as she had paced in Medraut's prison. She rehearsed what she was going to say, over and over. How she would react. What she would do—she had to take the offensive; the ground was all Arthur's. She had to force _him_ to react to what she said and did, not the other way around. She had to put him on the defensive.
She was rehearsing it all for the hundredth time when she heard the bar holding her in scrape across the door of the hut. The sound made her freeze, for it was neither dawn nor dusk. She turned, slowly, to face the little wooden door.
Two guards stood there, two of the Companions she was not familiar with. "Lady?" one said, hesitantly, peering into what must have been dark to him. His voice was very young. "Lady, you are to come with us—"
"I am Gwenhwyfar," she said, steadily. "Queen perhaps, war chief certainly. Not 'Lady.' "
She stalked out of the darkness of the hut and into the light, her eyes narrowed so that it didn't blind her, her back straight as a staff. "Lead on," she said evenly, taking in her surroundings as soon as her eyes adjusted. The island tor of the Isle of Glass loomed to her right, but it was more distant than she had thought, and all around her were the tents of a camp. This looked like a little farmer's hut, or a shepherd's, that Arthur had commandeered to hold her. So, she was not on the Abbey grounds, after all. Perhaps Arthur had wanted to put some distance between them and the Isle, for fear Gwyn ap Nudd would interfere in some way.
Which was foolish thinking. If Gwyn wanted to interfere, not the breadth of a kingdom would prevent him from doing so.
She eyed the guards; they were young. Very young. Evidently her good behavior had convinced Arthur that he need not put his stoutest warriors over her. They flushed as she looked them over. New armor, new tunics. With whom had they served before joining Arthur? Were they the younger sons of one of his allies? She wondered what they were thinking.
"Well," she said, when they didn't move. "If you are to lead me, then do so, if you please."
They flushed again, and one of them made an abortive gesture in the general direction of the largest tent in the encampment, which was, of course, precisely where she would expect Arthur's tent to be, since the encampment was laid out in the Roman style. She nodded and moved off at a deliberate pace, neither dragging her feet nor rushing. She didn't want these boys to have even a vestige of alarm about them because she had plans of her own.
Two more guards at the tent entrance held the flaps open for her. Just as deliberately she stalked inside and the canvas dropped in place behind her.
Arthur waited for her inside, flanked by Abbot Gildas and his foster brother Kai and two more pairs of guards. And before any of them could move or speak, she took the offensive.
Literally.
She crossed the space between them quickly, while they were still reacting to her presence, and slapped Arthur as hard as she could with the back of her hand. The _crack_ shattered the silence and shocked them all speechless. Which was exactly the way she wanted it.
"If I had a gauntlet, it would be at your feet, _husband,"_ she spat. "How dare you, _how dare you,_ take exception to anything _I_ have done, when you just spent the last seven months fornicating _with my sister?"_
Arthur's mouth dropped open in sheer shock; his eyes went wide and her handprint reddened on his cheek.
"My _sister,"_ she repeated, viciously, "Who also happens to be _married to Medraut._ While Medraut held me captive in _his_ villa, amused himself with me whenever he chose, and _you didn't even notice the difference."_
"Wait—" Arthur stammered. "What—"
"Ask Abbot Gildas," she said, crossing her arms over her chest. "He managed to deduce the truth without even having a decent conversation with the bitch. Or ask Lancelin—ah, no, wait, you can't, because you wanted to kill him, so to keep from harming so much as a hair on your head, he was forced to play the coward and flee. Because he knew you'd keep throwing yourself at him in a rage no matter what we said."
Arthur was not a fool; she had taken him by surprise, but he recovered quickly. "What kind of idiot do you take me for with this farcical tale of a sister like enough to you to be your twin?" he began. "And married to Medraut? Lady, you strain the bounds of—"
There was a not-very-polite cough from behind her. "I presume that you will take _my_ word as truth?" The Lady Aeronwen said, acerbically.
Arthur's face took on a look of confusion again. Not because he was confused by what the Lady had said—no, it was surely because he was trying to find a diplomatic way to respond.
Aeronwen did not give him time. "I can bring a hundred direct witnesses from Pywll, nay, more," she snapped. "Not to mention an equal number from Lothian. Gwenhwyfar of Pywll has always had a younger sister as like to her as a twin and separated from her by less than a year. So much like her that though the brat's given name was Gwyneth, she got the name Gwenhwyfach, and her true name was almost forgotten."
The number of dropping jaws around the tent far outnumbered those who could keep their countenance in the face of such information.
"Moreover," Aeronwen continued, "The girl was fostered to Anna Morgause and schooled by her and by Morgana in magic. She grew to womanhood in Lot's court and wedded Medraut." She raised an eyebrow. "Yes, Arthur. Your son by Anna Morgause wedded his foster sister, Gwenhwyfar's near twin, who was schooled in the same kind of magic his mother wielded. The same kind of magic that drew you to Anna Morgause's bed in the first place and brought about Medraut." The Lady stepped up past Gwen and stood in nearly the same position. "As to whether she was the one in your bed the last several months, that I cannot say. But it seems logical."
"And you _might_ ask yourself—and your men—just where Medraut is now," Gwen said angrily. "Where are _his_ men? And you _might_ ask yourself just what someone raised by Lot thought he was going to gain by putting his wife in your bed. And you _might—"_
But she got no chance to go further with that thought, for at that moment, there was a commotion outside the tent, and someone else shoved his way in through the tent flaps.
It was Gwalchmai, and beneath the beard and the dirt and blood, he was as white as snow. He clutched his shoulder, where red stained his armor and tunic. "The gods forgive me, Arthur—" he blurted, swaying where he stood. "Medraut—that misborn, misbegotten son of a witch and a demon—Medraut's on the way at the head of a Saxon army."
For one moment, there was no sound in that tent; it was as if the world had stopped dead in shock.
Except, perhaps, for Gwen. There was a part of her that had expected this moment, had known it was coming all along, and nodded in bitter recognition of that. That was why she recovered first and whirled, her gaze stabbing one of the two young warriors who had escorted her here. "You—" she snapped. "Get me armor to fit my frame. _My_ armor, if someone brought it here. And a sword. And most importantly, a bow and a horse of my father's breeding—my Rhys or Pryderi, if they are here."
Her voice seemed to jar them all back to life. The young man gaped at her and looked at Arthur. She frowned back over her shoulder at him. "You are going to need every warrior you have, Arthur. I saw your camp; most of your warriors are not here," she said, her tone clipped and precise. Maybe they were all doomed. Maybe they had been doomed from the beginning. But she would still fight right up to the moment that doom fell upon her. "Medraut must have been planning this for a long time. This is not a good ground to fight on; the only advantage you have is that it is equally bad for both sides."
Arthur looked gray, as if the ground had been cut out from under him. So Medraut's treachery cut him deeper than her defection? Well, so be it. That was just one more indication of how little he had thought of her and what she truly was, how little he had valued it. But he had his wits about him enough to see that she was right. "Do as Gwenhwyfar commands," he told the boy, and he turned to Kai. "Muster out the men. Send messengers. Gwalchmai, how many are there?"
"Same as last time." The old man—when had Gwalchmai gotten old?—clutched his shoulder as Kai pushed past him. "It's the full Saxon army, the one that retreated when we confronted them. That encounter was just a feint to test us and get our numbers. Medraut was planning this all along, planning to get you separated from the rest of your force. We're outnumbered, Arthur. Badly."
Arthur grimaced and grew paler. But he straightened, and Gwen saw that, like her, though doom fell upon them, he would fight to the last.
"Maybe not as badly as you think." Gwen's mind was racing. "Let me go to Yniswitrin. I'll see if I can call Gwyn ap Nudd out. You likely won't get fighters out of him, but he might make a passage for yours to come quickly. There's more than one tale of mortal armies passing through Annwn at need, and he _is_ one of your Companions and an ally King." Right now . . . she wished profoundly she could be the one to lead those armies here. But the King of Annwn would be the only one who could.
"I'll go with you," the Lady said quickly, before Arthur could say yea or nay. "With two of us, he is less likely to refuse."
Arthur looked for a moment as if he were going to refuse anyway, but then he shrugged. "Whatever can be done, we must do," he said, his face a mask of resignation.
Gwen didn't wait for him to change his mind. She strode out of the tent with the Lady sailing behind her.
There were several horses tethered beside Arthur's tent, and to her intense relief, one of them was her Pryderi, who tossed his head, whickered, and picked up his ears when he scented her. Whoever had appropriated him—well, too bad, he was going to have to find himself another mount. She ran to the picket line, pulled his reins loose, and hauled herself up into his saddle. The stirrups were set too long; she ignored them for now. The day she couldn't sit a horse for a straight run without stirrups would be a sad one indeed. As Aeronwen stood in the path, she rode up next to the Lady, and offered her hand. Aeronwen weighed next to nothing—did the Ladies never eat?—and Gwen was able to pull her up behind with just a little grunt of effort.
As ever, Pryderi responded as if he could read her mind; he danced a little and then leaped into a full gallop, answering her touch on the reins to arrow toward the distant isle, which rose above its perpetual mist as if it truly didn't belong in this world. Behind her, Gwen heard the camp coming to life, shouted orders and the frantic clashing of men getting armored and armed. In her ear, she heard the Lady softly chanting. What she chanted—well, Gwen didn't recognize it at all; it was older than any words she knew. But she felt it, felt the Power in those words, and felt that Power being drawn from somewhere ahead of them. Pryderi's ears swiveled, then pointed ahead again. He had never been disturbed by anything; she had schooled him to that.
They neared the mist, and the mist swelled and billowed out to meet them in a solid wall of white. Pryderi plunged into it without hesitation.
"Slow him," the Lady said in her ear, but she was already reining Pryderi in, lest he make a misstep, go tumbling, and kill them all. He tossed his head with rebellion, for he loved to run, but dropped immediately to a walk. The mist closed around them so thick that it was even hard to see the ground right under Pryderi. It clung to them, chill, damp, carrying with it a scent of water and green things.
Pryderi's hoofbeats sounded muffled, as if he walked on thick moss. Gwen looked about, and up, trying to catch the landmark of Yniswitrin, but there was nothing, nothing but mist—
"Give him his head," the Lady said. "Trust his instincts. If the King of Annwn is inclined to open his door to us—"
"The King of Annwn could not fail to welcome the Lady of the Cauldron Well and the White Apparition." Gwyn ap Nudd's voice came calmly out of the mist ahead of them. Pryderi stopped; the mist swirled a little, then parted, and then Gwyn stepped out of it, putting one hand on Pryderi's bridle. He looked up at Gwen. "So. Arthur needs his men. I can, and will, bring them through the doors of Annwn."
She let out the breath she had been holding at his answer and bowed in the saddle. "Then I thank you, Lord of Annwn."
He shook his head. "Do not thank me," he said, his eyes growing dark and sad; he released Pryderi and turned back into the mist. "I do them no favors, cousin, for I bring them to their deaths."
**Chapter Twenty-Five**
**G** **wen wished that** she could see Medraut's face. From where she sat on her horse, all she could see was the suit of armor and the blank faceplate of his helmet. There was no doubt it was him, though. The helm already had a golden coronet around it. It seemed he was very confident of victory over Arthur.
It was the first time she'd ever seen him in armor, although she had no doubt that he knew its weight well and knew the use of that sword he had strapped to his side. He had been one of Arthur's Companions, after all, and that wasn't just an honorary title. Medraut might avoid fighting whenever possible, but he clearly was able to give a good accounting of himself when he had to.
But right now, he surely found himself feeling disconcerted. He had come with his army of Saxons at his back expecting to find Arthur and no more than two hundred of his warriors. Instead, he found himself facing Arthur and every fighter that could be persuaded to cross the arcane gates into and out of Annwn to be here. And for Arthur's sake, that had been nearly all of them.
Even Lancelin.
Lancelin had arrived on his own, weary, on an exhausted horse. He had been taken straight to Arthur. She did not know what had transpired between the two men; she had not been privy to any of it, and he had made no attempt to seek her out, for explanations or otherwise. But Lancelin now held the left flank of the army, in his old position, as Kai held the right. Not by word or gesture had he even acknowledged that she was there, and by now, only the bands of her will held the pieces of her heart together. He had chosen. And as she had known he must, he had chosen the King.
The armies faced one another across a watercourse barely large enough to be called a river. The timely arrival of his men had allowed Arthur to move his forces to slightly better ground before Medraut's arrival; this place was called "Camlann," according to the local farmer who had guided Gwen to several good places to position archers.
But Arthur was determined to avoid a battle if he possibly could. He had hoped that a show of force would make Medraut change his mind; hoped that he could strike some sort of bargain with his son.
So now, two armies of nearly equal size faced each other across a tiny river swollen with spring rains.
Medraut's face was hidden behind a faceplate of blackened metal. Arthur wore only the open-faced helm of a Roman soldier that he had worn all his life as a warrior. _And so they are, on the field as in life. Medraut always concealing what he truly is behind a mask. Arthur never concealing anything . . ._
Except he had, of course. He had hidden so many things; his own birth had been concealed, he himself had been hidden until he had come of age to take back his father's kingship. He had hidden the fact that he had sired Medraut, hidden that he had tried to kill the infant. Hidden that he had caused the slaughter of who knew how many others in an effort to get the one he faced now. He had hidden that Medraut was his son . . .
_So many things hidden . . ._
It was as if they had conspired together to create this very situation, making one bad choice after another. One thing she would not do—she was not going to lay this at the feet of the gods. No, this was all the doing of mortals, people who had made decisions that ranged from ill-advised to evil. Including, if she was to be honest, some of her own.
An envoy approached Arthur's lines, a white pennon tied to his spear. Another, sent from Arthur, met him at the edge of the river. They conferred. Arthur's envoy returned, then came back and planted his pennon at the river's edge.
There was a flurry of activity, and a few moments later, Gwen felt her sleeve being pulled. She turned to see that fresh faced young man from Arthur's entourage. He blushed; he seemed to do that a lot. "You are wanted for the parley, L—warrior," he said, stumbling as he tried not to say "lady." She nodded and left one of her men in charge as she joined Arthur. Who still would not look at her. Well, let him sulk. She gazed defiantly at him before following him down to the river's edge, where Medraut already waited. The tension was intense; faces were strained, and hands hovered near weapons. It would not take much to cause these men to explode into violence.
She tried not to show her surprise to see that Gwenhwyfach waited there too, just behind Medraut. Arthur, however, did not restrain a start at seeing her sister, and, in fact, he finally glanced over at Gwen before looking back at Medraut's wife. Nor was he the only one. If it had not been that one was gowned and coiffed as a queen and the other had her hair bound up and was in armor, it would have been as if they were reflections of each other.
_So, all of you who didn't believe me . . . there you are. My dear sister, in the flesh, and looking more the queen than I do._
And that seemed . . . petty. Was there any reason for Gwenhwyfach to have dressed as if for a coronation?
Medraut pulled off his helmet and tucked it under his arm. His face was utterly unreadable. "Well, Father," he began, just a little too casually.
But anything he was going to say was interrupted by his wife.
Gwenhwyfach suddenly stormed across the grass between them, and before Gwen could even think to move or speak, slapped her so hard across the face that her lip split and she saw stars and tasted blood.
"You witless loon!" Gwenhwyfach hissed. "Fool! Idiot! All my life you were first. All my life I was second to you. Finally I was first! Finally _I_ was the one that someone loved! And you _ruined_ that!"
She seized Gwen's hair and wrenched her head around with shocking strength. "All he asked was for you to love him and be a true woman for him! All! And what did you do? You sat for months in his court and cried for your toy armor and sword like a spoiled brat! So I gave him what he wanted, and he loved _me!_ And you took that away from me!"
With a wrench, she flung Gwen to her knees. "You are no woman," she spat. "You're a half man. He should have been mine!"
Gwen stayed on her knees as her mind raced. Now she knew what it was that her visions in Medraut's cell had shown her. Little Gwen had not fallen entranced with Arthur—she had seen a way to take Gwen's place with a man who wanted what she was. She had probably been planning to betray Medraut—or at least, put this day off until Arthur died naturally, thus having her crown in both the present and future. But Gwen had escaped and spoiled her plan. Finally she rose, slowly, and looked into her sister's furious eyes. "Well, little sister," she said, weighing each word and casting them like weapons. "All my life you have coveted what I had, even when you didn't truly want it or were ill-suited to it. You wanted Medraut because you thought I wanted him and would be jealous of your married state, but your husband married you because he could not have me." She wiped away the blood from her lip with the back of her hand. "It must be causing laughter among the gods that my husband saw in you the reflection of what he wanted me to be and was enchanted. You rightly say that _you_ were the one Arthur wanted, and not me, though he knew it not. Given that, I believe that the scales are even between us."
Gwenhwyfach went white with fury. But before she or anyone else could say another word—
There was a cry and a flash of light on metal up on the slope, where the two armies had drawn near—dangerously near—one another.
And another great chorus of shouts and the cry of _"Treachery!"_ and the parley disintegrated into chaos as fighting erupted on that slope and, in a flash, spread over the entire field.
Screaming warriors charged from both sides and overran where Arthur's party stood. Gwen found herself separated from the rest and trying to beat her way back to her archers as the two armies surged forward and clashed. For a moment, before any real blows were struck, she felt hysterical laughter bubbling up inside her.
And then, as always, her world narrowed to the fighting in front of her, everything blurring into stroke and counterstroke, spin and blow and evasion. The noise was deafening; she shut it out. Once, she caught a glimpse of Lancelin riding through a sea of fighters, striking out on either side with his sword. Once, of Medraut and Arthur, fighting furiously like a pair of stags, oblivious to everything around them. Arthur's skill was greater than Medraut's, but Medraut was younger . . .
But mostly, it was just trying to stay alive, slipping in mud and blood, breathing the stink of spilled guts and voided bowels, with a stitch in her side and a burning gash across her forehead, with her arm growing heavier with every swing, and her heart in bits at her feet.
It all blurred together, until she was fighting in a kind of animal stupor, going on nothing but training and instinct.
And then, it seemed, she woke to find herself alone and without an opponent. And there was nothing more to fight. Somehow she had gotten to the edge of the battlefield, and as she looked about and saw no more enemies, her sword dropped from fingers too tired to hold it. Then she dropped to her knees, legs too weary to keep her upright. Numbly, she looked over the field again and saw nothing standing, nothing moving, nothing but the dead and a mist rolling over the battlefield to hide it. It was a vision of horror and carnage out of the end of some epic tale, one that does not end well for anyone—a tale that ends with all the heroes dead.
Despair overwhelmed her. She threw back her head and howled, sobbed, and keened a wordless lament, and she wasn't even sure who she was weeping for. Arthur? Lancelin?
Herself?
The end of the world?
For surely this was the end, the very end, of the world. After this, what could there be? Death, death, death; nothing left but darkness and death.
She sagged back on her heels, and the tears poured from that void where her heart had been. She had thought she had wept before. It had been nothing to this; the only thought left to her, if thought it could be at all, was that she would sit her forever, and weep forever, until she turned into a weeping stone and poured her waters into the little river that must now run red with blood until the end of time.
"Gwenhwyfar! _Gwenhwyfar!"_ Someone was calling her name. Shaking her. Would not let her mourn in peace. Shook her again, harder. Finally, to make it stop, she looked up through eyes so swollen with weeping they were only slits.
And the shock of what she saw, with mist weaving around them both, dried her tears in an instant.
"You—queen—" she gasped.
Arthur's second wife, cloaked and robed like one of Gildas' monks, put back her hood with an impatient hand. There was no doubt; it was the same woman who was supposed to be dead. "Yes, well, queen no longer, but yes, I was Arthur's second wife. Now get up and come with me. We have need of you."
"We—" She shook her head. This was impossible. How had anyone survived? "Who—"
"Come, warrior _._ I tell you, you are needed for the journey across Anwnn, and Gwyn ap Nudd cannot hold the door forever."
As if she had no will of her own, Gwen got to her feet and yielded to the phantom's urgent tugs on her arm. Though if the second Gwenhwyfar was a phantom, she was an uncommonly strong and solid one. "Where—"
"Gildas persuaded Arthur to put me aside. Melwas's _love_ didn't last past being confronted with an army." The queen's voice dripped with contempt, then softened. "Gildas is a good man. I have been . . . doing penance for my sins under his instruction. But Arthur needs us now. Arthur needs all of us now." Her voice cracked a little. "He is dying."
_I thought he was already dead . . ._
The mist swirled and billowed around them, making it seem as if they moved through a landscape of dream—or nightmare. They picked their way through tangled, motionless bodies and seemed to be heading for the single patch of light in the thickening shadows.
And then the mist parted before them. Lit by torches, Arthur lay on a crude stretcher, his head pillowed on someone's wadded-up tunic, surrounded by a handful of his Companions, all of them with faces contorted with grief. It was obvious to Gwen that no one could survive the terrible wound in his gut; it had been bound up, but from the amount of blood that had soaked the bandages, he could not have much longer.
Kneeling beside him, his hand clutched in both of hers, was Gwenhwyfach.
"And . . . you really are . . . the sister?" he was saying.
Little Gwen bent over his hand, weeping, and nodded.
He sighed. "Then . . . you are the one that I loved most truly, most dearly, and I could never be healed of that sickness of love," he said tenderly. "You are my true queen and ruler of my heart, who knew the desires of mine without my ever needing to speak them." His free hand moved feebly to the bandages, and his breath caught. "Medraut is dead; no one has ever survived a single blow of Caliburn, and I struck him nine times. But his return blow was as deep as mine, and full as fatal. I shall die soon—"
"No!" Little Gwen cried out. "No, no, you can't leave me! I need you! I'm meant to be your queen!"
He could only shake his head a very little, as his Companions wept.
A new figure loomed out of the mist. Gwyn ap Nudd, who nodded to the old queen and Gwen. "Arthur," he said, his voice deep and sonorous. "It is time."
Little Gwen looked up at him as if to protest, but at a single stern look from him, she shut her mouth, muffled her weeping, got up and stood aside. Four shadowy figures came from behind the King of Annwn; they approached the stretcher and took it up. Gwyn ap Nudd gestured to all three women to follow.
"You bear witness," said Gwyn, as the Companions watched, seemingly unable to move. "You see that these three queens, all beloved of Arthur, come to bear him through Annwn to the Isle of Glass."
The Companions stared; Gwen wanted to say something to them, but a power greater than she could deny pulled her after the others.
The mist closed behind them as they approached the riverbank. The shadow warriors put the stretcher gently on a boat that was tied to the bank; Gwyn gestured to the three of them to enter it as well. "I can go no further," Gwyn said. "But the gate is open for you, cousin, and by your bargain with my people, none will harm you in passage." Gwen went to the prow and stood there, facing the river and the mist; Little Gwen again took her place at Arthur's side and held his hand.
"And you, Queen-that-was, you know the way. Yours will be the guiding hand." The old queen took the tiller, and the shadow warriors, which all seemed to have the heads of beasts, stag, wolf, bear and otter, pushed it off.
For a long time, there was only mist and water, the splashing of waves interrupted only by Little Gwen's sobs. Gwen thought she saw vague shadows in the water and in the mist, but they never approached the boat, so she was never entirely sure what she saw. She felt empty and exhausted, as if she had left all of her emotions back there on the riverbank. And then, out of the mist, loomed a small wooden dock with more shadow figures on it, silhouetted by torches.
But these were not Gwyn ap Nudd's beast-men. Somehow, Gwen was unsurprised to see that they were robed in the garb of monks and that Abbot Gildas led them.
A good dozen hands reached for the boat and helped guide it to the dock and make it fast. More of them reached for the stretcher on which Arthur lay. As they lifted him out of the boat, to Gwen's shock, he opened his eyes and raised his hand.
"Wait," he whispered, and he beckoned to her.
She found tears pouring down her cheeks, again. "I—forgive me—" she choked out. "I never meant to harm you. I wanted to protect you from Medraut, and then—I thought you didn't care for me, I thought you would be pleased to see the back of me."
"It is you who should forgive me. I tried to make you—what you were not. I took a warhorse, and tried to fit it to a plow." Pain contorted his face for a moment. "Go, and be yourself again. I release you from—every promise, every duty, everything."
He waved his hand. The monks carried him away with Gwenhwyfach in close attendance, leaving Gwen and the old queen standing on the dock. And in that moment, a blankness came over Gwen, mercifully taking all thoughts with it.
Gwen came back to herself sitting in the Abbey church, with no recollection of how she had gotten there, nor how she had come to be clean of the mud and blood of combat and reclothed in another set of trews and tunic. The old queen was on her knees at the altar in the front of the church, but Gwen could not muster the strength or the will to move. It was dark in here, with only the candles on the altar and a small red lamp for light, but it was also dark beyond the windows. Somehow full night had fallen, not the strange twilight of the mist, while she had sat unaware.
Another blank came over her; this one was probably not as long as the last, for when it passed, Gildas was sitting beside her; he peered at her when she moved her head a little. "Ah," he said. "You are back among us."
She nodded and looked at the altar for the old queen. But she wasn't there.
"Arthur?" she asked, her throat sore and dry, her voice coming out as a hoarse whisper.
"He is gone," the Abbot said, simply. "And . . . so is your sister." He shook his head. "When Arthur died, she went mad. She was like a wild thing. She railed at us, that we had not tried hard enough to save him, that we had stolen her crown and her king." He blinked. "I can truly say that I have never seen such . . . such a strange and fearful sight. She was like one possessed."
Numbly, she shook her head. "Only by her own selfishness." He sighed. "She attacked my monks, clawing at them like a cat, in a frenzy. If she was not possessed, then surely she was mad."
Gwen blinked. "But you said—she was dead—"
"We managed to repel her and drive her out of the chapel. We found her in the morning at the edge of the lake, drowned. She died within moments of him, we think." He shook his head. "She must have fallen in at some deep point. She must have truly loved him to have been so frenzied."
She decided not to disabuse him of his notion. "Yes," she said slowly. "She did." _Or at least, she loved his crown._
"Then we will bury them together." He peered into her face. "Come. You should sleep."
"But—"
"The old queen—we call her Sister Blessed now—will hold vigil over them. And we shall have them buried by your Ladies, here, though not in ground consecrated to Christian use. Come." He took her hand and tugged at her. She stood.
And then there was another blank moment, and when she came out of this one, she was lying on a pallet, covered by a wool blanket, in a small wooden hut. The door stood open, and sunlight poured through it.
She was still numb, and her mind . . . wouldn't work. It was almost as if she were under the influence of one of Medraut's potions. Finally she just gave up trying to think at all. She let people lead her about, ate and drank what was put in her hands, did what she was told. She stood at the side of the grave as the monks laid Arthur and Little Gwen in it. That gave her a strange sense of dislocation—she felt a moment of utter terror as she looked at the dead face that was so like her own, could have been her own. For that moment, it seemed as if it were she, not Little Gwen, who was being covered over with earth . . .
But the moment passed, giving way again to numbness.
The numbness, the dullness, persisted. She spent days just sitting in the church or beside the lake, or at the Cauldron Well. If someone gave her something to eat, she ate it; if not, it didn't seem to matter. Nothing seemed to matter; not only her heart was broken, so was her spirit, and she was nothing but a hollow shell where once there had been a warrior with her name.
And so the days passed.
And then, one day she woke, and woke fully, and her mind worked again. She sat up and dressed quickly, feeling almost as if she had been very sick, and now the fever had broken.
Yet once she had dressed, she was at a loss for what to do. She had no idea what was going on beyond the boundaries of the Abbey. Had the Saxons overrun the country at last? Was there any resistance to them at all? Was there anything out there, beyond the deceptive peace of this place, or was it all a chaos of warfare and blood?
At least she could find the old queen, maybe, or Abbot Gildas, or one of the Ladies, and ask some sensible questions.
She ventured out into the morning sunlight, and that was when she saw him riding in along the path that led to the Abbey, looking worn and weary and as broken as she.
"Lancelin?" she faltered.
And although he could not possibly have heard her, he looked up, straight at her.
But his expression did not change. And although he dismounted, tethered a horse that looked as beaten and weary as he, and walked toward her, there was nothing of joy and nothing of love, in his face.
"Gwen," he said, stopping a little too far away from her to have taken her hand. "They told me you were here."
And there it was. That love, if love it really had been, had burned bright and guttered out. When she tried to find it in herself, all she could sense were cinders and ashes and regret. She nodded. "I have been ill," she said, and she released that dead love to fall to pieces in the aching void inside her. "I have heard of nothing since—"
"Ah." The silence hung awkwardly between them. "They never sing of these things, in the tales. Never talk about what happens after everything is over."
She swallowed. "And what does happen?" she asked.
His eyes held the wisdom of terrible sorrow. "Life goes on. Planting and harvest, birth and death, sun and rain. The world does not end for everyone. Just for a few." He sighed. "But you don't want to hear philosophy. The Saxons took a terrible beating, and no, they have not overrun the countryside. There is no High King, and things have broken down into squabbling among all the petty kings again. Most of the Companions are dead. Those that survived have retreated to their estates or taken places in the courts from which they came. Even Celliwig is mostly deserted, except for Kai and the few men that limped home from Camlann. Rumor says that you are dead, you are turned Christian and gone into retreat, or you have followed Arthur into Annwn, where you will both await a day that you are needed." He shrugged. "I came to see if the fourth rumor was true, that you were here, and if you were, to say farewell."
She stood awkwardly, hands dangling at her sides. Once she would not have been able to stop herself; she would have reached for him, begged him to take that farewell back. Now?
"Then do fare well, Lancelin," she said. _He forgave us,_ she wanted to say. But he probably would not believe that. He was the sort that flogged himself relentlessly with his faults. "What we did or did not do changed nothing. Medraut did not conjure up that army out of nothing. He had this planned—for years, I think. If it had not been now, it would have been soon."
Lancelin's lips thinned a moment; then, reluctantly, he nodded. He looked up at the stone tower on top of Yniswitrin. "Do you know," he said at last, his tone too casual, "What it was that caused the fighting to break out?"
"I was too far away to see. Only, there was a shout, and I think someone drew a sword—"
"When your sister struck you, half the men were ready to charge. It only needed an excuse. Someone saw a snake and drew his sword to slay it." He shook his head. "And someone saw the sword drawn and shouted treachery. That is what makes me think you are right. Nothing we did or did not do made any difference. This was a mighty storm, and we were but reeds in its path." He looked back at her. "I am going away. I am not sure where, just yet. Somewhere I can find some peace, I hope."
She closed her eyes against the pain in his. "I hope so too, Lancelin. Fare you well."
She kept them closed for a moment as a single tear forced its way beneath the lid of her right eye and moved down her cheek. If there was still anything, any spark in those ashes, he would see that tear, and he would touch it, or kiss it away, and—
But there was no touch, not of finger nor of lips. And when she opened her eyes again, it was to see his figure riding away, back as straight as a staff, yet head bowed beneath burdens he would not let go. It seemed too cruel that he was haloed by the sunlight of a perfect, peaceful day.
She wiped the tear away herself and walked to the little dock. The mist eddied and billowed over the lake, now showing, now hiding, the farther shore.
"And what will you do now, fair cousin?"
Somehow she was not surprised to find Gwyn standing beside her, though she had heard no one approach.
And that was when she realized what made her feel so hollow and so lost inside, so empty, and so broken. For the first time in her life, she had no direction, no purpose, and no certainty. She was a boat adrift, with no paddle and no tiller. "I don't know," she replied, and she closed her eyes on grief. "There seems no place and no need for me now."
He considered that in silence. "Have your hands lost their skill with blade and bow?" he said, finally.
"I don't—I don't think so." Yes, she did have that. And in the chaos that would come now, there would surely be a use for such skills. "But who would take me? I betrayed Arthur—"
"Those who are well aware you did nothing of the sort?" Gwyn replied. He put his hands on her shoulders and turned her to face inland. "Look there. That peaceful Abbey of the Christ followers. The Saxons too follow that path and will leave them in peace, but there are those who will not, who will hear tales of wealth and think it is the wealth of gold and silver, and not of wisdom. They will need a strong hand to help protect them. And look there." He turned her a little, aiming her at that hidden place that held the School of the Ladies and the Cauldron Well. "The Old Ways will die unless someone finds a way to hide them among the New. And the old queen, who is now called Sister Blessed, she would do that if she knew it was needed, for it was the Ladies who welcomed her as well as the Abbot. Or—" And now he turned her to face the mist. "—Or you can join my folk in Annwn. You will not be the first to join us, nor the last. And there is use for you there, as well. Or you can go into the wilderness and make a hermitage for yourself. Or return to your father and serve him and your sisters. Many choices are yours, more than most have now."
He turned her to face him. "You have work, cousin. But you will have to make it for yourself. You no longer serve anyone for the moment; you are your own master."
So there it was. _Be careful what you ask for—it might be what you get._ Hadn't she longed for just that in the days after she had escaped from Medraut? She was her own master.
Her mind stirred, moved again, turning like an old mill wheel too long left idle. Not her father; he had done well enough this long without her, and she could prove a liability, even a danger. There were men, like King March, who would hear of her being there and want to take and conquer her just to be known as the man who "owned" Gwenhwyfar. She would not bring that down on those she loved.
And not a hermitlike existence either. That would drive her mad.
But here . . .
Gwyn had said that he thought there was a purpose for her, past being a mere warrior. The Folk of Annwn had answered to her call. The Ladies themselves came out to defend her.
Abbot Gildas called her friend.
She _could_ be the bridge between the old and new. She was, perhaps, the only one who had all the skills and all the friends, to do so. She could not make Arthur's dream of one kingdom come true in this lifetime, but she could plant the seeds for it to grow when the time was right.
A lightness began to trickle into that emptiness inside her. "There is much that can be done here," she said slowly.
Gwyn nodded. "Yes, there is."
She took a deep breath and felt her spirit come back to life. "Then it is time to start doing it."
**Afterword**
**I** think every fantasy writer decides at one point or another to tackle "the matter of Britain," otherwise known as the legend of King Arthur. The genesis of my own stab at this came when I was looking into Welsh legends and came upon the curious Triad of "The Three Guineveres." Triad 56 of the Trioedd Ynys Prydein, translated as "The Triads of the Island of Britain," lists the "Three Great Queens" of Arthur's court.
Three Great Queens of Arthur's Court:
Gwennhwyfar daughter of Cywryd Gwent,
And Gwenhwyfar daughter of Gwythyr son of Greidawl,
And Gwenhwyfar daughter of (G)ogfran the Giant.
[Trans. By Rachel Bromwich]
Well that certainly piqued my curiosity, as did the mention of yet another "Guinevere," the "False Guinevere" or Gwenhwyfach, translated as "Little" or "Lesser" Guinevere. She is often said to be the bastard daughter of King LLuedd Ogrfan Gawr, or Ogrfan the Giant, born on the same day as her sister.
Yet another triad, Triad 53, describes the "Three Harmful Blows" of Britain and states that the third was when Gwenhwyfach struck Gwenhwyfar and caused the battle of Camlann.
And last of all I found this extremely interesting item in my researches, three stanzas found by Jenny Rowland _: "in the margin of the Dingestow 8 copy of Ymddiddan Arthur a'r Eryr (Aberysywyth, National Library of Wales, MS 5268, p. 461)."_
_[Gwenhwyfar speaks:]_
_Arthur fab Uthr of the long sword_
_I will say to you ?now/sadly the truth:_
_there is a master over every strong one._
_[Arthur speaks:]_
_Gwenhwyfar you are ?Gwenh[w]yfach._
_I have never been healed of love-sickness for you._
_Medrawd is dead. I myself almost._
_A surgeon has never seen a scar_
_where Caledfwlch [Excaliber] struck once:_
_I have struck Medrawd nine times."_
Now when you add in all the times that Guinevere seems to have been kidnapped, wandered away, run off with someone (not usually Lancelot!) and otherwise had any number of wild excursions, this seems a rather too active life for any one woman. Then you look at the places where she is childless, has one son, twin sons, and wonder which is true. And finally looking at how she supposedly died—where she is buried with Arthur or somewhere else, is killed by Arthur after running off with Melwas, gets married (by force or willingly) to Mordred, becomes a nun, or dies of a broken heart after Kai kills her son (or sons), I began to form a picture in my mind of not one, but three queens by that name.
Now I am not even going to pretend to be a Welsh/Celtic scholar, and I freely admit I made most of this up out of the little bits and pieces I found above. In my mind, I fastened on the third Guinevere, and I could easily see a scrappy fighter, much younger than Arthur, reluctantly wedded to a king quite old enough to be her father, as part of a bargain and power play—but who, schooled early on in the discipline and duty of princes, intended to make the best of it she could. And since the road to hell is paved with good intentions . . .
Therein lies the tale. I hope you enjoyed it.
Coming soon from DAW Books
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# **THE _why_ OF Work**
**HOW GREAT LEADERS BUILD ABUNDANT ORGANIZATIONS THAT WIN**
**DAVE ULRICH
WENDY ULRICH**
Copyright © 2010 by Dave Ulrich and Wendy Ulrich. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher.
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**TERMS OF USE**
This is a copyrighted work and The McGraw-Hill Companies, Inc. ("McGraw-Hill") and its licensors reserve all rights in and to the work. Use of this work is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hill's prior consent. You may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited. Your right to use the work may be terminated if you fail to comply with these terms.
THE WORK IS PROVIDED "AS IS." McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting there from. McGraw-Hill has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise.
## **CONTENTS**
Foreword
Preface
**CHAPTER 1** The Case for Meaning
**CHAPTER 2** The Making of Abundance
**CHAPTER 3** What Am I Known For? (Identity)
**CHAPTER 4** Where Am I Going? (Purpose and Motivation)
**CHAPTER 5** Whom Do I Travel With? (Relationships and Teams [Th]at Work)
**CHAPTER 6** How Do I Build a Positive Work Environment? (Effective Work Culture or Setting)
**CHAPTER 7** What Challenges Interest Me? (Personalized Contributions)
**CHAPTER 8** How Do I Respond to Disposability and Change? (Growth, Learning, and Resilience)
**CHAPTER 9** What Delights Me? (Civility and Happiness)
**CHAPTER 10** Implications for Executives, Human Resources, and Individuals
Appendix: Leadership Challenges and Actions as Meaning Makers
Notes
Index
## **FOREWORD**
Why? What is the why behind _The Why of Work_? Why should you read this book? Why should you care?
In 1979, my largest leadership development client was IBM, which was then (by a large margin) the most admired company in the world. I was a frequent visitor to IBM corporate headquarters in Armonk, New York. On most workdays someone could fire a cannonball down the halls of corporate headquarters at 5:15 P.M. and hit no one. Even the professional and managerial employees worked 35 to 45 hours per week, took time off when they had minor health problems, and enjoyed five weeks of real vacation—with no cell phones or personal computers. They took comfort in the belief that they could look forward to a lifetime of guaranteed job security.
Those days—and those jobs—seem like a distant dream. Today the employees in that same building work 60 to 80 hours per week, keep on working through most health problems, and take almost no real vacation. They are not counting on any guaranteed job security.
This year I was developing an executive education seminar for one of the world's most successful banks. I asked the coordinator of the session, "How many hours a week does the average executive in this program work?" His very sober answer was "Over 80!"
This book is written for leaders—and for professionals who aspire to be leaders. For both professionals and leaders the entire world of work has changed. Global competition, new technology, massive economic problems, and job insecurity have been factors in the creation of a new world of work. This new world of professional work is more challenging than at any time in my life.
If you are working 35 to 45 hours per week and take five weeks of real vacation, work-life balance may not be a huge issue. If you are working more than 50 hours per week and get almost no real vacation, then work-life balance has a very different meaning. For today's professionals, if life is somehow disconnected from work, lots of us won't have very meaningful lives.
This book would have been very important in 1979. This book is critically important today. It was needed then. It is really needed now!
In many developed countries, employee engagement is at an all-time low. It is past time for a turn-around.
I know of no couple who can address the _why_ of work better than Dave and Wendy Ulrich. Dave is one of the world's great business thinkers. I respect his work more than anyone in his field. Dave is an expert in understanding how organizations are impacted by individuals. Wendy Ulrich represents the "micro" to Dave's "macro." Wendy is a wonderful psychologist who deeply understands how individuals are impacted by organizations. Along with being great thinkers and professionals, Dave and Wendy are great human beings. They truly care about the organizations and people that they touch. They are dedicated to helping leaders created more effective organizations and helping human beings have more fulfilling lives. They wrote this book because they want to help you, the reader, and your organization achieve more abundance.
Peter Drucker once told me, "The leader of the past knew how to tell. The leader of the future will know how to ask." Today's leaders and professionals continually interact with knowledge workers. Peter taught us that knowledge workers are any employees who know more about what they are doing than we do. I guess that if we knew more about what was going on in other professional's work than they did, we could just tell them what to do and how to do it. In today's complex world, no leader or employee knows more than the knowledgeable professionals that surround us. We all have to ask for other people's ideas, listen, and learn.
Dave and Wendy have followed Peter Drucker's lead and organized this book around the asking of seven wonderful questions. By asking these questions—to ourselves and the members of our teams—listening to the responses and learning, we can create a more abundant world of work for both companies and the individuals who populate these companies.
The answers to the seven questions in _The Way of Work_ will help you and your organization: develop a positive identity, gain real commitment, build positive relationships, create a great environment, find deeper meaning, achieve continuous learning, and experience true happiness. What can be more important than that?
I want to end this Foreword with a challenge. Don't just read this book as a dispassionate observer; apply what you learn in each chapter to yourself and to your organization. Use these seven questions as a mirror to help you understand yourself and your organization.
The world will not become a better place because we learn—the world will only become a better place when we do.
What is the why in the work behind _The Why of Work_? Dave and Wendy Ulrich have years of invaluable experience in individual and organizational advising, research, study, and reflection. _The Why of Work_ is a wonderful synthesis of their years of learning. I can say without doubt that my life is better and more abundant because I have learned from Dave and Wendy. This book is intended to help you and your organization have a better and more abundant life.
Read _The Why of Work_ —and then do something that is much more important—do the work that is needed to help yourself, the people you love, and your organization have a better and more abundant life!
—Marshall Goldsmith is the author of the _New York Times_ and international bestsellers _Mojo_ and _What Got You Here Won't Get You There_ , the Harold Longman Award winner for Business Book of the Year. He lives in Rancho Santa Fe, California, and New York City.
## **PREFACE**
This book evolved out of a conversation between a business professor/consultant (Dave) and a psychologist (Wendy), a conversation that has seasoned more than 10 years of morning walks along the riverways of Michigan, the neighborhoods of Quebec, and the mountain trails of Utah. For more reasons than one, this conversation often leaves us breathless as we contemplate the challenges faced by leaders who create the organizations we respectively encounter. Theirs are the challenges we face as well: finding the _why_ to sustain the _how_ of our daily living. This book focuses on a simple question: How do great leaders create, for themselves and others, a sense of abundance (meaning, purpose, hope, pleasure) that not only engages employees but also delivers value to customers, investors, and communities?
Dave works to help organizations create value for employees, customers, investors, and communities. He coaches leaders on how to build corporate agendas, organizational capabilities, and the human resource infrastructures to achieve their goals and objectives Dave is also trained as a taxonomist who looks for simple patterns in complex phenomena. In these pursuits, Dave sometimes encounters leaders who formulate great strategies, structures, and processes but may overlook the heart and soul that make organizations meaningful places to work.
Wendy works to help people change and heal. With a background in psychodynamic, cognitive, and family therapy as well as positive psychology, she helps clients examine the patterns that have shaped their past so they can better choose their future. Her clinical practice and change workshops include both people with everyday struggles and people facing trauma or serious adversity. Some people in each group see primarily the senselessness and deficits of their lives, while others manage to find a sense of meaning and abundance. Her M.B.A. reminds her that real change means institutionalizing, not merely individualizing, abundance and meaning.
One of us works with organizations, the other with individuals. One wants to help organizations serve their customers and investors; the other wants to help individuals grow and find peace. But as we have worked together, we have found common ground. The questions both leaders and those they lead wrestle with and the answers they develop seem to overlap and connect around the search for _The Why of Work_ —the search for meaning, purpose. Finding that _why_ infuses organizations with a sense of abundance—having enough and to spare of what matters most.
Dave had a personal encounter with abundance a few years ago while we shared responsibilities directing a mission for our church in Canada. One day he met with a poor African immigrant family living in subsidized housing with shoddy furniture and too many people for the confined space. Despite these "deficits," this family had forged an emotional bond that emanated warmth and generosity. They cared about each other and the world. They were curious and compassionate. When it came to what mattered most, they had enough and to spare. Later that day, we had dinner in an executive's expensive, beautifully adorned home. Although the food was tasty and the furnishings elegant, the conversation and preoccupations of the evening were superficial and sterile. We both learned once again that meaning is tied less to belongings and more to emotional bonds, a sense of purpose, and using one's skills to serve the needs of others.
In organizations as well, meaning and abundance are more about what we do with what we have than about what we have to begin with or what we accumulate. They are more about finding the resources to deal with our challenges than about having unlimited resources to make work easy or effortless. Work will always be work—sometimes monotonous or routine, sometimes stressful to the max—but we believe work can still contribute more than just money to our lives. Leaders can develop the resources to make employees work harder and to make work work for employees. There is a strong business case for helping people find meaning at work. As employees find meaning, they contribute to the broadest purposes for which organizations exist: creating value for customers, investors, and communities. This book distills from a broad range of literature and research a set of resources leaders can use in that process.
As we have worked with college students and young missionaries, we have been infected with the rising generation's passion for purpose around both ideas and ideals. As we have worked with mature adults, we have learned that meaning seekers abound at all life stages. We have seen that people find meaning not only in their personal lives but also through the organizations where they learn, worship, socialize, and play. Meaning can be discovered in friendships, families, neighborhoods, religious communities, schools, service clubs . . . and work.
On a more personal level, we seem to be constantly asking ourselves, "What will we do when we grow up?" When younger we assumed this question would be well resolved by the time we were 30, but it has lingered into our children's 30s. Is meaning found in taking vacations, learning, giving, serving our neighbors, or building a business? The answer can be yes to each of these. And it can also be no. People find meaning in many places and activities, but for us and many we know, meaning itself is not optional. It is the object of a nearly universal search. Work is a nearly universal setting for engaging in this quest.
The problems we face as a consultant and a psychologist, the experiences we have had through serving others, and our personal meaning journey have occupied our thinking for a long time. As we tried to figure out what meaning means, why it matters, and how to develop it, we realized we had embarked on a complicated journey. Wendy has taught and supervised psychology graduate students, run workshops on personal abundance, consulted for a variety of organizations, and written books on forgiving ourselves and changing our mind-set. Dave has coached and trained countless executives and HR professionals on how to diagnose and build organizational capabilities and deliver value to customers, writing more than 20 books on these topics. In each of these forums, we interviewed people to find out how they interpret the sources of potential meaning in their lives. We asked flight attendants, janitorial workers, bus drivers, homemakers, and executives what they liked about their jobs and what gave meaning to their personal and professional lives. We looked for underlying patterns of individual and organizational meaning and success. We also went to our respective literatures for research and theory on meaning and living well. Many thoughtful people in many fields of inquiry have studied different aspects of how meaning and personal well-being are defined, experienced, and developed.
In the spirit of taxonomy, we culled our experience, our conversations, and the theory and research that informed our work and identified seven disciplines, each of which looks at meaning making through a slightly different lens: positive psychology, social responsibility, marriage and interpersonal relationships (including high-performing teams), employee engagement, culture and positive work environment, growth and learning, and happiness. The ideas and research from each of these disciplines contribute to the model driving this book: seven drivers, questions, and tool sets that leaders may use to build meaning, in turn creating a strong organizational purpose and identity that create value for customers, investors, and employees alike.
Two caveats are in order. First, we know we have not done justice to any of the disciplines we synthesize. Volumes of theory and research discuss positive psychology, social responsibility, marriage and interpersonal relationships (including high-performing teams), employee engagement, culture and positive work environment, growth and learning, and happiness. We have tried to pare down these vast literatures into a set of manageable tasks for leaders who want to help employees find meaning in their professional lives. Second, we realize we are writing about very personal issues within a professional setting. Consistent with that agenda, we have used a lot of personal stories to illustrate how to define and determine meaning. By personalizing meaning, we hope we can capture why and how leaders make meaning happen, build abundant organizations, and deliver value to stakeholders.
This brings us to the issue of the audience for this book: leaders. Whether talking to executives of global companies or therapy clients who struggle with loss and grief, we have found the search for meaning to be universal. It affects rich and poor; young and old; American, African, European, and Asian; those in big and small organizations, publicly traded firms and public agencies; employees close to retirement and employees just entering the workforce; those who volunteer in community organizations and those who lead large conglomerates; those who are unemployed and those who put in 80-hour weeks. Given our professional interests, we could have written to individuals at large, to employees, or to HR professionals (who generally accept the importance of meaning making and who build HR systems to sustain it). We decided to write to leaders.
_Leaders are meaning makers_ : they set direction that others aspire to; they help others participate in doing good work and good works; they communicate ideas and invest in practices that shape how people think, act, and feel. As organizations become an increasing part of the individual's sense of identity and purpose, leaders play an increasing role in helping people shape the meaning of their lives. Too many leaders focus on where they are going and how to get there, without paying much attention to how it feels to those on the journey with them. When leaders make work meaningful, they help create abundant organizations where employees operate on a value proposition based on meaning as well as money. Meaning becomes a multiplier of employee competence and commitment, a lead indicator of customer share, a source of investor confidence, and a factor in ensuring social responsibility in the broader community. We find that even the hardest-nosed leaders become interested in meaning when they realize its potential contribution to bottom-line realities. When leaders grasp the why of meaning, they then seek the how.
### **Our Meaning Makers**
We pay tribute to those who have helped us experience, think about, and attempt to understand and deliver meaning. We have each lost our father in recent months. To them we owe great gratitude for the lessons they taught by example and word. Our mothers continue to find meaning and enlarge it for others as their abilities allow, and they along with our wonderful siblings (Belinda, Carla, and Eric) and their families are models of grace, charity, humor, and hope. They have built abundant worlds for us, and we hope to pass that legacy to our children and theirs. We consider our children among our best colleagues, thought stimulators, and most abundant abundance enhancers: Carrie Kelley, Monika Ulrich, and Mike Ulrich, with his wife, Melanie Swenson Ulrich, and our sweet granddaughter, Maren. We dedicate this book to her as our tangible symbol of hope for our future and the world's future.
We have professional colleagues who are close friends whose ideas and care support and sustain us. The list is long, but we are grateful to insights and input from (in alphabetical order) the Alpine 6th Ward, Loretta Allen, Dick Beatty, Allen Bergin, Ginger Bitter, Karen Blake, Wayne and Nancy Brockbank, Kim Cameron, Ralph Christensen, Bob Eichinger, Kathleen Flake, Rich Ferre, Jac Fitz-enz, Marshall Goldsmith, Lynda Gratton, Michelle Holt, Bill Joyce, Steve Kerr, Dave Klimek, Dale and Gerry Lake, Ed Lawler, Mike Losey, Paul McKinnon, Susan Meisinger, Henry Mintzberg, Chris Packard, Jeffrey Pfeffer, CK Prahalad, Scott Richards, Bonner Ritchie, Libby Sartain, Judy Seegmiller, Norm Smallwood, Kate Sweetman, and Jon Younger. We owe a special thanks to Danny Stern, who advised us as a friend and agent. This book would not have come to fruition without the skillful shepherding of Mary Glenn and her staff at McGraw-Hill.
We are also indebted to professional colleagues who have written about these subjects with enormous insight and whose ideas inform our thinking: Viktor Frankl, whose marvelous book captures the search for meaning in impossible circumstances; Judy Bardwick, who has been so insightful at capturing many of these insights; Lynda Gratton, who brings a keen and kind eye to helping people find purpose at work; Kenneth Moore, who has the ability to bring spiritual insights into the work setting; Martin Seligman and his colleagues, who have shaped the field of positive psychology; and individuals such as Jacques Lusseyran, Teeda Butt Mam, Imaculee Ilibagiza, and Joseph Smith, whose stories of meaning making in the face of the most meaning-robbing forms of human suffering have encouraged us to believe that meaning making is not only always possible but also imperative.
We also thank our professional colleagues at the RBL Group (rbl.net) and Sixteen Stones Center for Growth (six teenstones.net), who touch our lives as both thought partners and advisers. We are most grateful to participants in workshops and retreats who have shared their stories, insights, and honest hopes for the future.
### **So, Why Have We Written This Book?**
We have written this book because we hope to synthesize and simplify mystical and complex approaches to meaning into focused questions and specific actions.
We hope to further a serious discussion of the nature of personal meaning at work.
We hope to show leaders that attention to meaning will help them reach their financial, customer, organizational, community, and strategic goals.
We hope to offer leaders specific ideas, tools, and practices for growing meaning and abundance.
We hope to redefine leaders' roles to include not only direction setting and structure providing but meaning making as well.
We hope to promote for all of us who go to work day in and day out a sense of greater abundance because we have a clearer sense of the meaning of our labor.
We hope to change the conversations between leaders and employees to focus not only on what needs to be done but also on how it feels to do it.
We hope to turn deficit-laden thinking into abundance metaphors and actions that will make a better world for our children, their children, and yours. For more information about this book, visit our website: thewhyofwork.com.
—Dave and Wendy Ulrich
Alpine, Utah
## **CHAPTER 1
The Case for Meaning**
This morning, people all over the planet got out of bed and got ready for work. Some headed out before dawn in high-end cars to claim high-rise offices with high-tech computers and highbrow clients. Some headed out before dawn to walk barefoot, wares on their head, to claim a choice spot in the dirt near the entrance to the village market. Some wrestled with the muses to create artistic masterpieces or solve perplexing scientific problems. Others wrestled with boredom to complete their shifts at cash registers, call centers, or assembly lines. Some pitched their résumés in business suits, looking for good benefits and a sure path to comfortable retirement. Some made their pitch in ragged jeans on street corners, looking for someone to rent their muscles for at least the day.
Some people in each one of these and many other categories by which we could define work found a sense of meaning, purpose, even abundance in their labor today. Others in each category found world-weary tedium, frustration, and despair.
Which were you?
Which were the people you lead?
Viktor Frankl was a budding psychologist following in the footsteps of Freud when World War II erupted. Frankl survived three years in a Nazi concentration camp, but upon his liberation he found his family, home, and writings gone. Before the war Frankl had been developing a system of psychotherapy based on our need for meaning. Once he was incarcerated, his previous philosophical speculations about what helps people heal and cope were no longer just interesting cerebral playthings; they were tested in the fire of a dreadful and lengthy ordeal. Frankl's book _Man's Search for Meaning_ , which has sold more than nine million copies, has become a classic. Against the backdrop of horrific adversity, his insistence on the possibility—even the necessity—of finding meaning in life becomes deeply credible. After all, adversity generally disrupts our sense of meaning and robs life of what previously gave it sense and purpose. In troubled times our search for meaning becomes both more difficult and more compelling. Frankl quotes the philosopher Friedrich Nietzsche: "He who has a _why_ to live can bear with almost any _how_."
He or she who has a _why to work_ can bear with almost any how as well. Obviously, people find meaning in many settings—in the privacy of homes and the expanses of nature, in churches, ballparks, and community centers, in family and friendship circles. But work takes the lion's share of our time and energy. Most of us spend more time at work than at play, at family gatherings, at religious meetings, or at hobbies. The organizations in which we labor are thus a primary setting not only for accomplishing assignments but also for finding an abiding sense of meaning in life. Work is a universal setting in which to pursue our universal search for meaning.
### **Meaning at Work**
This book is about both the _why_ and the _how_ of meaning at work.
The _why_ refers to the human search for meaning that finds its way into our offices and factories, a search that motivates, inspires, and defines us. The _how_ gets us into the practicalities of how leaders facilitate that search personally and among their employees. We offer many specific tools and principles to help leaders put meaning to work not only to build personal meaning but also to help companies succeed in the marketplace of human endeavor.
Thus the search for meaning adds value in two senses of the word. First, humans are meaning-making machines who find _inherent value_ in making sense out of life. The meaning we make of an experience determines its impact on us and can turn disaster into opportunity, loss into hope, failure into learning, boredom into reflection. The meaning we create can make life feel rich and full regardless of our external circumstances or give us the courage to change our external circumstances. When we find meaning in our work, we find meaning in life.
In addition to inherent value, meaning has _market value_. Meaningful work solves real problems, contributes real benefits, and thus adds real value to customers and investors. Employees who find meaning in their work are more satisfied, more engaged, and in turn more productive. They work harder, smarter, more passionately and creatively. They learn and adapt. They are more connected to customer needs. And they stick around. Leaders invest in meaning making not only because it is noble but also because it is profitable. Making sense can also make cents.
### **The Abundant Organization**
In this book we refer to companies that are meaningful in both of these senses of the word as _abundant organizations_. An abundant organization _is a work setting in which individuals coordinate their aspirations and actions to create meaning for themselves, value for stakeholders, and hope for humanity at large_. An abundant organization is one that has _enough and to spare of the things that matter most_ : creativity, hope, resilience, determination, resourcefulness, and leadership.
Abundant organizations are profitable organizations, but rather than focusing only on assumptions of competition and scarcity, abundant organizations also focus on opportunity and synergy. Rather than accepting the fear-based breakdown of meaning in hard times, abundant organizations concentrate on bringing order, integrity, and purpose out of chaos and disintegration. Rather than restricting themselves to narrow, self-serving agendas, abundant organizations integrate a diversity of human needs, experiences, and timetables.
In good times and in hard times, abundant organizations create meaning for both the employees who comprise them and the customers who keep them in business. Employees, customers, investors, and society benefit when employees find meaning at work and when companies give meaning to society. This logic applies to small and large organizations, to public agencies and private enterprises, to local storefronts and global conglomerates.
### **The Market Value of Why**
Even if you are not one of those rare folks blessed with a gift for finding joy in the concentration camps of life, you intuitively know that you and your work team would be more productive, more satisfied, and more creative if work engaged not only your head and your hands but your heart and soul as well. What most of us know intuitively research confirms: when employees find meaning at work, they care enough about it to develop their competence; they work harder and are more productive; they stay longer and are more positive about their work experience. But there is more: when employees are more positive, customers generally respond in kind. Employee attitude is a key lead indicator of customer attitude, and satisfied customers help the businesses they patronize to survive and thrive. In brief:
1. Employees who find meaning at work are more competent, committed, and contributing.
2. In turn, employee competence, commitment, and sense of contribution lead to increased customer commitment.
3. In turn, customer commitment leads to better financial results for the company.
Making meaning is an important cause and a lead indicator of long-term organizational success. So-called intangibles explain about 50 percent of the market value of publicly traded firms. Intangibles are the assets and capabilities of a company that cannot be touched or put on a balance sheet but give investors confidence in the future earnings of the company. Intangibles include nonthings such as leadership, talent, innovation, skill, and vision. Investors increasingly value these intangible organizational capabilities because they increase confidence in a company's future success.
Employee competence, commitment, and passion or energy are among these intangible assets. Employees can be competent, even committed, but still lack passion for their work. Meaning reinforces employees' passion for work because it ties what they do to a greater good that also pays off in the marketplace. Passion for work is an intangible asset that has a direct impact on a firm's market value.
Consider some additional data points on the value for both employees and customers of abundant organizations (exemplified here in organizations that employees like to work for, that investors admire, that invest in people, and that have positive work practices):
Over a 10-year period (1998 to 2008) "best companies to work for" have a 6.8 percent stock appreciation versus 1.0 percent for the average firm.
Over a seven-year period, the most-admired firms in _Fortune_ 's list of admired companies had doubled the market returns of competitors.
The probability of an initial public offering (IPO; a new company) succeeding goes from 60 to 79 percent when the new company invests in its people.
Sixty-one hospitals in the United Kingdom had a 7 percent decline in death rate when they invested in the well-being of their staff.
A one-standard-deviation increase in high-performance work practices yields $27,044 increase in sales per employee and $3,814 increase in profit per employee.
Only 13 percent of disengaged employees would recommend their company's products or services, compared with 78 percent of engaged employees.
Disengaged employees are 10 times more likely to say they will leave their company within a year.
Franklin D. Roosevelt, U.S. president during the Great Depression of the 1930s, said, "We have always known that heedless self-interest was bad morals. We know now that it is bad economics." This is even more true in today's transparent and fluid cultures.
### **Leaders as Meaning Makers**
So, how are abundant organizations created? This is the task of leadership.
Ultimately the crisis of meaning is always a crisis of leadership. We hope to structure for leaders the private conversations and corporate decision-making criteria that shape abundant organizations. Abundance is not only a prerogative for leaders of rich people, smart people, prestigious people, successful people. Meaning is not only in short supply for poor people, mediocre people, struggling people, hurting people. Great leaders recognize the vital importance of abundance and meaning to everyone in their organization. Including themselves.
The Great Place to Work Institute has conducted surveys of the best companies to work for in America since 1980. It now does work in more than 30 countries. Its surveys serve as a confirmation of the impact of _The Why of Work_ on business results. A portfolio consisting of all of the publicly traded companies on the Best Companies to Work For list each year from 1998 to 2008 would have earned an annual return of 6.80 percent, compared to just 1.04 percent over the same period for the Standard & Poor's 500. Even purchasing stock in companies on the list in 1998 and holding it for the ensuing 10 years would have achieved a return of 4.15 percent, which is also much higher than the comparable indices.
What do these companies do to maintain this outstanding performance? Of course they make money via excellent customer service and many other solid management practices or they would not survive. But in addition these high performers tap into the elusive quality of meaning in a variety of ways. For example, in the last 25 years, five companies have consistently been highly rated: Goldman Sachs, Nordstrom, Publix Super Markets, REI, and W. L. Gore & Associates. Goldman leaders build a culture of "smart people working together," or one of collaboration and synergy. Nordstrom has earned a reputation for exceptional customer service, hiring employees who delight in "anticipating and meeting customer needs." Publix Super Markets, founded in 1930, also has a strong customer focus, cultivating "servant leaders" who treat "associates" (not "employees") with respect and who become active in their communities. REI (a recreational equipment cooperative) trains leaders to build cooperation among employees and between employees and customers to accomplish its mission of "inspiring, educating, and outfitting for a lifetime of outdoor adventure and stewardship." Gore & Associates leaders encourage employees to pursue innovation by living by a set of guiding principles of "freedom, fairness, commitment, and waterline." In each of these exceptional companies, leaders endeavor to turn the meaning employees find in their work into sustained organizational abundance. Though each company has a unique take on how to make this connection, all develop leaders who help employees find meaning at work that contributes to organizational success.
The creation of meaning applies to countries as well as companies. Bhutan is a small country located in the Himalaya Mountains in South Asia. Although most countries use the Gross National Product index to measure national success, in 1972 King Jigme Singye Wangchuck of Bhutan instituted a Gross National Happiness (GNH) index to assess his country's progress. The king instituted social and economic policies to help Bhutan citizens find meaning and well-being in their lives. The GNH index includes measures of the progress of sustainable development, preservation of cultural values, conservation of the natural environment, and establishment of good governance. Even with low gross domestic product per capita, Bhutan citizens are among the happiest in the world, with over 50 percent of citizens reporting they are "very happy." Their lifespan is in the top 10 percent of nations worldwide. Bhutan became the world's newest democracy in 2008 as the king established parliamentary elections, Jigmi Thinley, the first Bhutan prime minister, has said, "material enrichment and consumerist ethics must not lead to spiritual impoverishment. True happiness and well-being lies in sustainable education, health, and living environments which include caring and sharing relationships where extended families serve each other."
In companies or in countries, leaders have the task of creating a direction for their organizations that is charged with meaning—that resonates with not only the minds and hands but the hearts of those they lead. In this book, we go beyond cases to synthesize and integrate theory, research, and experience from multiple disciplines to propose seven meaning drivers successful leaders have used to shape meaning. An individual leader might be predisposed to focus on one or two elements of an abundant organization, as shown in the preceding examples. We cull these and many other examples to offer leaders a menu of questions and activities to help them create meaning for employees and turn it into sustained organizational abundance.
### **Recessions of Meaning**
In either good or bad markets, without bottom-line results organizations will simply fold, leaving even able workers twiddling their thumbs. Organizations in any economy must also make sense to the people who compose them. When our organizations enact our highest values and embody our best aspirations, they inspire our best efforts, and nothing short of our best efforts will keep us afloat when storms are raging and the ship has sprung a leak— _or_ when fair winds lull us into lethargy and hubris.
In the 2009 recession, many governments bailed out companies with toxic assets. Bailing out sinking ships is a bad analogy for what makes organizations seaworthy, however. Before setting out for open seas, we must not only bail out the water but fix the leaks. Organization leaks occur not only when leaders fail to provide great products and solid returns, but also when they waver on ethical principles, isolate themselves from the consequences of their choices, abdicate responsibilities for strategy and innovation, or drop the ball of timely action. Organization leaks also occur when employees put in their time but don't invest their hearts, when they abandon creativity or integrity, or when they lose sight of the impact of their work. Organizations that survive in recessions and thrive during recovery will have leaders who consistently offer employees both economic well-being and an abundance of meaning and purpose.
In both lean and prosperous times, an organization's values are tested and forged, setting the stage for the future. Meaning is shaped or dissipated. Loyalties are won or lost. Talent and skill are honed or abandoned. Creativity and problem-solving skill are developed or undermined. And future sustainability is either ensured or threatened.
We need abundant organizations in deficit-dominated contexts that challenge our existing sense of meaning and growth-dominated contexts that give rise to expansion.
Even when the world economy improves, the ghosts of our "psychological recession" haunt us. Financial challenges are embedded in larger trends that permeate society. In downturns people feel an increasing sense of malaise, anomie, and isolation that robs them of meaning and direction. Crises in financial markets echo the crises in personal lives and social movements—crises that, almost by definition, undercut our ability to make sense of our lives and figure out what to do next. Crises sabotage the daily routines that have grown out of our values, beliefs, and past experience. Crises threaten the assumptions that we hold without even realizing it about what life means in both good times and in bad. In brief, crises increase our sense of malaise, anomie, isolation, or deficit, robbing us all of meaning and hope.
Frankl's _why_ and _how_ questions about meaning apply in both bad and good markets, at work and at home, in domestic settings as well as in organizations that span the globe. Good times can temporarily distract us from such questions, but the questions always come back around. As Frankl suggests, the search for meaning is more about how we think than about the circumstances in which we find ourselves. Deficit thinking can abound even in the midst of plenty.
### **The Prevalence of Deficit Thinking**
Have you ever been robbed? Our friend Rena's home was broken into. A small home safe containing her family heirlooms and personal papers was taken, along with some money, a computer, and jewelry. Rena is not a wealthy person. What was taken had relatively little economic value, but it included much that brought to her life a sense of meaning, identity, and connection with her past—a letter for her adopted son from his birth mother, Rena's father's World War II medals, a personal journal, a stack of prized letters from her mother, her grandmother's antique music box, the ring of a deceased friend. Rena lost her sense that she lived in a safe community, that her home was a haven, that a benevolent presence was protecting her family. As we can easily imagine, Rena became more skittish and vigilant, more protective of her children, more interested in home security ads on TV. Doors were locked more consistently. Sleep was interrupted by nightmares. Rena wished she could create an impenetrable wall to lock up her home, her family, her heart.
Like Rena, when employees lose what they have come to count on and expect—be it a person, an income, a position, or less concrete notions like security, identity, or direction—they are inclined to deficit thinking, a common problem when people stand to lose not only their personal treasures but also their retirement, their colleagues, their jobs. Deficit thinking is probably inevitable, perhaps even helpful, in some situations, but when leaders' thinking is dominated by an agenda of self-protection, deficit thinking itself becomes the burglar. Deficit thinking can lock us into a prison of our own making, a prison dominated by fear, isolation, disorientation, and competition for scarce resources. Even if we get back what we lost—even if the economy improves, the takeover is averted, or we end up with a better job than before—our deficit thinking can continue to cast a discomfiting spell over our lives.
The world of deficit thinking pervades both personal and organizational life. The thieves and robbers of crisis undermine the ability of leaders to foster abundance. Of course, economic hardships, political uncertainties, family disruptions, illness, death, and even horrific suffering are hardly new kids on humanity's block. Grim realities have always inhabited our collective neighborhoods. It is still quite another matter when they move into our basement, our spare room, even our master suite. Once we realize the pre-cariousness of the things we have come to depend on for security, security cannot be restored fully until our dependencies change. This is where great leaders come in.
At about age three, children in every culture begin badgering their parents with the question "Why?" The search for meaning begins early, but youthful philosophies that comfortably accommodated the distant existence of Trouble may require reevaluation when Trouble becomes our bed partner. Trouble may be as simple as a changed corporate policy or as complicated as a bankruptcy, as removed as an unhappy customer 3,000 miles away or as personal as losing a child. Leaders must refine and redefine their own answers to "Why?" and must help others do so as well. They must tackle not only the meaning of suffering but also the meaning of prosperity, opportunity, or just another day knocking on doors. When we need to solve complex problems, preserve the bottom line, and maintain motivation to try again, the search for meaning moves out of the domain of philosophers and theologians and finds its way to the top of the to-do lists of hard-minded corporate leaders.
Leaders spearhead the search for meaning in both good times and bad. In up markets, when talent is scarce, meaning matters because employees are essentially volunteers who can choose where to allocate their time and energy. In recessions, employee engagement or satisfaction scores would be expected to fall with the market; however, many organizations see false positives on such surveys because of a gratitude effect (employees compare themselves with their less fortunate colleagues or friends and are grateful to have any job at all, even if it is not especially meaningful). Either way, memories last longer than recessions. Employees who felt mistreated during a down market or whose meaning at work is found only in crisis containment are more likely to leave when things settle down and they have more options.
Consider the following cases of employees and leaders in different types of companies and at different career stages:
**Personal insecurities.** Vicki, a young professional with college diploma in hand, felt extremely lucky to win an ideal job at a top-brand company. She worked hard on assigned tasks and skillfully negotiated the daily politics of the office. But during a serious economic downturn her firm initiated first one and then a second and third round of layoffs in a matter of months. At first only lower-performing people were let go; then even talented, senior people were cut loose to face the shrinking job market. The atmosphere at the office turned from collegial to cynical and from cooperative to competitive. Vicki worked even longer hours to keep her job, and she worried incessantly about her future. The demands at work kept her away from hobbies and friends, invaded her relationship with her husband, and touched off old problems with depression and anxiety. The rhythms and routines of her life began to feel jagged and contorted almost beyond recognition, and all her stories became tinged with fear.
**Work/life balance.** Raj is a successful Indian entrepreneur, proud of the company he has built. The company he started 12 years ago has grown to more than 80 employees, with a strong brand and customer loyalty. But he knows that to go the next step of continued growth he will have to invest in becoming more global and even more innovative. This will require both personal energy and more time traveling in North America, Europe, and Asia, the most likely prospects for his company. With teenage children who are both happy to see him home and sometimes happy to see him gone, Raj knows he would pay a large personal price for the next phase of company growth. He debates whether he has the energy to do what it would take to move his company forward or should coast on previous successes for a while.
**Undermined security and flexibility.** Grant and Shirlyn have worked hard their entire professional lives. Grant started with his current company 25 years ago, right out of college. Shirlyn did substitute teaching until her children were older; then she began teaching full-time. They had hoped that when their last child left for college they would have more opportunities to travel and develop hobbies. Although Grant feels reasonably secure in his job, changing market conditions have led him to lay off 25 percent of his employees. Those who remain have to do not only their work but also the work of those who left. People are nervous about their jobs and frustrated about longer work hours. School budget squeezes have also led to increased class sizes and more stress for Shirlyn. Grant's and Shirlyn's retirement savings have been reduced about 20 percent in the declining stock market, and they will have to work for another three or four years to recover. Work has become drudgery as they face these unanticipated realities. But work also forestalls the necessary question: what will give meaning to my life when I retire?
**The liability of success.** Ivan was the successful one. In school he got the top grades, was popular, and was targeted as a future leader. At work he moved up quickly, becoming not only wealthy but powerful. He paid a personal price with two divorces and alienated children, but he hoped his kids would come back around as they matured. He savored the daily challenges of his work and put his mind and heart into it. Gradually, however, Ivan began to feel disconnected from the heart of his work. Sitting in his luxurious office, he realized it had been a long time since he had interacted directly with the customers who used to make him feel good about his company. He had not really visited employees on the front line in years, and when he met with them in formal meetings they seemed aloof. Those closest to him continued to tell him how talented and successful he was, and he was surrounded by all the trappings of success. But he started to wonder if he had lost touch with what he really loved. He saw himself resembling the Dickens character Scrooge more with each passing day.
Most of us as leaders have been or have had such employees in our organizations. Many of us have personally experienced both economic malaise and the pitfalls of success, either firsthand or among our families and friends. Unfortunately, these cases are not isolated; they represent developing patterns in today's world. Without overfocusing on depressing realities, leaders will recognize something of the depth and breadth of this malaise. Skim the following for a quick overview of some of these trends.
**1. Declining mental health and happiness.** Building on the work initiated in Bhutan, the New Economics Foundation, which has calculated happiness scores for 178 countries, concludes that most countries of the world face a crisis of unhappiness. More specifically, statistics on personal well-being indicate increases in clinical depression, anxiety, and addiction. Eight to 10 percent of Americans over age 18 suffer from some depressive disorder, while in developing countries depression affects 15 percent of the population with 80 percent of those afflicted untreated. Anxiety disorders (including panic disorder, obsessive-compulsive disorder, posttraumatic stress disorder, and social phobia) covary with depression, and about 18 percent of U.S. citizens face one of these anxiety challenges in a given year. Addiction disorders (including eating disorders and substance abuse) are also on the rise. Mental health disorders are the leading cause of disability in the United States for people aged 15 to 44, directly and indirectly affecting employee costs. People seem to be losing touch with their strengths as more lives are dominated by weaknesses with a focus on what is wrong.
**2. Increased concern for environmental demands, social responsibility, organization purpose, and individual motivation.** Scholars estimate that humans currently consume 30 percent more resources than the earth can produce. Between 1961 and 2006, human demand on the biosphere more than doubled. These demands threaten habitats, air quality, and climate stability. For example, between 1961 and 2001, the consumption of fossil fuels (coal, oil, gas) increased by almost 700 percent. At present rates of consumption, we could run out of these fuels in the next 25 years. In part because of their poor handling of environmental concerns, many social institutions face waning stakeholder respect. Institutional cynicism runs high in political, business, educational, and religious settings. People distrust organizations they believe do little to protect the earth or serve its poorest inhabitants. More than three-quarters (79 percent) of the world's most admired companies have seen their reputation decline in recent years. Eroding corporate reputation, increased institutional cynicism, and poor records on environmental responsibility underlie this loss, alienating many high-potential employees.
**3. Increased complexity of work.** Technology, globalization, and demographics all add to the complexity of the workplace. With technological advances, the half-life of knowledge has shortened. The Internet has newly become the standard source of information, with 60 percent of Internet users online daily and 70 percent of businesses having a website. Customers have more information and choice than ever about what and how to buy, and distant markets have replaced local markets in many industries. Global companies have 24-hour operations among their locations around the world. Workforce demographics are becoming increasingly diversified around race, ethnicity, social class, gender, sexual orientation, age, religion, and nationality. Corporations face the major challenge of how to respect and make good use of these differences in increasingly diverse workforces. For example, as GenMe or Generation Y employees (born between 1981 and 1999) move into the workforce, their values (like self-esteem, self-interest, and leisure time) often clash with those of the baby-boom generation, creating the need for policies and practices that appeal to and motivate various subgroups. All of these technological, global, and demographic trends make work more complex, necessitating both more specialization and more teamwork to respond. Teamwork requires unprecedented skill in cooperation, prioritization, and communication—skills often underdeveloped in an age of text messaging rather than in-person relating.
**4. Increased isolation.** Proliferating electronics, high mobility, and urban sprawl have all been blamed for increased social isolation. Those who spend hours in front of a computer screen spend less time with real people, Wiki and chat groups notwithstanding. U.S. households own an average of 2.24 televisions, with each television running for an average of 6 hours and 47 minutes per day and the average child watching TV 1,680 minutes per week (28 hours a week; 4 hours a day). Fewer Americans participate in civic movements like signing petitions, voting, or attending club meetings, and entertaining at home is half as common now as 20 years ago. The sense of isolation spreads to the workplace as job changes, international assignments, and constantly shifting work groups dominate the work landscape and undermine the sense of community. People lose the stories, the history, the heroes, and the routines of small interactions that form the bonds of connection. In a work setting, countering these trends means building a culture and work setting that unite and unify people.
**5. Low employee commitment.** A recent analysis of data by HR Solutions, Inc., found that an astonishing 50 percent of employees said yes when asked if they had thought of resigning in the last six months. According to a Saratoga Institute study of more than 19,000 U.S. workers in 17 industries, 72 percent of employees who quit leave because they feel they are not being recognized for their contributions or sufficiently respected and coached by their leaders. _Gallup Management Journal_ 's semiannual Employee Engagement Index shows that only 29 percent of employees are actively engaged in their jobs, while 54 percent are not engaged and 17 percent are actively disengaged. Right Management (a consulting firm) found similar results with only 34 percent of employees fully engaged while 50 percent are completely disengaged. Nine percent are engaged by their organization but not their job, and 7 percent are engaged by their job but not the organization. The cost of lost productivity in the United States is estimated to be between $287 and $370 billion. In the United Kingdom, research from YouGov on more than 40,000 employees reports that only half (51 percent) of employees feel fully engaged by their company. Disengaged employees are less likely to meet corporate goals or to stay with the firm. When only fear of unemployment keeps employees on the job, they are probably not giving their best.
**6. Growing disposability and change.** We live in a world of increasingly disposable products—from diapers to pens to shoes to electronic devices. Instead of repairing and reusing, we discard and replace. While disposability makes some things easier, it also carries a hefty environmental price tag. The disposability trend carries over into relationships, as speed dating, casual "commitments," and high divorce rates can land children and partners on the disposability heap. In the United States, about 45 percent of first marriages and over 60 percent of second marriages end in divorce. In Canada and parts of Europe the rates are even higher. The disposability of families has severe consequences for the financial stability, personal health, and emotional well-being of partners, children, and society as a whole. In recent years, the self-help movement, which often suggests these difficult problems have quick fixes, has burgeoned to become a $9 billion business. Many of these self-help books, tapes, or workshops offer false hope with few sustained successes. When desperate people seek easy solutions without doing the hard work of fundamental learning and change, resilience is undermined and real growth and learning fade.
**7. Greater hostility and enmity.** Road rage is up as people race to complete their journey ahead of others. Reality TV shows stage win-lose battles over everything from cooking to apprenticeships, while others make us voyeurs in domestic arguments. Political dialogue is less about solving problems and more about staking out a position and being louder than one's opponent. Bipartisanship is as outdated as rotary phones and landlines. In 1976, 26.8 percent of voters in the United States lived in a county where one presidential candidate won by more than 20 percentage points. The number of people living in these "landslide counties" increased to 38 percent in 1992, to 45.3 percent in 2000, and to 48.3 percent in 2004 and 2008. This partisanship indicates pockets of increasing homogeneity in our neighborhoods, reducing the opportunity to learn to get along with those who see the world differently. In personal relationships, getting our way gets in our way, as compromise and civility are replaced with contention and hostility. In work settings, we mistakenly see competing with each other as the pathway to competitive advantage. Win-lose battles crowd out win-win solutions. A false hope of the me-first mind-set is that winning will bring personal satisfaction, when it more often leads to emotional isolation. Civility and happiness come when people find delight in their work setting.
These daunting trends suggest that many people you lead face personal and societal demands that affect their well-being, their families, their communities, and inevitably their work experience. Even in the world's wealthiest nations, deficit thinking predominates. Workers at all levels respond by giving up on traditional dreams, isolating themselves, reducing their expectations, becoming dependent on government or others for support, or finding temporary escape in addictive behaviors. These responses are expensive and time consuming for employers and society. They can instigate vicious cycles of despair, withdrawal, and breakdowns in personal meaning and purpose.
And there is something organizational leaders—not just politicians, psychologists, parents, or priests—can and must do about it.
### **Leaders Who Focus on Meaning Create an Abundant Response**
A crisis is a terrible thing to waste. Fortunately, when crises stop us in our tracks they may also make us stop and think, and thinking can be the start of creating meaning at work and elsewhere. Crises can shock us into facing the questions we often sidestep: "Who am I? What am I trying to accomplish? What really makes me happy? What do I believe? What is my purpose? What matters most?" As leaders probe the whys of work, they empower employees to find personal meaning that creates value for customers, investors, and communities.
Abundance implies plenty: enough and to spare, fullness that overflows. If we focus attention on what we stand to gain from our crises, not just what we stand to lose, abundance thinking can replace deficit thinking even when deficits are the rule of the day. Abundance looks to future opportunity more than past disappointments, promotes hope over despair, suggests change for the future rather than languishing in the past, and fosters the creation of new meaning where old meanings have broken down. Abundance does not imply that things come easily or quickly but that we can make meaning even in the midst of challenges we face. Like the Gross National Happiness index in Bhutan, the abundance we imagine is not just an abundance of visible assets (money, prestige, security, or position) but an abundance of an intangible sense of purpose, identity, growth, and well-being. To reiterate: an abundant organization is a work setting in which individuals coordinate their aspirations and actions to create meaning for themselves, value for stakeholders, and hope for humanity at large.
For our friend Rena, whose home was broken into, a focus on the things robbers could not steal—memories, loving bonds, personal skills and talents, deep religious faith, opportunities for empathy and growth—allowed Rena to shift gradually from fear-based deficit thinking to a way of life that focused on all that she had, not all she had lost. On life's goodness and personal meaning, not just on its precariousness.
Many leaders see employees' search for meaning as their own affair, while productivity and bottom-line results are the business of business. We also advocate that companies exist to get work done. In fact, rather than define an organization by its structure, roles, or rules, we define it by its capabilities: what that organization is good at doing (Apple has the capability to innovate, Disney entertains, Marriott has the capability to serve, and Walmart delivers low prices). To survive, organizations must not only amass capabilities but must also turn internal capabilities into value for external stakeholders. For-profit enterprises must create products or services that customers value and investors trust. Government agencies must meet citizen demands and respond to legislative mandates. Not-for-profit organizations continue only if they embody and further societal values. Capabilities link what goes on inside the company to what customers will pay for and what investors trust.
But in this book, we also argue that organizational capabilities more readily lead to lasting value when leaders promote meaning making as well as moneymaking. As leaders weave affirming stories, find heroes and causes, embody ethical and trusted values, clarify principles that lend order and rationality to decisions and routines, and make visible the ways employees' efforts help the company contribute to a greater good, they create organizations that overflow with a sense of meaning and abundance. In the words of former U.S. president Woodrow Wilson, "You are not here merely to make a living. You are here in order to enable the world to live more amply, with greater vision, with a finer spirit of hope and achievement. You are here to enrich the world, and you impoverish yourself if you forget the errand."
Pockets of abundance can flourish in virtually any organization. The entire organization does not have to wait for a charismatic executive to push the abundance agenda. While we look to leaders to create organizational abundance, all employees also own the opportunity and responsibility to create an abundant work space for themselves and their team. Leadership is not confined to the executive suite.
As organizations become repositories of abundance, employees gain antidotes to some of the malaise, isolation, and crises of meaning discussed here. They also increase the organization's capability for doing what it does best. Apple researchers who experience abundance turn their personal creativity into Apple's product innovation. Disney "hosts" who experience abundance find a greater good in delighting theme park guests. Marriott hoteliers who experience abundance serve customers from resilient inner conviction more than easily derailed outward expedience. Walmart clerks who experience abundance can take pride in Walmart's commitment to low prices that help struggling families. While abundant organizations won't necessarily turn around divorce rates or stop drug addiction, they can be a societal force for meaning and purpose that counteracts ennui and despair both inside and outside company walls.
Whether you are an individual employee looking for a reason to get up for work every day, a manager of a team or division wanting to build employee productivity and engagement within your unit, or the leader of an entire organization committed to values, objectives, policies, results, and stories that make for great places to work, abundance is a relevant agenda. The next chapter provides an overview of seven questions and seven fields of inquiry that help promote this meaning-making, value-creating, hope-building process at all levels of organizational life.
## **CHAPTER 2
The Making of Abundance**
Abundance is neither a random act nor an isolated event. Leaders who intentionally create abundance at work build organizations that turn customer and investor expectations into daily employee actions.
### **Wrestling with Paradox**
In Chapter 1, we introduced Vicki, whose early career enthusiasm is moderated by cutbacks and office politics; Raj, whose personal and family demands goals may temper his ability to grow his business to the next level; Grant and Shirlyn, for whom peaceful progression toward the twilight of their careers has been derailed by the current economic context; and Ivan, whose success has isolated him from himself and others. The individuals in each of these cases might say, "I've got abundance at work, all right. An abundance of headaches and hassles."
Creating abundant organizations despite headaches and hassles requires leaders to struggle with paradoxical goals and values. These individuals must balance their professional dreams, career enthusiasm, family relationships, and retirement plans against business realities, office politics, the demands of growth, and larger economic contexts. Let's face it: leaders who attend only to personal needs (theirs or their employees') may create caring organizations that end up bankrupt. On the other hand, leaders obsessed only with making money will likely be socially and emotionally bankrupt if they fail at other things that matter: reputation, relationships, sustainable purpose, engaged employees, and the simple but invaluable experience of having fun at work.
Many insightful thinkers have attended to these issues. This chapter summarizes the remainder of the book by synthesizing and integrating diverse disciplines into our definition of how leaders create personal meaning and abundant organizations.
### **From Turnaround to Transformation**
Meeting both organizational and individual goals is seldom easy. Leaders effectively connect the two when they create a clear line of sight from employee meaning to customer and investor confidence. McKell, the CEO of a large global bank, survived the economic demands of turnaround by streamlining staff, cutting costs, managing risk, divesting toxic assets, and stabilizing profitability. McKell then realized that to go forward he needed not only to complete the economic turnaround but to begin a more fundamental transformation as well—to change how both employees and customers perceived and felt about the volatile but sometimes faceless bank.
McKell and his executive team continued to efficiently manage the bank's daily operations, but they also talked about where the bank was headed. McKell was a master of financial focus and discipline. But to put a friendly face on the bank he wanted to focus on feelings that shape meaning as well as facts that deliver results. This would mean not only continued efficiency but also relationships of trust with key clients and employees and better citizenship in the communities they served.
One of the executives jumped quickly on the bandwagon of good corporate citizenship with a proposal to invest in initiatives like microlending to underserved constituents. Another got enamored with building client trust and improving the bank's reputation for personal attention. Another felt passionate about efficiency and excellence in management processes. All three goals were ultimately about creating a sense of meaning as reflected in how people inside and out felt about their experience with the bank. And ultimately all three could help the bank's bottom line. After hours of debate McKell decided that only by embedding each of these goals in the other two would they shape a sustainable future identity. The individual values of these key executives needed to be coordinated and institutionalized for their goals to be realized.
As leaders they also needed to direct the emotional energy of employees, clients, and other stakeholders to these goals of citizenship, trust, and efficiency. Employees would need to gain a vision of how efficiency, client trust, and corporate citizenship could make their everyday jobs feel more like a personal mission and less like a duty to be endured. Clients and other stakeholders would also need a clear vision of what the bank was about and why.
When the executive team first became involved in the turnaround, they had a clear intellectual agenda for overcoming what was wrong with the bank's operations. As they began to look at transformation, however, their agenda shifted to building what was right—abundance thinking and an emergent emotional agenda. In many ways, transformation is more difficult than turnaround. In a turnaround, a pending financial crisis demands attention and thus dictates behavior. In a transformation, greater emphasis must be put on creating meaning to capture imagination and shape future behavior.
Statistics on the national economy or the corporate cash flow focus our attention on the deficits that dominate our lives, including deficits in time and money resources. But other deficits can be even more crucial to our sense of well-being—deficits in purpose, satisfying connections to other people, challenging work, resilience, and delight. Such deficits can add up to a deficit of meaning. Overcoming these deficits builds the agenda of abundance.
### **Discovering Meaning**
Abundance is not found in circumstances or events—in how big a raise we got or how many people report to us. Abundance is found in the value we place on those events and the way we interpret their impact on us. Meaning is not inherent in events; it is made by people. This is the good news and the not-so-good news. Good news: the meaning of our lives is not controlled by what happens—as Frankl discovered, we can find purpose, value, and also happiness in a wide variety of even unpleasant circumstances. Notso-good news: we have to work at this meaning-making process. It takes work to determine what work means, at either a corporate or a personal level. Leaders have the primary responsibility for this meaning-making process.
At a personal level, inner dialogues shape and construct this meaning. If I tell myself I'm not paid well because I'm not respected for my skills, I build a different meaning than if I tell myself how glad I am to work for an organization that is fiscally responsible. If I tell myself my boss's criticism means he is trying to help me improve because he values my contribution and wants me to succeed, I build different meaning than if I tell myself his criticism is a forerunner to my getting fired for incompetence. If I see my company as a major contributor to solving the energy crisis, I have a different feeling about the value of my labor than if I am just crunching numbers for someone else's selfish agenda. As the story goes, I feel differently about the meaning of my work if I see myself as a bricklayer than if I see myself as building a cathedral to God.
At a corporate level, leaders can help shape and construct the meaning employees assign to corporate realities, focusing corporate consciousness on opportunities instead of deficits. For example, when a corporation faces an industry downturn, people generally get nervous. Employees scramble to protect their budgets, make their own job perks sacrosanct, and push someone else between them and the corporate ax (remember Vicki's story from Chapter 1). But when leaders in one technology company made clear to employees that every $50,000 in savings could save one job, people enthusiastically rallied around cost cutting. As a result, employees were engaged, cooperative, and constructive. They had a clear line of sight between how their actions could deliver company goals while saving the jobs of people they cared about.
Because finding meaning at work is itself hard work, and because meaning is very personal, we can't promise leaders easy methods for replacing deficit thinking with abundance thinking. What we can offer leaders is a series of questions, which we will explore in the next section. We hope these questions will begin to structure conversations between leaders and their multiple constituents—conversations about what our organizations are trying to accomplish, why, and what those efforts suggest about the meaning of our lives.
These meaning-exploring questions are intended to produce the following outcomes:
Increasing clarity about identity and signature strengths
Gaining a sense of purpose to understand better what motivates us
Managing work complexity through teamwork
Replacing social isolation with positive work settings
Identifying and responding to challenges that we care about and that engage us
Growing from change by learning and becoming resilient
Building sources of delight and civility into our work routines
. . . and do all this within the fiscal constraints that help keep us honest about whether we are adding real value for customers, shareholders, and communities.
### **Why _These_ Outcomes?**
The questions that produce these outcomes have emerged from our reflection on two sets of ideas. First are the societal and business challenges or crises of meaning already laid out in Chapter 1:
Declining mental health and happiness
Increased environmental demands that shape social responsibility, organization purpose, and individual motivation
Increased complexity of work
Increased isolation
Low employee commitment
Growing disposability
Greater hostility and enmity
Second, a number of key concepts and even entire disciplines have arisen in response to—or at least of relevance to—these challenges. (See Figure 2.1.) The concepts we think are especially relevant to the preceding challenges are in the second column:
**FIGURE 2.1 Overview of Fields and Disciplines Contributing to the Concept of Abundance**
Our intent with the concept of abundant organizations is to both _synthesize_ and _complement_ insights and research around these key concepts, adding ideas that take each approach another step and focus it on leaders within an organizational setting. The questions and ideas that follow emerge from this synthesis. (See Table 2.1.) We provide an overview of these questions here, and the remaining chapters will probe these questions in greater detail. (See endnotes for more on the theories that provide answers to each question.)
**TABLE 2.1 Abundance Summary**
### **Seven Questions That Drive Abundance**
We propose seven questions to help leaders drive the abundance agenda—questions that help leaders make meaning, add value, create emotional energy, and foster hope while at work. These questions apply to leaders at the personal level (Am I finding abundance myself?), at the interpersonal level (Do we have an abundant work team?), at the organization level (Are we fostering abundance in this organization?), and at the societal level (Can our industry or community help humanity at large?). The key concepts listed on the right in the preceding list help us approach these questions. The key principles of an abundant organization emerge from these approaches. This is the architecture for abundance.
#### **1. What Am I Known For? (Identity)**
A sense of abundance is fostered by a clear sense of who we are, what we believe in, and what we are good at. In the bank example, McKell and his team were excited when they shaped their organization's future identity around efficiency, trust, and citizenship. They then had to turn this corporate identity or brand into personal action among the 30,000-plus bank employees.
Chapter 3 describes how leaders can shape an organ ization-wide identity and then help individuals use their personal strengths to foster that identity and succeed at work. It also describes how leaders shape organizational strengths (capabilities) to build an abundant corporate identity or brand, turning external stakeholder expectations into internal corporate actions.
The field of positive psychology helps leaders answer this primary question. The traditional approach of psychology to depression, anxiety, and addiction disorders has been to develop models and techniques for fixing what is wrong with us. Few theorists or clinicians also probed what is right. Into this space, Martin Seligman and his associates have inserted the proposal that the domain of psychology extends beyond fixing pathology to probing health and happiness. Positive psychology asks what makes people happy in the long run. Researchers in positive psychology have discovered that when we identify and regularly use our signature character strengths, life becomes more satisfying and meaningful. They further assert that even when we must cope with depression, anxiety, addiction, or other mental illness (and their corporate equivalents), building on our signature strengths fosters creativity and courage for tackling our challenges.
The abundant organization adapts principles of positive psychology to help leaders build both organizational strengths and the strengths of individual employees. In addition, we propose that leaders in abundant organizations not only recognize and build on strengths but also use those strengths to create value for external stakeholders. At both personal and organizational levels, the meaning we find from our strengths deepens as we not only build on our strengths but build on strengths that strengthen others too.
PRINCIPLE 1
Abundant organizations build on strengths (capabilities in an organization) that strengthen others.
#### **2. Where Am I Going? (Purpose and Motivation)**
Abundance emerges from a clear sense of what we are trying to accomplish and why. Too often employees' and employers' goals are at cross-purposes, resulting in both individual frustration and organizational underperformance due to employee cynicism and lack of perceived corporate vision. As McKell and his team worked through the paradoxical goals of trust, efficiency, and citizenship, they created a sense of corporate purpose that helped employees fulfill their personal purposes through their work at the bank. Employees who can meet their personal goals at work remain motivated and engaged; those who can't, go in a different direction, physically or emotionally.
Chapter 4 offers suggestions for how leaders create purposeful organizations that help employees' personal ambitions match organizational goals. When our personal goals align with the organization's goals, work feels like a meaningful extension of our private journey. As we both own and personalize our company's mission, we find opportunities to impact broad societal problems we care about.
Social responsibility and environmental activism are fields that speak to the importance of addressing society's biggest problems while investing in corporate citizenship. To manage scarce resources and rebuild organization reputations, many leaders have begun to pay attention to a "triple bottom line" of people (values and reputation), profits (financial return), and planet (e.g., carbon footprint). Environmental activists help corporations audit their carbon footprints and reduce energy consumption. Other organizations demonstrate a caring heart as they invest in philanthropic initiatives. These citizenship efforts underscore values of stewardship and accountability that help employees see how their personal values align with corporate values to make a real difference in the real world.
Just as the bank had to balance profit, purpose, and people, leaders in the abundant organization focus on sustainable profit as well as environmental sustainability. An organization that emphasizes social contribution without facing the economic realities of creating value for customers and investors will not survive. While bankruptcy will certainly reduce an organization's carbon footprint, it will also eliminate its ability to employ workers, make useful products, offer customers innovative solutions, and build communities.
PRINCIPLE 2
Abundant organizations have purposes that sustain both social and fiscal responsibility and align individual motivation.
#### **3. Whom Do I Travel With? (Relationships and Teamwork [Th]at Work)**
Our sense of abundance is enhanced by meaningful relationships. The increasing complexities of today's workplaces require combining people with different skills into cohesive and high-performing teams. As McKell and his team worked to shape the bank's direction, they found that their ability to work as a team turned individual strengths into organization capabilities. When they put aside individual biases for the good of the overall bank, they made the whole of the team more than the sum of the individual players. They worked to create this sense of teamwork throughout the organization.
Chapter 5 suggests specific ways leaders can strengthen positive work relationships that enhance teamwork. These work relationships make even difficult work more doable. Our meaningful work relationships include friendships, mentoring relationships, and professional networks. Research on high-performing teams explores the ways teams coordinate the efforts of many people to solve complex problems. Although teamwork is itself more complicated than working alone, it also allows team members to reduce complexity by specializing. Research suggests that high-performing teams operate with clear purposes, good governance, positive team member relationships, and the ability to learn.
While leaders must attend to teamwork in complex work settings, the concept of abundant organizations goes beyond teams that produce and perform their tasks well to teams that engender a kind of passion that allows for creativity, focused energy, trusting connections, and mutual respect. High-performing teams come from high-relating people. Research on successful marriages suggests patterns and stages of effective long-term committed relationships that can be applied to teams in organization settings. The best teams work through these stages and use these patterns to combat "organization divorce" characterized by burnout, turnover, and lost productivity. When leaders help their organization "families" move beyond the superficialities of getting along to struggling through conflict so that they can understand one another's strengths and weaknesses, they can approach the kind of synergy that occurs in the best of human relationships. They gain a competitive advantage over a less relationally sophisticated competitor. This means that leaders need to learn and model the skills of building good relationships at work. Lynda Gratton has captured this sense of team cohesiveness with the term _glow,_ which includes a cooperative mind-set, jumping across boundaries, and igniting latent energy.7
PRINCIPLE 3
Abundant organizations take work relationships beyond high-performing teams to high-relating teams.
#### **4. How Do I Build a Positive Work Environment? (Effective Work Culture or Setting)**
Abundance thrives on positive routines that help ground us in what matters most. While bad habits thrive on isolation and shame, positive routines help us connect with ourselves and others. As McKell and his team focused on their future identity, they wanted to establish a culture focused on building what is right, not just eliminating what is wrong. They wanted to replace backbiting with forward thinking, politics with collaboration, and self-interest with other-directed service.
Chapter 6 suggests ways leaders can create and sustain positive routines to foster effectiveness, efficiency, and meaningful connection. Leaders can tolerate cynical, negative, and demeaning cultures, or they can encourage constructive, affirming, and uplifting cultures. Leaders shape these cultures through their words and deeds. These cultures replace individual isolation with corporate connection.
Leaders who engender positive work environments promote good communication, development opportunities, and pleasant physical facilities to ensure a positive culture at work. Instead of building routines and patterns that encourage self-reflection, honest sharing, and the kind of consistency that brings people together, many of us build habits, addictions, and compulsive patterns that serve primarily to block out other people. Or we build almost no routines at all, leaving us untethered in time and space and making us unpredictable to those who want to connect. Routines and patterns driven by our deepest values help us stay grounded in what matters most and available to those who matter most. When leaders support individual and policy-level routines that help work _work_ , they create a positive environment that both sustains productivity and fosters connection.
Workplaces of all kinds use checklists and routines to ensure quality control. Checklists and routines that are chosen personally around core values and relationships lend predictability and stability to our lives. Instead of constantly fighting against time and space, we work with them in a mindful, realistic way. Whether personally or organizationally, flexible but consistent routines can help us know ourselves and others while countering both the perfectionism and the unpredictability that get in the way of connection.
PRINCIPLE 4
Abundant organizations create positive work environments that affirm and connect people throughout the organization.
#### **5. What Challenges Interest Me? (Personalized Contributions)**
It is hard to imagine abundance in the absence of challenge. The most engaged employees are generally those whose work gives them the opportunity to stretch while doing work they love and solving problems they care about. The bank executives gave employees a new challenge when they shifted the focus from turnaround to transformation through efficiency, trust, and citizenship. These three pillars of the bank's identity challenged employees to solve problems they cared about.
As leaders involve both teams and individuals in enjoyable challenges, they engage employees' hearts and their minds, as Chapter 7 discusses. Different people find different kinds of work easy, energizing, and enjoyable and different problems meaningful. Leaders need to adapt broad general challenges to individual requirements and predispositions.
The study of talent has evolved from a focus on employee competence ( _ability_ to do the work) to employee commitment ( _willingness_ to do the work). Employees who are competent but not committed will not perform to their full potential. Commitment comes from building an employee value proposition that engages employees to use their discretionary energy to pursue organization goals. Commitment or engagement grows when we work in a company with a vision, have opportunities to learn and grow, do work that has an impact, receive fair pay for work done, work with people we like working with, and enjoy flexibility in the terms and conditions of work.
Leaders in abundant organizations take employee competence and commitment another step—to employee contribution. Contribution focuses not just on activity but on the meaningfulness of the activity. For example, a teenager may be highly competent at video games (he wins them often), have a high commitment to video games (shown by playing them for hours at a time), but still not find real purpose and meaning in game playing. An employee may be competent (able to do the work) and committed (willing to work hard), but not have the sense of abundance that comes from also making a contribution to a greater good.
PRINCIPLE 5
Abundance occurs when companies can engage not only employees' skills (competence) and loyalty (commitment) but also their values (contribution).
#### **6. How Do I Respond to Disposability and Change? (Growth, Learning, and Resilience)**
Abundance acknowledges that failure can be a powerful impetus to growth and learning. When we face change and take risks to work outside our comfort zone, resist defensiveness about mistakes, learn from failure, and keep trying, we become not only more resilient but also more satisfied with life. McKell and his team knew that as they tried to implement their new organization identity and purpose they would make mistakes. Instead of hiding from and finding someone to blame for mistakes, they committed to facing and learning from them.
Chapter 8 reviews how leaders can encourage learning and resilience. Abundance is less about getting things right and more about moving in the right direction. Resilience reflects a positive outlook on work and shapes learning for the future rather than lamenting the past.
Research on personal resilience and learning organizations offers exciting insights into what helps people and institutions endure in the face of both suffering and setbacks. By studying what helps POWs survive and thrive, how Navy Seals can be trained to stay calm under attack, and what abused children who become successful have in common, we get hints about how leaders encourage learning under conditions of stress and challenge.
Unlike the assumption of disposability that governs so much of modern society, resilience and learning principles challenge us to "repair, reuse, and recycle" people, products, and programs rather than tossing them. In tough economic environments organizations will necessarily reduce staff, drop products, and cut nonessential programs; nevertheless, hiring freezes and reduced funds for research and development also mean we must work with whom and what we have. Abundance means we not only learn attitudes of resilience that help us thrive under stress; we also use these principles to make do with what we have. As we do so we come to realize that what we have is actually enough.
PRINCIPLE 6
Abundant organizations use principles of growth, learning, and resilience to respond to change.
#### **7. What Delights Me? (Civility and Happiness)**
Abundance thrives on simple pleasures. Sources of delight might include laughing at ourselves, appreciating excellence, relishing beauty, being present in the moment, and having fun at work. As McKell and his team laid out the bank's new identity, they encouraged employees to have fun in shaping this identity. Corporate fun included contests, celebrations, and communications about the new direction.
When leaders encourage civility and delight in how work is done, they go a long way toward creating a sense of abundance, as shown in Chapter 9. These sources of delight are highly personal, depending on the personality of the leader and the requirements of the employees.
The hostility rampant in modern life is itself under fire these days. The cry for tolerance demands that we outgrow our racial, religious, political, ethnic, and gender stereotypes. The cry for civility also calls on us to outgrow our we-they, win-lose, right-wrong, blame-and-shame mentality. As we move away from hostility and blame toward problem solving, listening, curiosity, and compassion, simple civility greases the skids.
Under the rubric of valuing differences, leaders are encouraged to understand, respect, and learn from the perspectives of people of different races, genders, backgrounds, or even professional training, replacing hostility with civility. We may also want to look for and rejoice in the different ways people find sweetness in life, going beyond civility to delight. Sensitivity to such differences helps us find a wide variety of ways to bring pleasure and delight into the work-place. For some perhaps a celebration of 10 years of service is meaningful; for others a renewing sense of delight is evoked by a note from the boss, a compliment, a shared joke, a favorite song, a different chair, a new dish at lunch, or simply a beautiful sunset shared on the way to the parking lot. Delight often comes in small packages, and when money is tight it helps to know that small and simple pleasures spread over time have more impact on our sense of well-being than grand one-time gestures.
PRINCIPLE 7
Abundant organizations attend not only to outward demographic diversity but also to the diversity of what makes individuals feel happy, cared for, and excited about life.
### **Organizational Application**
Much of what brings meaning into our personal and professional lives can be categorized under the preceding seven headings. When leaders help employees explore these questions, they help create abundant organizations with positive individual and organization results:
Higher commitment, better employee health, improved productivity and retention
A leadership brand that builds investor confidence
Increased customer commitment (because customer attitudes about an organization correlate with the attitudes of its employees)
Increased investor confidence in future earnings and higher market value (based on intangible assets like leadership and quality of employees)
Improved community reputation, merited by stronger social responsibility.
Table 2.2 provides an organizational assessment tool for abundance to help leaders parse out the components of abundant organizations and assess areas of strength and weakness. The remaining chapters of this book will address each area in more detail. These chapters will give leaders specific tools and concepts for increasing organizational abundance in teams, divisions, or companies.
**TABLE 2.2 Assessment of the Abundant Organization**
_Think of the organization where you work as you complete the following assessment. In a small company, this would be the entire organization; in a large company, it would be a division, plant, geography, or other work unit._
These principles apply at a personal level as well, as shown in Table 2.3. Questions on this individual assessment tool can help you and individuals you work with gauge your sense of _personal_ abundance and meaning at work. You will find more specific tools and concepts for increasing your personal sense of abundance at work in the chapters that follow.
Getting high scores on these questions does not mean that work will suddenly feel easy, people will get along instantly, customers will flock to buy products, or stock prices will soar overnight. Meaning does not ensure ease; it offers hope. Playwright and founding president of the Czech Republic, Václav Havel, writes, "Hope is not prognostication . . . It is not the conviction that something will turn out well, but the certainty that something makes sense, regardless of how it turns out." Abundance emerges from the growing conviction that what we are about "makes sense"—that it contributes to something larger than ourselves and that it is grounded in our deepest values. Such conviction does not forestall all problems, but it helps us confront problems with courage and integrity. And it is in that confrontation that meaning—abundance—flourishes.
In economically good times, abundant organizations matter. In tough times, they matter even more. When organizations address the key questions and build on the guiding principles of abundance, capable, committed employees also have the satisfaction of knowing their work makes a genuine contribution. Customers receive products and services that meet their needs. Investors have more confidence in the company's future. Communities and ecologies are sustained responsibly.
In short, there is enough. And to spare.
**TABLE 2.3 Assessment of Individual Abundance at Work**
_Think about your current personal experience with work as you complete the following assessment._
## **CHAPTER 3
What Am I Known For? (Identity)**
LEADERSHIP **IDENTITY** CHALLENGE
With rapid technological, demographic, political, and social change, organizations scramble to align employee strengths into a coherent organization identity that responds to evolving customer and societal requirements. Great leaders help individuals align their personal strengths with the organization identity (firm brand) and with customer expectations.
Jason Bourne is on the run (hear the insistent beat of the background music). Although struggling to clear a fog of amnesia about his history, he has not forgotten how to fight bad guys, break into Swiss banks, blow up cars, perform emergency medical procedures, gain the trust of wary women, or speak Russian, although he has no idea where he learned these things or why he needed to know them. Haunted by violent images, aware that others are out to get him, and spooked by his own instinctive capacities, he is horrified by the conclusion pressing upon him: he must be a killer for hire. Bourne has all the skills of a cold and highly trained assassin, but his moral values are deeply offended by such a possibility.
Jason Bourne is a fictional character: a highly skilled operative for an imaginary secret government agency gone bad, an agency that recruited him for his talent and patriotism, an agency he turns against and turns in as he realizes its corrupt leadership has deceived him. His predicament provides an interesting reminder that our identity does not consist only of the name we use, the stories we remember, or the people we know. Our identity is grounded in how we instinctively use our skills in the service of our deepest values. Although our lives do not play out to driving rhythms in tightly edited chase scenes, each of us is trying to figure out who we are, to analyze what we do well and whether it serves our deepest values.
At both a personal and an organizational level, a meaningful life is one that expresses who we are as articulately and honestly as possible, both with our words and through our actions. Who we are is not just about what we can do; it is about what we love and what we hate, what we desire and what we fear, what we know and what we are still trying to figure out. It is not enough for Jason Bourne to be good at what he does, even in the service of his own survival. He needs to know what end his skills serve, and he yearns for that end to be something he deeply believes in. When his institutional identity clashes with his personal identity, even when he cannot remember exactly why, his loyalty is lost and the institution he once served becomes the enemy.
Great leaders understand that the search for meaning that builds abundance is grounded in clarity about our truest individual and organizational values and how they align. Such leaders claim their values through their life choices and help others do the same. This is the beginning of an authentic and meaningful organizational experience.
### **Signature Strengths and Capabilities**
When we meet people, we often categorize them by where they work, what they wear, how they smile, or how they speak. These are at best superficial indicators of real values and competencies. Underneath our role, profession, appearance, or observable talents are what psychologists call _signature strengths_ : the character traits and values most central to who we are. Psychologists hypothesize that some core virtues are valued by virtually every culture and philosophy. (Examples would be gratitude, humility, courage, compassion, fairness, integrity, humor, forgiveness, and love of learning.) While we may agree that all such traits are important, typically we especially espouse and want to be known for a few. These signature strengths are likely to persist regardless of our role, profession, appearance, or talents. We also have skills, talents, and knowledge that are so embedded as to be instinctive, but our signature strengths are not just about talents and skills. Signature strengths are grounded in the moral values we espouse, the virtues we cherish. Like Bourne, we feel at odds with ourselves when our skills, however proficient, are not used in the service of our signature strengths—our deepest personal values.
Organizations also have identities and project images that shape the perceptions of both customers and employees. We call an organization's signature strengths its capabilities—what that organization does best in the service of its core purposes. Perhaps part of the success of _The Bourne Identity_ as a novel and a movie was its ability to capture the crisis we all face when our personal identity is at odds with that of an organization we once trusted and devoted ourselves to.
On a lighter note, Dave once did some consulting for Harley-Davidson, and the company kindly gave him a Harley-Davidson signature leather jacket. The jacket embodied all it meant to be Harley-Davidson: tough, fast, wild, and hard around the edges. Dave had fun wearing the jacket because it changed how others perceived him. No more Mister Nice Guy! Then our quiet, academically oriented 16-year-old daughter found the jacket. She wore it to school one day. She came home and said, "I met guys today I never knew existed before." We hid the jacket!
Harley owners have an identity that shows up in their clothes and actions. They are proud of their affiliation with the Harley brand, which aligns with their desired identity and values. Companies can spend millions of dollars creating and communicating these brand identities through creative marketing. Nike's swoosh stands for athletes in action; Walmart trucks and ads carry the slogan "always low prices"; the BP tagline bears the standard for "beyond petroleum" as BP tries to move into alternative energy sources. In the best companies, these public identities also translate into management actions inside the organization. Nike's corporate headquarters boasts gyms, tracks, and weight rooms, which employees are encouraged to use. Walmart holds executive retreats in modest surroundings to maintain its cost consciousness. BP leaders look for opportunities to work on energy outside traditional petroleum sources. Good companies know their signature strengths and their capabilities and align their services and their management practices with them. A company brand presents a point of view about the company, proposes a lifestyle consistent with that point of view, and shapes customer expectations.
Sometimes when employees' signature strengths intersect with the signature capabilities of their workplaces there is a seamless fit; other times there is a clash of values and goals. Have you ever been in an organization where you felt out of place? This happened when we entered an exclusive clothing shop on Rodeo Drive in Beverly Hills. We clearly did not belong. We knew it, and the staff knew it. Our personal identity did not mesh with their corporate identity. We would have needed more than a complete wardrobe overhaul to work in such a place; we would have needed a complete overhaul of our personal signature strengths.
As a leader, you create a more abundant organization when you help employees clarify their personal identity and enhance their signature strengths and then help them see how those strengths fit with the goals and values of the organization. As diagrammed in Figure 3.1, the steps in this process are:
1. Help employees define and grow their personal strengths.
2. Define and build organizational capabilities required for success.
3. Meld personal strengths and organizational capabilities.
**FIGURE 3.1 Melding Individual, Organization, and Customer Identity**
4. Determine customer and investor expectations.
5. Connect both personal and organizational identities with the needs of customers and investors.
We'll look at these five steps in more detail.
### **1. Help Employees Define and Grow Their Personal Strengths**
How does a leader help someone identify and build personal strengths? If deficit thinking focuses us on what is missing, abundance thinking focuses us on what is available and possible. As leaders we want to focus employees' attention on the latter, including a focus on their own identities.
Self-awareness is capricious. At times we are very aware of our flaws. When we look in the mirror, the zits or wrinkles jump out and overshadow our strong chin or fetching eyes. Not only do we magnify our flaws; we also ignore the strengths we have. Those with curly hair buy straightening irons; those with straight hair get perms. We once asked a group of young people to share what they saw as their physical flaws. One young man admitted sheepishly that his ears stuck out, which really bothered him. No one else in the group had ever noticed his ears sticking out. Even when this "flaw" was called to their attention, it quickly fell to the background when they interacted with him.
At other times we tend to flee from our flaws. Leadership researchers find that most leaders are better at identifying their strengths than their weaknesses. We run and hide from things we do not do well, out of embarrassment or uncertainty about how to change. Realism about both our strengths and our weaknesses is essential to a strengths-based identity. Great leaders build on their strengths but also bring their weaknesses to at least neutral. They help employees and companies to do the same.
Realism can hurt, but it also helps us invest our energy where it has the best chance of paying off. When Dave was younger, he liked basketball and played with enthusiasm. He had a dream that one day he might play college or even pro basketball. While this dream led him to hours of dedicated practice, it also gave him false hope. He eventually realized that he did not have the raw physical talent for professional basketball. He could continue to find great fun in community pickup games and watching others play, but being a professional athlete was not his strength. When Dave realized that he had other strengths that would give meaning to his life and pursued them with the same work ethic and enthusiasm (his real and enduring "signature strengths"), he was able to find sustainable meaning in his work.
When you as a leader help employees develop honest self-perceptions, you help them invest in the real dreams that bring meaning to life. You can help employees discover their identity through formal assessments, informal observations, conversations, and assignments.
#### **Formal Assessments**
Until we name and use them, we often take our strengths for granted. Innumerable personality tests depict who we are as colors, types, styles, initials, or aptitudes. Recently, two sets of scholars have worked to synthesize categories of strengths or core values that define us.
**Seligman and his colleagues.** Martin Seligman, the father of positive psychology, has identified six domains of personal strengths and 24 individual character traits within those domains. (See Figure 3.2.) As you look over this list, you may have a pretty good idea of which traits you value and exhibit most. Seligman's research suggests that people get a boost in personal happiness when they use their signature strengths regularly and in new and creative ways. When we deliberately structure our work and our interactions to build on our signature strengths, we feel like we have enough and to spare of what it takes to do the job at hand. (If you want a more scientific accounting, go to authentichappiness.org and take the _VIA Survey of Character Strengths_ to identify your signature strengths compared to other people. Use of this research site is free and can be used by you and your work team to determine and compare your strengths.)
**FIGURE 3.2 Seligman's Signature Strengths**
**Gallup organization.** Marcus Buckingham and colleagues in his firm and the Gallup organization have also developed an instrument that helps people assess work-related skills and characteristics. They find that such skills are difficult to train for but easier to hire for. They have identified 34 strengths a leader should consider when hiring an individual for a job—strengths that have little to do with specific work experience or job skill but a lot to do with the qualities it would take to work well in a specific culture or with a certain kind of customer. We list these strengths in Figure 3.3. (To take their test, buy _Now, Discover Your Strengths_ to obtain a code for the online test.)
As a leader, you might invite employees to take either (or both) of these tests as a way to quantify what comes naturally to them. While self-assessments have a certain self-bias, they still offer us a strengths language that facilitates discussion and self-awareness. They help employees see patterns that inform their identity. They also help you as a leader know what types of opportunities your employees are most likely to take joy and pride in at work.
**FIGURE 3.3 Buckingham's Strengthfinder Attributes**
#### **Observations**
To rephrase an old axiom, "We judge ourselves by our intentions, but others judge us by our behavior." While tests offer a quick way to identify how we view our strengths, other people are often more interested in our performance than in our intentions or dreams. When our son was in eighth grade, he came home excited and thrilled with his report card. We were anxious to see his grades and share his enthusiasm. He proudly displayed the report card boasting an A, B, C, D, and F. Our enthusiasm quickly waned. He explained that he had spent the semester working hard to "hit for the cycle" (a baseball term where a player gets a single, double, triple, and home run in the same game). He said that eighth grade was his last chance to do this before grades would count for admission to college and that he had worked hard to figure out how well to perform in each class to get the right grades for him (not us). We didn't much care about his intentions and dreams in this situation—we wanted performance!
Leaders can serve the important function of holding up a metaphorical mirror to help employees see how their behaviors are perceived by others. Formal 360-degree feedback assessments help employees learn how others perceive them on a set of leadership dimensions. Performance standards, quality reviews, and comments from others can help round out employees' self-perceptions.
Leaders may also help employees ascertain their identity by asking them to complete a time log and analyze the results. When we coach leaders, we often ask them to take the calendar test—to reflect on the last 90 days and consider:
What categories of activities make up your workday?
What issues have you spent the most time on?
Whom have you spent the most time with?
Where did you spend your time (in your office, in meetings, with customers)?
What reports and information do you spend time looking at?
What business issues capture your quiet time (keep you awake at night, float up when you are going to and/or from work, or surface often in conversations)?
As a leader, you should also be attuned to informal observations of your employees. Which employees tend to speak up first? Which employees have ideas that others follow? Which employees are listened to the most? Which employees are more bold, engaging, or creative? Which employees volunteer (or shy away from) certain assignments? Who does quiet service? Who works to engage others? As you thoughtfully observe employees, you can begin to see patterns that reflect each employee's identity.
Collectively, these observations reveal predispositions, strengths, and weaknesses that form an identity pattern, helping leaders know how to engage the hearts, not just the hands and heads, of their team.
#### **Conversations**
Leaders may not think much about conversations they have with employees, but these conversations are often extremely potent for employees. Some of these conversations occur in formal performance review settings, where you evaluate productivity and potential. Often more crucial conversations occur when you quietly share your observations with employees. Some of these conversations may be about negative behaviors; others are about positive ones.
Child behavior experts find that punishing conversations make children fearful or angry but do little to change children's behavior. Much more effective are parents who frequently and warmly pay attention to and point out behavior that is appreciated and appropriate and pay minimal attention to problems. Discipline works best when a privilege is withheld briefly from a child with minimal display of parental emotion or engagement. The most effective parents reserve attention (and negative attention is still attention) for behavior they want to see more of.
Leaders do well to follow a similar pattern, commenting on, praising, and rewarding constructive work behavior and mostly ignoring annoyances. When a serious problem must be corrected, it is best to do so with minimal engagement by withholding pay or privileges, not engaging in yelling matches or protracted threats or shaming, all of which build resentment, not change.
Identity-clarifying conversations will focus less on judgment and more on description. As a leader, you might ask your employees to share their perceptions of their strengths, describe times when they demonstrated their strengths, and explore how their strengths might be used to help others (including coworkers and customers). You can describe what you see and value in their behavior, the effect it has on others for the good, and additional options for building on strengths.
Other strength-identifying conversations might occur in a team setting. More and more work is performed by teams that bring differing skills to common problems. (See Chapter 5.) A valuable team exercise is to ask team members to describe examples of the strengths of each individual on the team. This affirming report generally results in team members bonding more tightly with each other.
#### **Assignments**
We learn by doing. When we perform familiar tasks, we demonstrate our skills and take pleasure in our expertise. When we act outside of our comfort zone, we may learn hidden strengths we did not know we had. At other times we may learn that what we had hoped would be our strengths are actually not (e.g., Dave's short-lived basketball career). When we ask people how they learned what they care about and are good at, they realize that this insight has often emerged from tackling assignments both in and out of their comfort zone.
All talent management begins with hiring people who have the right strengths for the job, and these "right strengths" are customer defined. An executive once elaborated to Dave how committed he was to managing people, to paying attention to their needs, and to helping them feel connected to the organization. He was a bit surprised when Dave suggested that helping his employees be happy was only the beginning point—hiring the right employees in the first place was another part of the journey. Such hiring is based on a simple criterion, not easily implemented: Are you hiring employees your customers would want you to hire? Are you the employer-of-choice of employees your customers would employ? Apple customers expect innovative design in their Apple products and service. Apple leaders need to make sure that new employees have creativity strengths and identity.
We don't always have the luxury of hiring the perfect employee or working at the best-fit job, however. We don't believe we have to start with a perfect fit in all cases or that we need to fire anyone whose signature strengths are not optimally aligned with corporate goals. For example, Raghu tended to be more comfortable in follower roles. His company was expanding and needed new leaders familiar with their customers and goals. They saw leadership potential in Raghu that he did not see himself. His manager began to assign him increasingly responsible leadership roles. He nervously accepted each assignment and did his best. Over time he recognized and developed his strengths as a leader and found great satisfaction and personal meaning in his new skills. He made valuable contributions to his company's emerging success.
Human resource systems like training and compensation may be used to help employees recognize and expand their strengths. Training opportunities provide forums to learn and apply new ideas, and pay programs may reinforce using those strengths.
As you help your employees recognize their identity and structure their work to build on strengths, don't ignore weaknesses. Building on strengths alone will not create leadership success. Dave hates to stretch, and Wendy hates to work up a sweat, but neither of us will be in great shape if we do only the physical activities that come naturally to us while ignoring all others. By helping employees recognize and face weaknesses, you also help them look honestly in the personal mirror and build an overall improvement process. As an identity builder, you offer employees a truer sense of self.
### **2. Define and Build Organizational Capabilities Required for Success**
How does a leader define an organization's strengths, or capabilities? Think about two restaurants, computer stores, sports venues, hair salons, or other companies you have visited. While two companies in the same industry might offer similar products or services, can you sense a difference in how the companies work? These differences reflect an organization's identity. Disney theme parks create an entire world of whimsy and entertainment while Magic Mountain gives customers daring rides. Shopping at a local hardware store is different from buying hardware tools at Costco or Carrefour. A deli in New York feels different from a bistro in Paris. Organizations have an identity. Just as an individual's identity is shaped by his or her strengths, an organization's identity emerges from its capabilities.
Capabilities represent what the organization is known for, what it is good at doing, and how it patterns activities to deliver value. These capabilities include many of the intangible assets that investors pay attention to, the firm brand to which customers can relate, and the culture that shapes employee behavior. These capabilities also become the identity of the firm, the deliverables of HR practices, and the keys to implementing business strategy. An organization's capabilities are rooted in its values and reflect its reputation or brand.
We have generated a list of capabilities an organization might have and examples of companies that demonstrate them, shown in Table 3.1. It is not hard to see that the individual strengths listed in Figures 3.2 and 3.3 can also show up in corporate identities. Within an organization, pockets of functional expertise may need different strengths. Your leadership challenge is to align capabilities with strategies, evolve capabilities, and make sure management actions reinforce key capabilities.
Abundant organizations not only help individuals deploy and use their personal identity—they shape organizations with a clear identity. When those who work in the organization bring their different skills to bear on a common problem, there is diversity with unity. These organizations avoid groupthink by valuing different perspectives and strengths, but also they coalesce individual interests into shared organizational goals.
As a leader, you can commission capability audits to determine which of the capabilities are most critical to your organization's reaching its goals. For example, consumer product firms thrive on product innovation. These firms need to replace old products with new and improved ones in a timely way. Firms in more cost-competitive industries like retail need to build their efficiency capabilities. Walmart's promise "always low prices" creates an identity in the mind of its customer but also guides its discipline in sourcing products, managing people, and building facilities.
**TABLE 3.1 Organization Capability Examples**
When employees, customers, investors, and other stake-holders know what the organization is known for and good at doing, these capabilities build trust that the organization has enough and to spare to accomplish its purposes.
### **3. Meld Personal Strengths and Organizational Capabilities**
How do leaders meld personal and organizational identity?
One of your leadership tasks is to help employees know whether and how they fit into the company. Sometimes fit or misfit is easy to define. The Federal Aviation Administration (FAA) is very clear that some people are more suited as air traffic controllers than others. Physical abilities (e.g., not being dyslexic) are prerequisites of course, but just as important (and harder to ascertain) are the strengths of managing stress, following detailed procedures, and remaining calm in a crisis. When the FAA started to source future air traffic controllers with police or military backgrounds (already practiced in these strengths), their retention and proficiency rates went up.
Disney theme parks communicate an identity. Their family-friendly, clean, and responsive image is upheld by employees around the globe who look and act in a particular way. They are less interested in creativity than in customer care, and they want employees who will play a role, enjoy the look of delight on a child's face, and handle repeated questions with courtesy—not merely work a register efficiently.
As a leader, you meld organization and personal identities by hiring, training, and compensating employees whose personal identity melds with the identity of the organization or its subparts. People find a sense of meaning, even abundance, when they are in an organization where they fit and feel valued for doing exactly what they do well. Leaders who are thoughtful about bringing in people who fit both technically and culturally help people find an abundant work setting.
In other cases, leaders meld personal and organization identity by shaping an individual's personal strengths into organization capabilities. The U.S. military acknowledges that it may not entice a lot of valedictorians as raw recruits. But the military is renowned for taking ordinary people and making them extraordinarily effective. Consistent and focused training and communication can change identities and shape how individuals respond to their situation.
Socialization of employees may begin on the first day of the job. As a new Ph.D. student, Dave was encouraged to attend faculty colloquiums where visitors would present their research and ideas. These seminars were seldom passive. Colleagues would push, prod, and challenge the work of the visitors to test the rigor and integrity of their ideas. By modeling to new Ph.D. students the importance of challenging ideas in a collegial setting, his faculty advisers mentored him into the role of a scholar scientist. They also learned which students would savor these inevitable clashes of ideas and which would run away. In contrast, Wendy's program was designed to train her as a psychologist. It focused on the student's willingness to look honestly at her own inner life with self-awareness and insight as a preparation for helping clients do the same.
As a leader, you may socialize employees through formal orientation programs where employees learn what is expected of them, but also through informal mentoring and coaching about unwritten rules and expectations for things like how to dress, how to show respect for others, how to deal with conflict, and what protocols govern decision making.
Go to dinner at your neighbor's. What are their routines? Who sits where? How is food passed? Does anyone say grace? (If so, who?) How are people dressed? How is the table set? Who cooks? Serves the food? Sits where? Who does dishes? Something as simple as having dinner at a friend's house demonstrates the many ways that two groups can differ in how they function. Fitting into someone else's family or work team or industry is seldom straightforward. In organizations with layers of complexity in history, rules, hierarchy, and routines, the job of helping others fit is much more difficult than serving a meal. But, when employees match their personal identity with the organization's identity, they are more able to use their strengths and to find meaning through work.
### **4. Determine Customer and Investor Expectations**
How do leaders segment targeted customers and investors and determine their expectations?
_Customer (and investor) segmentation_ means that not all customers or investors are equal. Companies who try to be all things to all customers generally serve none of them well. Segmenting customers means figuring out who are the target customers, those individuals or companies who will be critical to your future success. Segmentation may occur by product features, channel, desired service, or other features. Old Navy captured the essence of their targeted customer by putting a name on their prototype customer (Jenny), then making sure that employees throughout the organization know who "Jenny" was, what she wanted, and how best to serve her. Sharing customer information or creating a pseudo-customer helps employees know why they are in business and who they have to serve.
Once target customers are identified, leaders need to determine their buying criteria. Customers may pick suppliers based on price, service, quality, features, distribution, or brand. When leaders have a clear customer value proposition, they are able to enlist employees to meet those needs.
The same logic applies to investors. Figuring out who the investors are and their criteria for investing (e.g., growth versus value) helps leaders shape an organization agenda that meets those requirements.
### **5. Connect Both Personal and Organizational Identities with the Needs of Customers and Investors**
How does a leader make sure that the fit between the individual and the organization also fits with customers and investors?
_Fit for service_ does not just mean that individuals work well within their organizations but that there is a match between the employee inside and the organization's stake-holders outside. In the management literature the mantra "build on your strengths" has gained quite a bit of attention. When leaders help individuals shape their identity, clarify the organization's capabilities, and match individual strengths with organization capabilities, employees build on their strengths. But fully leveraging those strengths requires using those strengths to strengthen or serve others.
The movie _The Bucket List_ reports the ancient Egyptian belief that the gatekeepers of heaven ask new arrivals two questions about their lives on earth: (1) Did you find joy in life? (2) Did your life bring joy to others? The first question is about building on your strengths—necessary but not sufficient. The second question shifts the focus of joy to helping others find it—building our strengths that strengthen others.
We can see the importance of turning personal strengths into value for others with a personal example. In college, Dave majored in English and developed a knack for reading novels. Even today, he can read two or three novels a week—what a strength! But few people care about his novel-reading strength. He can't make much of a living exercising this strength. His strength doesn't bring joy to anyone but himself. What others want from Dave is his ability to analyze a situation in ways that help them reach their goals (not his). Reading and interpreting good writing is a sustainable strength when it informs his ability to diagnose and help others work through their problems.
Great companies are not built on the great strengths of their leaders or employees but on how those strengths build value for their customers. To turn personal and organizational strengths into value for others:
**Step 1: Be Clear About What You Want Your Organization to Be Known for by Your Best Customers**. As stated earlier, an organization has an identity that becomes its firm brand, or reputation among customers. As a leader, you should make sure your top team and other employees have the same perception of what you want to be known for as an organization by your customers. A simple exercise is to have all members of your team write down three things they want your organization to be known for by its best customers in the future. Cluster these answers by themes and then see what percentage of the answers coalesce into the top three categories. Ideally at least 80 percent of the answers will fall into these top three clusters. For example, if there are 15 members of your team, you have 45 total answers. If 30 of these answers fall into the top three clusters of answers, you have a 67 percent shared identity. Repeat the exercise until you get close to 80 percent shared identity, which means your team has a shared view of what you want to be known for by your customers. In Table 3.1, we conclude from their brand identity and reputation that Apple wants to be known for innovation, British Petroleum for social responsibility, and Walmart for efficient production.
**Step 2: Check It Out with Key Customers**. Validate your identity or firm brand with key customers. Does the identity you claim cause customers to buy more from you? Apple's "innovative design" brand gets customers to pay a premium for the company's smart phones. Disney's "family entertainment" brings people long distances to experience Disney theme parks. Make sure that what you want to be known for is what your target customer cares about. A telecommunication company that pledged that customers would be able to hear a pin drop over their phone lines found that most customers didn't care much about pins dropping as long as their calls were not dropped.
**Step 3: Make Sure That Organization Practices Inside Match the Intended Brand or Identity**. When the identity you are known for by customers is reflected in practices inside your company, employees have a line of sight between their daily work and future customer value. We have found four actions that weave external identity into internal action.
First, leadership behaviors should be consistent with what the company as a whole is trying to communicate to customers. We call this _leadership brand_. Employees should be able to recognize in their leaders' actions the customer needs they are trying to meet. Leaders at Apple will act to encourage innovation and design, while leaders at Walmart will work to reduce costs and drive efficiency.
Second, craft top-down and across-the-aisle communication to share with everyone what you are trying to do. Repeat your desired identity over and over in speeches, workshops, and informal discussions, and capture it in symbols, slogans, logos, and advertisements. Never forget that behavior will communicate more convincingly than words and logos.
Third, encourage bottom-up problem solving where employees make the brand real to them. A wise leader once said, "I teach people correct principles and let them govern themselves." Leaders set direction top down but enlist action from the bottom up. This could mean involving employees in town hall meetings about problems, letting them act on challenges in real time, or building rapid-response teams. Make sure employees are clear about the principles that should guide their self-governance and problem-solving options. Such principles will emerge from the corporate identity you are trying to foster among your best customers.
Fourth, upgrade internal processes to institutionalize customer expectations. Processes may include how your organization turns customer insights into products, allocates money, pays people, or develops talent.
These steps are simple but not easy. They require leaders to identify the organization's key strengths (capabilities) and use them consciously to connect with targeted customers. But when this happens, individual employees see better how their work makes a difference for real people. There is a line of sight between what they do on Monday morning and who gets helped on Tuesday afternoon. Working from their strengths, they know they have enough skills and to spare to get the job done right. Connected with their values, they have a sense of contributing something they care about. Grounded in their character traits and virtues, they feel their own goodness in operation. This is abundance in action.
**_Summary: Leadership Actions to Build an Identity_**
Help employees become more aware of their signature strengths through assessment, conversation, observation, and assignment.
Define your organization's required strengths (or capabilities) by doing a capability audit.
Make sure that employees' strengths serve the organizational capabilities they are hired to build.
Define your key customers and investors and determine their expectations of you.
Connect the identity of the individuals and organizations to the customers they serve, building on strengths that strengthen others.
## **CHAPTER 4
Where Am I Going? (Purpose and Motivation)**
LEADERSHIP **PURPOSE** CHALLENGE
In a world of information overload and centrifugal goals, employees and organizations often spin away from their basic sense of purpose and direction. Great leaders recognize what motivates employees, match employee motivators to organization purposes, and help employees prioritize work that matters most.
Lost in Wonderland, Alice approaches the grinning Cheshire cat to ask directions. When the cat asks where she is trying to go, Alice isn't quite sure. The cat provocatively states the obvious: it doesn't matter which road Alice takes if she doesn't know where she wants to end up.
Clarity about where we want to go and why is crucial to a sense of meaning and abundance. Where are we headed? What do we live for? Why do we do what we do? In the last chapter we looked at what we want to be known for—the strengths and personal values that become our hallmark. In this chapter we look at how leaders identify the end results that help us know which way to turn and motivate us to keep traveling.
Of course, the destinations we refer to are not found on maps. They are about the visions that call to us, the laurel wreaths that appeal to us, the relationships that matter to us, and the ideas that enthrall us. They are about our values, our desires, and the needs of humanity at large. One person's motivating destination is Olympic gold, while another's is gold in the bank. One person envisions a renewable planet; another values most a shining friendship and another an enlightening idea. Ultimately the abundant life seems to call us to the impossible—traveling toward many such destinations at the same time.
In this chapter we will explore how leaders establish a sense of direction or purpose that contributes to meaning inherent in the abundant organization.
### **Places to Go: Four Categories of Purpose**
We propose four categories of destinations to help employees find meaning in good times or bad. These categories build on work by Frankl and others. (See Figure 4.1.) Leaders with a clear sense of these four categories are better prepared to establish a compelling vision with a clear line of sight between the work and the world that receives the work, set and accomplish goals that add value across multiple scorecards, and articulate ideas that preserve the learning of the past and imagine solutions for the future.
**FIGURE 4.1 Types of Individual Purposes or Motivation**
We will come back to these leadership agendas later; first let's examine the four categories they are built on in more detail.
Two dimensions characterize these categories: a low or high focus on accomplishment and a low or high focus on relationships with people. The resulting four categories are independent, so an individual can ultimately be low or high in each of the four categories independent of the others. Every category also embodies opportunities for either abundant, meaningful living or self-serving, unfulfilling existence. These four categories apply as much in Mumbai as they do in Paris or Sao Paolo. Let's flesh out these four categories.
#### **1. Insight**
On the bottom left is _insight_. This category represents low interest in either external accomplishment or relationships with other people, but potentially high interest in self-awareness, the life of the mind, the world of ideas, or personal experience for its own sake. We might think of a monk meditating quietly in a cave, a camper enjoying a mountain hike, or a thoughtful student examining inner motivations and feelings. At its best, insight promotes awareness, thoughtfulness, creativity, and deep appreciation for what is good in this moment. This person looks at a baby's first smile and thinks, "Look at that! I wonder what is going on in that little mind of his."
There are also low-abundance versions of insight. At a less abundant level we might imagine a hermit who has withdrawn into a highly personalized but redundant world, a depressed individual ruminating over his inadequacies, or a couch potato in front of a television set. Low-abundance employees may drift through the halls of the workplace with little sense of passion for their work, doing the minimum, staying under the radar, going through motions with little sense of self-efficacy or even desire.
The movie _A Beautiful Mind_ portrays a range of possibilities from this quadrant. In this film an extremely intelligent and creative professor develops groundbreaking mathematical formulas and theories but also wrestles with the demon of schizophrenia and must fight against delusions and paranoia. At his worst, this individual becomes lost in the idiosyncratic world of his illness. At his best he becomes a Nobel Prize winner whose passion for his theories and formulas sparks creativity and insight in others.
People motivated by insight might find deep meaning in the world of ideas, in creating theories about themselves or the world, or in being mindful, present, and aware of their moment-by-moment experience. They know instinctively that self-awareness is the ultimate virtue. In this category we remember that all we really have is the present moment and that in that precise moment even great suffering can be bearable. Those who value insight find beauty or wonder in small details, exciting connections, or hopeful realizations.
In an organizational setting, individuals highly motivated by insight may provide thoughtful reflection on problems or opportunities. They may be involved in research and development—the search for new and creative solutions to old problems. They may provide the symbols, models, and connective images that capture people's imaginations and communicate powerfully. They are often motivated by the inherent value of a good idea and appreciate time to think and reflect. They remind us to appreciate the moment, learn from the past, or imagine the future. When things go wrong, their first instinct may be to say "Let's stop and think so that we can learn." Socially responsible individuals acting out of this quadrant focus on the data that shows the misuse and decline of the earth's resources. They write articles, give talks, and suggest policies that reflect the importance of sustainability.
Organizations motivated primarily by insight may include religious, philosophical, educational, or research institutions; yoga studios, cruise lines, or recreational facilities; museums, theaters, or national parks. They include industries focused on leisure arts, self-awareness, education, and self-improvement.
Not every organization will find its primary mission in the world of ideas. But every organization needs the abundance that comes from insight.
As a leader, consider where in your organization insight comes from: Who are the proponents of organizational self-reflection, self-awareness, and self-improvement? Who has new ideas, makes new connections, or comes up with suggestions for new ways to do business? Who creates the symbols that will inspire and instruct? Who stops to relish the moment and reminds others to do the same? Who remembers to honor the past? Who can imagine the future? Is the role of insight understood, valued, and promoted?
#### **2. Achievement**
On the top left is _achievement_. In this category are individuals who find meaning and purpose in doing, accomplishing, or just checking things off the list for the day. This quadrant is about getting something done and may include activities that are highly competitive or that require risk taking, discipline, and resilience in the face of failure. High-abundance members of the achievement group might include an athlete in training, an artist perfecting a painting, or a corporate executive planning an aggressive growth strategy for the company. Someone motivated by achievement looks at a baby's first smile and thinks, "How amazing! I wonder if she is developmentally on target for smiling."
Not all high-accomplishment activities are abundant with meaning. When achievement is devoid of moral values or becomes an end in itself, it may be characterized by ruthlessness, even cruelty. The TV show "The Apprentice," in which individuals compete in various business settings, suggests a high focus on achievement that becomes self-serving and callous. In the show competitors blame others for failures, see extravagance as the ultimate reward, and fear the boss's condemning words, "You're fired." Such an approach assumes that there is not enough to go around and that one person can win only when someone else loses. The deficit-oriented culture of "The Apprentice" dominates many corporations today.
In contrast, _Chariots of Fire_ is a movie about British athletes in the 1924 Olympic games, all motivated to excel at their sports. One of the athletes is discouraged from competing by his sister because she sees no value in sports and believes his destiny is to be a Christian missionary in China. He responds, "I believe God made me for a purpose—for China. But He also made me fast. And when I run, I feel his pleasure." People motivated by achievement love to accomplish for the sake of accomplishment. Corporations in which achievement takes abundant forms are among the most successful and admired of companies.
People motivated by achievement might find meaning in simply getting things done and in winning. They generally enjoy improving and may strongly identify with their skills and accomplishments. Thus they like setting and meeting goals, getting feedback and having clear scorecards for measuring success, and being recognized for their accomplishments. They want measurable action plans that track results. In this category failure is an impetus for learning and there is always room to improve. These folks know instinctively that unless the organization provides real value and succeeds economically it simply won't survive.
In an organizational setting, individuals highly motivated by achievement are generally hardworking and internally motivated. They often provide energy and drive to get the job done. They may flourish in competitive environments but are not necessarily trying to best others as much as solve problems and improve their own performance. Whether they are the rough carpenters who love getting the framework in quickly or fine craftsmen who relish detail work and fine finishes, people motivated by achievement take satisfaction in wielding their craft in ways others will respect. When things go wrong, their first instinct may be to ask, "What can we learn? How can we improve?"
Organizations motivated by achievement may focus on technology, sports, or the arts, but they will not just be along for a pleasant ride. They will be at the cutting edge, pushing the envelope of skill or design. They include industries focused on scientific progress, high return on investment, competition, or excellence in any domain. They may especially value high returns or good marketing but will get the biggest charge out of being among the best at what they do. "Winning" is their mantra, goal, and passion, and they write about and savor their triumphs and successes.
Not every organization will care to compete at the highest level. But every organization can benefit from the abundance that comes from achievement.
In your organization, where does achievement occur? Who are the proponents of achievement who push for learning and want to get better and better? Is achievement fostered by tailoring challenging assignments, providing clear feedback on performance (preferably with ways to actually count success or improvement), and recognizing improvement and success?
#### **3. Connection**
On the bottom right is _connection_ , which is characterized by less focus on achievement and higher focus on relationships. People in this category find meaning in life through people they meet and interact with. Some will be energized by a few intimate relationships, others by looser ties with many people, but the common thread will be satisfaction and meaning through relating to others. This person looks at a baby's first smile and thinks, "Oh, he likes me! Now we have a relationship."
Again, there are low-abundance and high-abundance versions of this category. Lower-abundance versions might be people who are interpersonally needy or codependent or who like parties and social events but don't develop real relationships of mutual trust, understanding, or care. These workers hang around at the watercooler but may be more invested in gossip or being liked than in getting the job done.
A higher-abundance version of connection might be a devoted parent, a trusted friend, or a skilled networker. Connectors find deep meaning in sharing life with other people, and people are the priority that gives meaning to everything else in their lives. At its best, connection motivates peace making, compassion, cooperation, and teamwork and fosters skill in listening, empathy, honesty, and service. Socially responsible connectors form advocacy groups, lobby for change, and rally support for environmental activism.
In an organizational setting, individuals highly motivated by connection grease the skids to help people get along at work. They consider the impact decisions will have on real people. They tune in to the needs and feelings of customers. They may have good intuition for solving interpersonal problems or creating systems to coordinate efforts of diverse groups. Under dire conditions, they endure so they can be reunited with or help those they love. They know instinctively that people matter more than things, more than policies, more than money, more than anything.
Organizations motivated by connection may include service-oriented industries of all kinds, clubs and sports leagues, neighborhood or civic groups, the social arm of religious groups, and extended family structures. They include industries focused on helping people meet, mediating conflicts, supporting families, and socializing the rising generation. Within companies human resource departments are often charged with concern for connection needs.
Not every organization finds its primary mission in getting people together. But every organization benefits from the abundance that comes from connection.
In your organization, where does connection live? Who are the proponents of people-oriented policies and programs? Whether or not your organization is explicitly service oriented, who pays attention to the needs of people both inside the organization and as customers and stakeholders? Any organization that does not provide real value to real people is unlikely to endure over time.
#### **4. Empowerment**
On the top right is _empowerment_ , characterized by a high need for achievement that is channeled into high investment in people, especially in working to overcome human suffering. A high-abundance version of empowerment would be the TV show "Extreme Makeover: Home Edition," where skilled designers and craftsmen use their talents and skills to redesign and rebuild an unworkable house for a deserving but impoverished family. They tailor the new house to the needs and personalities of the family, involving the whole community and working against the clock to finish the house in a week. The needs, feelings, and desires of people are foremost in such scenarios, but so are the skills, learning, and accomplishments of those who try to help. Other examples might be a skilled teacher who loves developing students, a talented political leader who finds creative solutions to real-world problems, and a hardworking religious leader who loves using her skills to empower others. An individual motivated by empowerment sees a baby's first smile and thinks, "This is the hope of the future. Children will change the world."
A low-abundance version of empowerment might involve overpowering others and attempting to enforce one's will through intimidation or force. Even if real problems are being addressed, the focus would not be on empowering others but on self-aggrandizement or personal ambition. Low-abundance employees who are motivated by empowerment may be dominating or demanding, more interested in garnering power than in sharing it.
People motivated by the abundant version of empowerment might find deep meaning in social responsibility pursuits like finding a cure, reducing world hunger, or freeing political prisoners. They may also find great meaning in cleaning up a local park, serving food at a homeless shelter, or teaching a child to read. _Empowerment_ may motivate someone to run for political office, become a high school teacher, or take over the lead of a troubled company. But high-abundance empowerment is not about accruing power over others; rather it is about helping others find their own voice, options, and personal clout.
In an organizational setting, individuals highly motivated by empowerment often gravitate to management/leadership or coaching/teaching positions. They like to see others succeed and want to make a difference for good. They may be good mentors, may be motivated to produce products that address a pressing problem, or may lead in charitable campaigns and community service.
Organizations motivated by empowerment may include political parties, nongovernment organizations, penal institutions, news agencies, volunteer groups, charitable organizations, or educational institutions emphasizing training and job skills. They include industries focused on medical advances and services, underserved populations, food production and distribution, ecology, energy production, and family services. Empowerment reminds us that suffering is unavoidable but that we can choose our attitude and response to suffering. We can ignore it, blame others, or give up in despair . . . or respond to it from our deepest values of compassion and courage. Empowerment is a powerful antidote to the societal plagues of isolation, despair, and ennui.
Not every organization will find its primary mission in humanitarian service. But every organization can benefit from a value proposition grounded in empowerment.
In your organization, where does empowerment percolate? Who are the proponents of social responsibility? Who helps everyone understand how his or her work is connected to the greater good and the needs of real people? Is there a clear line of sight between today's work and the world's problems?
### **Self-Awareness for Leaders, Employees, and Organizations**
These four categories suggest four destinations that motivate people and bring meaning to life. As a leader, you can bring these motivating purposes into your organization at four levels.
First, know yourself. Know which of the four destinations or quadrants is motivating to you personally, be familiar with how these motivations may have changed over your lifetime, and look for ways to expand your repertoire to include elements of all the quadrants.
Second, know your employees. You can help employees in your part of the organization to identify the destinations or quadrants that are most motivating to them, helping them make sure the work they do ties into that motivation. Placing insight-driven employees into achievement positions or tasks will both frustrate the individual and limit the quality of work done.
Third, know your organization. You can help define for your part of the organization the motivations most relevant to your work. You can also articulate for others how each of the four quadrants contributes to bringing meaning, direction, and motivation to work.
Fourth, position your organization to have a socially responsible agenda. You can connect individual goals to broader societal goals through philanthropy and giving programs (be a company with a caring heart), through social activism (monitor and control use of carbon and other resources), and through work/life policies (offer employees control and flexibility for their work).
To identify what motivates you, your employees, and your organization, we highly recommend the following exercise (even if insight is not your strong suit):
**PART 1**
For 20 minutes, write whatever comes to mind describing what your life would look like five years from today if you had become your best self and all your dreams were realized.
For an additional 20 minutes, write whatever comes to mind describing what your organization (or division) would look like five years from today if it had become the best it could be and all your dreams for it were realized.
Repeat this exercise tomorrow to give your thoughts time to percolate.
If you have _any_ interest in trying this exercise, which we hope you will, please do not read further until you do at least one of these writing exercises. You will glean a lot more information from Part 2 below if you do Part 1 first.
Psychologist David McClelland analyzed writing samples for evidences of what motivates human beings. He found that the needs for achievement, connection, and power showed up repeatedly in what people wrote, providing the basis for his theories about human motivation. While we won't try to be that scientific here, take a moment to look at the scenarios you created in this exercise.
**PART 2**
Looking through what you wrote, put an _I_ for _insight_ in the margin for any words from your success scenario that refer to creativity, imagination, symbols, self-awareness, balance, thoughtfulness, thinking for thinking's sake, or having great ideas.
Put an _A_ for _achievement_ in the margin for any words that refer to setting or achieving goals, learning so as to improve, developing skills, exercising resilience to keep trying at a difficult task, or gaining recognition for accomplishments.
Put a _C_ for _connection_ in the margin for words referring to good relationships with others, spending time with people, meeting people or bringing people together, deepening relationships, feelings of mutual care and support, or being with people you love.
Put an _E_ for _empowerment_ in the margin for words referring to solving world problems, making a difference, mentoring or developing others, seeing people succeed, providing resources or services to others, or gaining recognition for social responsibility.
Count up how many of each letter you have. And yes, you can count double for items that have high value to you or that you elaborate on.
Once you have used the exercise to identify the destinations you find most motivating to pursue, you will know more about the compelling whys that support the hows of your life. You can then deepen, expand, and focus to increase your sense of purpose and direction. You can help employees do the same. Let's explore these ideas further from a personal and leadership perspective.
### **Find the High-Abundance Version of Your Quadrant**
As noted, each of these quadrants has low-abundance and high-abundance versions. The difference often is found in the moral values of the individual. Responding from our highest moral values tips the scales in favor of abundance. For example, think of a challenge you faced in the past that was extremely difficult for you—either at work, in your family, or in your personal life. As you think back on that challenge, what do you feel best about in terms of how you handled it? Are you most satisfied with how you kept your calm, showed honesty or authenticity, showed your sense of humor, forgave, learned from mistakes, or perhaps just kept going and didn't give up? If you had it to do over again, what would you do differently (in 10 words or less)? What personal values show up in your answers?
Now think about the most pressing challenges in your life right now. Consider finances, family, health, losses, business downturns, tough relationships, transitions, etc. Now think of yourself looking back on this challenge from the perspective of many years from now. As you look back, what would you want to feel good about in how you handled the current difficulty? What values are most important to you to maintain and live from? What do you care most about in terms of your personal integrity in this situation? These are the values that saturate the high-abundance versions of the four quadrants—values like integrity, gratitude, humility, kindness, discipline, and compassion.
Now think about the most pressing challenges you face as a leader at work. How can you apply your personal values to these leadership challenges, helping others apply their personal values to meeting these challenges? When people apply their personal values to pressing business challenges, both individuals and organizations are more apt to succeed.
### **Expand into Other Quadrants**
Even though we concentrate our efforts in one quadrant or another to start, great leaders must have at least moderate proficiency in all four quadrants to motivate all types of employees and respond to all types of challenges. A good place to expand is into the quadrant on the opposite corner from the one you prefer. For example, if you work primarily in the achievement quadrant, consider bringing into your life a balancing experience with investing more in connection, spending time with people regardless of their usefulness. Or if you love empowerment, consider adding a component of insight to give yourself time for rest, self-reflection, and fresh ideas.
One of us (guess who!) feels very comfortable in the insight quadrant and loves the world of self-exploration and reflection. But she has learned over the years that the comfortable world of ideas is hard to justify unless she moves across the chart to the opposite corner—the world of empowerment, where ideas become real in the lives of other people. Unless she is writing, speaking, serving, and listening to the real problems of real people, her grand ideas quickly become sterile and boring. Other people's challenges challenge her to think differently about her own and push her to not only build on her strengths but also use them to strengthen others.
To some extent movement from one quadrant to another is a developmental process. We may need to concentrate our desires in one quadrant for a time, but over a lifetime can shift energy into new desires.
The other one of us (guess again!) majors in the quadrant of achievement, with a strong minor in insight. He spent many of his early professional years exploring exciting ideas, writing books, and developing a reputation as a thought leader in human resources and leadership. He loves crossing things off the daily to-do list and feels energized by his internal scorecard for accomplishments for the day. But in more recent years he is discovering the abundance that comes in investing more in family, friends, and community. Professionally he has moved more into both executive coaching and consulting with governments and international companies, trying to make a difference for good in people's lives.
Few people start out with motivation in all four quadrants. To raise a family a person might concentrate on relationships for a time, putting achievement needs on hold. Another may invest heavily in achievement in the early stages of a career and then become more motivated by insight and the need for self-reflection later on. As we become aware of the limits of the quadrant we have been in, we may feel regret, even guilt, about not having balanced our lives better. But every life involves compromises and trade-offs, and few of us have the energy to support all four quadrants equally at the same time, especially early in life. Over a lifetime we can expand our repertoire of motivations and desires to include all four quadrants, even if we will always lean toward one or two.
It has been said that the abundant life begins when we give up all hope of ever having a better past. Many of us do not realize that clinging to the hope of a better past keeps us from finding meaning and purpose today. We covertly act as though if we are frustrated and unhappy enough about our regrets somehow life will take pity on us and undo them. Facing this false hope for what it is and willingly relinquishing it opens up the time frame in which real hope lies: the present.
In a similar way, a company cannot afford to be motivated indefinitely by one quadrant at the expense of the other three. Social responsibility initiatives for protecting the environment or serving the underprivileged (empowerment) must be informed by thoughtfulness and awareness of our limitations (insight). Human capital and employee initiatives (connection) must be tempered with the need for profitability, market penetration, and capital investments (achievement). Different divisions or employees may be charged with championing the whys associated with a particular quadrant but must remember that cooperation is needed to ensure that all the quadrants are accounted for in the organization's overall structure and direction. Many European organizations measure their success by financial, customer/employee, and societal results—the so-called triple bottom line, often called the 3-Ps of performance, people, and planet. Corporate balanced scorecards help leaders match employees' desired destination with their organization position.
### **Find the Right Fit**
Leaders need to help employees and organizations find a good fit between the purposes that motivate the individual and the purposes that motivate the business as a whole. The higher leaders are in the organization, the more broadly they need to think about the purposes or destinations the organization seeks and the more they need to "walk in four directions at once" while keeping a clear sense of their overall purpose.
Sylvia was a talented human resources manager with an Ivy League education and a passion for women's rights. She was hired in part because of her organization's commitment to equality. But when Sylvia's passion took over every aspect of her work to such an extent that she could talk of little else, her empowerment motivation ran amok, untempered by other business realities. While higher-ups valued her passion for equality, they also needed to attend to other purposes to keep the business profitable and contributing value for all of its constituents. Her single-focused why might have been a terrific fit in a government human rights agency, but it did not serve her (or others) well in her capacity as a business leader who needed to attend to all four quadrants.
While no organization will endure for long if it is not firmly grounded in empowerment agendas, ultimately the goal is to empower, serve, and create value for customers and stakeholders, not just to stroke the empowerment agendas of individual employees. Having said that, the more firmly grounded an organization is in the quadrant of empowerment—highly focused on both accomplishment and people—the more that organization can keep a clear line of sight between what it does well and the needs of customers.
### **A Leadership Agenda**
While leaders need to walk in four directions at the same time, it is important to learn how to manage priorities and results across the four quadrants. Herbert Simon, the Nobel prize-winning economist defined the principle of satisficing. Satisficing suggests that some quadrants, though worth doing, may not be worth excelling at. There are things that are worth doing but worth doing poorly. Those quadrants that define our identity and purpose require our maximum efforts and energy. Like Kobe Bryant's commitment to winning basketball games, these will be the essence of our game, the desires and strengths we rely and build on for success. Other quadrants we will satisfice, meeting basic criteria so these things won't interfere with other goals rather than looking for the very best way to approach them. Like Bryant's jump shots, we need to do these things moderately well but not superbly. In a world of limited resources of time, funds, and energy, it is crucial to know the primary motivations and purposes to which we will give our best effort and the secondary motivations and purposes that we will make do on. Then we to make peace with the compromises we all must make about where we spend limited energy.
Leaders can bring direction and purpose to their organizations and employees by asking:
**What are the insights we need to succeed as an organization?** Who spends time thinking and reflecting on these insights? Who has responsibility for new ideas, learning from the past, and reflecting on our current situation? How do we make room for pondering, reflection, learning, and creativity?
**What achievements and goals will keep us in business?** Who spends time clarifying those goals, working toward their accomplishment on a daily basis, and acknowledging and rewarding their accomplishment? How do we promote efficiency and clarity to help people do their work with commitment and competence?
**What types of relationships will help us get our work done?** Who spends time investing in people, listening to their ideas, building congenial teams, caring about the individual, and keeping people connected? How do we build skills of communication, compassion, respect, and cooperation?
**What human problems are we trying to solve?** Who spends time creating a clear line of sight between what we do and what our customers, stakeholders, and the world at large need? Who makes sure employees understand how the work they do makes a difference for real people? How do we communicate our empowerment agenda to all?
**Which are the most pressing motivations of this organization, and where do they fall among the four quadrants of insight, achievement, connection, and empowerment?** Which of the four quadrants will we excel at, and where will we satisfice?
It is easy to lose track of our primary motivations and where we are going in the rush of work, the complexity of the world, or the press of adversity. But when we start wondering what the point of all our labor is, remembering the whys that delineate our destinations helps us put up with the hows. In the words of Viktor Frankl:
_It did not really matter what we expected from life, but rather what life expected from us. We needed to stop asking about the meaning of life, and instead to think of ourselves as those who were being questioned by life—daily and hourly. Our answer must consist, not in talk and meditation, but in right action and in right conduct. Life ultimately means taking the responsibility to find the right answer to its problems and to fulfill the tasks which it constantly sets for each individual._
**_Summary: Leadership Actions to Articulate a Purpose_**
Help employees recognize what motivates them (insight, achievement, connection, empowerment).
Match the employees' motivation with the organization task they are assigned to perform.
Create an organization aspiration that declares a socially responsible agenda and translates that agenda to individual action.
Help employees satisfice in those tasks that are worth doing poorly and prioritize tasks that are important to do well.
## **CHAPTER 5
Whom Do I Travel With? (Relationships and Teams [Th]at Work)**
LEADERSHIP **RELATIONSHIP** CHALLENGE
Despite increasingly competitive and isolating work settings and declining interpersonal skills, much work has to be accomplished with others and within teams. Great leaders help employees build skills for professional friendships between people and among teams.
Ask 10 people what brings them joy, and chances are good at least half will refer to people they love. One of the saddest experiences of Wendy's career was talking to a client who was extremely distraught by the 9/11 phone calls that a man on one of the hijacked planes made to say good-bye to his wife. She too was upset by this image, wondering what it would feel like to receive such a call. But that wasn't what had upset him. "You don't get it," he said. "What is so hard for me is that if I had been on that plane, I would have no one to call." It is hard to imagine abundance or meaning in life without people to share it with. Friendship helps not only our leisure time teem with abundance but our work teams as well.
While much of the joy in daily life comes from sharing it with others, the challenges of getting along have not diminished with all of our technology for connecting. In fact, the anonymity of e-mails, Tweets, Web-based bulletin boards, and blogs often intensifies the challenge as it removes the personal touch so central to meaningful relationships. Globalization and equal hiring initiatives mean more and more of us work with people of different cultures, backgrounds, orientations, races, and life stages. Increasingly complex work necessitates coordinating efforts among people of diverse professional training to bring products to fruition or provide the range of services expected. Getting along with people who differ from us in either overt or subtle ways requires skill, patience, self-awareness, curiosity, and empathy. And getting along with others is catching. When one person is happy, others share the joy, and vice versa. Students with more depressed roommates become more depressed, and students with more optimistic teachers become more positive.
And yet we seem to have less and less opportunity to develop the very relational skills we need. Spending our days in front of screens and hooked into earphones reduces face-to-face contact and visual cues for reading one another, so we get less practice in real-time talking and listening. What we see on those screens increasingly involves gamesmanship, overt hostility, partisanship, backstabbing, and cutthroat competition, with few role models for healthy relating.
Fortunately, as we come to value the human element at work, some of the old rules about not fraternizing are starting to soften a bit. When research suggests that people with at least one really good friend at work are more apt to like their job and stick with it, friendship at work becomes an asset rather than a liability. Research by the Gallup Organization reveals that employees who have a best friend at work are _seven times_ more likely to be highly engaged at work than those who do not. Those with a close friend at work are almost _twice_ as likely to be satisfied with their pay, and that number stretches to _three_ times as likely for those in the _lowest_ -paying jobs. People with close friends at work are 27 percent more likely to see their strengths as aligned with the company's goals. These friendship claimers are also statistically more likely to satisfy customers, get more done in less time, have more fun on the job, have fewer accidents at work, innovate and share ideas more, and simply show up more consistently. Those with three or more close friends at work report even more increases in work and life satisfaction. While work friendships can create problems as well, the advantages of having strong friendships and good relationships at work seem to far outweigh the disadvantages.
Effective leaders play an important role in helping subordinates make friends, build strong teams, resolve conflicts, get along with customers, and build relationships of trust, support, and _abundance_ throughout the organization. Effective leaders also reap the benefits of personal engagement and satisfaction when they have close friends at work.
One plant manager who was worried about abysmal scores on employee engagement measures (along with high customer complaints, high absenteeism, a poor safety record, and low overall plant performance) decided she had little to lose by trying to foster friendship among her employees (who were all men, almost all over 40, and described as hard-nosed manufacturing line workers). She began talking about the importance of caring for each other, set up a social fund to give employees money for outings with coworkers and their families, kept communication open, and openly encouraged friendship among her employees. The attitude and feeling at work changed, people started having more fun at work, and the plant became simply a more pleasant place to be. These "soft" changes also translated into hard improvement in productivity and customer perceptions. A year later the employee engagement scores were up dramatically, as were productivity and plant safety. Customer complaints decreased 50 percent, and absenteeism dropped. These trends continued the following year.
Just as good parents let their kids work out their friendship squabbles on their own if they can, effective leaders get out of the way of other people's relationships. But effective leaders also provide opportunities for people to get together, and they model good listening and sincere apologies, demonstrate caring, and when necessary help mediate problems. Relationships are too important to our sense of abundance and meaningful life to ignore. When people come together to make ideas grow, ideas improve and the people find more meaning. What's more, research like that just cited suggests that good work relationships mean good business.
### **A Relationship Playbook**
What makes for good relationships at work? It is one thing to get along while we veg out in front of the TV with someone. It is quite another to get along while designing a new Web page, coordinating efforts to clean up an oil spill, or hammering out the details of a merger. What are the keys to getting along while getting things done?
Historically, folk wisdom, family role models, and religious teachings have been humanity's primary sources of information about what makes relationships survive and thrive. In recent years, researchers have made relationships a scientific agenda, complete with video cameras, statistical analyses, and brain imaging techniques to help us understand the nitty-gritty of how people interact. We've sampled that literature with a simple question in mind: What are the most important skills that grease the skids of human connection? We looked for fundamentals, but fundamentals with a punch—with proven results, solid research, and sensible theory to back them up. We wanted the essential skills that will allow someone to play the relationship game with a reasonable chance of success, both so relationships can thrive and so work can get accomplished.
We've grouped our findings into five learnable skill sets that seem to capture much of what it takes to promote genuine connection. As individuals develop these skills, leaders emulate them, teams adopt them, and organizations foster them, the magic fairy dust of human connection can increasingly sprinkle down on the practical world of work. These five skill sets are:
1. Make and respond to bids
2. Listen and self-disclose
3. Navigate proximity
4. Resolve conflict
5. Make amends
#### **Make and Respond to Bids**
Irene felt lucky to land a job right out of college, even if it meant a move to a new area. While Irene anticipated an adjustment period, she was unprepared for the cool reception she received at her new job. She enjoyed her clients, but the other employees seemed preoccupied and distant. The secretary smiled vacantly and showed her the copy machine but had little to say. Staff meetings consisted of the office manager reading off policy changes or calendar events while everyone listened in polite boredom. Irene resented being expected to spend many uncompensated hours each week completing paperwork as part of a new initiative, but when she raised the issue in the staff meeting, the supervisor gave everyone a lecture about budget cuts and how lucky they were to have jobs. Irene needed the money, but she began to wonder about the "lucky" part.
Whether we are new to a company or have worked there for 20 years, the process of finding supportive relationships, building good teams, or making "best friends" at work begins with making and receiving "bids." Relationship expert John Gottman defines a bid as a request for attention. A bid might be a smile or a touch, simply looking someone in the eye, saying hello, offering a compliment, sharing something personal, requesting help, or asking a question. In the world of relationships, nothing happens until someone makes a bid. At Irene's company the art of bidding had apparently been absorbed into the holes in the soundproofing tile: no one had much interest in anyone else at work.
Equally important in the bidding process is the response we get to our bids. If the other party does not respond by paying attention to our bid in a positive way, the game stops, like a ball that dies when a tennis serve is not returned. Unlike the tennis serve, the goal of a bid is not to defeat the opponent but to encourage a volley. In fact, even in established relationships people are not very apt to keep bidding if we don't hit the ball back. Gottman's research found that an overt bid that is not responded to is almost never repeated. This suggests that it is just as important that we respond to other people's bids as that we make bids.
Both making and responding to other people's bids are crucial when we are new or when others are new to our organization. But even when people are established, relationships founder when no one is bidding or when bids are ignored. Even with old friends or family, unrequited bids are unlikely to be repeated. This doesn't mean we have to accept every lunch invitation or agree to help everyone who asks, but our response to these bids needs to acknowledge the bidder and give positive attention even if we can't go along. "I'm swamped" does little to grease the skids of emotional connection but will leave the bidder feeling exposed and ignored, where "Darn, wish I could. Could we reconnect in three weeks when this project is further along?" might save the volley. Even "I'm almost always committed for lunch, but have you thought of asking Tom?" might successfully redirect the ball to a more suitable player while keeping the bidder in the game.
When we raise concerns or work issues, we are also bidding for a kind of attention. The staff meetings in the preceding example were littered with the rejected bids of staff members whose concerns or questions had been virtually ignored. These dropped bids cluttered the emotional court of the staff meetings, resulting in employees who felt little commitment to the workplace, little involvement with one another, and little confidence in management.
Arina, a supervisor in a large social service agency, noticed that even though many of the employees were friendly and connected, others seemed to operate on the sidelines. Many of the latter were talented individuals whose work benefited the agency, but Arina felt like they were not having a great experience at work and wondered how long they would stay once other opportunities opened up. She took time during a training meeting to discuss the concept of bids, gave a playful demonstration of making and receiving bids, and invited discussion about what happens when bids are ignored. She encouraged everyone to pay more attention to both making and responding to bids and made sure she modeled the changes she was hoping for. She continued to bring up the concept of bids often, asked the less connected employees about their experience with bidding and responding to others' bids, and deliberately set up time for people to connect informally. The atmosphere at the agency began to warm up, and at least some of the folks she had worried about losing started to make better connections at work.
Think about a bid for attention you have made today. What did you do? How did the other person receive your bid? Did he or she keep the volley going? Who made a bid for your attention today? Did you return the serve or let the ball bounce off the court while you looked something up on the Internet or rushed to meet a deadline? We have encouraged people to set a goal of having at least one meaningful encounter with a person each day. While this sounds easy, it often requires consciously making and receiving bids rather than falling back into personal isolation.
How would you rate the confidence people in your organization feel to make and respond to bids? Do you make a point as a leader to greet and engage people in conversation, respond attentively to their bids, and encourage others to do the same? Or are too many balls dropping out of play, making the workplace feel cool and flat? Do people at all levels understand the importance of simply making and responding to bids?
#### **Listen and Self-Disclose**
Once a relationship has been opened by a bid, two simple skills help deepen the connection: good listening and appropriate self-disclosure. These are the skills that allow close friendships to develop out of mere acquaintances. And close friendships not only lead to more engagement and satisfaction at work; they lead to a sense of meaning or abundance.
While we often think our best friends are people we have a lot in common with, research suggests that proximity is really the more important variable in who will become a close friend. Our friends are more likely to be the people who live next door than the people who live just a block away, more likely to be people in our office than one building over, more likely to be people we sit next to in a class than those across the room. Sure, among the 150 or so people we interact with regularly we will often choose to get closer to those who like the things we like or who see the world as we see it, but in almost any group of 150 we can find such people with a little effort.
In addition to good eye contact and an open posture, many good listeners take the time to restate what they are hearing to make sure they understand both the content and the feelings involved. "Wait a minute; let me make sure I understand. So you think . . . Am I understanding that right? What am I missing?" This simple three-part formula communicates real listening:
1. I'm hearing . . .
2. Is that right?
3. Is there anything else?
This formula comes in especially handy when feelings are strained or emotions run high, but it is also valuable in any kind of negotiation, including the negotiation of a new relationship.
Of course, even the best of listeners won't get anywhere unless someone else talks. Work doesn't always feel like a safe place to disclose the things that keep us awake at night or that are at the core of our innermost feelings. Nor do we especially care to hear the details of everyone else's colonos-copy, marital discord, or high school basketball career. But people don't get the benefit of having close friends at work unless they are willing to take some risk in letting people know a little more about them than what is on their résumé. And that means work has to be a reasonably safe place for people to be honest.
Leaders can help create that sense of safety by listening carefully to others and restating others' opinions and feelings, especially when conflict or tension exists. They can also model appropriate self-disclosure by sharing their values and experiences from time to time, either one on one or in public. But self-disclosure without self-awareness or without being interested in others as well can backfire. If one person reveals too much too fast or too often while the other only listens, the "friendship" will feel more like therapy or parenting than genuine two-way connection.
Self-disclosure requires real self-awareness so one person does not dominate conversations or throw work meetings off track with too many personal stories. Everyone wants to know what the leader thinks, but only to a point. A leader who hijacks meetings with personal opinions, stories, or dramas will soon be resented by those who have no choice but to listen. Friendship is based on reciprocity, with roughly equal amounts of talking and listening on both sides and with roughly equal levels of self-disclosure. One relationship expert recommends setting a goal of three genuine connections each day. What would happen to our experience of personal abundance if we made a point to really connect in an honest and meaningful way at least three times every day?
To what extent do people who work together in teams or in your organization respectfully listen to each other at both a factual and a feeling level? Do people feel heard? Are leaders especially careful to listen, not just pontificate? Is it safe to say what is really on one's mind? Such an atmosphere helps foster the good listening and appropriate self-disclosure that fosters deeper friendships as well as healthy work environments.
#### **Navigate Proximity**
So what happens to work while all this love is being passed around? Fortunately for our pocketbooks, human beings need more than symbiotic clinging to one another to be happy. We not only want connection—sometimes we also want to be left alone. Linguist Deborah Tannen reminds us, "There is comfort in being understood and pain in the impossibility of being understood completely. But there is also comfort in being different—special and unique—and pain in being the same as everyone else, just another cog in the wheel."
Relationships are always working at cross-purposes to some extent because people have conflicting needs for both involvement and individuality, time together and time apart. As our need for closeness is met, we begin to feel more keenly our need for solitude, for achievement, or for respite from the anxiety of relating. When we get too far into our own heads or work, we start to long for contact with others. But when we get too much of that good thing, we start to long for time apart. Tannen goes on to say, "It's a double bind because whatever we do to serve one need necessarily violates the other. . . . Because of this double bind, communication will never be perfect; we cannot reach stasis. We have no choice but to keep trying to balance independence and involvement, freedom and safety, the familiar and the strange—continually making adjustments as we list to one side or the other."
In navigating these competing needs, Tannen finds that women in conversation often emphasize how people are alike, while men more readily point out differences. When we don't play our expected gender role when talking with our own gender, we may create mistrust or confusion without anyone really knowing why. Likewise, when men and women talk together, they may wonder why they end up feeling at cross-purposes. Regardless of gender, our competing needs for solidarity and solitude, sameness and uniqueness are probably easier to balance if they are explicit to us and others.
Another aspect of closeness and distance is also important to consider in work relationships. To illustrate, ask yourself whom you would be most likely to turn to if you needed a creative solution to a problem—a close friend or a relative stranger. While we would probably feel more _comfortable_ turning to a close friend, research by Mark Granovetter suggests that we will probably get a more creative solution from the stranger. People we don't know as well are more likely to think of something we haven't thought of, to bring fresh perspectives and unusual information to bear on our problem.
For the introverts among us who see little value in "wasting time" networking or making small talk, this is a helpful insight. I may get more feel-good support from people I've known long and well, but I'm more likely to get unexpected approaches to old problems from people on the fringes of my comfort zone. These are folks who are less likely to already think like I do. Doris Kearns Goodwin determined that President Abraham Lincoln's political genius included his willingness to bring together a "team of rivals" to staff his cabinet—people who not only had _not_ supported his presidency and his viewpoints but who were his major competitors.
We don't need the complexity of trying to work with people who intensely dislike us to get the benefits of peripheral contacts, however. Jeff is a volunteer employment specialist in the church group we attend. Of the 100 or so families who attend our congregation, roughly 10 have lost jobs, another 10 need upgraded employment, and at least 10 more have seen real economic losses in their family businesses. Jeff decided to see if the members could help each other, so he opened his home on a Sunday evening meeting to everyone who wanted to come to share ideas for improving his or her work situation. The dozen people who showed up included a realtor who was thriving on foreclosures and wanted to help others, a colonel ready to retire and wondering what to do next, a small retail shop owner struggling against new competition, and a talented carpenter who couldn't get enough work after the housing market crashed. Jeff invited each person to share his or her situation and needs in just a couple of minutes and then invited brainstorming from the group for 10 to 15 minutes per person. By the end of two hours each of the six people who had come with a challenge had at least two or more solid ideas for new contacts, offers to help with a specific problem, or new directions to consider. A couple of people connected around an idea for a new business venture. Customers of the retail store gave its owner specific suggestions for improvement. The carpenter knew someone who was a great contact for the colonel, and the realtor gave the carpenter ideas for getting in on the foreclosure market. A random group of people with no obvious similarities in job interests were able to help everyone in the group in some way, and everyone came out grinning and energized.
This simple experiment reminds us of the value of investing in both close friends and broad social networks. Cross-functional teams, neighborhood groups, or random collections of those taking severance packages could well have answers for one another's problems that their closest friends and colleagues do not. As a psychologist Wendy has learned that she gets better ideas by attending conferences on the periphery of her interests than those she thinks will be most central to her work. She knows a lot about things she's really interested in, so it is harder to learn something new, whereas she gets tons of new ideas that she can apply in creative ways when she gets training from people who approach the world very differently.
Connecting us with others is one of the roles of "vital friends" at work, according to research by the Gallup Organization. We all need at least some friends who play the important role of connecting us with people we don't necessarily claim as best friends. Malcolm Gladwell's "tipping points" are fueled by such people, who always seem to know somebody who knows somebody who . . . As these folks share information and bring people together, trends are born, deals are made, and ideas are cross-germinated.
Are there ample opportunities for people in your organization to come together for support and ideas and also to work independently with sufficient privacy? Are you including on your teams people whose backgrounds and ideas differ? Where do people with divergent viewpoints come together to learn from one another? Who are the connectors, and are they valued and encouraged? What problems are people facing today that others from completely different backgrounds might shed light on if brought together to brainstorm?
#### **Resolve Conflict**
When one of our kids was about seven, we overheard her in conversation with a young friend who had come to play. They were squabbling about some now-forgotten offense, and the friend threatened to "tell." Our daughter, unmoved, replied, "It won't do any good. They'll just tell us to work it out ourselves." We didn't know whether to be happy or sad about our daughter's assessment. On the one hand, we hoped it meant she understood that people, even young people, could work out their problems and that we had confidence in her ability to do so. On the other hand, we wondered if our daughter felt a little _too_ alone with her relational challenges—if she thought we were unwilling to get involved and that she was on her own.
We rely on our rational thinking and empathy for others to resolve conflicts creatively and compassionately, but people vary greatly in their skill at these basic tasks. Our conflicts with one another are sparked by all kinds of differences in how we think, feel, and see the world. We have come to appreciate more and more how much people need help to learn to get along. The skills of resolving conflict and remaining cool under a perceived attack are complicated, but they can be learned.
Understanding some of the physiology of the human brain as we respond to conflict can help us have more empathy for ourselves and others in times of disagreement. First, it helps to know that special cells called _mirror neurons_ help us imagine, empathize with, and mimic the emotions of others. When we feel connected with people with good emotional and relational skills, our mirror neurons help our own skills improve. Just modeling how to be cool under fire and skilled at conflict management is an asset of good leadership.
Once a conflict surfaces and we decide we are under threat (and what we find threatening varies greatly from person to person), high-power hormones like cortisol and adrenaline (epinephrine) kick in. These hormones empower the body with quick self-defensive responses—a great boon when we need extra energy or faster response time against a genuine attacker. But the same hormones, especially if chronically elevated, have a disastrous effect on learning, problem-solving skill, and empathy for others. While a certain amount of pressure or expectation increases our learning, work performance, and problem-solving ability, once we get past this optimum level of demand our performance begins to decline. Adding more pressure will not help us do better; it will only undermine our performance more.
When people have been exposed to trauma, abuse, or neglect in their early years, their brains tend to become much more sensitive to threat, abandonment, shaming, or stress, pumping out the stress hormones more readily. Such individuals then respond more self-protectively or aggressively, and they take longer to calm down after a conflict. Under the best of conditions, however, the brain circuits that promote empathy and impulse control don't always mature until the early twenties or beyond. All of these variables affect our ability to soothe ourselves when we get upset, feel empathy for others, and think objectively in the midst of conflict.
Mirror neurons are especially sensitive to the moods and perspectives of people with power, making the emotions of leaders particularly contagious at work. Leaders who are shaming, critical, or grumpy may evoke a lot of action, but not necessarily a lot of learning and real productivity. In an experiment with simulated work teams, the mood of the leader impacted not only the moods of the team members but their productivity and cooperation as well. The grumpy bosses' teams also made poorer decisions and chose less effective strategies in their panic to please the grouchy boss. Fuming and moodiness from a leader may get more work done, but it will probably not be better work. What's more, people remember negative interactions with a boss far longer and with more emotion than they remember the positive ones, so it takes a lot of positive interactions to make up for one emotional zinger. In contrast, feeling a sense of security, trust, and connection at work makes it easier to take tough feedback, solve problems creatively, take smart risks, and work through obstacles without giving up.
It is amazing how often relationships stagnate or conflicts escalate simply because people do not feel heard and understood. If you doubt this, think about an important relationship in your life. Ask yourself what the other person doesn't really "get" about you. If this person were to really listen to your thoughts and feelings on this topic, restate both the content and the feelings until you agreed that he or she had it right and had not missed anything important, would you feel more willing to really try to listen to the other person's point of view as well? Chances are good that if someone is just not listening to us, we can help the situation by really listening to him or her first.
Leaders who practice participative management recognize that participation does not always produce consensus. When two employees disagree, a leader can invite each to restate the other's point of view until mutual understanding is reached. The leader may then make a decision and move forward.
Dave learned this in working with a senior executive who had laid out an agenda for his organization in correspondence to Dave. Dave thought the executive had missed a significant point and shared this with the executive. The executive expressed appreciation for the input but trusted his own instincts. At first Dave felt ignored, but then he realized that the executive had both listened to and understood Dave's perspective. He just did not agree, and the call was his to make. Dave gave his full support to the decision. Participative management does not mean that we get our way but that we have been respected and heard. An executive once said, "I am putting you on my team because you and I do not think alike. If we both think alike, one of us is not necessary . . . and it won't be me! But when we go public, we go with one voice."
Marriage researchers wired each partner up to equipment for monitoring physiological signs of stress or relaxation and then asked them to discuss a recent disagreement. In one common pattern, one partner begins to distance from the other, showing outward signs of disinterest and withdrawal as things heat up. The other partner gets frustrated and ups the ante, raising the volume, moving closer, determined to make the distancer come back and face the music. Observers can see that the pursuer looks anxious and frustrated, and the monitors confirm that blood pressure is rising and adrenaline is pumping. But the monitors also pick up something quite unexpected about the cool, disinterested distancer. That partner's physiological signs of stress (blood pressure, adrenaline response, activation of the part of the brain that responds to a threat), though unseen, are also extreme. While the two display their stress differently on the outside, both are being flooded by intense feelings of anxiety and stress. In fact, the apparent escape artist's stress levels are so high as to interfere with clear thinking and problem-solving skill. Being chased by the outwardly upset spouse only makes the problem worse.
Some of us have seen similar patterns at work, even if the outward display of emotion is more restrained there. Only when both individuals agree to come back to the problem at a later time when their physiology has calmed down are they likely to get very far with a resolution.
Spouses, bosses, and friends can go a long way to improve the emotional climate in a given setting by avoiding what John Gottman calls the "four deadly horsemen" of criticism, contempt, defensiveness, and stonewalling. These characteristics so powerfully undercut marriages that if they show up steadily in the first three minutes of a marital conversation, researchers can predict with 96 percent accuracy that the conversation will end badly. The long-term prediction for divorce or deep dissatisfaction with the marriage follows the same pattern. In contrast, whether at work or in marriage, if conflict is managed with humor, empathy for the other person, willingness to listen nondefensively, a focus on solving the problem rather than blaming, and attention to creating an environment of emotional safety and trust, long-term satisfaction with the relationship is very likely.
As a leader, how well do you create a positive emotional atmosphere at work? (See more ideas in Chapter 6.) How well do you bring to the surface differences and conflicts inherent in any team? Are you willing to ask how people would rate you (anonymously) on how consistently and skillfully you demonstrate empathetic listening, emotional trustworthiness, appropriate humor, and encouragement of others and on how consistently and skillfully you avoid criticism, contempt, defensiveness, and stonewalling? When conflict erupts, are you a resource for helping people calm down their physiology instead of escalating their stress? Do you encourage a focus on problems and solutions instead of blame?
#### **Make Amends**
A perfect leader or a perfect friend would always demonstrate accurate and total empathy. He or she would always understand, always connect, always help. This individual would be completely trustworthy, always responding to our needs out of a deep understanding of what drives us or hurts us. Around such a person workers would always feel known, understood, and liked. Their sense of personal safety would skyrocket, along with their learning, productivity, and creativity. This is in principle only, of course. In actuality, we learn to deal with stress, problems, and conflicts in part through experience with being misunderstood, frustrated, and left—in moderate and tolerable amounts.
Unfortunately we don't live in this perfect world. Fortunately, there is a Plan B for all of us less-than-perfect mortals: apologize.
Apologizing gets a bad rap with many people, who feel ashamed, weak, or foolish when they apologize. As a result, many people have grown up with little or no experience with a sincere apology. They have yet to learn how powerful an apology can be in making up for lapses in empathy and trustworthiness. Fortunately, apologizing is a skill that can be learned, and it is almost never too late for a sincere apology to begin its healing work.
Legal departments have been nervous about admitting guilt when things go wrong for fear of lawsuits if people get the smell of blood. But current evidence suggests that doctors who apologize sincerely for even fatal mistakes are actually _less_ likely to be sued, and politicians and companies are following suit. People will often see through self-serving or manipulative apologies, but many folks are deciding that apologizing is not just the economically smart thing—it is the right thing. It is still nice to know that people will not generally punish us for doing that right thing.
Of course, if apologies are not deemed sincere, they won't go far. Genuine empathy for the hurt feelings of the other person is the basis of sincerity. Once we are willing to tune in to that hurt, the steps of an effective apology are really pretty simple: (1) Say what you did wrong (if you don't know, or you don't think it was wrong, just go to the next step); (2) say what you understand the other person might be feeling and that you are genuinely sorry; (3) say what you will do to try to make it up to the person or what you will do differently the next time this type of problem comes up; and (4) ask if there is anything else you can do to make it right. After the apology, take upon yourself the onus of responsibility for helping the other person regain trust in you, especially if the problem was serious. These steps are generally effective at many levels, both personal and corporate, and generally go a long way in helping individuals, companies, even nations to let go and move on.
### **Abundant Relationships**
There you have it: five basic skill sets that grease the skids of friendship, positive relationships, and teamwork that will promote the attendant benefits of increased engagement, productivity, and meaning. As leaders model, promote, ask about, teach about, encourage, and make room for people to care about each other, not just increased productivity, increased productivity may actually follow. High-performing teams derive from high-relating individuals.
**_Summary: Leadership Actions to Foster Relationships and Teams [Th]at Work_**
Develop good friendships at work and encourage others to do so too.
Learn, teach, and model the skills of
Making and receiving bids
Listening and self-disclosing
Navigating proximity
Resolving conflicts
Making amends
Apply these skills to relationships between people and among teams.
## **CHAPTER 6
How Do I Build a Positive Work Environment? (Effective Work Culture or Setting)**
LEADERSHIP **POSITIVE WORK ENVIRONMENT** CHALLENGE
Organizations develop unconscious patterns of how work is done that, left unattended, may lead to cynicism, disorganization, redundancy, or lethargy. Great leaders recognize and establish positive work environments that inspire employees, meet customer expectations, and give investors confidence.
How long does it take to get a feel for the atmosphere in a work setting you walk into? Think of walking into a doctor's office, a store, a restaurant, a classroom, or a plant. Within minutes or at most hours you have a pretty good sense of what it feels like to work there. Companies track employee attitudes, productivity, and retention to put numbers behind these gut impressions, but leader and customer perceptions of a work environment are often spot on. What exactly is it we are picking up on? Does it have to do with the pictures on the walls? The looks on people's faces? The casual conversations in the halls?
We've learned from personal experience (ahem!) that long-term weight loss is less about any particular diet and more about changing our lifestyle, emotional patterns, and relationship with food. Likewise, a work unit's work environment consists of the lifestyle, emotional patterns, and relationships between the people and the work that goes on there. Sometimes leaders sponsor events to try to shape how work is done (a town hall meeting, training program, annual bonus, new logo, poster and cards with vision statements, etc.), but until events become patterns, the work environment remains unchanged. The work environment reflects the organization's consciously chosen identity, brand, or culture (Chapter 3) but also shows up in the less conscious and unwritten norms, expectations, and rules—the "muscle memory" of how people think and act at work.
Most of us have personally experienced both a negative and a positive work environment. A negative work environment comes with cynicism, frustration, and gossip. Employees spend more time backbiting, protecting turf, resisting, or blindly obeying than solving problems and helping the company add real value for customers. There is an assumption of deficiency and not enough to go around of all the things that matter: resources, respect, information, opportunity. People dread work and look for excuses to be away.
In contrast a positive work environment inspires, invigorates, and challenges. Employees have positive relationships with each other (Chapter 5) and savor the work itself (Chapter 7). They see work as adding to their quality of life and personal well-being, not detracting from it. There is a feeling of abundance—enough and to spare of what matters most in our lives: good relationships, meaningful work, learning and growth, and positive impact on the world. A positive work environment is one in which:
Employees are committed, productive, and likely to stay with the company
Customers pick up on employee attitudes and are more likely to do business with the company
Investors have confidence in the company's future, giving it a higher market value
The company's reputation in the community is enhanced
In this chapter, we lay out 10 attitudes that underlie an abundant work environment and what leaders can do to foster them. Table 6.1 at the end summarizes these 10 attitudes and highlights the cynical and abundant options for each. It also enables you to score your organization on each attitude.
#### **1. Attitude Toward Success: Arrogance Versus Humility**
Recently Dave was asked to speak to a combined group of business and religious leaders. They asked his view about the dramatic economic decline that gripped the world. Not being an economist or financial markets expert, he chose to talk about the impact of leadership on this decline. When governments came to the aid of financially stressed companies with a "bailout," the metaphor badly missed the real issue. As discussed in Chapter 1, we bail out a boat taking on water or people in jail. In either case, bailouts don't solve the underlying problem of the hole in the boat or the crime committed. If the holes are not fixed or people's lives are not put in order, bailouts accomplish little.
One hole in the boat that led to recession was a lack of effective leadership. We believe one of the important qualities of effective leadership is humility. As shown in Figure 6.1, when leaders act with a sense of humility, even in the midst of success, prosperity continues. But when leaders become arrogant, prosperity reverses and declines. In many cases the success of companies and countries causes leaders to respond with arrogance, taking credit for the prosperity, seeing themselves as invincible, or focusing more on enjoying the present windfall than learning for the future. This arrogance is the pride before the fall. Humble leaders continue to improve and respond to changing conditions. And humility becomes part of the culture of the firm—the work environment we can sense when we walk in the door of a company.
There is a liability of success, and it causes many successful companies to fail. There is a rapid turnover of firms in the U.S. Fortune 500 (almost 50 percent every 10 years). Twenty years after _In Search of Excellence_ was published, many of the 43 original firms had not lived up to the criteria that placed them in the "excellent" category. Researchers Ulrike Malmendier and Geoffrey Tate found that CEOs who received superstar status as evidenced by public CEO awards (from _BusinessWeek_ , _Financial World_ , _Chief Executive_ , _Forbes_ , _IndustryWeek_ , Morningstar.com, _Time_ , Time/CNN, and the like) actually performed 15 to 20 percent worse than comparable CEOs for the three years after winning their award, suggesting that if such awards promote arrogance they do their recipients and their employees a real disservice.
**FIGURE 6.1 Leadership Arrogance, Decline, Humility, and Prosperity**
The liability of success can be overcome as leaders avoid arrogance and complacency and remain learning focused and service oriented. (See Figure 6.1.) Humble leaders take the blame for mistakes and share credit for success. They talk less about personal accomplishments and more about others' achievements. They focus on giving rather than receiving service. They don't boast about what has been but focus on the challenges yet ahead. Jim Collins in _Good to Great_ notes the importance of leadership humility, labeling it a key factor in "Level 5 leadership." Humble leaders have also been called _servant leaders_ , who don't need to always get their way, who admit that others may be right, who express appreciation for insights, who seek to learn, and who help others do their job.
Humility helps create a positive work environment of learning, service, appreciation, and growth.
### **2. Attitude Toward Value and Values: Implicit Versus Explicit**
One of Yogi Berra's (an American athlete known for his witticisms) notorious restatements of the obvious was "If you don't know where you are going, you might wind up someplace else." Many terms have been used to articulate a direction: _strategy_ , _mission_ , _vision_ , _purpose_ , _goals, intent_ , and _aspiration_. Underlying these concepts is the importance of making both value and values explicit. _Value_ refers to the worth, importance, or significance placed on something by key stakeholders. _Values_ are ethical norms that guide behavior. A direction statement not only positions the organization with stakeholders in the future but also suggests the beliefs and moral behaviors that will guide action to fold the future into the present. Value is about what matters to others; values is about what matters to me. A positive work environment is shaped by leaders who intentionally and thoughtfully build both value and values.
Abundant leaders must create clear and explicit value propositions for several groups: employees, customers, investors, and communities. An employee value proposition clarifies what employees give to the organization and in turn what good employees get back in return. In a positive work environment, an employee knows what is expected and what he or she can expect for meeting (or not meeting) those expectations. Negative work environments persist when employees don't know for sure what they should do or understand what happens if they reach or miss goals.
A customer value proposition clarifies what the organization intends to offer customers and what customers can expect from the product or service they purchase. Customer value propositions make explicit whether the customer should expect excellent service, high quality, technological innovation, or low prices. A high-priced restaurant will receive more complaints than a low-priced restaurant because its patrons expect better service, ambience, and food and so are more readily disappointed.
An investor value proposition states why investors can expect the company to maintain market share, remain profitable, and increase stock price. Some investor value looks back at financial results; other investor value looks forward to confidence in the ability to deliver future results. A community value proposition ensures the reputation of the organization as a contributor to the common good and a participant in civic events.
In addition to making value propositions explicit, abundant leaders have clear values statements that refer not only to ideals but also to actions. Most companies have drafted some formal statement of their values, but fewer companies have turned those value statements into leadership behaviors, organization practices, and customer expectations. In abundant organizations leaders' actions are consistent with their espoused values, turning internal values into real value for customers. A number of companies we have worked with have taken their value statements to their key customers and asked three questions:
**1. Are these the values you would like us to have?** By inviting customers to comment on the values, leaders make sure they are creating an identity consistent with customer expectations. One company started with three key values: to be the most profitable in the industry, with great people, and great customer service. But customers didn't care if the company was the most profitable in the industry—in fact, more profit for the company meant less cash in the customer's pocket. They wanted reasonable profit so the company stayed in business but were more interested in innovative products and consistent quality.
**2. What do we have to do to live these values?** When customers help operationalize the behaviors associated with values, they become more real to everyone. Customers who operationalized _innovation_ as "bold new designs" have different expectations from those who think _innovation_ means "consistent improvement."
**3. If we live these values as you expect, will you buy more from us?** Values can lead to increased customer share because customers have more confidence in the firm's ability to serve them over time.
When leaders talk and act on their espoused values both inside and outside the company, employees and customers have more confidence in them. They have a sense of this being a company where there is integrity that can be trusted—enough and to spare.
### **3. Attitude Toward Service: Self-Interest Versus Selflessness**
In the classic prisoner's dilemma game, the following scenario occurs:
Two suspects are arrested by the police. The police have insufficient evidence for a conviction and, having separated both prisoners, visit each of them to offer the same deal. If one testifies against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a 5-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?
This dilemma can be summarized as:
Clearly, the best outcome for both parties is obtained if both remain silent. Each will serve six months but no more. But if one prisoner takes a chance on this option and the other does not, that individual will pay for his choice with 10 years of his life while his squeaky accomplice goes free. Acting selflessly is the best policy if everyone plays by this rule, but it is risky. If we don't trust others to act selflessly as well, we all pay a higher price. This is especially true if we play the game over and over, as companies do in real life. In that scenario people quickly learn whether trust and selflessness pay off or self-interest is the rule of the day.
We play many versions of the prisoner's dilemma in life . . . in divorce courts, political parties, neighborhood squabbles, and corporate mergers. Work-related examples of the prisoner's dilemma:
In compensation decisions about a fixed bonus pool, do leaders take a larger portion of the bonus or distribute it more widely?
In decision making, do leaders call the shots or include others in the process?
In allocating perks (parking space, travel funds, office space), do leaders send a message of self-interest or selflessness?
In assigning credit for successful projects, do leaders take or share credit?
When leaders consistently act out of self-interest, employees do the same. Over time, such leaders contribute to negative work environments for everyone. In contrast, leaders who emphasize other-service more than self-interest demonstrate a real commitment to treat people with fairness and respect. They help create work environments where people look out for and serve each other because people trust that the small sacrifices they make for the public good will be reciprocated, not taken advantage of. There is goodwill to spare.
### **4. Attitude Toward Ideas: Criticized Versus Invited**
A few years ago Dave helped facilitate a town hall meeting in which employees were charged by their business leader to generate solutions to some real business challenges. After employees winnowed their ideas into recommendations, they were to present these ideas to their business leader. These employees spent most of a day generating and filtering their top priorities for sparking and supporting more innovation. When the business leader came at the end of the day to hear their recommendations, the employees were excited to share. But when the spokeswoman for the group shared the group's first recommendation, the leader slammed the table and said, "Is that all you've got to show for a day of working on this? We've tried that, and it doesn't work. I hope you have something better than that!" Needless to say, the employees' enthusiasm turned to silence and the anticipated sharing of ideas quickly evaporated. Without intervention, the work environment in this unit would sour dramatically.
Colleagues have suggested that ideas are the new economic currency. The money of new ideas grows on the trees of imagination and is nurtured by encouragement, good listening, and respect, followed only later by careful, respectful pruning. Leaders who build positive work environments encourage the growth of good ideas by creating listening posts where employees share and discuss options. These listening posts may be a café-type conference area, an electronic blog, or a town hall meeting. Town hall meetings work well when leaders create a positive work environment by acknowledging employee creativity, expressing gratitude for their work, inviting open discussion of new ways to act, and making real-time decisions that demonstrate their willingness to try new things.
Being open to new ideas means that leaders ask questions and seek to learn. In contrast, one leader shared his experience with a corporate executive on a two-day tour of the local facility. During the two days the local leader asked countless questions about the executive's background, experience, and suggestions for improvement. The executive, intent on sharing his wisdom and making recommendations, never asked a single reciprocating question about the local leader's perceptions or experience. At dinner on the last evening the local team shared some of its local innovations and awards from the community for its successes with plant operations. The corporate leader was surprised to learn what the local leader had done but did not pursue trying to learn about these local innovations. At the end of the trip the executive returned to headquarters satisfied that he had shared what he knew. But the local innovations were not brought into the rest of the system, and the work environment of the local team was affected more negatively than positively by the visit.
Leaders who listen and learn create an environment where ideas can be surfaced, debated, and tried. One executive is known for the yellow legal pad that he carries everywhere, to note not problems but insights from conversations in which he is always inquisitive and trying to learn. Another leader followed the flow of her product into her customer's hands, starting in her customer's purchasing department and asking why purchasing had chosen her product over others and how they could improve . . . then going to the receiving dock to determine whether her product had been shipped to the customer in ways that made it easy to work with . . . then visiting the assembly area to see how her product fit into the customer's product . . . then following up with visits to sales, marketing, and service, each time learning how her product was accessed and used by the customer. When the leader returned to her organization, she met with each group of employees to share with them the customer's comments, compliments, and suggestions about their particular area. Each group of employees felt like the leader brought fresh ideas that connected them with their customers.
A positive work environment is supported by routines that foster openness to new ideas. Employees can voice opinions and even bad news without fear of others killing the messenger. Leaders ask more questions and become a clearinghouse for innovation. Ideas are valued and sought out.
### **5. Attitude Toward Connections: Impersonal Versus Personal**
A positive work environment is rooted in how people treat each other. In one fast-food company, local leaders had a three-step protocol for determining the friendliness of the franchise:
**1. Do our employees smile at customers?** Greeting customers, smiling at them, and making eye contact shows a commitment to friendliness.
**2. Do customers smile back?** When customers reciprocate and smile back, the friendliness is two-way and customers are probably enjoying that employee.
**3. Do customers smile at each other?** When customers engage with each other without going through the employees, they are fully enjoying the restaurant.
By analogy, employees may be seen as a leader's most important set of customers. Do leaders engage their employees in positive interactions? Do the employees engage back? Do the employees engage with one another? A positive work environment reflects all of these levels of engaged personal connection.
Ideas for creating a connected workforce are elaborated in Chapter 5. In addition, leaders build a positive work environment through caring connections by focusing on what is right more than what is wrong, expressing appreciation and gratitude, and creating ways to celebrate both people as individuals and the work unit as a whole.
Leaders can use what we call _gratitude enhancers_ to help connect employees. One leader created a language that employees could use to describe their day—a simple rating scale of 1 to 10—and he would often ask, "So how is your day going, 1 to 10?" or "Did you have a 10 day today?" Another leader encouraged people to remember others' birthdays and special events. Another wrote letters complimenting employees to their spouse, children, or parents. Another started most staff meetings with a "good news moment" where people could briefly share a personal or work-related highlight. A leader who graduated from Duke University sent "blue devil" stuffed animals (the Duke mascot) to employees who had done a good job. Another leader wrote notes on personalized stationery that expressed appreciation. Another provided funds for employees to go bowling together. Another invited employees to brainstorm ways they could support a teammate with cancer. Such ideas (and many others . . . see the excellent examples by Bob Nelson) help employees feel close not only to the leader but also to each other.
Obviously, leadership is not just about affirming but also about making corrections. However, we have a three-to-one rule of thumb. For every correcting comment we encourage leaders to make a bare minimum of three positive and affirming comments. This encourages everyone to focus more on what is right than on what is wrong, building a positive work environment.
The characteristics of a work environment come into high relief at times of crisis, which might include physical harm to an employee, product malfunctions, family illnesses, work-related threats, and other debilitating circumstances. At such times leaders in abundant organizations offer personal and organizational support and resources. Sanlam Investment Management is a South African investment firm. When one of its employees was tragically kidnapped and murdered, the business leader immediately reached out to her family. He also communicated to employees openly about the tragedy and offered them counseling and support. Posthumously, the deceased employee received public recognition and awards for her service, which had great meaning to her family. By recognizing and talking about the tragedy, the leader was able to help other employees pull together and cope with very difficult circumstances.
### **6. Attitude Toward Involvement: Hands-Off Versus Hands-On**
Belinda is a middle-school principal of students aged 12 to 14. A key symbol of her leadership is her tennis shoes. She spends much of her day wandering around the school. She greets students (mostly by name) when they disembark from their bus; she stands in the hallway talking to students between classes; she visits classrooms while teachers teach; she eats in the lunchroom; and she attends many after-school activities. Her tennis shoes symbolize her leadership on the run, spending time with students, teachers, and parents. Belinda's leadership priorities have resulted in lower teacher and staff turnover and higher student test scores over the course of her tenure. The atmosphere at her school has improved as teachers who are committed to education feel supported and encouraged. When Belinda's father passed away, many teachers and students attended the service to support her in turn.
While people do not appreciate a leader who microman-ages, a hands-on leader can make a powerful contribution to a positive work environment. Hands-on leaders are accessible, go to employees rather than requiring employees to come to them, and get on the floor where employees are on the job. They learn what employees are doing and become more sensitive to their needs. On a recent United flight, a well-dressed passenger helped the flight attendants serve throughout the flight. Dave learned that that passenger was one of the corporate officers. Whenever he flew, he felt it was his opportunity to support the in-flight crew. Word about such efforts spreads quickly and helps employees see that they are supported.
Leaders also create positive work environments by building enthusiasm for upcoming initiatives. When Belinda greets students and teachers during the day, she often reminds them of "coming attractions" at the school. The school dances that she sponsors have high attendance because the students have been looking forward to them for many weeks. We all need things to look forward to and dream about. As leaders point people toward future opportunities, they build positive energy.
Hands-on leaders can also learn a lot about the company's work environment by becoming its customers. One company asked its leaders to call in a complaint through the normal customer service channels without identifying themselves as executives. They found gaping holes in the quality of service and preparation—holes they could set about plugging with training and supervision. The overall work environment is more positive when people know they are providing good service.
### **7. Attitude Toward Accountability: Enfeebling Others Versus Empowering Others**
A new head of a U.S. sales operation presented his plan to the senior executive team. He was a bit embarrassed that he did not have a dramatic new program to increase sales in a tough market. What he proposed was "Management 101"—having each salesperson set clear goals for sales and make practical plans about which customers to meet with, what products to offer, and how to spend time to reach the goals. He prepared a simple one-page accountability form to use to follow up with each direct report each week. Nothing dramatic, no fancy program, not a lot of fanfare. But no one was surprised when after three months revenues began to increase. As employees began to realize that their new leader had clear, reasonable expectations and held them accountable for results, they came to trust that they could succeed.
Employees want leaders to lead, not just be peers or friends. Leading includes setting clear goals and expectations and then following up to make sure people are accountable for results. When employees participate in the expectations, they have more ownership for them. When leaders offer direct and clear feedback and help employees analyze their performance strengths and weaknesses, employees learn and move forward. When employees succeed, they have a better experience at work.
Dave was invited into a company that had gone through four new performance appraisal systems in four years, and he was asked to recommend new performance appraisal system number five. If four out of four systems do not work, it may not be the systems that are at fault but their implementation. He quickly discovered that leaders at this company were not holding people accountable for goals they set. When leaders shirk candid conversations about accountability, no system will work. We suggest three phrases that can help these conversations go better:
**1. "Help me understand."** These words put the leader in a coaching stance where the leader wants to learn, not boss. "Help me understand what went wrong" and "Help me understand what went right" both spur helpful discussions.
**2. ". . . the data."** Sharing with the employee the specific data that indicate problems or successes helps everyone get results focused (e.g., missed deadlines, low customer service scores, low quality scores, low revenues).
**3. ". . . so that we can solve the problem?"** gets the conversation focused on fixing the problem, not finding someone to blame. The focus is on _we_ , not you or me.
When employees consistently make mistakes they don't learn from, leaders need to move decisively to replace them. When Dave interviews leaders who have been through a transformation, he asks, "If you had to do it over again, what would you do differently?" Inevitably the answer is "I would move quicker. I knew early on that X did not have the skills or commitment we needed, but I stayed with X for too long, hoping he [or she] would adapt and change."
When leaders ensure accountability, a positive work environment follows because our best experiences at work generally occur when we know we got the job done and done well. Clear accountability coupled with support for learning from mistakes helps empower people to succeed.
### **8. Attitude Toward Communication: Reduced Versus Increased**
A common finding from employee attitude surveys is that communication rates low: employees often feel out of the loop about ideas leaders think are well understood. A positive work environment is fostered by communication that is redundant, two-way, and affectively charged.
Effective communication requires _redundancy_. When complex or new ideas are involved, it probably takes 10 units of communication for every unit of understanding. This means that leaders need to overcommunicate through multiple media. A senior leader Dave worked with crafted a detailed plan for her company. She then spent almost as much time figuring out how to share this plan as she had spent creating it: through formal webinars, teleconferences, blogs, town hall meetings, training programs, compensation programs, videos/DVDs, and staff meetings. In addition, she shared the plan informally as she talked to employees throughout her division. She invited employees to comment on the direction and to commit to the actions necessary to make it happen. At first employees were uncertain and skeptical about her agenda, but her consistent and redundant communication helped them understand the plan and see her commitment to making it work.
_Two-way_ communication helps employees both see where the company is headed and contribute to its success. They know they have the ear of those shaping that agenda, and they are empowered to help. For example, Sony regularly encourages employees to offer suggestions for improvement and seeks to implement over 90 percent of the ideas. Do workers in your company have the opportunity for this kind of impact? When employees have easy access to those who enact policies and procedures and their ideas are routinely implemented, they not only help the company succeed but know too that they are making a difference to that success.
_Affect_ implies that information has emotional appeal. One way information becomes memorable and impactful is for leaders to share personal feelings or stories about the information. The leader described earlier who shared her plan over and over also talked about how it would affect her and others and shared her feelings about the intent and benefits of the plan. She shared stories to help employees realize that her commitment was not passive and that the plan had real consequences in people's lives.
Communication that is redundant, two-way, and affectively rich helps shape a positive work environment in which people know they matter and are motivated to contribute to the whole.
### **9. Attitude Toward Conflict: Run and Hide Versus Run Into**
Wendy is affectionately known in our family as "conflict averse." She hates political talk shows, resists correcting employees, and hopes that if she ignores a conflict it will go away. It is always amazing to her when people confront a conflict openly and something good actually comes of it. While it is entirely possible to create conflict unnecessarily, when we run and hide from differences, conflict often festers.
Leaders build a positive work environment by facing and running into conflict rather than avoiding and hiding from it. This does not imply escalating conflict through blame, contention, or yelling. Quite the contrary. Running into conflict rather than away from it means respectfully airing multiple points of view, being transparent about problems, and moving quickly toward problem solving when things go wrong.
Conflict may require difficult decisions. A firm saw a 30 percent drop in revenues in a recession, which led to the need for cutbacks on staff, compensation, and training opportunities. Rather than hide from this difficult conversation, leaders in this company became very transparent. They went to employee groups and shared industry conditions, customer demand, and their company's financial woes. Leaders then asked employees to help them find ways to survive the downturn. Instead of resisting and posturing, employees were highly motivated to find creative ways to reduce costs. They minimized travel, gave back vacation days, managed supplies better, and implemented dozens of other cost-cutting ideas in an effort to save jobs. When this was not enough, employees also recognized that some job cuts were necessary for the company's survival, so morale was not overly compromised.
Conflict may also occur between individuals within a work team. Leaders who sense a conflict among employees need to teach and model skills for conflict resolution. It is easy to fall into shouting, blaming, and seeing only one side of an issue. Leaders manage conflict by inviting the parties into a dialogue where they seek to understand and verbalize the other's point of view until each can state the other person's position as well as the person presenting it. If clear understanding does not lead to compromise, leaders may need to make a decision, acknowledging that it may not equally please each side of the conflict. Win-win decision making requires understanding and buy-in, not agreement with all aspects of the resolution.
Setting the stage for organization-wide or individual conflict resolution means that leaders learn how to disagree without being disagreeable, accept tension without fostering contention, and allow differences while seeking common ground. When differences can be exposed and discussed, organizations have a more positive work environment because people feel safe disagreeing.
### **10. Attitude Toward Physical Space: Haphazard Versus Chosen**
Take a quick look at your physical surroundings at work. What do they communicate about your leadership style and your company's culture? A telling example of work space sending a message is the boardroom set of the television show "The Apprentice." In each episode, contestants for a high-powered apprenticeship perform work tasks and then gather in the boardroom to meet the boss. During the boardroom showdown one of the contestants is "fired." The boardroom is dark, with no visible windows, no personal effects on the walls or table, and colors that communicate wealth and status. The board table is rectangular, with the boss and his lieutenants on one side and the aspirants on the other. The boss sits in a larger chair than anyone in the room, and he enters through a private door next to his chair so he does not have to come close to the potential apprentices. All of these visual cues signal that the boardroom is serious and the boss is in charge, surrounded by symbols of power. The use of physical space sends messages about the nature of the work environment. Here the space communicates forcefully that the boss is a man to be feared, whose word is final . . . and who needs lots of external props to reinforce his ego.
A company's work space sends an implicit message to customers and employees alike about what matters. To dissect that message more explicitly, consider layout, worker safety, lighting, color, personalization, upkeep, and symbols.
Physical _layout_ can hinder or facilitate relationships, communication, efficiency, and innovation. Modular workstations let people quickly reconfigure space to meet changing requirements. What does it communicate when a company has mobile walls so that employees can organize space to form small task forces? Or when filing systems are portable to allow employees to transport materials from office to office?
Layout should include consideration of which units need to communicate or work together. If you want closer cooperation between sales and engineering, put their offices next to each other. If you want to boost creativity among your innovative spark plugs, move them near each other. The layout inside an office or plant also speaks volumes about expectations: a U-shaped table with an LCD projector in a conference room normalizes a one-way presentation to passive recipients, while a round table with flip charts and an overhead projector implies team problem solving, responsiveness, and influence based on mutual insight.
"No message" is also a message. Office layouts communicate management style and culture more clearly than any speech or culture change program. A top-floor corner office communicates a different leadership approach than a bottom-floor office near the main entrance. A leader who sits behind a desk that takes up almost half his office sends a very different message from another leader who had the desk removed entirely and works at a small table in a corner. The former meets visitors across an imposing barrier; the latter turns and interacts directly with guests.
_Worker safety_ also plays a part in managing physical space. Investing in seating and work surfaces that fit the individual worker may be more costly than one-size-fits-all office furniture but can pay for itself in workers' compensation alone (back pain leads to almost a quarter of workers' comp claims and a third of the dollars spent). A work environment that encourages employees to move around during the day rather than spend unbroken hours at their desks can make a difference in employee health. A work environment that emphasizes employee safety communicates clearly that employees are valued and their well-being is paramount.
_Lighting_ both creates a mood and allows people to function at work. Four types of lighting may be used in the office environment: (1) daylight from windows, skylights, and glass doors; (2) ambient light from ceiling- or furniture-mounted light sources; (3) task light from lamps focused on a particular area; and (4) accent or display lighting to add visual interest and define space. Natural lighting in office space helps people connect with the world outside the office and helps prevent or alleviate seasonal affective disorder, a type of depression.
_Color_ also sends messages. Some companies pick light colors for an open feeling; others equate social status with darker colors. Red, orange, and yellow tend to stimulate and excite. Pale greens, light yellows, and off-white are calming (think doctors' offices). Water colors seem to cool things down; fire colors seem to warm the space.
People like to _personalize_ their work space with favorite colors, pictures of loved ones, and mementos of hobbies or interests. Even in temporary "hotelling" offices where employees share space and furniture, some personal touches appear. Companies that ban personalization not only reduce employees' sense of ownership in their office space but risk reducing ownership in the company as a whole.
The _upkeep_ of the work setting also sends a message. Is the workplace clean, freshly painted, and safe? Are the gardens kept up? Are the windows clean? These tangible details of the workplace signal commitment to quality and to employee well-being.
_Symbols_ can also intentionally and sometimes unintentionally send powerful messages about a company. The first impression sticks: a traditional stone chalet in a forest communicates a different message from a modern glass office building downtown. The whole physical plant—architecture, location, landscaping, signage, maintenance—will be read as an indication of the company's values. Leaders with larger offices, customized wall hangings, plush carpets, rich paneling, and expensive artwork send powerful messages that fit the needs of hierarchical organizations very well. Retaining such physical accoutrements in a theoretically flat and agile organization sends the unintended message that influence is a function of position rather than a function of insight, information, and contribution.
Using these tools, leaders can thoughtfully use physical space to communicate their values nonverbally. Is the use of physical space contributing to a constraining, cold, and isolating message or to a positive, inclusive, and caring one?
### **Positive Work Environment in Action**
Creating a positive work environment is important in all types of organizations—large and small, private and public, domestic and global. Let's look at how organizations in different settings have used the 10 attitudes (plus principles discussed in other chapters) to ensure that affirming routines replace cynical ones and that positive patterns outlive any single event.
_Merck_ has articulated a commitment to a positive work environment with the following public statement:
_A positive working environment is essential to allow our employees to achieve their potential. It helps attract new employees to Merck and motivates them to stay. Components of our working environment include numerous opportunities for employee development and professional growth, competitive compensation and benefits, our focus on health and safety, and our approach to diversity and inclusion. 12_
Their leaders then leverage the above tools to signal these values and make this aspiration a reality.
_ConocoPhillips_ also has made a public commitment to its work environment:
_We are committed to providing a workplace free of harassment that values employees and respects their rights. Our code of business ethics and conduct, along with our equal employment opportunity policy, set consistent global standards for providing equal opportunities and fair treatment in recruiting, compensation, professional development, and advancement. Regional policies determine how these standards are implemented in compliance with local law. 13_
Conoco leaders make this commitment real by training supervisors to communicate openly with employees, resolve employee conflicts, and track employee attitudes. The impact of this training shows up in the work environment:
_The City of Brisbane_ (Australia) commits to providing employees "a positive and supportive working environment," fostered by valuing diversity of people who are hired, making decisions founded on a set of values, and paying enormous attention to workplace health and safety issues. The city has publicly committed to "zero harm" to anyone in the workplace or in public places and to the health and well-being of employees through wellness programs. It offers free gyms and fitness centers in major centers. It also claims "vibrant, open office spaces that offer exciting new environments."
_Health care_ research has shown that a nurse-friendly environment leads to improved measures of not only nurse retention but also patient care. The nurse-friendly environment includes safety, control, professional development, recognition, and accountability (dimensions we highlight in this chapter). When nurses experience these "friendly" practices, patient care improves, as do indicators of nursing satisfaction, commitment, and retention.
_The University of Bristol_ 's leadership team implemented a positive work environment initiative (PWE) in response to survey results from university employees. The PWE was built on five commitments to staff:
**Staff support and development.** This includes clearly articulated standards and expectations as well as opportunities for development of employees.
**Leadership and management.** This includes coaching leaders to engage employees and work closely with them.
**Communication.** This includes websites and other information sharing.
**Physical environment.** This includes paying attention to physical space.
**Monitoring and evaluation.** This includes regular reporting of progress on PWE efforts.
As a result of these initiatives, university staff commitment scores have gone up and the university was awarded the _London Times Higher Education Leadership and Management award_.
### **An Exercise**
Walk back into your work space. Take a look around. Notice the written and verbal messages, the faces of employees, the layout of the offices, the attitudes and priorities communicated, the symbols. Take the checklist from Table 6.1 with you to help you quantify your gut impressions. Ask employees and customers to do the same. Are the messages being communicated consistent with your company's chosen values and beliefs?
Work environments matter. The work environment outlasts any individual leader in shaping how employees and customers respond to the company. Positive work environments are fostered by leaders' investment in the 10 attitudes we have described.
**_Summary: Leadership Actions to Create a Positive Work Environment_**
Pay attention to the work environment as patterns of how things are done.
Regularly monitor the work environment using the diagnostic in Table 6.1.
Pick two or three of the items from your diagnosis and focus on them.
Ask newcomers to your work environment their impressions of what is positive and what is not.
Make public statements about your commitment to shaping a positive work environment.
**TABLE 6.1 Summary of Cynical Versus Abundant Attitudes and Routines**
## **CHAPTER 7
What Challenges Interest Me? (Personalized Contributions)**
LEADERSHIP **PERSONALIZED CONTRIBUTIONS** CHALLENGE
Too often employees feel emotionally disconnected from the work they do; their work may capture their talents and time, but not their heart and soul. Great leaders personalize work conditions so that employees know how their work contributes to outcomes that matter to them.
When their work is too easy, people get bored. When it is too difficult, they get anxious and give up. Somewhere in between, a moderate level of challenge and clear feedback help us stay engaged in our work, even lost in the trance of creativity and effective problem solving. This state of flow is associated with high energy, engagement, and a sense of doing something we love, thus finding meaning that leads to abundance. Beyond the _level_ of challenge, people want to work at the _type_ of challenge they care about and under the _conditions_ that make that challenge enjoyable. In previous chapters we discussed how identity, direction/purpose, and relationships increase the likelihood that we will find a type of work that brings us a sense of meaning. In this chapter we focus on the parameters of the work we do—the contexts and conditions that shape a specific job.
We describe in this chapter several ways of categorizing work that can help leaders home in on the type of work that works for specific employees. For example, Wendy sees herself as a healer (identity), and she finds abundance by identifying insights that help her clients change (purpose and direction). But how, where, and with whom she does her work also matter to Wendy. Does she work autonomously in a private practice or in a regulated health care system? Does she work with a narrow or broad range of clients (differentiated by age, marital status, or presenting problem)? Does she deepen expertise in a single therapeutic methodology, or does she work from a large range of counseling approaches? Does she value a consistent work schedule or want flexible hours? Such questions address the nature of her work and complement the abundance she finds from the work itself. The way she goes about doing her work has a big impact on how she feels about it.
Leaders personalize work for each employee by:
1. Understanding what outcomes matter to the employee
2. Creating a clear line of sight between what employees do and the outcomes they desire
3. Helping employees discover the intrinsic value of their work
4. Shaping work conditions and matching employees to conditions that appeal to them
Let's explore these four actions in more detail.
### **1. Understand What Outcomes Matter to the Employee**
Often we try to motivate people by showing them how their work produces outcomes we desire without figuring out the outcomes that matter to them. Think of a parent trying to motivate a teen to clean his room, something that teenagers generally see no inherent value in and that feels to them like pretty hard work.
**DAD:** Your room is a mess. Better clean it up.
**TEEN:** I don't have time. I have a paper due.
**DAD:** You'll feel better if your room is clean.
**TEEN:** No, I won't. I like it this way.
**DAD:** But how can you find anything in there?
**TEEN:** I know where everything is.
**DAD:** This is ridiculous—human beings just don't live this way.
**TEEN:** This human being lives this way and thinks it is just fine.
**DAD:** Don't your friends find this disgusting?
**TEEN:** No. My friends' rooms all look like this.
And so the conversation goes. The parent wants the room clean, couldn't find anything in the room if he wanted to (he doesn't), thinks human beings shouldn't live this way, and knows _his_ friends would find this room disgusting (and they are arriving tomorrow), so he assumes that these factors will motivate the teenager. But none of these things matter to the son. He is motivated by entirely different goals: avoid difficult work that adds no value to my life and get my paper done. Dad is trying to motivate the son to work toward outcomes that matter to Dad, but the son has other aims.
Employees are no different. The things about a job that matter to them may be entirely different from what matters to an employer or to another employee. If the leader (Dad) wants to impact the son's behavior, he needs to figure out what matters to the son and show him what behavior will lead to that outcome.
**DAD:** Your room is a mess. Better clean it up.
**TEEN:** I don't have time. I have a paper due.
**DAD:** That's important. When is it due?
**TEEN:** Tomorrow. I've been working on it, but I still have a lot to do.
**DAD:** How can I help?
**TEEN:** Well, could you proofread it for me when I'm done?
**DAD:** Sure. I'll proofread if you'll work on your room. You'll need a break from writing by that point anyway. Deal?
**TEEN:** Deal.
Other goals and interests that might motivate a teenager to clean his room: Son wants to join the Marines—Dad knows that the Marines expect a high level of personal neatness. Son wants to impress his girlfriend—Dad suspects that dirty underwear on the floor will not be a turn-on. Son wants the car—Dad can tie this privilege to room cleanliness.
Leaders who know the goals and outcomes that are important to their employees can help employees get what _they_ want, not just what the leader wants. Of course employees want to be paid and to keep their jobs, but what else do they want that is impacting their behavior? Leaders can find out:
What problems are most pressing for this employee (or group of employees)
How the behavior they need from this employee might help him or her solve those problems
What goals or desires this employee holds
How the behavior they need might help him or her reach those goals
A number of years ago, Dave had an M.B.A. student who met the rigorous criteria for being accepted into a top M.B.A. program. The student often came late to class, wasn't prepared, and did not do well on papers. Dave labeled this student unmotivated, uncommitted, and unlikely to set and meet goals. Then one day he learned that this student had spent the night camping out in the cold to get early tickets to the school's football game, painted his body in school colors, and led cheers throughout the game. This individual was highly motivated and committed; it just took the right social setting to activate the "engagement gene." When Dave worked to help the student better identify with the social aspects of learning (working in teams, doing presentations, being involved in class discussions), the student became more engaged. Individuals have different ways of contributing to work. Employees may be competent (this student had high admission scores) and committed (this student chose to attend the rigorous M.B.A. program) but still need ways to contribute that work for them (this student had more passion about the social than intellectual elements of the degree).
### **2. Create a Clear Line of Sight Between Actions and Outcomes**
When there is a clear line of sight between what we do and what we value, we find work more meaningful. When living in Michigan a number of years ago, Dave and his dad decided to attend a public broadcast of a championship boxing match from Las Vegas. One of the fighters was from Michigan and a hometown favorite. The rowdy fans watching the broadcast were loudly supportive of his efforts. At about the third round, Dave leaned over to his dad and said, "I don't think he can hear us in Vegas!" All of the fans' yelling was having no impact on the outcome of this fight. This obvious conclusion dampened the enthusiasm Dave and his dad felt. Without a line of sight between their yelling in Michigan and their favored boxer's ability to perform in Vegas, their interest eroded. The hometown advantage of crowd support dissipates when the crowd cannot be heard.
In a training program, a leader did a presentation to employees on the company's stock price over the last decade. He charted stock price against earnings, competitors, capital structure, strategic initiatives, and market conditions. Participants were convinced that a higher stock price was in their best interests—they knew a higher stock price meant more money and job security for them—and they were highly motivated to make the stock price go up. But when they were asked how they could impact the stock price with their actions over the next 90 days, they were mostly stymied. Their interest and desire for higher stock prices remained high, but when they could not plainly connect their daily actions to the longer-term goal, they were like the Michigan fans at the Las Vegas boxing match: the stock exchange could not "hear" them from New York. They would look at the daily stock price, hoping that it had gone up but having little sense of influence. Not exactly a recipe for feeling that one has enough and to spare of what it takes to make a difference.
Leaders create a line of sight by crafting "if . . . then . . . " logic:
If my team identifies targeted customers key to our future success, then we can build better customer relationships.
If we create better customer relationships, we will be better able to predict and meet those customers' needs.
If we better meet customer needs, our revenue from those customers will increase our profitability.
If we are more profitable, our market share will increase.
If we gain market share, we will have more predictable and stable growth in earnings.
If we have sustainable earnings, we will gain a better reputation from investors and our stock price will increase.
If stock prices go up, the price of my stock options will increase, my salary will go up, or I will be more likely to keep my job.
These if/then statements help employees understand how their actions today lead to being "heard in Vegas." Employees who see how their actions today impact who wins tomorrow are motivated to keep yelling.
### **3. Help Employees Find the Intrinsic Value of Their Work**
When leaders build a line of sight between action and outcome, employees are motivated because they want those outcomes. When work has intrinsic value, employees do the work not only because of the outcomes of the work but also because they value and enjoy the work itself. To help employees discover the work challenges they value most, regardless of outcomes, leaders can pose these questions:
If you were guaranteed success, what work would you do?
What do you love doing so much you'd pay to get to do it?
What do you do that makes you feel most alive?
When the plant manager can see how her work helps her get to her desired purpose/destination of _achievement_ and _impact_ and enacts her identity as an arranger and maximizer, her work has value in itself apart from how many reports she completes, how much she is paid, or what hassles she confronts. Leaders who tune in to what employees want and love help them discover the intrinsic value of the work itself.
Some athletes play a game only to win; others learn to enjoy how the game is played. Athletes who play only to win may not continue to play unless success is guaranteed, but those who savor the game itself enjoy mastering techniques or team camaraderie even if no one keeps score. On the other hand, some athletes care so much about the game that they are afraid to try for fear of failing. They are highly motivated by the game, but also highly motivated to avoid the anxiety of not doing well. Great leaders help people both find what they love and manage the anxiety associated with growth and potential failure.
Work that is intrinsically motivating will generally be relatively easy, energizing, and enjoyable for that individual.
##### **Easy**
_Easy_ does not mean without effort, but rather consistent with the employee's abilities and interests. As we mentioned earlier, Dave learned early on that his desires to be a professional basketball player were not matched by his abilities. No matter how hard he worked out, practiced shooting, or did basketball drills, he did not have the natural ability to become a professional basketball player. For him to play pro ball would be like running up a sand dune: the effort to get to the top of the hill would simply be too great. Leaders who have honest dialogues with employees about what work falls within the employee's zone of opportunity help the employee avoid sand dunes.
On the other hand, Dave had some natural talent as a teacher, and teaching came more easily to him than to others. Still, he spent (and still spends) hours observing, thinking about, and experimenting with how to better present materials when he teaches. Dave may be a "natural" at teaching, but this natural ability is supported by enormous effort. He still has to expend great effort to get to the top of his teaching game, but this is a mountain he can reasonably expect to climb.
##### **Energizing**
Intrinsically motivating work will generally be energizing. What energizes one employee may vary (insight versus accomplishment versus connection versus empowerment), but there is a high payoff for leaders who find out what gives an employee passion for the job: Is this salesman energized by making a difficult sell or raking in low-hanging fruit? Does this medical researcher care more about curing diabetes or chronic pain? Does this computer programmer get excited about really complex technical problems or really useful applications? In any work setting, individuals who find their work energizing are more engaged and more likely to be productive. Tests of work passion include the extent to which an employee wakes up excited about coming to work rather than dreading work, the extent to which an employee talks about work with a sense of possibilities rather than limitations, and the extent to which an employee gives discretionary energy to the task at hand.
##### **Enjoyable**
Intrinsically motivating work is enjoyable. _Enjoyable_ does not mean liking all of the work all of the time. Every job has aspects that become routine, tiring, or draining. But big chunks of the work will be inherently satisfying. Dave likes to create words and images to make complex ideas simple and memorable. One day he was listening to a group of about 10 senior HR executives talk about their challenges. Dave noticed that many of the executives described their work using frameworks and vocabulary Dave and his colleagues had developed. He had a private moment of enjoyment in seeing his ideas have impact, even though no one attributed them to him or knew where they came from.
When leaders help channel employees into work that is easy, energizing, and enjoyable for them, their sense of abundance increases.
### **4. Shaping Work Conditions to Offer Abundance to Each Employee**
Wendy likes one-on-one meetings with ongoing clients; Dave finds abundance in working as a presenter with large groups of strangers. Much of Wendy's work has occurred in a small office; Dave's requires extensive travel and large venues. Wendy's work requires deep connections with a few people; Dave's requires looser connections with many. Both Dave and Wendy are motivated by the purposes of _insight_ and _impact,_ but their preferred work parameters vary considerably. Leaders build abundance when they help each employee discover and actualize the work conditions that matter most to them. These specific work conditions vary along four parameters:
What type of work am I doing?
Where do I work?
How do I work?
When do I work?
People will answer these questions differently. A friend (Kathleen) wants to work as a toll booth operator. She imagines a job without stress that at the end of the day she can leave to pursue what really matters to her. Her skills of discipline, integrity, and comfort with routine make the toll booth her ideal job. Another friend (Leslie) graduated from a top university program. She enjoyed writing and found a seemingly ideal job at a top publishing house. But the job entailed less creative writing and more editing on a deadline. She wanted to create new ideas, not edit others' work. She was competent and hardworking, but the work did not give her much sense of meaning. She soon left. Kathleen and Leslie have very different orientations toward work and would each hate the other's ideal job. One prefers more routine and structured tasks, the other more creativity and flexibility. Each finds more abundance at work when her leaders recognize and respond to her individual preferences in four key areas—what, where, how, and when.
##### **Work Condition 1: What Work Do I Prefer Doing?**
Work can be categorized along three dimensions: intellectual, physical, and relational.
_Intellectual_ work focuses on making knowledge productive. Knowledge workers analyze problems, discover alternatives, shape thinking, and create innovative solutions. Words and ideas become the basic elements of work that can be shaped and molded to change how people think and act. Employees who like intellectual work enjoy debates about how to shape problems and discover interesting solutions. Leslie enjoyed the pursuit of ideas, and demonstrating good use of words and insights would differentiate her as a high-performing employee in such fields. Leaders may discover their employees' predisposition to intellectual work by probing how they think about complex problems, assigning them to present verbal or written recommendations, or engaging them in a dialogue about how to assess and improve work processes. Intellectual work results in intangible outcomes that may not always be seen or measured easily.
_Physical_ work emphasizes tangible results that are visible and traceable. Physical work emphasizes concrete, touchable results. Physical work might include figuring out what materials to use in a design, making mock-ups, and seeing products through the manufacturing and sales process. It might include on-site visits to observe how work is done. Kathleen leans toward tangible work in the toll booth, where she receives money and makes change. Employees who enjoy physical work take pride in design and production and turning ideas into actions.
_Relational_ work emphasizes connecting with others and getting work done through others. Relational work includes helping others reflect or learn, organizing people to accomplish a task, or just bringing people together. The M.B.A. student stood out in the social setting of the football game and could bring this interest in people into his work in class. Those predisposed to relational work may like working in teams, sharing ideas with others, and creating social networks. They are connectors and brokers who engage and involve others. Leaders who recognize this social gene may help social employees become guardians of social networks and good work relationships.
While few positions are exclusively intellectual, physical, or relational, a leader may use the survey in Table 7.1 as a self-assessment to determine his or her preferred type of work or as a way to talk with employees to determine their preferred work type.
##### **Work Condition 2: Where Do I Work?**
Work occurs in many places. Traditionally, employees are "at work" when they are in the office or on the job. Sometimes employees signal their commitment by being first in or last out of the office. In a clever "Seinfeld" episode, George (the vagabond friend) had his car break down in the company parking lot. When people showed up early, his car was already there, symbolizing to them that he must be a diligent worker. When the manager left late at night, George's car was still in the parking lot, which reinforced his hard-worker image. George told Jerry (his friend), "I don't even need to go to work! Everyone thinks I'm there because my car is!" Clearly there are more ways to be "at work" than to be parked in the employee lot. We suggest three sets of options that may (or for some employees may not) affect feelings of abundance at work: remote location versus office, inside versus outside, and domestic versus international.
**TABLE 7.1 Assessment of Types of Work**
**Remote Location Versus Office**. Some people like the formal transition from and to work, and going to an office or job site helps create boundaries between work and personal lives. But with technology, many tasks can now be done in remote locations. The boundaries of work are less about physically showing up at the office and more about delivering the desired outcomes.
A senior IBM official shared with us that at any point in time, 40 percent of IBM employees are working at customer sites, in hotels, at home, or at conferences, rather than in an IBM office. JetBlue reservationists generally work from home, where they don't have to commute or dress up to handle customer calls. Best Buy gets increased productivity and engagement when employees are free to focus on sales results, not hours in the store. These strategies work well if leaders rigorously hold employees accountable for outcomes, quality, and timeliness. George cannot leave his car in the parking lot as a surrogate for commitment if the focus is on work outcomes, not hours worked. Leaders also need to consider the social elements of work, which may be neglected without face time on the job. Independent employees may become socially isolated and miss the subtle connections that make work meaningful over time.
**Inside Versus Outside**. The physical work environment is crucial to some people. Our contractor friend would dread work if he had to come in in a suit and tie and spend all day indoors. He thrives on working outside, moving from one project to the next, and in a casual atmosphere. We have other friends who enjoy the security and stability of their office space, perhaps using light, color, and other design elements to creatively shape the work setting.
A variant of this bias are those who travel extensively instead of working in a single location. Those who would prefer the stability of an office might find travel hassles daunting and draining; those who relish fresh challenges would find office politics demoralizing and destructive. Leaders need to help employees recognize the requirements of work and the extent to which employees and employers are able and willing to adapt to those requirements.
**Domestic Versus International**. Some like the comfort of a familiar culture, language, and home country. Others like the stimulation of international assignments. In a global marketplace, more people will be given opportunities to work across boundaries. Some people are energized by the challenge to adapt to new geographic contexts. Travel is a price they willingly pay to do work they enjoy. Others find travel isolating, demanding, and draining. Some homebodies can come to enjoy an international opportunity with adequate support, training, connections, and incentives.
Leaders who are aware of all these variants are less likely to impose their work style on their employees. Leaders who like to come to the office, spend time in meetings, or take global assignments will have employees who do not. When the leader adapts to the employees' preferred work setting, the chances for abundance increase. Of course, every job has certain parameters, and these are not always flexible. Periodically people tell Dave they would love his consulting job but would want to do it without all the travel. A consultant who doesn't travel is like a doctor who doesn't see patients. But the parameters of work are not always as fixed as they appear: not many doctors make house calls these days, but this used to be expected.
##### **Work Condition 3: How Do I Work?**
It is difficult if not impossible to synthesize volumes of theory and research on the nature of work into a few key principles, but let's try. We see four dimensions of how work is done that may help leaders create more abundance for their employees: innovation, autonomy, opportunity, and visibility.
**Innovation**. Work may vary along a continuum of routine (similar work repeated over and over) to creative (doing a variety of work tasks that require innovation). Some jobs lend themselves to one extreme or the other. For example, air traffic controllers need more discipline than creativity (no one really cares if an air traffic controller can land a plane looking in a mirror between his legs). On the other hand, creative writers or product designers would not last long if unable to define and pursue blue sky opportunities. While some individuals are predisposed to and interested only in either creative or routine jobs, most are in between. Good leaders both tap employees' creative energies and help them settle in comfortably to more routine aspects of work.
For example, when Helen came in from the outside as a principal of a middle school, she discovered that many of the teachers had fallen into routines that were not really conducive to learning. They may have started teaching with high levels of creativity and innovation, but over time their teaching had become rote. To encourage innovation, she moved every teacher's classroom assignment over the summer. Some teachers who had been in the same classroom for many years resisted, but Helen used this symbolic change to signal new beginnings and encourage innovation. Even people on assembly lines endure the rigors of routine better if they can talk to friends, listen to music, control the pace of the line, or approach their work with humor.
**Autonomy**. Work may vary depending on how much control an employee has over the work done. A friend worked part time at a men's clothing store. He soon became bored with the job—who could get meaning out of selling clothes? However, the store owner was continually challenged and engaged with the work and found it stimulating and exciting. The salesperson saw his job as primarily taking orders from customers. The owner worked to figure out what clothing and styles sold the most, to create advertisements and marketing to solicit new customers, and to manage inventory to make money. The self-employed often work longer hours and have more demanding and stressful jobs than their employees, but they find more meaning in their work because they have control. Employees can sometimes feel the same sense of ownership if they participate in an aspect of the work that they can control and benefit from, if they see the complete job versus one element of it, or if they have a say in key elements of their work experience.
At the other extreme, one executive team (which will remain unnamed) told us they as executives had vast experience within their industry that enabled them to solve problems better than anyone else in their firm. They isolated themselves to define what should be done and how to do it and then shared their wisdom with their employees. Describing this highly centralized governance process, an executive quipped, "We sort of believe in 'designed by genius, implemented by idiots.'" It is not a shock that their organization had higher employee turnover, lower morale, and less productivity than competitors.
When employees participate in defining and solving problems, they are more committed to their decisions. We refer to shared decision making as the fingerprint test. A leader wants a lot of employee fingerprints on a project or initiative so that employees are a part of the governance process and multiple perspectives and types of expertise are included in solutions.
**Opportunity**. Work varies according to how much the employee can grow from the work. While some employees prefer steady jobs with little change, most want the chance for growth and challenge. The more common opportunity choice is the extent to which an employee wants to either broaden or deepen skills. Some employees would like to become deep specialists who have extensive expertise in a particular area. Other employees like the chance to learn a little about many types of work. To determine how employees define opportunity, Beverly Kaye suggests leaders have a "stay" interview with employees where they ask, "What would it take to keep you both on the job and passionate about the job?"
A senior manager asked his financial head this question and discovered that she wanted the chance to run a business. When reassigned as a business leader, she flourished. She not only grew the business beyond expectations but also experienced personal growth in her new role. Employees have opportunities for growth through temporary job changes, project assignments, professional development experiences, promotions, or other challenges at work. Leaders give employees opportunities for growth by asking employees to do difficult things that might be outside their comfort zone. Then leaders need to give employees transparent and honest feedback on what worked and what did not. While outwardly inconsistent with the "build on your strengths" mantra, this approach assumes that employees who do new things may build new strengths.
**Visibility**. Work may vary according to how much visibility or recognition the employee gains from doing the work, both inside and outside the company. In Philosophy 101 we ask, "If a tree falls in the forest and no one hears it, did it make a sound?" In Abundance 101, leaders ask, "If an employee did a good job and no one noticed, did it contribute to the employee's sense of abundance?" Sometimes employees are so self-motivated that they only want to prove to themselves what they can do. But more often employees want to be recognized for their contributions. If the Olympics were held in private, Michael Phelps might still have won 14 gold medals, but his impact on the world of sports and its impact on him would have been reduced.
Leaders need to recognize good employee performance appropriately and publicly. Some of this visibility shows up in reward systems as bonuses and promotions, but the visibility also comes from immediate feedback and public praise for doing something well. Small comments and sincere expressions of thanks can make a difference. When a participant in an executive program in China complimented Dave on his course, Dave joked that the participant should tell Dave's mother. Dave was surprised and pleased when a week later his mom told him she had received a call from someone in China who had been in his course and wanted to thank her for her son's work. Visibility, recognition, praise, and positive feedback allow leaders to communicate gratitude to employees for their work.
Just as soldiers in the heat of battle think more about saving their friend than saving their country, workers who feel valued and appreciated by those they work with are more engaged even if their jobs seem relatively detached from their broadest values. When leaders structure positions, match people to positions, design management processes, and communicate broadly about innovation, autonomy, opportunity, and visibility, employees can tune in to ways that their work matters to both the world at large and to the individuals they work with.
##### **Work Condition 4: When Do I Work?**
Dave and Wendy each have pioneer ancestors who crossed oceans and continents to colonize a new land. In today's work world, pioneer boundaries are less about space and more about time. Time has often become people's scarcest resource and most valued asset, and many companies today are pioneers in its use. How we spend our time communicates our values and priorities.
**Calendar Test.** When Dave coaches senior leaders, he often asks them to do a time audit or "calendar test":
In the past 30, 60, or 90 days, what would you say were your top priorities?
What did you talk about in your public speeches?
What were your stated goals?
What percentage of your time did you spend on these issues?
Whom did you meet with, and what were the topics of conversation?
What were the agenda items in your meetings?
What else did you spend time on, and how important were those things?
This calendar test helps leaders know if their intentions are consistent with their actions. A leader once said that his priorities were building stronger customer relationships, but his calendar made clear that he spent most of his time inside his organization in meetings and planning sessions. Another leader claimed managing cost was the priority, but this priority did not show up in her calendar.
Hypocrisy is a leadership killer. Employees pay more attention to behavior than rhetoric and will observe what leaders do more than what they say. Leaders build abundance by living up to the values that give meaning to work, including the value of integrity between their intentions and their calendars.
A new leader wanted to send a message to his organization about the importance of inclusion in the workplace. Instead of just talking about the value of inclusion and diversity, he regularly scheduled meetings with employees in underrepresented groups, asked for data on the careers of these employees, and sponsored projects that communicated inclusion. Wendy often ends a session by asking the client how he or she might spend fifteen minutes to make progress on goals. Even busy people can find 15 minutes, and without at least some commitment to action more talking only fosters the illusion of change without the reality. Dave likes to end his workshops with a cartoon of a group of turkeys who have just attended a training seminar where they learned to fly. They spent time flying and soaring among the clouds. Then, the caption says, "at the end of the seminar, they all walked home." Dave often asks workshop participants to share the action items they have calendared and to schedule a phone call or e-mail follow-up with a peer to ensure accountability for the result.
**Satisficing**. Herbert Simon, a Nobel Prize–winning economist, used the term _satisficing_ to describe decision making based on meeting the minimal criteria rather than on searching for an optimal solution. Leaders should also help employees invest their time, not just spend it. We have used a simple formula, "return on time invested," as a time quality check. In one company, when leaders make a request of employees, the employees are encouraged to ask "how much time is this request worth?" By answering this question, the leader can signal the amount of time and the rigor of the decision the request warrants. Sometimes leaders make innocuous requests that create volumes of work among employees because leaders are not clear about the return on time invested and what should be satisficed versus optimized.
Most of us have learned to satisfice (versus optimize) some personal decisions. We might satisfice making our bed or taking care of our yard while optimizing our relationship with our children. We might satisfice on breakfast and optimize on dinner. Leaders can help employees know when to satisfice and when to optimize by having the "return on time invested" discussion. Some organization initiatives and decisions are so important to do that they are worth doing well (e.g., safety in manufacturing, customer relationships), but other still-important decisions don't require as much precision.
**Flexibility**. One key to managing time is schedule flexibility. Many employees want flexibility so they can respond to demands from their personal life. This does not mean that they will work fewer hours, but it may mean that they can have some say in when they work those hours. As employees make choices on work flexibility, they are constrained by business realities (not many in a grocery store want to work on Friday or Saturday nights, but someone must). But employees are often very motivated to find creative ways to get work done well if they can have some say about when to do it. Many organizations have options for four 10-hour days or even three 13-hour days to allow employees to build a work-week that works for them.
### **Abundant Work**
A relative of ours has a fridge magnet that states: _Life's greatest tragedies occur when we give up what we want most for what we want now._ Sometimes what we want now is so basic to survival that putting off what we want most is a noble sacrifice and not a tragedy at all. But generally speaking, our work feels most abundant when we get both some of what we want now and much of what we want most. Even in good times no one has a perfect job, and even great jobs have unpleasant aspects. In a down economy the type of work we can get and the parameters of that work may be even more constrained, leaving employees feeling that they are giving up more and more.
In good times or bad, great leaders can help employees find a line of sight between the work they do and the outcomes that matter to them. They can help them find the intrinsic value in doing work that matches their skills and interests. They can help shape the work space and the duty roster to increase options, control, and flexibility for employees. They can help employees connect with the aspects of the work that come most naturally and that are energizing and enjoyable. The assessment tool in Table 7.2 offers a template for doing this diagnosis and matching.
An abundance-seeking employee can also use this assessment tool to think through what conditions of work matter most and what conditions can be satisficed—finding a reasonable option rather than a perfect one. He or she will also recognize that production requirements dictate many aspects of work, making compromise necessary. An employee can create a personal work scorecard based on this assessment that informs work choices.
As leaders and employees work together to match tasks and people, there will always be gaps and snags—aspects of the work that are unpleasant, unclear, or uninteresting to almost everyone. As employees participate in these discussions, they can often find creative solutions for sharing such tasks or changing their parameters. When leaders don't take this initiative, they risk losing good employees over sometimes trivial aspects of work that are more flexible than they realize or that people would feel better about doing once they knew they had been heard and their suggestions considered. Of course a leader should be clear about what must be done to deliver results, compete in the marketplace, and fairly distribute rewards. But engaging employees in shaping their work where possible empowers them to get some of what they want now and much of what they want most. This is abundance at work.
**TABLE 7.2 Work Characteristics Assessment**
**_Summary: Leadership Actions to Ensure Personalized Contributions to Work_**
Learn what outcomes matter to employees: How does this job relate to their identity, values, and purpose?
Help employees articulate the line of sight between what they do and the outcomes they value.
Help employees discover the intrinsic value of their work and what they enjoy in the work itself.
Shape work conditions and match employees to conditions that appeal to them (where, when, with whom, and how they work).
## **CHAPTER 8
How Do I Respond to Disposability and Change? (Growth, Learning, and Resilience)**
LEADERSHIP **GROWTH, LEARNING, AND RESILIENCE** CHALLENGE
As changes compound and the risk of failure increases, people may fade, fail to adapt, and get demoralized, which leads to organization stagnation. Great leaders relish change and help employees grow, learn, and be resilient to bring new life to their organizations.
Change happens.
Consider the following from Tim Clark's research detailed in his book _Epic Change: How to Lead Change in the Global Age_.
The cost of a gigabyte of computer memory dropped from $10 million in 1956 to $7,700 in 1990 to $13.30 in 2000 to $1 in 2006.
Sales of white bread in the United States fell slightly from $2.3 billion in 2001 to $2 billion in 2005. In the same time period tortilla sales rose from $81 million to $1 billion—a 12-fold increase.
One in eight couples married in the United States during 2005 met online.
In 1976, Americans drank an average of 1.6 gallons of bottled water per year; in 2006, the average was 28.3 gallons.
More than half of the Ph.D.s awarded in the United States in science and engineering go to students from China, India, Korea, and Taiwan.
Ed Lawler also found that between 1973 and 1983, 35 percent of the top 20 companies in the Fortune 500 were new; 45 percent were new between 1983 and 1993; 60 percent were new between 1993 and 2003; and if the last five-year trend holds, over 70 percent of the top 20 Fortune 500 companies will be new to that list for 2003 through 2013.
All of these changes and the millions more they represent take us into new territory, where the likelihood of failure increases. Deficit responses to change are rooted in fear, stagnation, and withdrawal, born of the belief that failure is a threat to success. Abundant responses to change focus on learning and resilience, born of the belief that failure is a path to success.
A classic example of this second mind-set is Thomas Watson, Jr., who headed IBM in the 1960s. A manager reporting to Watson ran a business unit that lost $10 million. Watson called him into headquarters. The guy walked into Watson's office weak-kneed. Watson said, "Do you know why I called you here?" He responded, "I assume you called me here to fire me." Watson said, "Fire you? Hell, I just spent $10 million educating you. I just want to be sure you learned the right lessons."
Another story is told of Jonas Salk, the inventor of the polio vaccine. When asked where he got the resilience to persevere through multiple scientific failures, he referred to his mother. He remembered a time as a child when he was eating cookies and milk while zooming a toy car around the table. His mother warned him repeatedly to move his milk away from the edge of the table so he wouldn't spill it, but he ignored her. Predictably, he knocked the milk to the floor. He looked up, chagrined. Most parents would have scolded a child for ignoring warnings. Salk remembers his mother simply asking, "So, what did you learn?" The importance of learning from failures stuck.
These stories exemplify an abundant response to failure. Rather than use change and setbacks as an excuse to scold, punish, give up, or give in, leaders who build abundance focus on learning and resilience.
No one becomes a better musician, teacher, scientist, carpenter, dentist, accountant, or manager without stretching outside of their comfort zone. The only way to avoid the setbacks and disappointments inherent in this unfamiliar territory is to avoid trying new things. Frankly, if you are not failing at something, you are probably not pushing yourself hard enough. What's more, failure should be disappointing. If there is no disappointment, the work you tried was probably not that important to you. We have coached leaders to "rejoice in disappointment" because disappointment means they are working on things that matter to them.
Our self-esteem and capacity to cope have more elasticity, or capacity to stretch without breaking in response to stress, when we have a learning mind-set. Just as a savings account gives us elasticity in the face of unexpected expenses, Stephen R. Covey refers to an "emotional bank account" that gives us elasticity in the face of unexpected setbacks of other kinds. When people learn how to learn from mistakes, they can cope better with the stress of change. Setbacks become opportunities to grow rather than reasons to give up. Leaders build this elasticity, this sense of having enough stretch and to spare in one's emotional bank account when they teach employees how to learn from both good and bad experiences. A learning focus puts _new meaning_ on failure and change in general, turning it from a threat to an opportunity. This learning focus, rich with meaning making, is a key building block of the abundant organization.
### **Learning**
Think of someone you would characterize as a gifted learner. Why? What are this individual's personal attributes? What can this person do?
Rand is one of our most precocious learning friends, as he exemplified when traveling with us to a foreign country. First, he was constantly inquisitive, engaging the local residents to find out more about their lifestyles and beliefs. Second, he wanted to try new things: on our one-week trip he learned the alphabet of the local language and began to learn the basics of the language so that he could communicate better with the people. Finally, he could use insights from one setting to understand another: he enjoyed contemplating how the experiences of the Maccabees in the first and second centuries B.C. apply to today's political environment. Rand demonstrates not only high intelligence but learning agility—the ability to inquire, experiment, and extrapolate in flexible and productive ways.
Organizations need learning agility as well—an organizational capability for making knowledge productive. Organizations with high learning agility are not only more interesting places to work but also more profitable. Dave has defined _organizational learning agility_ as the ability to generate × generalize ideas with impact. At either a personal level (our friend Rand) or an organizational level, these two principles help people build a learning response to change:
**Generate.** Leaders who encourage learning seek new ways to do new things. In the face of change, they are open to experimenting, adapting, and improving.
**Generalize.** Leaders who learn transfer ideas from one area to another. They have the ability to see patterns that may apply elsewhere.
In a world of increasing change, a learning focus both increases employees' elasticity for responding to setbacks and opens up new opportunities for growth and contribution.
### **Principle 1: Generate New Ideas**
As change occurs in the business environment, yesterday's rules of thumb become outdated. When leaders encourage the generation of new ideas and procedures, they build learning agility. We have identified four ways leaders generate new ideas: self-reflection, experimentation, continuous improvement, and boundary spanning.
#### **Self-Reflection**
Learning leaders are self-aware. They recognize that their choices have consequences, and they constantly review both the choices they make and the consequences of those choices. They ask themselves questions such as:
What can I learn about myself from what just took place (in a meeting, conversation, or presentation)?
What did I do in this setting (meeting, conversation, work effort) that worked? Why?
What did I do that did not work? Why not?
Is this how I generally respond to similar situations? What are my common patterns?
What could I try instead? What am I afraid might happen if I change?
If I am sometimes successful at a different approach, how could I be more consistent?
By asking these types of questions, leaders enhance their learning agility. They also model for employees how to be inquisitive, open to suggestions, and committed to improving.
Self-reflection shows up as well in leaders' willingness to be accountable. When they make mistakes, learning leaders run into them rather than away from them. They also help others reflect on their goals and take responsibility for reaching them. When goals are missed, learning, not blaming, becomes the priority.
#### **Experimentation**
Leaders encourage experimentation and innovation by asking employees for their input and encouraging employees to try out their ideas. Employees with successful track records get more latitude in experiments. Experiments are bounded in time and space and audited rigorously to determine how well they work. Experiments may occur in a number of areas: product design and features (e.g., Microsoft Office), service (e.g., FedEx), channel of distribution (e.g., online purchases), operations (e.g., Walmart's supply chain), cost management (e.g., lean manufacturing at Herman Miller), customer experiences (e.g., Starbucks), management processes (e.g., virtual teams at Nokia), business model (e.g., direct distribution at Dell), or industry redefinition (e.g., iPod at Apple). Experiments that don't work should be abandoned, with lessons learned transferred to other settings and without lingering investments in the unsuccessful experiment.
Learning leaders also accept difficult and new assignments where they ask lots of questions and are resourceful and creative in approaching traditional problems. They are open to alternatives rather than locked into habits. These leaders generally have many interests both inside and outside of work.
Google employees work aggressively on building a culture of experimentation or innovation. They have identified 10 attitudes for innovation that capture their commitment to experimentation:
1. Ideas can come from anybody.
2. Share everything you can (new ideas and projects are put on the Internet).
3. Dare to recruit somebody more powerful and insightful than you.
4. Have a green light to your dreams: commit one day a week to contribute to the company the way you like (50 percent of new initiatives are developed during this day).
5. Look for quick wins.
6. Provide less "I like it" and more analytics.
7. Do not kill an idea; transform it.
8. Innovation requires constraints like budgets and timelines.
9. Care about the end customer first, not the money.
10. Identify your "twin" in the company . . . an innovation sparring partner.
With these attitudes and actions, Google has a remarkable track record of experimentation and innovation.
Based on work in the innovation literature, we have identified a six-step protocol for experimentation. (See Figure 8.1.) Leaders who use these steps help employees discover that there is always enough and to spare of great ideas.
#### **Continuous Improvement**
Continuous improvement programs are just what they sound like: efforts to institutionalize the focus on constant improvement. Leaders encourage continuous improvement through both formal programs and informal conversations.
A great example of a formal continuous improvement program is Alcoa's suggestion system where thousands of suggestions are made and about 60 percent are implemented. Over 40 years, Toyota's suggestion system has received more than 20 million suggestions or about one per employee per week, the vast majority of which are used. The GE Work-Out initiative and town hall meetings were designed as a disciplined way for employees to share ideas for removing unnecessary work and improving work processes. While no system is flawless and mistakes and recalls may happen, these approaches enable employees to feel personal ownership and accountability for business results.
**FIGURE 8.1 An Experimentation Protocol**
Leaders can also sponsor continuous improvement informally through what they attend to and ask about. One of the most useful questions leaders can ask when an employee poses a problem or question to them is "What do you think?" Generally (not always), the employee has spent more time thinking about the problem and potential solutions than the leader. When leaders give employees license to solve the problems they identify, employees find more meaning in their work.
#### **Boundary Spanning**
Leaders can look for best practices both inside and outside their organization. It is not enough to share a best practice, however; we must also consider the system in which the practice works. For example, many copied GE's town hall meeting initiatives, only to find that they were not as successful unless accompanied by many of the other GE management practices (incentives, succession planning, leadership training, teamwork, etc.). Also, copying someone else's best practice automatically means trailing in generating new ideas. Even better is to leapfrog a best practice, improving it before implementing it to move beyond what others have done.
Steve Kerr introduced us to a learning matrix methodology to determine best practices inside a company that can be shared across geographic, functional, or business boundaries. (See Figure 8.2.) This matrix uses five steps:
**1. Complete this statement: To be world class at X, we must . . .** X can be anything the corporation is committed to doing well (e.g., service, quality, customer focus, cycle time, or training). This steps identifies 10 to 12 factors critical to success in X. A small research team, task force, or other group can define these 10 to 12 critical success factors, which become the columns at the top of the matrix.
**2. What are the units where these factors could be demonstrated?** These units are organizational entities (functions, plants, divisions, geographical areas, etc.) where the critical success factors could be demonstrated. These units become the rows listed on the left side.
**FIGURE 8.2 Learning Matrix**
**3. For each cell, rate that business unit on that critical success factor as follows:**
0 = not applicable
1 = not good at all
2 = below average
3 = average
4 = we think we are good (self-report)
5 = others think we are good (certified by someone else as excellent or world class)
This assessment can be done either by an organizational unit leader or by an external rating team (e.g., a corporate group that inspects the unit or an outside rating agency). Scores of 0–4 can be provided by members of the organization unit; a score of 5 must come from outside.
**4. Combine the individual assessments by rows or columns.** The ratings for each cell may now be combined to create a learning matrix for a particular initiative (X). The average score for a row indicates how the particular business unit fares. The average score for a column indicates how well the entire organization is doing on that particular factor. This matrix helps pinpoint pockets of excellence as well as an overall corporate score for a particular initiative. It can be used to track progress on initiative X across business units or across factors.
**5**. **Create processes for sharing ideas from high scorers with lower scorers.** Mechanisms for sharing knowledge and experience across cells include:
Make the higher-scoring business units "best practice" sites where others can learn.
Create cases from the higher-scoring cells for others to draw on.
Move talent from higher- to lower-scoring business units.
Create incentive systems for sharing knowledge (e.g., bonuses, awards).
Assign someone from corporate to oversee the entire matrix process and ensure that a larger percent of cells are 5s in each successive year.
This learning matrix offers a disciplined way to share best practices within an organization.
When leaders use a mix of self-awareness, experimentation, continuous improvement, and boundary spanning, they help their organizations learn from rather than be overwhelmed by change.
### **Principle 2: Generalize Ideas**
_Generalization_ simply means the movement of ideas or knowledge across boundaries like space or time. For example, our friend Rand readily transfers his skill at learning languages into new geographic settings and brings his understanding of ancient civilizations into today's political processes.
Most of us are not nearly this good at generalizing knowledge or skills. The biggest challenge in education is not to get kids to learn math but to get them to remember to apply the math skills they have learned when they go to the grocery store or restaurant. Research on continuing education programs suggests that most participants, even though they spend a lot of time and money and even if they rave about the program, will change very little as a result of their investment and enthusiasm. Helping employees (and ourselves) generalize learning by applying it in new settings and spreading it around is not easy. But without this key step, generating great ideas is a waste of time.
In organizations, leaders move knowledge across many boundaries: vertical (from the top to the bottom of an organization), horizontal (from one function, department, or business to another), external (from supplier or customer), global (from one geographic site to another), or temporal (from one time period to another). Leaders generalize learning across these boundaries by buying and building talent, creating incentives, and using information systems.
##### **Talent**
Organizations are only as gifted at generalizing ideas as the individuals who compose them. Robert Eichinger and Michael Lombardo have identified 68 competencies of talented employees. These competencies are based on a content analysis of dozens of studies and competence models. Specific competencies of individuals who help organizations generalize ideas across boundaries include:
**12**. conflict management
**27**. informing
**32**. learning on the fly
**33**. listening
**36**. motivating others
**46**. perspective
**48**. political savvy
**51**. problem solving
Firms can either _buy_ or _build_ these generalizing competencies. To _buy_ these generalizing competencies firms can hire outside talent either full time (as employees) or part time (as contracted consulting or outsourced partnerships). A _build_ strategy for competencies involves training or developing existing employees. A build strategy assumes that with appropriate nurturing, current employees can acquire competency at sharing knowledge. Moving talent across units is a common build practice for sharing knowledge, such as through a succession planning system that lets employees apply for jobs or projects throughout an organization. Using training events as forums for sharing ideas and turning them into action also facilitates generalization. Some innovative companies today are not only moving people across units within their company but also doing executive exchanges between their company and customers or suppliers. Procter & Gamble high-potential leaders who need more savvy in technology may exchange roles for two to six months with Hewlett-Packard executives who want to improve on brand management. These and other ideas are listed in Table 8.1.
##### **Incentives**
The old adage "People do what they are rewarded for" is half helpful. Without doubt, incentives change behavior. But incentives work to accomplish business goals only when they are based on clear and explicit standards. A better adage would be "Incentives promote business goals when people are rewarded according to clear and measurable standards relative to those goals."
When incentives link rewards to clear standards for learning agility, learning agility will increase. Start by measuring learning agility (perhaps using relevant criteria from this chapter); then build this measurement into the performance management system. Once standards and measures are established, allocate rewards for meeting those standards. Some rewards are financial (e.g., base pay increases, bonuses, stock options), and others are nonfinancial (e.g., recognition awards to managers who anticipate competency needs or demonstrate learning strategies). As long as rewards tie to the measures of learning agility, accountability for learning increases. A good example of an integrated system for innovation and learning agility is 3M's "vitality index," which measures the percentage of revenue that comes from products introduced in the last five years. This vitality index encourages experimentation, risk taking, and sharing of ideas. In this light, measures and rewards may also be used to encourage cross-boundary behavior. One company requires that 20 percent of the bonus money available to a leader to distribute must be given to someone outside his direct chain of command. This money pool allows leaders to rewards boundaryless behavior.
**TABLE 8.1 Checklist for Acquiring Talent for Learning**
#### **Information Systems**
Many large professional service firms have created the position of "Director of Knowledge Management," whose primary responsibility is to move information across units. Accenture (a consulting firm) excels at leveraging technology best practices across business sites. On completing an assignment, each Accenture consultant answers basic questions about the assignment:
What was the presenting problem?
What methods were used to deal with the problem?
What were the results?
What were the lessons learned?
These answers are merged into an ever-evolving data set that other consultants may draw on. Accenture's consultants live and work all over the world, but they still form a community of values because they share so much information. The Accenture database they draw on becomes a carrier of the values of the firm.
The two principles we have laid out—generate and generalize—help leaders build elasticity in employees by increasing learning agility. With a broader range of skills, employees can better cope with change. They come to see change as offering opportunities for growth more than excuses for failure. When employees learn, they have enough and to spare of the information, confidence, and skills not only to perform but also to contribute at work.
### **Resilience**
Resilience is the ability and courage to bounce back and try again when faced with change. One of the greatest examples of resilience is U.S. president Abraham Lincoln. Born into poverty, Lincoln faced defeat throughout his life. He lost eight elections, failed at two businesses, and suffered a nervous breakdown. Here is a sketch of Lincoln's road to the White House:
1816: His parents were forced out of their home. He had to work to support them.
1818: His mother died.
1831: He failed in business.
1832: He ran for the state legislature and was defeated.
1832: He lost his job. He wanted to go to law school but couldn't get in.
1833: He borrowed money from a friend to begin a business and lost it all by the end of the year. He spent the next 17 years paying off his debt.
1834: He ran for the state legislature again and won.
1835: He was engaged to be married when his fiancé died and his heart was broken.
1836: He had a total nervous breakdown and was in bed for six months.
1838: He sought to become speaker of the state legislature and was defeated.
1840: He sought to become elector and was defeated.
1843: He ran for Congress and was defeated.
1846: He ran for Congress again and won. He went to Washington and did well.
1848: He ran for reelection to Congress and was defeated.
1849: He sought the job of land officer in his home state and was rejected.
1854: He ran for Senate of the United States and was defeated.
1856: He sought the vice presidential nomination at his party's national convention and got fewer than 100 votes.
1858: He ran for the U.S. Senate again and was defeated.
1860: He ran for, and was elected, _president of the United States._
Clearly, Lincoln not only learned from setbacks but demonstrated almost inconceivable resilience. His biographers have described the emotional strengths that contributed to his enormous resilience:
**Empathy:** He could put himself in the place of others and appreciate their point of view.
**Humor:** He used self-deprecating humor and storytelling to put people at ease.
**Magnanimity:** He held no grudges against those who disagreed with him.
**Generosity of spirit:** He publicly admitted mistakes and took blame for administrative errors.
**Perspective:** He put things in context, always seeing the big picture.
**Self-control:** He controlled his public emotions, sometimes by writing a letter to himself and then tearing it up.
**Balance:** He was able to relax and entertain friends even in the midst of stress.
**Social conscience:** He tirelessly worked to serve others.
Lincoln's resilience enabled him to cope with huge setbacks and try again, somehow maintaining the perspective that he had enough and to spare of what it would take to succeed.
Consider three sources of resilience that leaders manage to create meaning from loss or failure: personal, social, and organizational.
#### **Personal Resilience**
Leaders facing the same challenge may respond with despair or resilience. Personal resilience, the ability to bounce back from defeat, increases when leaders can do the following:
**Maintain an optimistic attitude.** Resilient leaders see opportunity even in the midst of dramatic change. Lincoln used humor and stories to communicate optimism in the face of the enormous challenges facing the Union. For an immediate boost to your sense of well-being, try this exercise that will likely have demonstrable results: Each night for a week, write down three good things that happened that day and why you think they happened. Stopping to notice things we like about the day, especially when we also notice what caused the good moment, is a great routine that builds hope and connection.
**Live out of a strong moral code.** Many of the most resilient victims of hurricane Katrina and 9/11 attributed their response to their faith and moral compass. In times of distress leaders can turn to lasting moral principles to get their bearings and rally others. Lincoln appealed to moral values in his memorable speeches, placing present action steps in that context:
_With malice toward none, with charity for all, with firmness in the right, as God gives us to see the right, let us strive on to finish the work we are in; to bind up the nation's wounds; to care for him who shall have borne the battle, and for his widow and his orphan—to do all which may achieve and cherish a just and lasting peace among ourselves and with all nations._
**Face fears head-on.** We have a friend who gets very anxious in social settings. Rather than run from the fear, she invites people to her home. She has done the same with her fear of needles by training to be a phlebotomist; of exercise by committing to do a triathlon; and of performing by auditioning for community theater. Leaders who face anxiety or other fears or challenges directly increase their resilience and skill.
**See patterns and put events in context.** When the Union lost a battle, Lincoln continued to focus on winning the war. He knew the long-term outcome that he desired and could accept periodic setbacks as long as he moved forward. Leaders see beyond single events into longer term patterns.
**Stop worrying and start living (quoting Dale Carnegie).** To gain resilience in the face of change we have learned to ask ourselves, "What is the worst thing that can happen?" Once we identify and stare down the worst-case scenario, we can better move forward. When leaders accept the possibility of the worst and then act to create the best, they move forward with more resolve.
**Manage risk.** One of the liabilities of transparency is that leaders' private actions become fodder for public discussion. Transparency demands may reduce the willingness to take risks, and bold actions that create innovation may be tabled. Resilience is, almost by definition, willingness to take risks. Our formula for risk taking is _will to win divided by fear of failure._ Will to win often comes from personal predispositions and the ambition or drive that an employee might have. Leaders can ensure a high will to win by selecting and placing the right people in the right jobs, but they may take more directive actions to reduce the fear of failure. Rather than punishing mistakes, leaders need to help people learn from them. The Tom Watson story at IBM is one of many examples of leaders who reduce the risks of failure by focusing on learning rather than blaming.
**Move on.** Sometimes resilience comes through managing the transitions associated with change. William Bridges points out that a transition is more than a change of behavior; it is a change of identity and patterns. Real transitions require emotional processes, not just behavioral modifications. These emotional processes include:
Letting go of old identities, activities, assumptions, and relationships; mourning the loss of the "old normal" that will not be regained
Putting up with a sometimes lengthy period of confusion, uncertainty, and redefinition of roles; gradually coming to imagine and experiment with new patterns, identities, and ways of making decisions
Allowing something new to be born, institutionalized, and valued as a "new normal" rather than clinging to the past
Symbolic acts can help facilitate this difficult transition process. Belinda, the school principal, changed teachers' classrooms as a symbol of a "new world order" at school. Another new leader facing a major corporate transition asked employees to list on a card the things they had done to contribute to the company's past success. He encouraged employees to share these stories with friends and family for a weekend. On Monday morning he invited everyone to write him a personal memo on what he or she would do to help implement the new agenda. Then they all burned the cards representing the past. Leaders who take seriously their meaning-creating role of honoring the past and boldly envisioning the future help others complete the transitions related to change.
#### **Social Resilience**
A few years ago, one of Dave's books was reviewed on Amazon. Here is the verbatim review:
**Stupid title. Stupid theory. Stupid book.** , _September 15, 2003_
_Reviewer:_ **PT Kearns** _from UK_
_We all need to worry when "top" academics are telling us that the bottom line isn't. At last, the vacuity of Dave Ulrich's work is plain for all to see. Any book which states that the "big, new idea is connecting leadership to market value" (p.259) has to win the award for the most fatuous statement of the blindingly obvious._
_I was going to give this 0 stars, but the system does not allow it._
Ouch. When Dave read this review, he was mortified, angry, and hurt. His first reaction was to cover the computer screen with his hand so no one would see it. But of course the review was already in the public domain, hanging out there for all to see. So instead of pretending to hide the review, he started to share it. He learned that most people did not agree with this reviewer (thank goodness), and he got social support to cope with the negative comments.
Another time, Dave received a prestigious award. A later write-up of the ceremony began, "Dave Ulrich, a large and homely man . . ." Again, he shared the unflattering description with his wife and friends, who jokingly said that he might someday change one of these two factors (large), but he was stuck with the other (homely). Sharing difficult situations lets close friends laugh with us and give us perspective—or perhaps help us change. When Dave decided to become "less large," he publicly shared his commitment to a large group of young adult missionaries he was supervising at the time. He held up an Oh Henry! candy bar and said, "I am working to lose weight and not eat any more of these great candy bars. If you catch me eating an Oh Henry! bar, you can drive my car for a day." Over the next few weeks, Oh Henry! bars appeared in his briefcase, car seat, pockets, office, and nightstand with the names of those making the offers attached. But, with his public commitment (and car insurance premiums) on the line, he was able to resist.
We all need social support to be resilient in managing change. As we have discussed in previous chapters, there are two types of social support: close and loose. Close friends support us and remind us that we are cared for even if we are "large and homely." What a privilege to have friends who don't care as much about what we do as about who we are. Leaders and employees who surround themselves with close friends get support for change. But, in addition, we need loose connections with more distant acquaintances who teach us new things. After 35 years of marriage, Dave and Wendy can order for each other at restaurants and often fill in the blanks of open-ended sentences. We need new associates who offer new ideas on how to approach old problems. We can find new connections through professional associations, extended social groups, and new assignments. By having close friends who support them and new acquaintances who teach them, leaders can find social support to manage change.
A final way to build social support for change is to help someone else manage change. When we help others, we often become more able to cope. We build a goodwill account with others that we can later draw on. We see the change through someone else's eyes and get a different perspective. During a crisis, those who join groups to help others gain support themselves. Mothers Against Drunk Driving (MADD) is indispensable to many who have lost a loved one in a car accident. By serving others, they become more resilient. Those who formed similar groups after 9/11 coped better with the painful transitions of that crisis. Leaders can ask those struggling with a transition to help others through it. By serving others and giving back, those experiencing difficulty may cope better.
#### **Organizational Resilience**
Leaders who build organization systems that reinforce resilience and increase capacity for change practice three principles.
**Principle 1: Make the Unspeakable Speakable**. Anyone in a long-term relationship has discovered that without candid conversation the relationship withers. To build a relationship, caring partners need to talk. This is especially true for things they don't want to talk about—things that make them embarrassed, resentful, or doubtful. But only when we make the unspeakable speakable do real understanding and empathy occur.
In almost every organization "unspeakability" viruses limit successful change. These unwritten and unspoken norms dictate activity and prescribe choices without full awareness or choice. Dave and his colleagues have identified more than 30 such viruses, including these:
**Activity mania.** Our badge of honor is a full calendar, even if it excludes thinking and results; we hide behind our busyness.
**Have it my way.** We insist things be done as we want, not allowing other styles.
**False positives.** We hide behind nice-talk, even when we disagree.
**Authority ambiguity.** We are not sure who is responsible or accountable, so no one is.
**Turfism.** People defend their turf, sometimes to the detriment of the overall organization.
**Full sponge.** We are overflowing with too many changes going on at once; we are burned out and stressed out on change.
**Overmeasure.** We measure everything, even to a fault; our dashboards are way too complex.
**Undermeasure.** We don't have indicators to track important stuff; we measure what is easy, not what is right.
**Going for the big win.** We look for the mega-change that will solve all problems instead of starting small with low-hanging fruit to build momentum.
When leaders can identify, name, and discuss such viruses openly, they can be cured. New employees often see these viruses most readily, just as we see the clutter in someone else's home more readily than in our own. Teams can have fun naming, drawing, and mocking viruses lurking in their organization. One team drew their most prevalent viruses, then posted these drawings in their offices while they worked to disable them.
**Principle 2: Turn What We Know into What We Do**. In managing change in organizations, most leaders can accurately list within two minutes 7 to 10 keys to successful change. In our work, we have synthesized a number of keys to successful change, including the following:
**Leadership.** Change requires a strong leader who sponsors and champions the change.
**Felt need.** When the need for change is palpable, it helps overcome the natural resistance to change.
**Vision.** A clear and compelling vision based on clear values and with specific goals and action steps facilitates change.
**Commitment.** Get people to act as if they are committed, and commitment will follow.
**Decisions.** Build a decision protocol that breaks the vision of tomorrow into decisions today; start with small, visible changes to let success build success.
**Systems.** Institutionalize a change through wise investments in people, communication, rewards, information and data, and budget.
**Measures.** Monitor how the change is going to ensure learning and adaptation.
Knowing what it takes to make change happen does not mean we will do it, however. Leaders help people turn what they know into what they do by bringing the discipline of a change checklist to any project and initiative. Pilots, surgeons, merger specialists, and fast-food restaurant managers all use checklists to ensure consistent performance. Leaders can use a change checklist to determine what keys to successful change are already in place or where to invest more resources. For example, in one company, the first three keys to change from the preceding list (leader, need, and vision) scored high, but decision protocols, systems, and measures scored low. This team did not need to spend more time on selling the change but did need to invest in how to make it happen. In another case, leaders scored high on all the change disciplines, but employees did not. In both cases, change checklists helped leaders ensure that knowledge about change was turned into action.
**Principle 3: Make Change a Pattern, Not an Event**. Ultimately, organizational resilience and learning in response to change is not about a single incident but about creating a new pattern. Learning cannot be something that just happens in a workshop, team meeting, or process review; it must become part of the soul of the organization, something that occurs naturally and continuously during all work activities. A pattern implies that a new culture has been created, a new vision institutionalized.
Corporate cultures that abound with resilience and learning inside generally focus on customers outside. Customers' needs, values, options, and dreams always take us to the cutting edge of innovation and improvement. When this customer focus is embedded throughout the organization, learning and resilience become systemic. Change is not an idle hazing meant to distract employees, but an essential link to keeping up with customer expectations and delivering value in the marketplace.
### **In Conclusion**
Change happens.
How we respond to change matters. (See Table 8.2.)
**TABLE 8.2 Change Assessment**
An executive recently said that a business that took 50 years to build could be lost in 2 if it does not respond to change. Individuals, teams, and organizations that respond to change with learning and resilience have a chance to succeed; those that do not may lose the ability to catch up. As leaders institutionalize the ability to generate and generalize ideas with impact, organizations become resilient at individual, social, and organization levels. Patterns of learning and resilience equip organizations to respond to external demands, create higher intangible market value, implement strategies, and plan for the future. They also create excitement and a sense of abundance among employees by infusing them with a sense that this organization has enough and to spare of the intellectual, social, emotional, and organizational resources to meet real needs and make a difference for good.
**_Summary: Leadership Actions to Facilitate Growth, Learning, and Resilience_**
Have a positive attitude about change; trust that you can learn from it and be resilient when facing it.
Learn how to generalize new ideas through:
Self-reflection
Experimenting
Boundary spanning
Continuous improvement
Learn how to generalize, or share, new ideas by:
Moving talent across boundaries
Sharing information across boundaries
Building incentives to encourage shared behavior
Become resilient in the face of change by:
Making the unspeakable speakable
Turning what you know into what you do
Changing events into patterns
## **CHAPTER 9
What Delights Me? (Civility and Happiness)**
LEADERSHIP **DELIGHT** CHALLENGE
Partisanship sometimes affects organizations where there is more hostility than civility and where a we-they, win-lose, right-wrong, blame-and-shame mentality persists. Great leaders move away from hostility and intolerance toward multiculturalism through problem solving, listening, curiosity, diversity, and compassion and by bringing creativity, pleasure, humor, and delight into their organizations.
Recently, Dave's father, Richard Ulrich, passed away. As the family gathered to celebrate his life, we were joined by an interesting assortment of individuals whose work was far removed from anything Richard did professionally: bank tellers, produce managers, teachers, and folks who worked the window at McDonald's. Why? Because when Richard went to the grocery store for peaches, he did not just see someone putting out produce. Richard saw an individual with a name, a story, and a personality. He saw someone he could get to know, make smile, sing a song to. His favorite song was "You are my sunshine, my only sunshine, you make me happy when skies are gray . . . ," and he sang it off key but with gusto. By the end of his life he walked only with the help of braces and a cane, yet he regularly gathered day-old baked goods from local grocery stores, as he had done for over 20 years, loaded them into his old truck, and delivered them to shelters and soup kitchens all over town. He never missed his grandkids' games. He picked up stranded strangers and gave them a lift. He brought flowers to his wife every week (until she pointed out to him that she was allergic to them). Of the hundreds of people at his funeral, virtually every one had received a personal letter from Richard, usually written at 3:00 A.M., thanking them for some small service or offering some tidbit of counsel or encouragement. In his honor, we gave everyone who came to the funeral a McDonald's coupon to give away to someone who needed a hamburger or an ice cream cone. Kind of a silly thing to give away at a funeral, but Richard loved to give such things away. Richard was a character, but he knew how to find delight in the world and loved sharing it with others.
So what does giving out McDonald's coupons or singing to the bank teller have to do with how leaders build your company's bottom line? Just this: Customers who are delighted with their interaction with our products come back for more. So do employees. In an understated, backdoor way, delight seems to go to the heart of finding a sense of abundance at work. Delight teaches us that life's goodness is not found in money or fame but in simple pleasures, meaningful connections, and a sense of discovery. Delight reminds us that no one has nothing to give, that relishing diversity and multiculturalism is good business, and that there is always something of which we have enough and to spare. Employees who find delight at work are often employees who stick around, who make a difference, and who invest their discretionary energy in the creative and challenging aspects of work.
When we talk to leaders about the ideas in this book, the idea of making room for delight sticks. It smacks of creativity, playfulness, pleasure, and fun. It is approachable, reachable: "I'm going to bake cookies and take them to work tomorrow—that'll shock people!" "I'm going to learn more people's names, and not just the people above me on the organizational chart." "I'm getting a book on tape for the commute home and turning off the talk radio." "I want to thank someone sincerely every day." "I am going to have a dress down day at the office." "I am going to begin staff meetings with a good news, non-work-related moment." These simple choices remind them that harder choices can also be broken down into more manageable pieces, that they are not alone, that they have a capacity for creativity and change that doesn't emerge only when strong-armed by relentless production schedules or hefty rewards.
Delight is not just about jokes or cookies, although it is about jokes and cookies. Delight is about noticing little things, breaking out of ruts, feeding creativity. Delight is about appreciation, about beauty, about playfulness and fun. Delight is picking up the cell phone to check in—or maybe turning off the cell phone to check out. Delight is doing someone a favor, choosing a new screensaver for our computer, taking day-old bread to a battered-women's shelter, picking berries with the kids. Delight is about appreciating and learning from people who come from different backgrounds and cultures. Delight may start with a leader's sense of humor or from a group of employees who find joy at work. And delight can turn a tough day on a tough job into something tolerable, something laced with hope. While delight is inherently personal, we can manage a common process to figure out what it is. Leaders can do this exercise alone or with their employees. Take out a pencil and a piece of paper. Ready?
Number from 1 to 10. As quickly as you can, list 10 random changes you could make to bring more delight into your life. And if you find yourself resisting this suggestion, let us warn you that there are more of these exercises to come in this chapter, so, hey, humor us. It will take only two minutes, and it might be delightful. Go.
Did you do it? If not, why not? Need some suggestions to get started? Here's Wendy's list: take a walk after dinner, offer to babysit our grandbaby once a week, write a novel, walk through the backyard, take a yoga class, go to the farmers' market, get a new pen, call my sister more, trace my genealogy, drive up the canyon with good music on.
Here's Dave's list: spend time weekly with each of our children and our granddaughter, walk up the canyon, offer tips ($10 or $20) to good flight attendants, take a bike ride, read a novel, attend more Jazz (basketball) games, check in daily with Mom, Google an interesting topic just to learn about it, exercise regularly, give talks on new subjects, take time off to stroll along a beach.
Maybe some of the things you wrote down require a hefty amount of disposable income, but we're guessing that much of what brings you delight is about small and simple things, not big and expensive things. In fact, research on what makes people happy backs up that idea. If they were to get a windfall of $20,000, most people think they would get the biggest kick out of shooting the wad on a big vacation or plastic surgery or front-row tickets to a play-off game. And it is true that the big purchase would get your attention and give you a huge thrill and a lasting memory. But the research suggests that after two years you would have gotten a lot more satisfaction and a bigger boost to your overall happiness by investing $100 a week in lots of smaller hits: small vacation breaks, dinners with friends, gifts for people you like, handouts to someone in need, a membership at a gym, fresh flowers, a new basketball, a painting class—especially if you keep the small hits consistent with your values and interests.
So, how many of the items on your list were related to or done at your work? Too often, delight is found outside of the daily demands of work. In a workshop, senior leaders were asked to write their personal leadership point of view. In almost every case, when leaders talked about values and things that brought meaning and delight to them, they referred to things outside of work—their children, families, hobbies, and service activities. When they talked about work, they referred to their ability to set goals and get things done. Simply stated, we want to bring meaning and delight into work, without minimizing the seriousness or intensity of the work we must do.
Delight at work does not have to be expensive either, and employees will generally appreciate lots of small investments in their well-being and delight at work more than grand gestures on rare occasions. As a leader you set a tone for cultivating and modeling delight at work. You can also ask others to brainstorm about what they could do to make work more fun for them or what the company could do at minimal cost that would be meaningful to employees to bring delight to work.
Let's look at four sources of delight that can make work, and life, more enjoyable: creativity, pleasure, humor/playfulness, and civility. Then we'll talk about how fostering delight at work among employees can also create a climate of delight for customers.
### **Creativity**
Delight is both an outcome of and a contributor to creativity. This is a chapter about finding delight, not using delight to build creativity, but the process certainly can go both ways. If we know we want to foster creativity at work, then providing people with rich images and evocative raw materials will invite the creative part of them to come out and play. We do our best sustained creative work under moderate, not severe stress, when the heat is on but we are not in the pot. As long as the challenges of staying in business and keeping a job are sufficiently motivating, an atmosphere of playfulness, humor, and support can keep things from boiling over.
But creativity is also delightful! When we have a creative breakthrough, a moment of innovation or novelty, we often get a huge charge out of it. It sparks delight to see a solution that has evaded us, to realize a connection we hadn't made before, to be surprised by truth. If we want to find work delightful, even small doses of creativity enrich the stew.
In many organizations creativity is the domain of research and development. It is not really fostered on the plant floor or in the accounting office, where in fact creativity is suspect. Who needs a creative accountant? You do. Even if you don't think accounting creativity will help your bottom line, it can help your employees, who can help your bottom line. Like this:
Creativity experts Julia Cameron and Mark Bryan describe Jerry, an accountant for a Big Six accounting firm. Jerry reports, "My life was lackluster. I knew it but lacked the will and resources to change it. I crunched numbers by day, in a place that felt like a tomb, and I ate cookies at night to calm my fears of being dead." Jerry took a course in creativity from Julia and Mark and was assigned to spend time each week feeding his creative interests. He couldn't think of any. He did other assignments, but he was not experiencing the usual jump in delight that came as people invest in their creative lives.
Then Jerry remembered a long-forgotten curiosity about Oriental rugs. He began to explore rug stores on his day off. He was fascinated. The romance and timelessness of caravans moving across the deserts sparked his imagination. Being the good accountant he was, he began to study the rugs, learn the rules about what made them valuable, and run the numbers on rugs he liked. One day he found a rug in a secondhand store that he quickly realized was a steal. He bought it, took it to work, and put it in his office. He writes, "That first rug transformed my office and my life. It gave me something to talk about with clients, and I suddenly understood in a visceral way what my job really was. I was supposed to help clients turn their money into beauty, things they dreamed of. I suddenly had new respect for my job and new respect from my clients. I learned to listen to the beauty in the numbers. . . . I help clients manifest their dreams."
Creative accountants not only help find creative answers to problems that bore most of us; they bring a sense of meaning and delight to colleagues and customers. Creativity on the plant floor may mean the difference between turnover and retention, between business as usual and innovation, between line-stopping problems and back-saving solutions. People shouldn't have to work for Disney to have the chance to be imaginative, innovative, or inspiring at work.
_Creativity_ with a capital _C_ may be the domain of artists, scientists, and high-paid marketing firms, but garden-variety creativity is what lets everyday people know and _feel_ we are alive. It is what helps us figure out what to do when our kids won't do their homework or our employees won't finish their paperwork, without alienating either. It is what opens doors to new relationships and new endeavors. It is not just about doing something we have never done, like eating a grasshopper or swearing at the president. Creativity is about bringing divergent ideas together to solve a problem, articulate truth, capture beauty, or form a promising connection that leads to new products and better ways of doing business. And that sparks a sense of delight in everyone who touches it.
Creativity expert Eric Maisel writes:
_Creativity] can have its own splendid rewards, but the goal is to produce work that has meaning and makes meaning in the universe, that touches and transforms others, that speaks to others, that decorates or enriches the lives of others, that bears witness—that, to put it in the most old-fashioned way possible, is both beautiful and true . . . each of us knows that the special marriage of truth and beauty, where witness is borne and material crafted, is the very definition of deep work and high achievement.[ 2_
Both playfulness and civility can be seedbeds for creativity. Playfulness invites irreverent questions and fresh approaches that spark new ideas, while civility moderates the tone of harshness or criticism that can keep innovation from growing. To be sure, not every brainchild is worth developing, but even the best ideas do not see the light of day without encouragement and protection. Creativity requires curiosity and reflection. It requires working outside your comfort zone and attempting things where you may not be qualified today. It requires hard work and deep honesty. Most of all, it requires us to learn to tolerate anxiety. Eric Maisel states:
_While anxiety is the greatest impediment to aliveness, in order to create you must invite anxieties into your life and live anxiously. . . ._ If you are to create you must invite anxiety in. _But then you must manage it. 3_
Do you remember anyone in school or your early job training teaching you about the anxiety that accompanies honest, creative work? Do you remember anyone telling you how to manage that anxiety, tame it, work despite it? Most of us don't. This is often the great leader's job: to help people tame and tolerate the anxiety inherent in the process of doing good work, creative work, meaningful work. Leaders can warn people about difficulties, stir up hope in the face of obstacles, and hold open the space between a vision and its realization to help people trust that it can happen. Great leaders not only help shape that vision or identify those problems but also help people muster the stamina and courage to keep trying, to keep staring down their self-doubts or fear or boredom until they get somewhere new.
Questions for you:
**Who are your most creative employees?** What do they need to work creatively? (More clarity about what is needed or its parameters? More help? More experience? More license? More encouragement? More protection from criticism in the early stages? More realism?)
**Who are your least creative employees?** What do they need to work more creatively? (Consider the same possibilities.)
**Which category do you fall into?** What do you need to work more creatively?
### **Pleasure**
Positive psychology guru Martin Seligman has identified three sources of happiness: things we find deeply meaningful, things that are deeply engaging, and things that simply feel good. While lasting happiness is not found in pleasure alone, in balance with meaning and engagement pleasure contributes a lot to our sense of well-being, including at work.
Number your sheet of paper from 1 to 10 again. What are 10 things you could do to make work more pleasurable that would cost nothing or less than $20? Ignore all judgments about whether these ideas are practical or even possible—just brainstorm and see what comes up. Go!
If you are having trouble getting started, try deliberately including at least one item from each of the following categories of pleasure: physical, intellectual, spiritual, social, and emotional/aesthetic.
Here are some of the things we've heard:
**Physical.** Play air Ping-Pong with Fred in the hallway on breaks, take a walk at lunch, burn scented candles in the lobby, keep a golf ball and a putter behind the door, stash chocolate, organize a yoga class, rearrange my office furniture, do sit-ups.
**Intellectual.** Ask people about their favorite books, get a new iPhone application, learn new vocabulary words, set up a friendly debate, study a language, look more stuff up on the Internet, Google myself or a friend, attend a conference or class in a field I don't know much about, read more, listen to people I disagree with until I can clearly articulate their position.
**Spiritual**. Organize volunteers for Habitat for Humanity, privately pray for coworkers, pool money with officemates to support a disadvantaged child, play Gregorian chants in the elevator, fast for world peace, give fast-food coupons to homeless people, post and practice the values our team believes in, plant trees, get out the vote.
**Social.** Invite some new employees to a picnic lunch, start a sudoku contest, tip a good flight attendant, go bowling as a work team, become a better listener, compliment people more, do an act of unsolicited service for someone you care about, make a real connection with someone every day, respond more to others' bids, share ideas more.
**Emotional/Aesthetic.** Smile more, take good pictures and share them, plant flowers, find a great screensaver, get colored file folders, bring in a headset and some good music, get an office pet, sponsor a company talent show, write in your journal and share it with your family or friends, have a poetry contest, make more jokes, tell patriotic stories.
Will any of these things save the economy or improve your market share? Not immediately. Could bringing pleasure to work get out of hand? Of course. But somewhere in between saving the world and disintegrating into an overgrown frat house, pleasure has a role to play in making work a place where people feel good about being alive and being at work. Leaders set an important tone in encouraging, modeling, participating in, and sometimes toning down or rechanneling pleasure and delight at work so they serve a greater good.
Do you know what the primary sources of pleasure at work are in the preceding categories for each person on your team?
Do you know which departments have the most turnover? What are the sources of pleasure at work that matter most to those who leave? To those who stay?
### **Humor and Playfulness**
Everybody had a favorite teacher at school. Occasionally these were people who were intellectual giants or deeply caring mentors, but often our favorite teacher was the one who was funny. Humor and a sense of playfulness can make the serious work of business more palatable for everyone. John Kotter at the Harvard Business School is a world expert on change. He has written a number of important volumes on the process of change, books that get quoted in academic articles and look impressive on bookshelves but don't sell a lot of copies. Then Kotter decided to write a lighthearted parable about penguins who realize their iceberg is melting and something will have to be done. Embedding his message about the steps of corporate change in an approachable and playful little story would not work very well if Kotter didn't have something worthwhile to say, but adding humor and accessibility to his considerable academic credibility allowed Kotter to significantly broaden the impact of his ideas. _Our Iceberg Is Melting_ has sold more than 500,000 copies.
Of course, if your work setting already struggles to get people to put down the whoopee cushions and get down to business, you will have to take this section with a grain of salt (or maybe consider how to channel that lightheartedness into friendly competition or great customer relations). If your office needs to present a high degree of decorum to convey an appropriate professionalism to clients, playfulness may have to be reserved for the commute home (or maybe ask yourself whether all clients really want _all_ that propriety _all_ the time). To start, put an _X_ to indicate where you would currently put your company or team in terms of playfulness, humor, and fun:
Frat house wannabe **1 2 3 4 5 6 7** Funeral home on Valium
Now, where do you think your best customers would like you to be? Circle that number. Finally, what would your best employees prefer? Put a big _E_ on the line for them. If there is a mismatch, consider a few suggestions for how to shift the balance toward a little more playfulness. Or, if you need to tone it down, consider the next section on civility for some ideas.
Wendy: Dave is the playfulness expert in our family and hands down the hardest worker of any of us. Thanks to him, each of our kids has developed an ability to have fun along with a solid work ethic. For Dave, the two are closely related. Dave is certainly able to put in long hours at thankless work when necessary, but he also gets a huge kick out of much of what he does. He thinks the process of creating a new presentation or engaging a challenging business problem is fraught with fun. I learned early on that Dave was both hardworking and playful, but we were married for several years before I realized he was also funny. Maybe that says more about me than it does about him, but I honestly don't think Dave was always that funny. He developed his sense of humor to become a better teacher and a better person. He works at being funny, and sometimes he bombs. He doesn't let that stop him. When he finds a good one-liner, like all good comedians, he uses it again. He watches good comics in action. Not everyone is a natural at humor and playfulness, but most of us can get better at humor if we nurture it a little, see it as valuable, and lose a few of our inhibitions about what others will think of our beginning efforts.
How would you rate yourself on the humor and playfulness scale (1 to 10)? If you see room for improvement, it might be helpful to examine your attitudes about humor and fun. Fill in the following:
When I was a kid, I thought people who were playful were
__________________________________________
The thing that makes me nervous about humor is
__________________________________________
I would be more fun if
__________________________________________
The arena where I could use more playfulness is
__________________________________________
I think people who are funny are actually
__________________________________________
People get hurt by humor when
__________________________________________
I have been hurt by joking or humor when
__________________________________________
To be more playful I would need to
__________________________________________
I am funniest when
__________________________________________
The person who would most appreciate it if I lightened up is
__________________________________________
I could show this person my lighter side by
__________________________________________
Learn anything? Has your sense of humor been injured by ridicule or excesses? If so, what have you also learned about how humor can help without hurting? Have you seen people victimized by humor so that it has turned you off? If so, it may be time to collect the baby back from the bathwater and reinvest in your lighter side. Have you channeled your playfulness too narrowly? If so, it might be time to let more people see this side of you. Does your humor become mean-spirited, overly sarcastic, or crude? See if you can develop other aspects of your humor repertoire.
Consider who in your organization is great at humor and playfulness while still being a credible and contributing employee. How does he or she pull this off? What can you learn from this person?
Wendy: I'm not as good at humor as Dave, but I believe in the power of play. In my work as a psychologist I often invite adult clients to experience working in trays of sand, using miniatures to create whatever they like. Sand tray therapy is a powerful educational technique as well, helping people express without words what the nonverbal and most creative part of the brain knows but cannot articulate. The great psychologist Carl Jung once said, "Often the hands will solve a mystery that the intellect has struggled with in vain." This is true for big grown-up problems, not just little-kid problems, but big grown-ups often consider play beneath them. When I can get people to simply play in the sand and then tell me about their creations, they are often stunned at what they learn that they had no idea they knew. And this learning usually sticks far better than word learning alone.
Play has many uses for creative problem solving and innovation. Not only can we play directly at solving problems or imaginative innovation by drawing, crafting, or just manipulating objects, but sometimes taking a break from a pressing problem to go bat a ball around or knit for a while will allow creative solutions to kick in.
Pick up that pencil once again and number your piece of paper from 1 to 5. How could you enhance the atmosphere of appropriate humor, fun, and playfulness as a leader in your work setting? If nothing comes to mind, make this a group brainstorming exercise and see what others come up with.
Some possibilities:
Smile and laugh more.
Have your next team meeting with everyone sitting on the floor.
Give everyone poker chips to reward one another for going the extra mile.
Tell funny stories on yourself.
Give out prizes for the happiest desk or the most unflappable response to an irate customer.
Use window crayons and markers to brainstorm or draw solutions on the windows.
Wear costumes for Halloween and hand out candy.
### **Civility**
Recently we spent a night at a posh private club in New York City as guests of a friend. We giggled at the list of stuffy rules: no flip-flops, no tennis shoes, only jackets and ties in the lobby or dining areas, no talking on cell phones or using computers in public spaces. But as we went to the breakfast buffet all scrubbed and suited, we couldn't help noting the air of . . . well . . . civility and delight. We got into a conversation with the waiter, an older man who talked and looked like Rocky Balboa's hard-nosed manager, who had worked at the club for 15 years and loved it. "Why?" we wondered. "Because the people here are just so _nice_." As people who prefer gym clothes over all other attire and would go barefoot to the mall if we could, we are unlikely to buy a membership at a private club with a formal dress code anytime soon. But we did find ourselves wondering if there is a time and a place to turn off the cell phone and put out some flowers. We did wonder if civility is a lost art worth cultivating.
In political debates where strongly held positions often lead to degrading others' points of view, civility has too often been replaced by hostility. As a result, the gears of the political process become stuck and no one benefits. Wise politicians can disagree without being disagreeable and have tension without contention. Political, organization, and personal civility shifts the debate from how we differ to how we can come to agreement, from how the other person is wrong to what we can learn from the other person, and from demeaning others to respecting them (even if we disagree).
Civility doesn't have to be stuffy or punishing, of course, and the type of civility we recommend should be neither. Instead of upturned noses or lots of rules, think writing notes of appreciation, acknowledging birthdays or personal events, offering little acts of kindness and respect, exhibiting basic politeness, smiling. Civility that is warm and friendly can help grease the skids of working at close quarters with people we don't always agree with. It won't work very well to expect sales reps to be sincere and polite to customers if we are not sincere and polite to them. Rate yourself (1 = low, 5 = high) on the following:
_________ I promptly and sincerely thank people for good work or extra effort, often in writing.
_________ I am appreciative and friendly to people who perform menial tasks.
_________ I say please, thank you, and "I goofed—I'm so sorry" to both colleagues and customers.
_________ I make it easy for others to tell me the truth because of how I respond.
_________ I attend weddings and funerals (literally and figuratively).
_________ I dress appropriately for the occasion.
_________ I avoid sexist, racist, or mean-spirited jokes or comments.
_________ I work to put people at ease around me.
_________ I listen to understand other people's point of view.
_________ I can disagree without being disagreeable and have tension without contention.
_________ I don't use anger or petulance to get my way.
The form civility takes in a Marine fighting unit may vary from that of a flower boutique, but civility has a place in both. Genuine civility generally brings out the best in people, who bring out the best in their colleagues and customers.
Ask your team members how they would rate you on the preceding criteria. How would they rate themselves? Do they think these are the right criteria for their work setting? What others would they substitute?
### **Customers and Delight**
Our daughter Carrie, who does not consider herself a very techy person, recently decided to replace her outdated computer. She had put the decision off for a long time because both learning new technology and setting up a new computer intimidate her, and she has no idea where to begin in making computer-related decisions. She asked her brother, a statistician computer-geek, for advice. He talked her into an Apple, his personal favorite. She went to the Apple store, made her purchase, set up the computer, transferred all her files, and had a completely positive experience. She can't stop talking about how much she loves her new computer, how much fun it is to go back to the store for their computer classes, how hassle-free the purchase process was, and did we mention how much she loves her new computer?
We got curious about how a computer can meet the needs of both our tech-savvy son and our tech-avoidant daughter so well. As near as we can figure, both of them find a simple sense of delight in a product that is both technically advanced and deliciously intuitive. The screen is beautiful. The experience is tactile and inviting. They don't have to stand in line at the store, because every sales rep carries a little credit card reader around his or her neck. The computer synchs with the phone. And have you seen the cool way the icons swell enthusiastically when you run the cursor over them?
Most companies that make a living by attracting customers want people to experience that sense of delight because they know it translates into customer loyalty. Customer delight, may come from store layout, product features, a great bargain, or attentive service, and customer delight is a constantly moving target, but if companies can deliver on delight, they can usually count on people to come back. Companies that deliver on delight can usually count on their pick of creative employees as well.
A study done many years ago at a large retail firm with thousands of stores found that every 10 points of increase in employee engagement translated into a 4-point increase in customer satisfaction. We anticipate a similar connection between employee delight and customer delight. As leaders make room for employees to experience both big _C_ and little _c_ creativity, enjoy little pleasures, find work conducive to a sense of humor and playfulness, and practice civility, employee satisfaction can turn into customer satisfaction.
You may not be able to afford a fancy gym or day-care center for your employees, but a yoga class or a Ping-Pong table might fly. Salaries may be frozen, but someone could still thaw out the cookie dough. Delight doesn't have to mean expensive artwork or fancy furniture, and it is not something people have to wait for management to provide—as long as thoughtful leaders are opening up the windows to let a little delight blow through.
### **An Unexpected Lesson in Delight**
When the Khmer Rouge, a totalitarian Communist regime, took over Cambodia in the late 1970s, they emptied the capital city of Phnom Penh of its 2 million inhabitants in a matter of hours, sending everyone to the country to work in rice fields and on farms in makeshift huts and with no training or provisions. An estimated 1.5 million of the 7.1-million-person population died from torture, starvation, disease, and forced labor during the five years of Khmer Rouge rule, probably half from execution, making it the most lethal government of the 20th century. Schools, hospitals, banks, communication systems, and industry all came to a complete halt, with intellectuals, professionals, the educated, those with leadership skill, and city dwellers among the most suspect and the first to be executed. Children were separated from parents and trained in torture. The oft-repeated phrase from the government to the populace was "To keep you is no benefit. To destroy you is no loss."
Teeda Butt Mam and her family were among those evacuated from the city and sent to the rice fields to eke out a meager existence. Despite being well-educated professionals, they survived by working hard, adapting skillfully, and carefully hiding their background. As they became more aware of the relentlessness of their oppressors and the impossibility of escape, however, Teeda became more and more despondent. Though suicide meant sure punishment to surviving family members, when Teeda's friend was raped brutally and repeatedly until she died, Teeda began plotting her own death. Life had lost all meaning, and she felt dead inside. The months and years of horror and exhaustion seemed impossible to endure any longer, even for the sake of her mother and siblings. But then the story takes an unusual turn. Teeda states:
_Then, unexpectedly, on my way to the rice fields one morning, I glanced up, just as the sun rose over the paddies. The sheer beauty of heavy ripening rice silhouetted against the glorious orange sky took my breath away. A massive, plodding buffalo moved across the scene, giving a sense of the continuity of life from former times to now—an instant lesson in patience and perseverance. All nature affirmed that some things were beyond Angka Loeu's the Khmer Rouge's] power to control. Neither sunrise nor storm, neither cloud nor wind nor bamboo, nor I, would be controlled by Angka. Angka Leou was not omnipotent. I felt—for the first time in months—that life might still hold something worthwhile.[ 4_
A tiny moment of delight, of beauty, declaring that "life might still hold something worthwhile," held Teeda steady through this moment of crisis and gave her a memory that held her through many others. She and her family eventually escaped Cambodia and started a new life in the United States.
If a small moment of delight can bring hope to someone in such circumstances, affirming that life is a precious gift even under the hand of unspeakable oppression, surely such moments can bring meaning to those of us with much less to overcome, much more to live for.
**_Summary: Leadership Actions to Foster Delight_**
See and test the connection between employee delight and customer loyalty.
Find ways to delight yourself at work and encourage your employees to find delight through:
Creativity
Pleasure
Humor/playfulness
Civility
## **CHAPTER 10
Implications for Executives, Human Resources, and Individuals**
So, how do the seven principles and actions of _abundant organizations_ apply to business executives leading organizations, to human resource professionals who work to institutionalize these ideas, and to individuals who seek meaning from the work they do?
### **Two Cases**
Rodney Smith is the president of a small liberal arts university in rural Virginia. The idyllic campus was purchased about 15 years ago from a failing finishing school for girls, with the idea of creating a small Eastern mission-based university for members of the Church of Jesus Christ of Latter-day Saints—Mormon kids who more typically head to church- or state-run colleges in the West. Southern Virginia University has grown slowly under its current business model, and it is now home to about 650 students—about 400 shy of capacity. President Smith and his faculty and staff are passionate about their mission and deeply proud of their accomplishments: on average, entering students come in at about the 68th percentile academically and leave at the 93rd, with 55 percent going on to graduate programs. The students also graduate in less time, are significantly more satisfied with almost every aspect of their college experience, and are better prepared for jobs and graduate schools than comparable students attending competitor schools.
Southern Virginia University is ringing wet with meaning and organizational abundance. Like many start-ups, it faces inevitable financial struggles. Small, more expensive than its competitors, and in a remote location, SVU faces a constant uphill battle to pay the bills and come to the attention of prospective students. President Smith's business challenge is not about how to motivate employees with a compelling vision, great colleagues, challenging opportunities, or a positive work environment; SVU is already steeped in all the drivers of meaning. His task is to convincingly share with potential students and donors the particular world of meaning he and others have created so compellingly and to ground that meaning in fiscal disciplines and organizational capabilities to sustain it. Like many start-ups or purpose-driven enterprises, meaning is at the heart of SVU's very existence, but alone it will not be sufficient to ensure its success.
At perhaps another extreme would be a large business conglomerate in existence for a long time. We recently rented a car from an airport kiosk of just such a large national agency. While waiting for the paperwork to be processed, we asked a young employee standing nearby how she felt about her job. She candidly but somewhat sheepishly reported that she liked all the downtime when she could catch up on her favorite TV shows. A second, older woman who had apparently been there much longer was busy processing our rental documents, overheard our question, and volunteered _her_ answers: she really liked chatting with customers, adding that she learned a lot from people she talked with. When Dave asked her if she had a bigger car available that might fit him better, she thought carefully about the available options and made a good recommendation; redid the paperwork without a grumble; gave us quick, accurate directions to the small, distant town we were headed to; and gave us clear, intuitive instructions for finding our car.
Working at a rental car kiosk is not exactly a job fraught with meaning, nor did the younger employee seem to need a compelling vision or challenging growth opportunity to get her to show up for work that day. She was content with a paycheck and the chance to watch TV. The question is, will she last? Will she attract and retain long-term customers? Will the agency's investment in training her pay off in their bottom line? Our guess would be that unless she can find more meaning in her work—as her more seasoned colleague seemed to have done—she will neither endure long nor contribute significantly to the company's success. Nor will it have much impact on hers.
Organizations face different challenges around meaning. Leaders of start-ups may put their stake in the ground precisely because they are hungry to fill a niche they care about and invest it with their passion and energy. They have plenty of meaning, but they need to find ways to communicate that meaning to stakeholders and support it with sound business practices. Leaders in established companies with proven track records and ingrained business practices may struggle more to keep their founding meaning fresh and growing, invest it with the energy and skill of established employees, and communicate it compellingly to new hires. And many companies line up somewhere in between on all these dimensions.
In this final chapter we will review why meaning is a crucial foundation for organization capability in all types of businesses and how top leaders, human resource professionals, and employees can create—returning to our original definition of abundant organizations—work settings in which individuals coordinate their aspirations and actions to create meaning for themselves, value for stakeholders, and hope for humanity at large.
### **The _Why_ of Meaning at Work**
In either personal therapy or leadership coaching, we generally start with a "presenting problem." In personal therapy the presenting problem might be symptoms of depression or anxiety, addiction, marital discord, or learning problems. For business leaders, this presenting problem might be a business challenge like loss of market or customer share, falling stock price, the need for more revenues in emerging markets, low customer service scores, technology changes in the industry, loss of key talent, or the need to grow through new markets or innovative products. To adequately address the presenting problem, one must identify and resolve its underlying causes. Treating only symptoms delivers only short-term gains that do not become sustainable solutions.
We believe that the underlying cause of many presenting problems in business today is a deficit of meaning. Our logic:
Presenting problems generally show up as an organization's _inability to respond to external requirements_. Presenting problems might be:
Inability to meet customer needs—evidenced by falling customer share, market share, or customer service scores
Losing investor confidence—evidenced by lower financial returns or lower stock values
Poor community reputation—evidenced by erosion of brand confidence or inability to attract or retain employees
Underlying causes of these presenting problems are _lagging organization capabilities_. An organization capability is what the organization is good at and known for, such as the ability to:
Change quickly
Innovate
Serve customers
Operate efficiently
Collaborate and build teams
Learn
Manage risk
An organization's capabilities are a collection of the _competencies and commitment_ of individual employees. Organizations do not think or act; people do. When people think and act in a skilled, cohesive way, organization capabilities follow.
Individual competencies (ability to do the work) and commitment (willingness to do the work) are sustained and leveraged when employees see how their work makes a genuine _contribution_ to people and causes they care about (finding meaning in the work).
To reverse this logic:
Employees' ability to find meaning in their work leverages and sustains their competencies and commitment.
The collective competence and commitment of employees creates organization capabilities.
These capabilities address the presenting problems facing organizations today, leading to sustained organizational success.
Employee meaning is, therefore, a lead indicator of not only organizational abundance but also organizational prosperity. **_Why_** meaning? Because meaning has both inherent value to individuals and market value to companies. Leaders who diagnose, invest in, and improve meaning address underlying causes, not symptoms, so their solutions endure beyond quick-fix activities.
### **The _How_ of Meaning**
Leaders help employees find meaning at work as they learn and apply the seven drivers of meaning we have presented. These seven drivers tap into the inherent value or meaning people generally find in:
Evolving their identity by using their personal values and strengths at work
Staying grounded in a purpose and a direction that connects personal drives to a common good
Enjoying satisfying relationships where they feel respected and attached
Creating positive work environments that sustain their productivity
Tackling challenges that invite growth and innovation
Finding value even in setbacks as they learn and bounce back
Appreciating the daily delights of civility, creativity, humor, playfulness, and pleasure
The **_why_** and **_how_** of meaning have implications for (1) leaders at all levels of a company, (2) human resource professionals, and (3) individual employees. All three can use these meaning drivers throughout an organization to promote both _personal values_ and _bottom-line values_.
### **Leadership Implications**
Our primary audience throughout this book has been leaders. Leaders set the tone for their organizations. Leaders make choices and investments that determine how organizations work. Leaders model what others follow. Sometimes employees consciously choose to follow their leader's intentional directives; other times the leader's behavior provides subtle cues about what is permissible or expected. When leaders focus on meaning-making activities, employees more readily sense that their experience at work matters to someone and that their contribution is valued.
Leaders at all levels can help make meaning happen.
#### **Boards of Directors**
The primary task of a board of directors is to monitor and ensure fiscal responsibility to shareholders. Some argue that organizations should also demonstrate social responsibility as an end in itself, even if doing so ignores profitability. While we admire the intent of this work, we believe it does not reflect the reality of competitive organizations. Competitive organizations that are socially responsible and make people feel good but don't serve customers and investors simply will not (and should not) survive. Even not-for-profit organizations succeed and survive only by delivering value to communities and constituents. But we don't have to rely on a social conscience to justify spending time building meaning. Research (reviewed in Chapter 1) compellingly suggests that meaning making for employees can be money making for shareholders. Employees who find meaning in their work have more positive attitudes, which in turn predict not only employee retention but also customer attitudes and shareholder confidence. If boards are serious about sustained financial success, they will attend to the creation of meaning. As shareholder representatives, boards often oversee financial results, product innovations, strategic choices, and customer satisfaction; we suggest boards also assess leadership depth, talent processes . . . and employee meaning.
To track meaning, boards pay attention to both formal indicators and informal observations. Retention of key talent, productivity indices about company outputs per unit of employee input, or employee survey scores on the meaning dimensions we reviewed in Chapter 2 each may be used to assess the extent to which employees find meaning at work. Board members may also use informal observations to track a sense of employee meaning. They may observe:
How employees treat outsiders (customers, board members, guests) who visit the company
How employees show pride in their work setting (e.g., in cleanliness)
What employees want to talk about when asked about their work
How much employees use the products or services the company offers
How many company symbols employees use
What reputation the company has with outsiders
None of these queries or observations is perfect, and if employees are coached overtly to parrot the "right" answers or put on a show, these measures will become meaningless. But board members who ask, listen, and accept the answers given can get a feel for the degree of organizational abundance of a company. Board members who attend to employee signals and who openly discuss meaning making help connect social consciousness with sustainable economic success.
#### **C-Suite Executives ( _C_ for Chief, as in Executive, Financial, Technology, Marketing, or Human Resource Officer)**
Senior executives model and monitor their organization's level of abundant or deficit thinking. They live in glass houses, and their words and actions are scrutinized and mimicked. Senior leaders model a commitment to meaning by communicating, personalizing, and tracking meaning at work.
In formal settings like board meetings, annual reports, websites, performance reviews, training programs, and monthly staff meetings, leaders communicate priorities by what they spend time on and how they work through issues. In informal hallway conversations, leaders signal what matters most to them. When leaders are transparent about not only what is happening but also how they feel about it, when they face difficult issues head-on, and when they connect the creating of meaning to the making of money, they legitimate employee efforts to attend to and discover meaning at work. Leaders who share positive _affect_ have positive _effect_.
Senior leaders personalize meaning and spread it around by sharing their aspirations and helping others do the same. A new president of a large state university began his first senior management retreat by asking everyone to tell a story about why he or she worked there. People talked about how education had enriched their personal lives, how their parents had sacrificed to provide them with schooling, how education had helped their children or siblings progress and contribute, or how they felt when they personally experienced students' learning and growth. These touching personal stories captured the shared identity and purpose of the university, reminding leaders why they did the work they did. The stories formed a foundation of meaning and shared vision that lent legitimacy and urgency to subsequent discussions of budget, curriculum, procedures, and staffing. When senior executives share how they feel about their work, they build a foundation of meaning that grounds their organizational efforts.
Communicating and personalizing meaning is not enough. Senior executives must help their organization turn aspirations into actions to sustain that meaning foundation. If the organization's values and goals are lauded but not materialized, meaning dissipates quickly.
Senior leaders need not only advocate and institutionalize meaning but also audit it. In addition to financial, customer, and organization reviews, leaders might ask questions such as these:
How do you feel about the work you do?
How do customers feel as they receive the outcomes of your work?
How do you use your strengths and values at work, and how often?
How do you see your work contributing to things you care about?
What are you learning about yourself in this job?
How do you explain what you do at work to your closest friends and family?
How much energy and passion do you feel for your work?
These questions focus on the emotion, values, and meaning inherent in work. They legitimate conversations about meaning at work. Of course, executive openness and accessibility will accentuate the grumbling of the disaffected, but thoughtful executives can use this to forestall bigger problems and make course corrections, as well as to ferret out more positive patterns. Sometimes listening comes from face-to-face employee visits in town hall meetings, at site visits, or on employee road shows. With technology, leaders can also get a sense from blogs, Web chat rooms, and employee networks. In all these listening posts, it is critical not to over-or underreact. It is also crucial not to "teach to the test" (rewarding the "right" comments rather than allowing comments to reflect real feelings). As leaders move around asking about meaning, they will raise awareness and accountability among others for its creation. In addition, senior executives can do organization meaning audits using the questions we laid out in Chapter 2 to determine whether their organization encourages meaning in each of the seven dimensions.
#### **Leaders as Models**
People say that charity begins at home. The same is true for meaning. To become a leader who shapes and creates meaning for others, start with a personal meaning audit:
How do I feel about my work?
What aspects of my job are the most meaningful to me?
What am I trying to accomplish that feels connected to a greater good I value?
Which of the seven drivers of meaning matters most to me?
Which of the seven drivers of meaning could I invest in to make a difference in how I experience my job?
What could I do in the next 30 to 90 days to help myself and my employees find more meaning in our work?
A leader's small meaning-promoting acts can enhance a sense of personal meaning. When budget cuts at one company meant eliminating snacks at corporate off-sites, the top executive personally baked cookies to pass around at the next retreat. In another company, a leader wrote personal thank-you notes to those who made unique contributions to a product or customer success. Another executive observed special events (birthdays, work anniversaries, children's graduations, funerals) with personal cards or notes. Another wrote gratitude letters to employees' significant others (spouses, partners, children, parents) to personally acknowledge the employees' good works. Such small and simple actions signal a sense of sharing values and of valuing employees. This is not to suggest in any way that a leader has to be every employee's best friend or that pragmatic financial issues be taken lightly. But the leader who attends to making meaning will likely find more support in meeting financial, customer, and other business goals as well.
Leaders communicate both formally and informally the things that matter most to them. When communications include not only facts but feelings, leaders can touch hearts as well as minds. At the large state university off-site where the president invited stories about why people cared about education, he gave each leader a Newberry Award–winning children's book and invited them to give the book to a child they knew. They were asked to write a personal note to this recipient to explain why learning mattered to them. This symbolic act helped them directly experience the joy of sharing the value of learning with someone they cared about. The university off-site ended with a video of current students telling their stories of how the university had helped them. Sharing customer experiences with a company's products or services helps employees connect with the impact of their work on real people—always a meaning builder.
### **Human Resource Implications**
Dave has spent much of his career figuring out how to build human resource (HR) systems that deliver value—both inside the company to employees and managers and outside the company to customers, investors, and communities. He has helped focus HR on the outcomes or value it creates for others rather than on internal HR activities and practices. HR work that focuses on adding value becomes a means for leaders to sustain desired results. Dave is frequently asked why he chose to invest in HR. His response is simple: HR practices form the infrastructure that makes sustained organizational success possible.
Early in his career, Dave facilitated versions of a t-group, where members of a team got together over a weekend to share their personal feelings about work, each other, and the company. Late Saturday night, as fatigue set in, people's defenses often fell, and they tended to open up and be honest with each other, sometimes to the point of rudeness. Often a false sense of genuine emotional intimacy resulted. Unfortunately, this temporary intensity of sharing real feelings was frequently lost by Monday morning, when they all returned to work and the organization patterns they had established. Dave realized that sustained change did not come through emotive weekends but through institutionalized HR practices around recruitment, promotion, development, compensation, communication, and organization design. When these systems were changed, organization capabilities emerged that outlasted any single event or leader.
If employee meaning is a lead indicator of organization capabilities, financial results, customer service, and community reputation, it should also be a key outcome of good HR work. HR practices related to (1) people, (2) performance, and (3) organization can be designed to create and sustain meaning.
#### **People Practices**
Meaning should be a key consideration when hiring, training, developing, promoting, or outplacing employees. Hiring people who are technically competent and intellectually committed is not enough. Leaders and HR professionals should also examine the fit between the worker's values and passions and the job hired for. We have discussed under identity, purpose, and the nature of work signals that suggest employees are coming to work with not only their brains, hands, and feet, but also their hearts and souls. In monitoring these signals it is important to remember that many wonderful, contributing employees are not demonstrative extroverts who wear their passion for work on their sleeve. Signals may vary from person to person and should be used as just that—signals—not as ends in themselves to be rewarded or punished.
Training and development opportunities for employees should be initiated by both management (so employees acquire skills to do their work well) and employees who desire to learn and grow. Career moves should include consideration of what the employee feels passion about. Moving into a more senior position for the sake of salary and status alone does not always lead to sustained motivation. Employees are more likely to sustain energy and passion for their career moves if their signature strengths match their new roles. When it is necessary to let someone go, it should be done with care and concern, so that those who remain feel there is justice in the process.
#### **Performance Practices**
Total reward systems begin with clear expectations for both work outcomes (financial or customer results) and the behaviors that lead to them (such as the seven meaning drivers we have identified). Money is a big motivator, often a primary motivator. But money often has as much value as a symbol of importance or prestige as it does in buying power itself. Nonfinancial rewards like work flexibility, growth opportunities, access to valued relationships, and positive work environments are frequently at least as important as money in shaping employee meaning.
#### **Organization Practices**
Over time, organizations become institutionalized through their policies, structures, and physical settings. HR can also shape work policies and practices to support employees. We have seen companies offer:
Concierge services to help employees with daily logistics
A speaker series where employees could hear industry thought leaders
Tutoring services where employees help other employees' children with homework
Venture capital advice for employee spouses who wanted to start their own business (side note: when spouses used the business advice, the employee almost always stayed with the company)
Leaders can and should turn to their HR professionals to help design and deliver HR practices that instill meaning, linking these practices to presenting business problems. To promote meaning making, HR can architect choices, coach leaders on intended and unintended consequences of their actions, facilitate the processes of change, perform meaning audits, and help craft an employee value proposition that focuses not just on the terms and conditions of work but also on the emotional appeal and opportunities for contribution that the work provides.
HR practices institutionalize good intentions. Most of Dave's work has focused on creating and sustaining customer and investor outcomes of HR, and the creation of employee meaning is both a lead indicator of these outcomes and a valued outcome in and of itself.
### **Employee Implications**
The importance of meaning to the next generation came into sharp focus in the spring of 2009 when almost half of the M.B.A.s graduating from Harvard Business School took a pledge to "do no harm," "serve the greater good," and "act with the utmost integrity." While symbolic more than binding, this ambitious pledge sent a clear signal about the hopes and ambitions of a talented and capable elite group. They expect work to make a difference for good in the world, they expect to make a difference at work, and presumably they expect work to make a difference to them. We see this social responsibility pledge as a worldwide tsunami with more and more business-oriented students wanting to both make money and do good.
In a very different setting, a colleague shared how he applied some of the concepts presented in this book with an entirely different audience:
_Last week I used your ideas (with some modification) to youth who are sentenced in a Detention Center. Their ages run from 10 to 18 years old. I first showed them pictures of several famous people—leaders and celebrities—and asked them what attributes come to mind when they thought of each particular person. After a few minutes of discussion I had them think of a person they knew personally who has made a significant difference in their lives and who has helped them find meaning. I had them list their attributes. Some shared a great deal—it was very touching at times. I then told them to listthe characteristics of their "ideal significant person." This next part was a bit abstract and I was worried that it would not work. I then told them that the attributes they listed for the "significant person" exercise were really their values, the attributes that they could aspire to. I spent a long time on the idea that those attributes often become hidden under much baggage, but if they focused on bringing meaning into their lives, they could find it. They "got it." Finally, I asked them to recognize the meaning they bring to the world and their families. I saw tears and many who recognized that they had worth within them—maybe for the first time. These were boys who were in jail who now had something in their hand, affirmed by them, which said that they brought something to us all. By exploring how others gave them meaning, they found meaning in who they were. So thanks. Some CEOs will benefit greatly from your book—but for 20 boys in a detention center it made a tremendous difference._
The search for meaning applies equally to Harvard M.B.A.s with bright futures and young adults with tough histories trying to identify who they are in a complex world. While skilled leaders can help guide that search, it falls to individual employees to pick up the trail if leaders do not. Abraham Lincoln is often quoted, "Most people are about as happy as they make up their minds to be." We would tweak this a bit: "Most people find about as much meaning in their lives as they make up their minds to find."
Employees make many choices that can enhance meaning in their personal and professional lives. Some employees might drop out of the corporate world and live more simply. Others will invest deeply in their careers and their companies. Whether exploring options for a first job, a job change, or just the job they get up for on yet another Monday morning, employees can make more thoughtful meaning choices about their professional lives by considering the seven questions we have suggested:
**What will I be known for?** How can I express my core values in my daily work? Which job, career, or life choice will build on my strengths and best match my identity with the organization brand?
**Where am I going?** What impact do I want to make on what types of problems? Which job, career, or life choice will help me reach my goals and accomplish things that are important to me?
**Whom do I travel with?** How do I build the skills of good relating? Which job, career, or life choice will help me build relationships that matter to me?
**How do I build a positive work environment?** What can I do to make my work environment more conducive to my work style? Which job, career, or life choice will be pursued in a work setting that I personally enjoy?
**What challenges interest me?** How can I calibrate the level of challenge to stay optimally engaged and make a significant contribution? Which job, career, or life choice will offer me opportunities to do work that is easy, energizing, and enjoyable for me personally?
**How do I respond to disposability and change?** How do I do a better job of making what I have enough? Which job, career, or life choice will help me grow, learn, and develop resilience when facing change?
**What delights me?** How can I make more room for pleasure, playfulness, creativity, and living in the moment? Which job, career, or life choice will bring a sense of joy and delight to my personal and professional life?
We have asked these questions of hundreds of people facing choices among jobs, companies, and careers. These questions are timeless and work in both up and down markets to help people find a sense of meaning in their work lives. The seven meaning drivers also apply in families, neighborhoods, social groups, and volunteer associations. Wherever people work together to accomplish a shared goal, meaning matters.
### **A New Value Proposition**
Traditional employee value propositions have focused on terms and conditions of work, often around pay and working conditions. While money will always matter, the new employee value proposition is also about meaning. In Chapter 1, we presented bleak statistics about the deficit that many people face in their personal and professional lives. In contrast to these deficits, this book explores how an abundance mentality focused on creating meaning can help employees in all kinds of circumstances find enough and to spare of what matters most. We believe that the heart of leadership is fundamentally about the creation of meaning and that leaders have a primary accountability to work with their employees to unleash it. A focus on meaning can yield employees who are more productive and committed, who build the organization's capacity to respond to business challenges, and who help their organizations succeed.
In up markets, when talent is scarce, meaning matters because employees are essentially volunteers who can choose where to allocate their time and energy. In down markets, some organizations experience a gratitude effect and get false positives on employee engagement scores from employees who gratefully compare themselves with less fortunate colleagues. But memories last longer than recessions. Employees who felt mistreated or taken advantage of during the down markets may look elsewhere when options open up. Companies that succeed at helping employees find meaning in downturns often create a cadre of resilient and motivated contributors who will be the problem solvers and innovators of future success.
We have had a number of candid conversations with leaders and employees at all levels about the changing role of leadership in today's business world. Often what we sense is increased cynicism. People distrust leaders who make personal gain more important than organizational and societal responsibility. Some will shy away from leadership opportunities because of this cynicism or because the price and risks of leadership feel too high in a transparent world, where leaders' privacy is lost to YouTube and leader decisions are debated endlessly on blogs and talk shows. There is an increasing and pressing need for good and great leaders at all levels of organizations and society—leaders who not only deliver results but also foster meaning, whose leadership agendas include both fiscal responsibility and social responsibility, who organize to both solve existing problems and imagine new possibilities. Leadership is a noble stewardship.
Meaning should be a real option for every worker who values it, and not just in not-for-profit organizations that have been its traditional province. Whether our future employees are graduating from the Harvard Business School or the local detention school, meaning matters. It matters not only for the profit of investors and the needs of customers but also for the hearts and souls of the millions of people who get up and go to work every day. Delivering on that hope is one of the most important opportunities facing business today.
## **APPENDIX
_LEADERSHIP CHALLENGES AND ACTIONS AS MEANING MAKERS_**
### **Leadership Identity Challenge**
With rapid technological, demographic, political, and social change, organizations scramble to align employee strengths into a coherent organization identity that responds to evolving customer and societal requirements. Great leaders help individuals align their personal strengths with the organization identity (firm brand) and with customer expectations.
#### **_Summary: Leadership Actions to Build an Identity_**
Help employees become more aware of their signature strengths through assessment, conversation, observation, and assignment
Define your organization's required strengths (or capabilities) by doing a capability audit
Make sure that employees' strengths serve the organizational capabilities they are hired to build
Define your key customers and investors and determine their expectations of you
Connect the identity of the individuals and organizations to the customers they serve, building on strengths that strengthen others.
### **Leadership Purpose Challenge**
In a world of information overload and centrifugal goals, employees and organizations often spin away from their basic sense of purpose and direction. Great leaders recognize what motivates employees, match employee motivators to organization purposes,and help employees prioritize work that matters most.
**_Summary: Leadership Actions to Articulate a Purpose_**
Help employees recognize what motivates them (insight, achievement, connection, empowerment)
Match the employees' motivation with the organization task they are assigned to perform
Create an organization aspiration that declares a socially responsible agenda and translates that agenda to individual action
Help employees satisfice in those tasks that are worth doing poorly and prioritize tasks that are important to do well.
### **Leadership Relationship Challenge**
Despite increasingly competitive and isolating work settings and declining interpersonal skills, much work has to be accomplished with others and within teams. Great leaders help employees build skills for professional friendships between people and among teams.
**_Summary: Leadership Actions to Foster Relationships and Teams [Th]at Work_**
Develop good friendships at work and encourage others to do so too
Learn, teach, and model the skills of making and receiving bids, listening and self-disclosing, navigating proximity, resolving conflicts, and making amends
Apply these skills to relationships between people and among teams
### **Leadership Positive Work Environment Challenge**
Organizations develop unconscious patterns of how work is done that, left unattended, may lead to cynicism, disorganization, redundancy, or lethargy. Great leaders recognize and establish positive work environments that inspire employees, meet customer expectations, and give investors confidence.
**_Summary: Leadership Actions to Create a Positive Work Environment_**
Pay attention to the work environment as patterns of how things are done
Regularly monitor the work environment
Pick two or three of the items from your diagnosis and focus on them
Ask newcomers to your work environment their impressions of what is positive and what is not
Make public statements about your commitment to shaping a positive work environment
### **Leadership Personalizing Contributions Challenge**
Too often employees feel emotionally disconnected from the work they do; their work may capture their talents and time but not their heart and soul. Great leaders personalize work conditions so that employees know how their work contributes to outcomes that matter to them.
**_Summary: Leadership Actions to Ensure Personalized Contributions to Work Personalizing and Contributing Work_**
Learn what outcomes matter to employees; how does this job relate to their identity, values, and purpose
Help employees articulate the line of sight between what they do and the outcomes they value
Help employees discover the intrinsic value of their work and what they enjoy in the work itself
Shape work conditions and match employees to conditions that appeal to them (where, when, with whom, and how they work)
### **Leadership Growth, Learning, and Resilience Challenge**
As changes compound and the risk of failure increases, people may fade, fail to adapt, and get demoralized, which leads to organization stagnation. Great leaders relish change and help employees grow, learn, and be resilient to bring new life to their organizations.
**_Summary: Leadership Actions to Facilitate Growth, Learning, and Resilience_**
Have a positive attitude about change, that you can learn from it and be resilient when facing it.
Learn how to generalize new ideas through self-reflection, experimenting, boundary spanning, and continuous improvement
Learn how to generalize, or share, new ideas by moving talent across boundaries, sharing information across boundaries, and building incentives to encourage shared behavior
Become resilient in the face of change by making the unspeakable speakable, turning what you know into what you do, and changing events into patterns
### **Leadership Delight Challenge**
Partisanship sometimes affects organizations where there is more hostility than civility and where a we-they, win-lose, right-wrong, blame-and-shame mentality persists. Great leaders move away from hostility and intolerance toward multiculturalism through problem solving, listening, curiosity, diversity, and compassion and by bringing creativity, pleasure, humor, and delight into their organizations.
**_Summary: Leadership Actions to Foster Delight_**
See and test the connection between employee delight and customer loyalty.
Find ways to delight yourself at work and encourage your employees to find delight through creativity, pleasure, humor/playfulness, and civility
## **NOTES**
### **Chapter 1**
1. This research is summarized in: Ulrich, D., and N. Smallwood (2003). _Why the Bottom Line Isn't_. Boston, MA: Harvard Business Press.
2. These five companies are the only ones listed in both editions of the book _The 100 Best Companies to Work For_ (1985 and 1993) and then on every list published in _Fortune_ magazine since 1998.
3. Keynote address by Honorable Lyonchhen Jigmi Y. Thinley, prime minister of Bhutan, at the World HRD Congress 2010, Mumbai, 12 February 2010.
4. Bardwick, J. M. (2007). _One Foot Out the Door: How to Combat the Psychological Recession That's Alienating Employees and Hurting American Business._ New York, NY: AMACOM.
5. Marks, N., A. Simms, S. Thompson, and S. Abdallah. (2006). _The Happy Planet Index: An Index of Human Well-Being and Environmental Impact._ London, UK: New Economic Foundation. happyplanetindex.org.
6. Evans, V. (2008, February 29). _Depression Statistics—Just the Facts._ Retrieved January 22, 2008, from http://ezinearticles.com/?Depression -Statistics—Just-The-Facts&id=1017816. Kessler, R. C., W. T. Chiu, O. Demler, and E. E. Walters. "Prevalence, Severity, and Comorbidity of Twelve-Month DSM-IV Disorders in the National Comorbidity Survey Replication (NCS-R)." _Archives of General Psychiatry_. The World Health Organization. _The World Health Report 2004: Changing History_ , Annex Table 3: Burden of Disease in DALYs by Cause, Sex, and Mortality Stratum in WHO Regions, Estimates for 2002. Geneva: WHO, 2004.
7. Kessler, R. C., W. T. Chiu, O. Demler, and E. E. Walters. "Prevalence, Severity, and Comorbidity of Twelve Month DSM-IV Disorders in the National Comorbidity Survey Replication (NCS-R)." _Archives of General Psychiatry_ , 2005 Jun;62(6):617–27.
8. Andersen, A. E. (1995). "Eating Disorders in Males." In: Brownell, K. D., and C. G. Fairburn (Ed.), _Eating Disorders and Obesity: A Comprehensive Handbook_ (pp. 177–187). New York, NY: Guilford Press. Spitzer, R. L., S. Yanovski, T. Wadden, R. Wing, M. D. Marcus, A. Stunkard, M. Devlin, J. Mitchell, D. Hasin, and R. L. Horne (1993). "Binge Eating Disorder: Its Further Validation in a Multisite Study." _International Journal of Eating Disorders,_ 13(2), 137–53. Yager, J., M. J. Devlin, K. A. Halmi, D. B. Herzog, J. E. Mitchell, P. S. Powers, and K. J. Zerbe (2000). "American Psychiatric Association Work Group on Eating Disorders: Practice Guideline for the Treatment of Patients with Eating Disorders (revision)." _American Journal of Psychiatry,_ 1–39. Bruce, B., and W. S. Agras (1992). "Binge Eating in Females: A Population-Based Investigation." _International Journal of Eating Disorders,_ 12, 365–73.
9. See World Wide Fund for Nature (wwf) report _Living Planet Report, 2008._ http://assets.panda.org/downloads/living_planet_report_2008.pdf.
10. See World Wide Fund for Nature (wwf) report _Living Planet Report, 2008._ http://assets.panda.org/downloads/living_planet_report_2008.pdf.
11. Fan, D., R. Wyatt, and K. Keltner (2001). "The Suicidal Messenger: How Press Reporting Affects Public Confidence in the Press, the Military, and Organized Religion." _Communication Research_ , 28(6). Paxton, P. (1999). "Is Social Capital Declining in the U.S.? A Multiple Indicator Assessment." _American Journal of Sociology_ , 105(1).
12. Gaines-Ross, L. (2008). _Corporate Reputation: 12 Steps to Safeguarding and Recovering Reputation._ New York, NY: Wiley.
13. Office for National Statistics. (2007, March 15). _Focus on the Digital Age._ Retrieved January 20, 2009, from statistics.gov.uk/focuson/digitalage.
14. Friedman, T. (2005). _The World Is Flat._ New York, NY: Farrar, Straus and Giroux.
15. In the 2000 census, approximately 30 percent of the U.S. population was "nonwhite," increasing in all states. Aguirre, A. (2003). _Racial and Ethnic Diversity in America: A Reference Handbook (Contemporary World Issues)._ Oxford, UK: ABC-CLIO.
16. Gundling, E., and A. Zanchettin (2006). _Global Diversity: Winning Customers and Engaging Employees Within World Markets._ London, UK: Nicholas Brealey Publishing.
17. Twenge, J. M., and W. K. Campbell (2002). "Self-Esteem and Socioeconomic Status: A Meta-Analytic Review." _Personality and Social Psychology Review_ , 6(1), 59–71.
18. Lancaster, L., and D. Stillman (2003). _When Generations Collide: Who _They Are. Why They Clash. How to Solve the Generational Puzzle at Work._ New York, NY: HarperCollins._
19. Nielsen, A. C. (2007). _Television Statistics_. Retrieved January 20, 2008, from The Sourcebook for Science Teaching, csun.edu/science/health/docs/tv&health.html#tv_stats.
20. Putnam, R. (2000). _Bowling Alone: The Collapse and Revival of American Community._ New York, NY: Simon and Schuster. Putnam, R. D. (2007). " _E Pluribus Unum:_ Diversity and community in the twenty-first century. The 2006 Johan Skytte Prize Lecture." _Scandinavian Political Studies,_ 30(2), 137–74. Retrieved January 20, 2009, from blackwell-synergy.com/doi/full/10.1111/j.1467-9477.2007.00176.x.
21. Branham, L. (2005). _The Seven Hidden Reasons Employees Leave_. New York, NY: American Management Association.
22. _Employee Engagement Report._ (2008). Retrieved from blessingwhite.com/EEE__report.asp.
23. 2006 Gallup study: Engaged employees inspire company innovation. _Gallup Management Journal._
24. Gallup study: Engaged employees inspire company innovation. _Gallup Management Journal._
25. YouGov (2009): yougov.co.uk.
26. Bernthal, P. (2004). Measuring Employee Engagement Development Dimensions International Inc. White paper.
27. Retrieved 20 January 2009 from divorcerate.org.
28. Seltzer, J. A. (1994). "Consequences of Marital Dissolution for Children." _Annual Review of Sociology, 20,_ 235–66. Clark-Stewart, A., and C. Brentano (2007). _Divorce: Causes and Consequences._ New Haven, CT: Yale University Press.
29. Starker, S. (2002). _Oracle at the Supermarket: The American Preoccupation with Self-Help Books_. Piscataway, NJ: Transaction Publishers.
30. Salerno, S. (2005). _Sham: How the Self-Help Movement Made America Helpless_. New York, NY: Crown.
31. Bishop, B. (2008). No we didn't. Retrieved 5 March 2009 from slate.com/blogs/blogs/bigsort/archive/tags/2008+election/default.aspx.
32. Wilson, W. (1913). Swarthmore College, Swarthmore, Pennsylvania. 25 October 1913. Wilson, W. (1956). _The Politics of Woodrow Wilson: Selections from His Speeches and Writings._ New York, NY: Harper & Brothers. (Republished in 1970 by Harper & Row, Publishers, Inc.)
### **Chapter 2**
1. There are many books on positive psychology: Seligman, M. E., and M. Csikszentmihalyi (2000). "Positive Psychology: An Introduction." _American Psychologist_ , 55, 5–14. Seligman, M. (2004). _Authentic Happiness. Using the New Positive Psychology to Realize Your Potential for Lasting Fulfillment_. New York, NY: Free Press. Lyubomirsky, S. (2008). _The How of Happiness: A Scientific Approach to Getting the Life You Want_. New York, NY: Penguin.
2. Asplund, J., S. J. Lopez, T. Hodges, and J. Harter. (2009). _The Clifton StrengthsFinder® 2.0 Technical Report: Development and Validation_ [technical report]. Lincoln, NE: Gallup.
3. Cameron, K. S., J. Dutton, and R. E. Quinn (2003). _Positive Organization Scholarship: Foundations for a New Discipline._ San Francisco, CA: Berrett-Koehler. Mroz, D., and S. Quinn. (2007). "Extraordinary Teams: Beyond High Performance." _Strategies._ http://competingvalues.com/competingvalues.com/wp-content/uploads/2009/07/Extraordinary-Teams-Beyond-High-Performance.pdf.
4. Savitz, A. W., and K. Weber (2006). _The Triple Bottom Line: How Today's Best-Run Companies Are Achieving Economic, Social and Environmental Success—and How You Can Too._ San Francisco, CA: Jossey-Bass.
5. Harter, J. K., and N. Blacksmith (2009). "Employee Engagement and the Psychology of Joining, Staying in, and Leaving Organizations." _Oxford Handbook of Positive Psychology and Work._ New York, NY: Oxford University Press. Sekerka, L. E., and B. L. Fredrickson (2009). "Working Positively Toward Transformative Cooperation." _Oxford Handbook of Positive Psychology and Work._ New York, NY: Oxford University Press. Richardson, J., and M. A. West (2009). "Dream Teams: A Positive Psychology of Team Working." _Oxford Handbook of Positive Psychology and Work._ New York, NY: Oxford University Press.
6. Wageman, R., D. A. Nunes, J. A. Burruss, and J. R. Hackman (2008). _Senior Leadership Teams: What It Takes to Make Them Great (Center for Public Leadership)._ Boston, MA: Harvard Business School Press. Hack-man, R. (2008). _Leading Teams: Setting the Stage for Great Performance._ Boston, MA: Harvard Business School Press.
7. Gratton, L. (2009). _Glow: How You Can Radiate Energy, Innovation, and Success._ San Francisco, CA: Berrett-Koehler.
8. Mroz, D., and S. Quinn (2007). "Extraordinary Teams: Beyond High Performance." _Strategies._ http://competingvalues.com/competingvalues.com/wp-content/uploads/2009/07/Extraordinary-Teams-Beyond-High-Performance.pdf.
9. Ulrich, D. (1998). "Intellectual Capital = Competence × Commitment." _Sloan Management Review,_ 15–26.
10. Stairs, M., and M. Galpin (2010). "Positive Engagement: From Employee Engagement to Workplace Happiness." _Handbook of Positive Psychology and Work._ New York, NY: Oxford Press.
11. Warren, S. (2010). "What's Wrong with Being Positive?" _Oxford Handbook of Positive Psychology and Work._ New York, NY: Oxford Press.
12. Warren, S. (2010). "What's Wrong with Being Positive?" _Oxford Handbook of Positive Psychology and Work._ New York, NY: Oxford Press.
13. Lyubomirsky, S. (2008) _The How of Happiness: A Scientific Approach to Getting the Life You Want_. New York, NY: Penguin.
14. Harter, J. K., and N. Blacksmith (2009). "Employee Engagement and the Psychology of Joining, Staying in, and Leaving Organizations." _Oxford Handbook of Positive Psychology and Work._ New York, NY: Oxford University Press. Wright, T. A. (2010). "More Than Meets the Eye: The Role of Employee Well-Being in Organizational Research." _Oxford Handbook of Positive Psychology and Work._ New York, NY: Oxford Press. Stairs, M., and M. Galpin (2010). "Positive Engagement: From Employee Engagement to Workplace Happiness." _Oxford Handbook of Positive Psychology and Work._ New York, NY: Oxford Press.
15. Ulrich, D., and N. Smallwood (2003). _Why the Bottom Line Isn't._ New York, NY: Wiley. Ulrich, D., and N. Smallwood (2007). _Leadership Brand._ Boston, MA: Harvard Business Press.
### **Chapter 5**
1. Fowler, J. H., and N. A. Christakis (2008). "Dynamic Spread of Happiness in a Large Social Network: Longitudinal Analysis Over 20 Years in the Framingham Heart Study." _British Medical Journal._ 337: a2338.
2. Rath, T. (2006). _Vital Friends: The People You Can't Afford to Live Without_. New York, NY: Gallup Press.
3. Ibid., 67–70.
4. Gottman, J. M. (2001). _The Relationship Cure: A Five-Step Guide to Strengthening Your Marriage, Family, and Friendships._ New York, NY: Three Rivers Press.
5. Tannen, D. (1986). _That's Not What I Meant!—How Conversational Style Makes or Beaks Relationships._ New York, NY: Ballantine Books.
6. Ibid., 20.
7. Tannen, D. (1990). _You Just Don't Understand: Women and Men in Conversation_. New York, NY: Ballantine Books.
8. Granovetter, M. S. (1973). "The Strength of Weak Ties." _American Journal of Sociology,_ 6(78).
9. Goodwin, D. (2005). _Team of Rivals: The Political Genius of Abraham Lincoln._ New York, NY: Simon and Schuster.
10. Rath, T. (2006). _Vital Friends: The People You Can't Afford to Live Without._ New York: Gallup Press.
### **Chapter 6**
1. Ackman, D. (2002). "Excellence Sought and Found." _Forbes_ , October 10, 2002.
2. Malmendier, U., and G. Tate (2008). _Superstar CEOs._ Working paper from University of Berkeley.
3. Collins, J. (2004). _Good to Great: Why Some Companies Make the Leap and Others Don't._ New York, NY: HarperCollins.
4. Many people have written about servant leaders: Blanchard, K. (2003). _Servant Leader._ New York, NY: Thomas Nelson. Autry, J. (2004). _The Servant Leader: How to Build a Creative Team, Develop Great Morale, and Improve Bottom-Line Performance._ New York, NY: Three Rivers Press. Greenleaf, R., and L. Spears (2002). _Servant Leadership: A Journey into the Nature of Legitimate Power and Greatness._ Mahwah, NJ: Paulist Press.
5. Stewart, T. (1998). _Intellectual Capital: The New Wealth of Nations._ New York, NY: Broadway Business. Stewart, T. (2007). _The Wealth of Knowledge: Intellectual Capital and the Twenty-First Century Organization._ New York, NY: Doubleday Business. Sveiby, K. E. (1997). _The New Organizational Wealth: Managing and Measuring Knowledge-Based Assets._ San Francisco, CA: Berrett-Koehler.
6. Ulrich, D., R. Ashkenas, S. Kerr, and T. Jick. _The GE Work-Out._ San Francisco, CA: Jossey-Bass.
7. Nelson, B. (2002). _The 1001 Rewards and Recognition Fieldbook: The Complete Guide._ New York, NY: Workman Publishing. Nelson, B. (2005). _1001 Ways to Reward Employees_. New York, NY: Workman Publishing. Nelson, B. (1997). _1001 Ways to Energize Employees_. New York, NY: Workman Publishing. Kaye, B., and S. Jordan-Evans (2008). _Love 'Em or Lose 'Em: Getting Good People to Stay._ San Francisco, CA: Berrett Koehler.
8. This story comes from Raymond Schkolne who was the head of HR for the business at the time.
9. Miller, J. (2003). _The Suggestion System Is No Suggestion._ Gemba Research. Retrieved from gemba.com/uploadedFiles/The%20Suggestion %20System%20is%20No%20Suggestion.pdf.
10. National Safety Council (1992). Accident facts. Chicago, IL: National Safety Council. Herman Miller, Inc. (2002). _Body Support in the Office: Sitting, Seating, and Lower Back Pain._ Herman Miller Inc. Retrieved from hermanmiller.com/hm/content/research_summaries/wp_Body_Support.pdf.
11. Herman Miller, Inc. (2001). _Lighting in the Workplace._ Herman Miller, Inc. Retrieved from hmeurope.com/WhitePapers/wp_Lighting_in_Wkpl.pdf.
12. Merck & Co, Inc. (2009). _Building a Positive Work Environment: Advancing the Dialogue Toward a Healthier Future._ Merck & Co, Inc. Retrieved from merck.com/corporate-responsibility/basics/employees/employees-benefits-compensation-training/home.html.
13. Conoco-Phillips. (2008). _Conoco-Phillips Company._ Retrieved from conocophillips.com/SusDev/ourpeople/promoting/index.htm.
14. Brisbane City Council. Joint City Council/Planning Commission Special Meeting. Meeting held 9 April 2007 in Brisbane, California. Minutes taken by Sheri Marie Schroeder, City Clerk.
15. Meraviglia, M., S. J. Grobe, S. Tabone, M. Wainwright, S. Shelton, H. Miner, and C. Jordan (2009). "Creating a Positive Work Environment Implementation of the Nurse-Friendly Hospital Criteria." _Journal of Nursing Administration,_ 39(2), 64–70.
16. TSL Education Ltd. (2009). _Times Higher Education._ Retrieved from timeshighereducation.co.uk/hybrid.asp?typeCode=340&pubCode=1&nav code=98142.
### **Chapter 7**
1. Connecting actions and outcomes comes from classic work called _expectancy theory._ In this theory, if an individual believes a task can be done (expectancy), if the individual sees a high probability that doing the task will result in a meaningful outcome (instrumentality), and if the outcome is valuable (valence), then the individual will commit more discretionary energy to the task. Vroom, V. (2005). "On the Origins of Expectancy Theory," in Smith, K., and M. Hitt. _Great Minds in Management: The Process of Theory Development._ Oxford University Press, 239–58.
2. Business Week (2006). Smashing the clock: No schedules. No mandatory meetings. Inside Best Buy's radical reshaping of the workplace. _Bloomberg L.P._
3. There are a number of studies of antecedents of engagement and what employees want: Magnuson, D., and L. Alexander (2008.) _Work with Me: A New Lens of Leading the Multigenerational Workforce_ , Personnel Decisions International. Morgan, L. (2004). Corporate Leadership Council (2004). _Driving Performance and Retention Through Employee Engagement._ Holbeche, L., and N. Springett (2004). "In Search of Meaning at Work" (report).
4. Kaye, B., and S. Jordan-Evans (2008). _Love 'Em or Lose 'Em: Getting Good People to Stay._ San Francisco, CA: Berrett Koehler.
5. Simon, H. A. (1957). _Models of Man: Social and Rational_. New York, NY: Wiley. Simon, H. A. (1978). "Rationality as a Process and Product of Thought." _American Economic Review,_ 68, 1–16. Simon, H. A. (1983). _Reason in Human Affairs_. Stanford, CA: Stanford University Press.
### **Chapter 8**
1. Clark, T. R. (2008). _Epic Change: How to Lead Change in the Global Age._ San Francisco, CA: Jossey-Bass.
2. Lawler, E., and C. Worley (2006). _Built to Change: How to Achieve Sustained Organizational Effectiveness._ San Francisco, CA: Wiley.
3. Zasky, J. (2009). "Going out of Business Tales: Learning from Inexcusable Business Failures." _Failure Magazine, LLC._ Retrieved from http://failuremag.com/index.php/site/print/going_out_of_business_tales.
4. Jarvis, J. (2009). _What Would Google Do?_ New York, NY: HarperBusiness.
5. Ashkenas, R., D. Ulrich, T. Jick, and S. Kerr (1995). _Creating the Bound-aryless Organization._ San Francisco, CA: Jossey Bass.
6. These individual competencies for organizational learning come from the combination of the organization architect and career architect tools by Lominger. In organization architect, one of the 16 organization capabilities deals with the ability to share information (cluster 7). Lominger then tied this organizational capability to the specific individual competencies most likely to make it happen.
7. The concepts on measures and rewards are drawn from Lawler, E. E. (1990). _Strategic Pay._ San Francisco, CA: Jossey-Bass. Kerr, S. (1988). "Some Characteristics and Consequences of Organizational Reward" in Schoorman, F. D., and B. Schneider (Eds.). _Facilitating Work Effectiveness: Concepts and Procedures_ , Lexington, MA: Lexington Books.
8. Kearns, D. G. (2006). _Team of Rivals. The Political Genius of Abraham Lincoln._ New York, NY: Simon and Schuster. Donald, D. H. (1996). _Lincoln_. New York, NY: Simon and Schuster. McPherson, J. (2009). _Abraham Lincoln._ London, UK: Oxford University Press.
9. Carnegie, D. (2004). _How to Stop Worrying and Start Living._ New York, NY: Pocket.
10. See MADD.com, where those who are bereaved can share their stories and experiences to gain support.
11. Some of the 9/11 support groups include Adam's Angels, adamsangels.org;Long Island 9/11 Memorial, li911memorial.org; 9/11 Memorial Bracelets, http://nleomf.com/html/products/9100l, memorialbracelets.com; Pentagon Memorial Project, http://memorial.pentagon.mil; Reclaiming the Sky, reclaimingthesky.com; The Peter M. Goodrich Memorial Foundation, goodrichfoundation.org; Tuesday's Children, tuesdayschildren.org; Windows of Hope, windowsofhope.org.
### **Chapter 9**
1. Bryan, M., J. Cameron, and C. Allen (1998). _The Artist's Way at Work: Riding the Dragon._ New York, NY: William Morrow.
2. Maisel, E. (1995). _Fearless Creating: A Step-by-Step Guide to Starting and Completing Your Work of Art_. New York, NY: Tarcher/Putnam.
3. Maisel, E. (1995). _Fearless Creating: A Step-by Step Guide to Starting and Completing Your Work of Art_. New York, NY: Tarcher/Putnam.
4. Criddle, J. (2004). _To Destroy You Is No Loss: The Odyssey of a Cambodian Family._ Auke Bay, Alaska: East/West Bridge Publishing House.
## **INDEX**
_Page numbers followed by_ f _or_ t _refer to figures or tables respectively._
Abundance, –36t
assessment of individual, at work, –52t
civility and, –47
commitment and, –44
happiness and, –47
identity and, –38
motivation and, –39
personalized contributions and, –44
positive routines and, –43
purpose and, –39
questions that drive, –47
relationships and, –41
responding to disposability and change and, –45
summary, –36t
teamwork and, –41
work culture and, –43
Abundant organizations
assessment of, –49t
creating, –28
defined,
identity and,
meaning and,
overview of fields and disciplines contributing to, f
process of melding individual, organization, and customer identity, , t
value of,
Abundant relationships,
Abundant work, –84
Accountability, attitude toward, positive work environments and, –43
Achievement, –88
Affect,
Alcoa,
Amends, making, relationships and, –24
Apple, ,
Arrogance, leadership, –29, f
Assignments, leaders and, –69
Berra, Yogi,
Best Buy,
Bids, –11
Boards of directors, meaning and, –51
Bottom-up problem solving,
BP, –57,
Bridges, William, –8
Brisbane, Australia, –52
Bryan, Mark, –25
Buckingham, Marcus, , –64f
Calendar test, –79
Cameron, Julia, –25
Capabilities, defining and building organizational, –72, –72f
Carnegie, Dale,
Change
assessment, –16t
responding to, –45
Checklists, for quality control,
Civility, –37
abundance and, –47
creativity and,
Clark, Tim,
Collins, Jim,
Commitment, abundance and, –44
Communication, attitude toward, positive work environments and, –44
Conflict
attitude toward, positive work environments and, –46
resolving, relationships and, –22
Connection, –90
Connections, attitude toward, positive work environments and, –39
ConocoPhillips,
Contempt,
Continuous improvement programs, –94
Contributions, personalized, abundance and, –44
Conversations, leaders and, –67
Courage, t
Covey, Stephen R.,
Creativity, –28
Crises,
Criticism,
Customer segmentation,
Defensiveness,
Deficit thinking, prevalence of, –23
Delight, –24
customers and, –39
leadership actions to foster,
unexpected lesson in, –41
Dell,
Disney, ,
Disposability, responding to, –45
Eichinger, Robert,
Emotional bank account,
Employee attitude,
Employee Engagement Index,
Empowerment, –92
Engagement, –21
Experimentation
leaders and, –92
protocol for, –94f
Federal Aviation Administration (FAA), –73
FedEx,
Fit for service,
Flexibility, scheduling,
Frankl, Viktor, , –12, , ,
Friendships, at work,
General Electric (GE), –92,
Generalization, –99
Gladwell, Malcom,
Glow,
Goldman Sachs,
Goodwin, Doris Kearns,
Google, –92
Gottman, John, –9,
Granovetter, Mark,
Gratitude enhancers,
Gratton, Lynda,
Gross National Happiness (GNH) index, ,
Happiness
abundance and, –47
sources of,
Happiness scores,
Harley-Davidson,
Havel, Václav,
Herman Miller,
Hewlett-Packard,
High-performing teams, –41
Humanity, t
Human resource practices, –59
Humility, leadership, –30, f
Humor, –35
Hypocrisy,
IBM,
Ideas
attitude toward, positive work environments and, –37
generating new, –90
Identity
abundance and, –38,
leadership actions to build, –80
Incentives, –202
Innovation, leaders and, –92
Insight, –86
Intangibles, –6
Intellectual work,
Involvement, attitude toward, positive work environments and, –41
JetBlue,
Jigme Singye Wangchuck, king of Bhutan,
Jigme Thinley,
Jung, Carl,
Justice, t
Kaye, Beverly,
Kerr, Steve,
Knowledge, t
Kotter, John, –31
Lawler, Ed,
Layout, physical, –48
Leaders
agenda for, –102
assignments and, –69
conversations and, –67
encouraging friendships at work and, –6
experimentation and, –92
finding right fit and, –100
focusing on meaning and, –26
helping employees defining and grow personal strengths and, –64
as meaning makers, –10
melding personal strengths and organizational capabilities, –75
as models, –55
observations and, –66
personalizing work for employees and, –84
self-reflection and,
Leadership actions, summaries of
to articulate purpose,
to build identity, –80
to create positive work environments,
to ensure personalized contributions to work,
to facilitate growth, learning, and resilience,
to foster delight,
to foster relationships and teams that work,
Leadership brand,
Learning, –89
checklist for acquiring talent for, t
leadership actions to facilitate,
Learning matrix, –98, f
Lighting, physical space and, –49
Lincoln, Abraham, –5,
Lombardo, Michael,
Maisel, Eric,
Malmendier, Ulrike,
McClelland, David,
Meaning
abundant organizations and,
boards of directors and, –51
discovering, –32
employee implications of, –62
how of, –49
human resource implications of, –59
leaders and, –53
leaders focusing on, –26
making,
new value proposition and, –63
recessions of, –12
senior executives and, –53
why of, –48
Meaning-exploring questions,
Merck,
Microsoft,
Mirror neurons, ,
Motivation, abundance and, –39
Navigating proximity skills, for relationships, –17
Nietzsche, Friedrich,
Nike,
Nokia,
Nordstrom,
Nurse-friendly environments,
Observations, leaders and, –66
Organizational learning agility,
Organizational resilience, –14
Organizations. _See_ Abundant organizations
Personalized contributions
abundance and, –44, –59
leadership actions to ensure,
Personal resilience, –8
Phelps, Michael,
Physical layout, –48
Physical space, attitude toward, positive work environments and, –50
Physical work, –69
Playfulness
creativity and, –27
humor and, –35
Pleasure, –30
Positive psychology,
Positive routines, abundance and, –43
Positive work environment initiative,
Positive work environments, –55
in action, –52
attitude toward accountability and, –43
attitude toward communication and, –44
attitude toward conflict and, –46
attitude toward connections and, –39
attitude toward ideas and, –37
attitude toward involvement and, –41
attitude toward physical space and, –50
attitude toward service and, –34
attitude toward success and, –30
attitude toward value and values and, –32
exercise for,
leadership actions to create,
Presenting problems,
Prisoner's dilemma game, –34
Problem solving, bottom-up,
Procter & Gamble,
Publix Super Markets,
Purpose, –82
abundance and, –39
categories of, –92
leadership actions to articulate,
Quality control, checklists and routines for,
Questions, meaning-exploring,
Redundancy, communication and,
REI,
Relational work,
Relationships
abundance and, –41
abundant,
leadership actions to foster,
listening and self-disclosure skills for, –13
making amends and, –24
making and responding to bids skills for, –11
navigating proximity skills for, –17
resolving conflict skills for, –22
Resilience, –5
leadership actions to facilitate,
organizational, –14
personal, –8
social, –11
Roosevelt, Franklin D.,
Routines
positive, abundance and, –43
for quality control,
Salk, Jonas,
Satisficing, , –80
Segmentation,
Self-awareness, , –62t
for leaders, employees, and organizations, –95
Self-disclosure,
Self-reflection,
Seligman, Martin, , ,
Senior executives, meaning and, –53
Service, attitude toward, positive work environments and, –34
Signature strengths, –58, –62t
Simon, Herbert, ,
Socialization of employees, –75
Social resilience, –11
Southern Virginia University, –46
Starbucks,
Stonewalling,
Strengths, assessing, –63, –64f
Success, attitude toward, positive work environments and, –30
Symbols, power of, –50
Talent, –200
checklist for acquiring, for learning, t
Tannen, Deborah, ,
Tate, Geoffrey,
Teamwork, abundance and, –41
Teeda Butt Mam,
Temperance, t 3M,
Tipping points,
Toyota,
Transcendence, t
Transformation, –30
Two-way communication,
Ulrich, Richard, –20
University of Bristol,
Value, attitude toward, positive work environments and, –32
Values, attitude toward, positive work environments and, –32
Walmart, –57, –72, , ,
Watson, Thomas, Jr., –87,
Why, market value of, –7
Wilson, Woodrow,
Wisdom, t
W.L. Gore & Associates,
Work
assessment of individual abundance and, –52t
assessment of types of, t
characteristic assessment of, –83t
intellectual,
meaning at, –3
physical, –69
relational,
Work conditions, shaping, –80
Work culture, abundance and, –43
Worker safety,
## **ABOUT THE AUTHORS**
Organizations exist to create value both inside to employees and outside to customers, investors, and communities. When internal leadership and human resource practices align to external expectations, organizations survive and thrive.
Dave Ulrich is a professor at the University of Michigan Ross School of Business and a partner at The RBL Group, a consulting firm focused on helping organizations and leaders deliver value. He studies how organizations build capabilities of leadership, speed, learning, accountability, and talent through leveraging human resources. He has helped generate award-winning databases that assess alignment between strategies, human resource practices, and HR competencies. His writing, teaching, and coaching have helped shaped the role of human resources in global organizations. His work has helped leaders both become more personally effective and build better leadership throughout their organizations. He has helped to redefine organizations more by the capabilities they deliver to customers and investors than by their structure and systems.
Dave has published more than 150 articles and book chapters and 22 books. He edited _Human Resource Management 1990_ and has served on editorial board of four professional journals, on the Board of Directors for Herman Miller, and on the Board of Trustees at Southern Virginia University. He is a Fellow in the National Academy of Human Resources. He has won numerous lifetime honors and been consistently ranked among thought leaders in business and human resources. He has consulted and done research with over half of the Fortune 200.
Recent publications include:
_Leadership in Asia_ (2009, edited book, published by McGraw Hill)
_HR Transformation_ (2009, with Justin Allen, Wayne Brockbank, Jon Younger, and Mark Nyman, published by McGraw Hill)
_Leadership Code_ (2008, with Norm Smallwood and Kate Sweetman, published by Harvard Business Press)
_Companion for Strategic Human Resources_ (2008, with John Storey and Pat Wright, published by Routledge)
_HR Competencies_ (2008, with Wayne Brockbank, Dani Johnson, Kurt Sandholtz, and Jon Younger, published by SHRM and RBL Group)
_Leadership Brand_ (2007, with Norm Smallwood, published by Harvard Business Press),
_Human Resource Value Proposition_ (2005, with Wayne Brockbank, published by Harvard Business Press)
_The Future of Human Resource Management_ (2005, with Michael Losey, Sue Meisinger, published by Wiley & Sons)
_Human Resources Business Process Outsourcing_ (2004, with Ed Lawler, Jac Fitz-enz, James Madden, published by Wiley & Sons).
Contact information: e-mail: _dou@umich.edu_ , websites: _rbl.net and thewhyofwork.com._
Humans are meaning-makers who find _inherent value_ in making sense out of life. In addition to inherit value, meaning has _market value_ in work settings. Making sense makes cents.
A licensed psychologist in private practice for twenty years, Wendy Ulrich brings a personal touch to corporate complexities. She focuses on helping leaders create meaning at work that contributes real value to employees, customers, and investors. Employees who find a why to work are motivated and productive co-developers of abundant organizations with enough and to spare of the things that matter most: creativity, hope, resilience, determination, resourcefulness, and leadership . . . all in the service of customer commitment and financial performance.
Wendy helps organizations build personal strengths and people skills to succeed: communication, problem-resolution, change, creativity, resilience, civility, forgiveness, and happiness. She speaks to thousands of people every year on these topics.
In addition to counseling and coaching of individuals, Wendy has provided training and consulting for such organizations as General Electric, the U.S. Army, Johnson & Johnson, and the United Way. She is the founder of Sixteen Stones Center for Growth (sixteenstones.net), offering seminar-retreats for individuals and groups on topics such as forgiveness, loss, and creating an abundant life. She has taught psychology and organizational behavior at the University of Michigan, Northrup University, and Brigham Young University and is a fellow and former president of the Association of Mormon Counselors and Psychotherapists.
Wendy holds a Ph.D. in education and psychology from the University of Michigan and an M.B.A. specializing in organizational behavior from UCLA.
Recent publications include:
_Weakness Is Not Sin: The Liberating Distinction That Awakens Our Strengths (2009)_
_Forgiving Ourselves: Getting Back Up When We Let Ourselves Down_ (2008)
Contact information: e-mail: wulrich@rbl.net, websites: sixteenstones.net and thewhyofwork.com.
|
{
"redpajama_set_name": "RedPajamaBook"
}
| 1,247
|
package fakes
import (
"sync"
"istio.io/istio/pilot/pkg/model"
)
type ConfigStoreCache struct {
ConfigDescriptorStub func() model.ConfigDescriptor
configDescriptorMutex sync.RWMutex
configDescriptorArgsForCall []struct{}
configDescriptorReturns struct {
result1 model.ConfigDescriptor
}
configDescriptorReturnsOnCall map[int]struct {
result1 model.ConfigDescriptor
}
GetStub func(typ, name, namespace string) (config *model.Config, exists bool)
getMutex sync.RWMutex
getArgsForCall []struct {
typ string
name string
namespace string
}
getReturns struct {
result1 *model.Config
result2 bool
}
getReturnsOnCall map[int]struct {
result1 *model.Config
result2 bool
}
ListStub func(typ, namespace string) ([]model.Config, error)
listMutex sync.RWMutex
listArgsForCall []struct {
typ string
namespace string
}
listReturns struct {
result1 []model.Config
result2 error
}
listReturnsOnCall map[int]struct {
result1 []model.Config
result2 error
}
CreateStub func(config model.Config) (revision string, err error)
createMutex sync.RWMutex
createArgsForCall []struct {
config model.Config
}
createReturns struct {
result1 string
result2 error
}
createReturnsOnCall map[int]struct {
result1 string
result2 error
}
UpdateStub func(config model.Config) (newRevision string, err error)
updateMutex sync.RWMutex
updateArgsForCall []struct {
config model.Config
}
updateReturns struct {
result1 string
result2 error
}
updateReturnsOnCall map[int]struct {
result1 string
result2 error
}
DeleteStub func(typ, name, namespace string) error
deleteMutex sync.RWMutex
deleteArgsForCall []struct {
typ string
name string
namespace string
}
deleteReturns struct {
result1 error
}
deleteReturnsOnCall map[int]struct {
result1 error
}
RegisterEventHandlerStub func(typ string, handler func(model.Config, model.Event))
registerEventHandlerMutex sync.RWMutex
registerEventHandlerArgsForCall []struct {
typ string
handler func(model.Config, model.Event)
}
RunStub func(stop <-chan struct{})
runMutex sync.RWMutex
runArgsForCall []struct {
stop <-chan struct{}
}
HasSyncedStub func() bool
hasSyncedMutex sync.RWMutex
hasSyncedArgsForCall []struct{}
hasSyncedReturns struct {
result1 bool
}
hasSyncedReturnsOnCall map[int]struct {
result1 bool
}
invocations map[string][][]interface{}
invocationsMutex sync.RWMutex
}
func (fake *ConfigStoreCache) ConfigDescriptor() model.ConfigDescriptor {
fake.configDescriptorMutex.Lock()
ret, specificReturn := fake.configDescriptorReturnsOnCall[len(fake.configDescriptorArgsForCall)]
fake.configDescriptorArgsForCall = append(fake.configDescriptorArgsForCall, struct{}{})
fake.recordInvocation("ConfigDescriptor", []interface{}{})
fake.configDescriptorMutex.Unlock()
if fake.ConfigDescriptorStub != nil {
return fake.ConfigDescriptorStub()
}
if specificReturn {
return ret.result1
}
return fake.configDescriptorReturns.result1
}
func (fake *ConfigStoreCache) ConfigDescriptorCallCount() int {
fake.configDescriptorMutex.RLock()
defer fake.configDescriptorMutex.RUnlock()
return len(fake.configDescriptorArgsForCall)
}
func (fake *ConfigStoreCache) ConfigDescriptorReturns(result1 model.ConfigDescriptor) {
fake.ConfigDescriptorStub = nil
fake.configDescriptorReturns = struct {
result1 model.ConfigDescriptor
}{result1}
}
func (fake *ConfigStoreCache) ConfigDescriptorReturnsOnCall(i int, result1 model.ConfigDescriptor) {
fake.ConfigDescriptorStub = nil
if fake.configDescriptorReturnsOnCall == nil {
fake.configDescriptorReturnsOnCall = make(map[int]struct {
result1 model.ConfigDescriptor
})
}
fake.configDescriptorReturnsOnCall[i] = struct {
result1 model.ConfigDescriptor
}{result1}
}
func (fake *ConfigStoreCache) Get(typ string, name string, namespace string) (config *model.Config, exists bool) {
fake.getMutex.Lock()
ret, specificReturn := fake.getReturnsOnCall[len(fake.getArgsForCall)]
fake.getArgsForCall = append(fake.getArgsForCall, struct {
typ string
name string
namespace string
}{typ, name, namespace})
fake.recordInvocation("Get", []interface{}{typ, name, namespace})
fake.getMutex.Unlock()
if fake.GetStub != nil {
return fake.GetStub(typ, name, namespace)
}
if specificReturn {
return ret.result1, ret.result2
}
return fake.getReturns.result1, fake.getReturns.result2
}
func (fake *ConfigStoreCache) GetCallCount() int {
fake.getMutex.RLock()
defer fake.getMutex.RUnlock()
return len(fake.getArgsForCall)
}
func (fake *ConfigStoreCache) GetArgsForCall(i int) (string, string, string) {
fake.getMutex.RLock()
defer fake.getMutex.RUnlock()
return fake.getArgsForCall[i].typ, fake.getArgsForCall[i].name, fake.getArgsForCall[i].namespace
}
func (fake *ConfigStoreCache) GetReturns(result1 *model.Config, result2 bool) {
fake.GetStub = nil
fake.getReturns = struct {
result1 *model.Config
result2 bool
}{result1, result2}
}
func (fake *ConfigStoreCache) GetReturnsOnCall(i int, result1 *model.Config, result2 bool) {
fake.GetStub = nil
if fake.getReturnsOnCall == nil {
fake.getReturnsOnCall = make(map[int]struct {
result1 *model.Config
result2 bool
})
}
fake.getReturnsOnCall[i] = struct {
result1 *model.Config
result2 bool
}{result1, result2}
}
func (fake *ConfigStoreCache) List(typ string, namespace string) ([]model.Config, error) {
fake.listMutex.Lock()
ret, specificReturn := fake.listReturnsOnCall[len(fake.listArgsForCall)]
fake.listArgsForCall = append(fake.listArgsForCall, struct {
typ string
namespace string
}{typ, namespace})
fake.recordInvocation("List", []interface{}{typ, namespace})
fake.listMutex.Unlock()
if fake.ListStub != nil {
return fake.ListStub(typ, namespace)
}
if specificReturn {
return ret.result1, ret.result2
}
return fake.listReturns.result1, fake.listReturns.result2
}
func (fake *ConfigStoreCache) ListCallCount() int {
fake.listMutex.RLock()
defer fake.listMutex.RUnlock()
return len(fake.listArgsForCall)
}
func (fake *ConfigStoreCache) ListArgsForCall(i int) (string, string) {
fake.listMutex.RLock()
defer fake.listMutex.RUnlock()
return fake.listArgsForCall[i].typ, fake.listArgsForCall[i].namespace
}
func (fake *ConfigStoreCache) ListReturns(result1 []model.Config, result2 error) {
fake.ListStub = nil
fake.listReturns = struct {
result1 []model.Config
result2 error
}{result1, result2}
}
func (fake *ConfigStoreCache) ListReturnsOnCall(i int, result1 []model.Config, result2 error) {
fake.ListStub = nil
if fake.listReturnsOnCall == nil {
fake.listReturnsOnCall = make(map[int]struct {
result1 []model.Config
result2 error
})
}
fake.listReturnsOnCall[i] = struct {
result1 []model.Config
result2 error
}{result1, result2}
}
func (fake *ConfigStoreCache) Create(config model.Config) (revision string, err error) {
fake.createMutex.Lock()
ret, specificReturn := fake.createReturnsOnCall[len(fake.createArgsForCall)]
fake.createArgsForCall = append(fake.createArgsForCall, struct {
config model.Config
}{config})
fake.recordInvocation("Create", []interface{}{config})
fake.createMutex.Unlock()
if fake.CreateStub != nil {
return fake.CreateStub(config)
}
if specificReturn {
return ret.result1, ret.result2
}
return fake.createReturns.result1, fake.createReturns.result2
}
func (fake *ConfigStoreCache) CreateCallCount() int {
fake.createMutex.RLock()
defer fake.createMutex.RUnlock()
return len(fake.createArgsForCall)
}
func (fake *ConfigStoreCache) CreateArgsForCall(i int) model.Config {
fake.createMutex.RLock()
defer fake.createMutex.RUnlock()
return fake.createArgsForCall[i].config
}
func (fake *ConfigStoreCache) CreateReturns(result1 string, result2 error) {
fake.CreateStub = nil
fake.createReturns = struct {
result1 string
result2 error
}{result1, result2}
}
func (fake *ConfigStoreCache) CreateReturnsOnCall(i int, result1 string, result2 error) {
fake.CreateStub = nil
if fake.createReturnsOnCall == nil {
fake.createReturnsOnCall = make(map[int]struct {
result1 string
result2 error
})
}
fake.createReturnsOnCall[i] = struct {
result1 string
result2 error
}{result1, result2}
}
func (fake *ConfigStoreCache) Update(config model.Config) (newRevision string, err error) {
fake.updateMutex.Lock()
ret, specificReturn := fake.updateReturnsOnCall[len(fake.updateArgsForCall)]
fake.updateArgsForCall = append(fake.updateArgsForCall, struct {
config model.Config
}{config})
fake.recordInvocation("Update", []interface{}{config})
fake.updateMutex.Unlock()
if fake.UpdateStub != nil {
return fake.UpdateStub(config)
}
if specificReturn {
return ret.result1, ret.result2
}
return fake.updateReturns.result1, fake.updateReturns.result2
}
func (fake *ConfigStoreCache) UpdateCallCount() int {
fake.updateMutex.RLock()
defer fake.updateMutex.RUnlock()
return len(fake.updateArgsForCall)
}
func (fake *ConfigStoreCache) UpdateArgsForCall(i int) model.Config {
fake.updateMutex.RLock()
defer fake.updateMutex.RUnlock()
return fake.updateArgsForCall[i].config
}
func (fake *ConfigStoreCache) UpdateReturns(result1 string, result2 error) {
fake.UpdateStub = nil
fake.updateReturns = struct {
result1 string
result2 error
}{result1, result2}
}
func (fake *ConfigStoreCache) UpdateReturnsOnCall(i int, result1 string, result2 error) {
fake.UpdateStub = nil
if fake.updateReturnsOnCall == nil {
fake.updateReturnsOnCall = make(map[int]struct {
result1 string
result2 error
})
}
fake.updateReturnsOnCall[i] = struct {
result1 string
result2 error
}{result1, result2}
}
func (fake *ConfigStoreCache) Delete(typ string, name string, namespace string) error {
fake.deleteMutex.Lock()
ret, specificReturn := fake.deleteReturnsOnCall[len(fake.deleteArgsForCall)]
fake.deleteArgsForCall = append(fake.deleteArgsForCall, struct {
typ string
name string
namespace string
}{typ, name, namespace})
fake.recordInvocation("Delete", []interface{}{typ, name, namespace})
fake.deleteMutex.Unlock()
if fake.DeleteStub != nil {
return fake.DeleteStub(typ, name, namespace)
}
if specificReturn {
return ret.result1
}
return fake.deleteReturns.result1
}
func (fake *ConfigStoreCache) DeleteCallCount() int {
fake.deleteMutex.RLock()
defer fake.deleteMutex.RUnlock()
return len(fake.deleteArgsForCall)
}
func (fake *ConfigStoreCache) DeleteArgsForCall(i int) (string, string, string) {
fake.deleteMutex.RLock()
defer fake.deleteMutex.RUnlock()
return fake.deleteArgsForCall[i].typ, fake.deleteArgsForCall[i].name, fake.deleteArgsForCall[i].namespace
}
func (fake *ConfigStoreCache) DeleteReturns(result1 error) {
fake.DeleteStub = nil
fake.deleteReturns = struct {
result1 error
}{result1}
}
func (fake *ConfigStoreCache) DeleteReturnsOnCall(i int, result1 error) {
fake.DeleteStub = nil
if fake.deleteReturnsOnCall == nil {
fake.deleteReturnsOnCall = make(map[int]struct {
result1 error
})
}
fake.deleteReturnsOnCall[i] = struct {
result1 error
}{result1}
}
func (fake *ConfigStoreCache) RegisterEventHandler(typ string, handler func(model.Config, model.Event)) {
fake.registerEventHandlerMutex.Lock()
fake.registerEventHandlerArgsForCall = append(fake.registerEventHandlerArgsForCall, struct {
typ string
handler func(model.Config, model.Event)
}{typ, handler})
fake.recordInvocation("RegisterEventHandler", []interface{}{typ, handler})
fake.registerEventHandlerMutex.Unlock()
if fake.RegisterEventHandlerStub != nil {
fake.RegisterEventHandlerStub(typ, handler)
}
}
func (fake *ConfigStoreCache) RegisterEventHandlerCallCount() int {
fake.registerEventHandlerMutex.RLock()
defer fake.registerEventHandlerMutex.RUnlock()
return len(fake.registerEventHandlerArgsForCall)
}
func (fake *ConfigStoreCache) RegisterEventHandlerArgsForCall(i int) (string, func(model.Config, model.Event)) {
fake.registerEventHandlerMutex.RLock()
defer fake.registerEventHandlerMutex.RUnlock()
return fake.registerEventHandlerArgsForCall[i].typ, fake.registerEventHandlerArgsForCall[i].handler
}
func (fake *ConfigStoreCache) Run(stop <-chan struct{}) {
fake.runMutex.Lock()
fake.runArgsForCall = append(fake.runArgsForCall, struct {
stop <-chan struct{}
}{stop})
fake.recordInvocation("Run", []interface{}{stop})
fake.runMutex.Unlock()
if fake.RunStub != nil {
fake.RunStub(stop)
}
}
func (fake *ConfigStoreCache) RunCallCount() int {
fake.runMutex.RLock()
defer fake.runMutex.RUnlock()
return len(fake.runArgsForCall)
}
func (fake *ConfigStoreCache) RunArgsForCall(i int) <-chan struct{} {
fake.runMutex.RLock()
defer fake.runMutex.RUnlock()
return fake.runArgsForCall[i].stop
}
func (fake *ConfigStoreCache) HasSynced() bool {
fake.hasSyncedMutex.Lock()
ret, specificReturn := fake.hasSyncedReturnsOnCall[len(fake.hasSyncedArgsForCall)]
fake.hasSyncedArgsForCall = append(fake.hasSyncedArgsForCall, struct{}{})
fake.recordInvocation("HasSynced", []interface{}{})
fake.hasSyncedMutex.Unlock()
if fake.HasSyncedStub != nil {
return fake.HasSyncedStub()
}
if specificReturn {
return ret.result1
}
return fake.hasSyncedReturns.result1
}
func (fake *ConfigStoreCache) HasSyncedCallCount() int {
fake.hasSyncedMutex.RLock()
defer fake.hasSyncedMutex.RUnlock()
return len(fake.hasSyncedArgsForCall)
}
func (fake *ConfigStoreCache) HasSyncedReturns(result1 bool) {
fake.HasSyncedStub = nil
fake.hasSyncedReturns = struct {
result1 bool
}{result1}
}
func (fake *ConfigStoreCache) HasSyncedReturnsOnCall(i int, result1 bool) {
fake.HasSyncedStub = nil
if fake.hasSyncedReturnsOnCall == nil {
fake.hasSyncedReturnsOnCall = make(map[int]struct {
result1 bool
})
}
fake.hasSyncedReturnsOnCall[i] = struct {
result1 bool
}{result1}
}
func (fake *ConfigStoreCache) Invocations() map[string][][]interface{} {
fake.invocationsMutex.RLock()
defer fake.invocationsMutex.RUnlock()
fake.configDescriptorMutex.RLock()
defer fake.configDescriptorMutex.RUnlock()
fake.getMutex.RLock()
defer fake.getMutex.RUnlock()
fake.listMutex.RLock()
defer fake.listMutex.RUnlock()
fake.createMutex.RLock()
defer fake.createMutex.RUnlock()
fake.updateMutex.RLock()
defer fake.updateMutex.RUnlock()
fake.deleteMutex.RLock()
defer fake.deleteMutex.RUnlock()
fake.registerEventHandlerMutex.RLock()
defer fake.registerEventHandlerMutex.RUnlock()
fake.runMutex.RLock()
defer fake.runMutex.RUnlock()
fake.hasSyncedMutex.RLock()
defer fake.hasSyncedMutex.RUnlock()
copiedInvocations := map[string][][]interface{}{}
for key, value := range fake.invocations {
copiedInvocations[key] = value
}
return copiedInvocations
}
func (fake *ConfigStoreCache) recordInvocation(key string, args []interface{}) {
fake.invocationsMutex.Lock()
defer fake.invocationsMutex.Unlock()
if fake.invocations == nil {
fake.invocations = map[string][][]interface{}{}
}
if fake.invocations[key] == nil {
fake.invocations[key] = [][]interface{}{}
}
fake.invocations[key] = append(fake.invocations[key], args)
}
var _ model.ConfigStoreCache = new(ConfigStoreCache)
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,183
|
package com.github.horai.tasktracker.runner;
/**
* Created by yh on 2016/11/30.
* 额外的任务信息,一般为tasktracker信息或在tasktracker上生成的信息
*/
public class TaskExtInfo {
// 任务在本节点已经重复的次数
private int retryTimes = 0;
// 任务执行日志存放地址
private String taskLoaPath;
// 任务日志最大长度
private int logSize;
public int getRetryTimes() {
return retryTimes;
}
public void setRetryTimes(int retryTimes) {
this.retryTimes = retryTimes;
}
public String getTaskLoaPath() {
return taskLoaPath;
}
public void setTaskLoaPath(String taskLoaPath) {
this.taskLoaPath = taskLoaPath;
}
public int getLogSize() {
return logSize;
}
public void setLogSize(int logSize) {
this.logSize = logSize;
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,105
|
South Dakota: Major Marijuana Legalization Drive Underway
Activists are ramping up for a major signature gathering effort to once again put legalization on the ballot for 2022
Addiction Center
South Dakota • Legalization
South Dakota marijuana activists are ramping up for a major signature gathering effort to put legalization on the 2022 ballot. Meanwhile, the state Supreme Court continues to consider a case on the fate of the legal marijuana measure that voters already approved last year.
Advocates are still holding out hope that the state's top court will issue a positive ruling in the case. But on Thursday's weekly decision day, the justices announced no action, reports Marijuana Moment. And time is running short to mobilize a ballot campaign to qualify for 2022.
The group South Dakotans for Better Marijuana Laws is now soliciting volunteers to prepare for a massive signature collection drive. The drive will support any of the four proposed legalization initiatives that the group has filed.
MPP: 'We Must Prepare For The Worst'
The Marijuana Policy Project (MPP) has played a leading role in Cannabis law reform efforts in South Dakota, The group's deputy director, Matthew Schweich, told Marijuana Moment that advocates "remain hopeful" the court will uphold the will of voters. But activists said they aren't taking anything for granted.
"We must prepare for the worst," Schweich said. "So we are building a grassroots volunteer signature drive operation across the state in order to qualify another cannabis legalization initiative for the 2022 ballot."
Activists already set things into motion in July. That's when they filed the four reform measures with the state Legislative Research Council.
Four Initiatives, Four Unique Approaches
The four potential initiatives share some basic provisions. Each, however, takes a unique approach to the policy change. For a summary of what each of the four initiatives would do, click here.
Activists have also filed a fifth measure to eliminate a single-subject rule for the ballot process—a policy that led to a state judge deeming the 2020 recreational measure unconstitutional. Just as happened in another conservative state, Mississippi, judges relied on arcane legal questions to nullify the vote of the people.
Activists face a challenging timeline to get any of the measures approved for circulation. Even once they clear that hurdle, they must to collect enough valid signatures to qualify. The Supreme Court is weighing the fate of 2020's voter-approved initiative. Meanwhile, the campaign is encouraging prospective volunteers to fill out a form to get prepared for signature gathering.
South Dakota AG, Secretary of State Must Approve
The Legislative Research Council has already approved the four initiatives. Now the state attorney general and Secretary of State must do the same before signature gathering. At that point, advocates will have until November 8 to collect signatures. They'll need at least 33,921 valid signatures for a constitutional proposal and 16,961 for a statutory measure. The number depends upon what method they choose to use.
The February ruling that nullified the 2020 adult-use legalization vote frustrated activists, of course. The ongoing delay in the Supreme Court's decision on upholding or overturning that nullification has frayed a few nerves as well. But they see a ray of light. The separate medical marijuana measure that voters also approved approved took effect in July.
https://leafmagazines.com/news/legalization/south-dakota-major-marijuana-legalization-drive-underway/
Published September 17, 2021 October 15, 2021
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 8,143
|
\section{INTRODUCTION}
\indent
A spinning magnetized neutron star provides huge electric
potential differences between different parts of its surface
as a result of unipolar induction \citep{gol69}.
A part of the potential difference may be expended on an
electric field along the magnetic field somewhere in the
magnetosphere. Although a fully self-consistent model for the
pulsar magnetosphere has not yet been constructed, several promising
models have been proposed. Among them, the polar cap model
\citep{stu71, rud75} assumes that an electric field
$E_\parallel$ parallel to the magnetic field lines exists just
above the magnetic poles.
The electric field accelerates charged particles up to TeV energies,
and resultant curvature radiation from these particles produces copious
electron-positron pairs through magnetic pair production.
These pairs are believed to be responsible for radio emission.
The extremely high brightness temperature of pulsar radio emission
requires a coherent source for this radiation.
In the past decade, various maser processes have been proposed and studied:
for example,
curvature emission induced by curvature drift or torsion \citep{luo92,luo95}
and emission due to the cyclotron-Cerenkov and Cerenkov drift instabilities
\citep{lyu99a,lyu99b}.
In most cases these models are sensitive to the magnetic field strength
or other parameters.
Although the torsion-driven maser process \citep{luo95} is not so sensitive
to the physical parameters, we have no definite ideas to achieve
the required inverted energy spectrum of particles and twisted field lines.
Therefore, there is still no widely accepted model
of maser emission.
On the other hand, one of the simplest mechanisms of radiation
is the coherent curvature radiation
from bunches of electron-positron pair plasma,
which was discussed mainly in the 1970s.
If $N$ particles are in a bunch of some characteristic size $\lambda$,
emission with wavelengths longer than $\lambda$ will be coherent.
Then the particles in the bunch
radiate like a single particle with charge $N e$.
The brightness temperature becomes $N$ times that
estimated from the intensity when the $N$ single particles radiate incoherently.
\citet{che77} suggested that the bunching arises from
the electrostatic two-stream instability of electron
and positron streams.
However, \citet{ben77} found that the growth time
of the instability is far too long.
Although some other mechanisms to excite instabilities
\citep[e.g.][]{gol71,ass80, ass83,uso87}
have been proposed, the problem remains unsolved so far.
Another serious problem in the polar cap model
is the screening of the electric field.
The localized potential drop in the polar cap region
is maintained by a pair of anode and cathode regions.
For a space charge-limited flow model
\citep{faw77, sch78, aro79},
where electrons can freely escape from the stellar surface,
i.e., $E_\parallel = 0$ on the stellar surface,
an anode has been
considered to be provided by pair polarization.
However, as \citet{shi98, shi02} found,
the thickness of the screening layer is restricted to be
extremely small,
in order to screen the electric field consistently.
A huge number of pairs must be injected within the small thickness.
The required pair multiplication factor per primary particle
is enormously large and cannot be realized in the conventional pair
creation models.
In addition to the above problems, there are various unsolved problems
in pulsar physics; for example, the current closure problem
is a representative one.
It may be worthwhile to explore the possibility of a novel model,
even if the model has some ambiguities at present.
Recently, \citet{asa04} (hereafter AT) have
proposed a new mechanism to screen the electric field.
In the AT model, nonrelativistic protons are supplied
from the corotating magnetosphere to flow toward the stellar surface.
Protons can provide an anode to screen an electric field
the standard polar cap model supposes.
Injected electron-positron pairs yield an
asymmetry of the electrostatic potential around the screening
point. The required pair creation rate in this model is
consistent with the conventional models.
The existence of the proton counterflows
is also favorable for the bunching of pair plasma.
The existence of protons apparently
makes excitation of two-stream instability easier \citep{che80}.
In this Letter, we show that the pair and proton flows in the AT model
excite electrostatic waves,
which can explain the pulsar radio emission through coherent
curvature radiation.
In contrast to most modern theories of pulsar radio emission,
the bunch models have been so much discussed from the early days
of pulsar research and have received several criticisms,
such as insufficient growth rates and rapid bunch dispersion due to
random motion of bunching particles (see, e.g., Melrose 1995).
However, reconsideration of this old idea without any prejudice
may be valuable \citep{gil04} in order to
overcome present difficulties in pulsar physics,
although the maser models are still an alternative possibility
of the radiation mechanism.
Another interesting reason to reconsider the bunch model is that
space charge density waves appear outside the screening region
in the AT model, even though the velocity dispersion of pairs
is taken into account (see also Shibata et al. 2002).
The two stream instability discussed here may be useful
to excite non-linear radiation processes in a relativistic plasma
\citep{lyu99a,lyu99b}.
In \S 2, we show that the two-stream instability
is easily excited in the AT model.
The excited wavelength is long enough to bunch particles.
In \S 3, we discuss counteraction of the excited waves
on the pair flows.
\S 4 is devoted to a summary and discussion.
\section{TWO-STREAM INSTABILITY}
In this section, we discuss the two-stream instability
for the situation the AT model supposes.
In the AT model, protons are assumed to flow from the corotating magnetosphere
toward the stellar surface.
The primary electron beam is accelerated
from the stellar surface.
Electron-positron pairs start to be injected
at a certain height above the polar cap,
and the electric field is screened there.
Outside this point, two-stream instability may be
excited, and the resultant bunching of pair plasma
yields coherent curvature radiation.
The AT model requires that the proton current $J_{\rm p}$
is of the order of the Goldreich-Julian (GJ)
current $J_{\rm GJ} \equiv -\mathbf{\Omega}_* \cdot \mathbf{B}/
2 \pi$, where $\mathbf{\Omega}_*$ and $\mathbf{B}$ are the angular velocity
of the star and magnetic field, respectively.
Hereafter, we assume $\mathbf{\Omega}_* \cdot \mathbf{B}>0$.
In the case of opposite polarity, the electric fields are not screened
in this model.
There is no observational evidence for two classes of pulsars
due to the polarity, as expected.
The polarity problem remains unsolved so far for all pulsar models.
The proton flow is mildly relativistic
(the average velocity in AT $\simeq -0.4 c$) in the pulsar frame.
The current of the primary electron beam
from the stellar surface is also of the order of $J_{\rm GJ}$.
The Lorentz factor of pairs at injection is required to be more than $\sim 500$.
From the above assumptions,
we obtain the proton number density $n_{\rm p} \simeq \Omega B/
2 \pi c e$.
Then the proton plasma frequency,
$\omega_{\rm pp}^2 \equiv 4 \pi e^2 n_{\rm p}/m_{\rm p}$, becomes
\begin{eqnarray}
\omega_{\rm pp}/2 \pi \simeq 100 T_{0.3}^{-1/2} B_{12}^{1/2} \quad
\mbox{MHz,}
\end{eqnarray}
where $T_{0.3}$ and $B_{12}$ are the rotation period of the pulsar
and $B$ in units of 0.3 s and $10^{12}$ G, respectively.
In order to simplify the situation, we consider one-dimensional
homogeneous flows of protons and electron-positron pairs.
Since the Lorentz factor of the primary beam of electrons
from the stellar surface
is too large to contribute to the dispersion relation,
we neglect the beam component hereafter.
The distributions of protons and pairs are functions of the
4-velocity $u=\beta/(1-\beta^2)^{1/2}$, where $\beta=v/c$.
In the linear perturbation theory,
the dispersion relation for electrostatic waves \citep{bal69}
is given by
\begin{eqnarray}
1+\sum_a \frac{4 \pi q_a^2}{\omega m_a}
\int d u \frac{\beta}{\omega-k v}
\frac{\partial f_a}{\partial u}=0,
\end{eqnarray}
where $f_a$, $q_a$, and $m_a$ denote the distribution function,
charge, and mass of the particle species $a$, respectively.
Solutions of the dispersion relation usually
yield a complex frequency $\omega=\omega_r+i \omega_i$.
The imaginary part $\omega_i$ of $\omega$
corresponds to the growth rate of waves.
A positive growth rate $\omega_i>0$ implies an exponentially
growing wave, while a negative $\omega_i$ implies an
exponentially damped wave.
In the cold-plasma limit
the distribution function of the proton flow may be written as
$f_{\rm p}=n_{\rm p} \delta(u)$ in the rest frame of the proton flow.
We assume that the number densities and flow velocities of pair electrons and positrons
are the same.
In this case, the contributions of pair electrons and positrons
are degenerate, so that we write the total pair distribution
as $f_\pm=n_\pm \delta(u-u_\pm)$.
We neglect the injection of pairs,
although the pair injection continues outside the polar
cap region in general.
Then we obtain
\begin{eqnarray}
1-\frac{\omega_{\rm pp}^2}{\omega^2}
-\frac{\omega_{\rm p \pm}^2}{(\omega-k v_{\pm})^2 \gamma_\pm^3}=0,
\end{eqnarray}
where $\omega_{\rm p \pm}^2 \equiv 4 \pi e^2 n_\pm/m_e$,
and $\gamma_\pm=500 \gamma_{\pm,5}$ is the Lorentz factor of pairs.
The charge density wave due to pairs is constructed
by the density waves of electrons and positrons
with displaced phases of $\pi$.
We normalize $k$ and $\omega$ by the proton plasma frequency
as $\tilde{k}=c k/\omega_{\rm pp}$ and
$\tilde{\omega}=\omega/\omega_{\rm pp}$.
We write $\omega_{\rm p \pm} \equiv \xi \omega_{\rm pp}$.
The current of the primary electron beam (we have neglected here)
is also of the order of $J_{\rm GJ}$.
The number of pairs one primary electron creates
may be $10^3$--$10^4$.
Therefore, $n_\pm/n_{\rm p} \equiv M$ may be in the range of $10^3$--$10^4$.
As a result, $\xi=\sqrt{M m_{\rm p}/m_{\rm e}}$ is in the range of 1400--4300.
The condition to yield a pair of complex solutions is given by
\begin{eqnarray}
\tilde{k} \beta_\pm <(1+\zeta)^{3/2},
\end{eqnarray}
where $\zeta \equiv \xi^{2/3}/\gamma_\pm$.
Since $\gamma_\pm$ is required to be larger than $\sim 500$
in the AT model,
we assume $\gamma_\pm=500$--1000.
In this case,
$\zeta$ is in the range of 0.1--0.5, and $\beta_\pm \simeq 1$.
Thus, the threshold of $\tilde{k}$ is close to unity
irrespective of the parameters.
The phase velocity of the excited wave is obtained as
\begin{eqnarray}
\frac{\omega_r}{k} \simeq \frac{v_\pm}{1+\zeta}.
\label{phase}
\end{eqnarray}
The maximum of $\omega_i$ is given
by $\tilde{k}$ smaller than and close to the threshold
$(1+\zeta)^{3/2} \sim 1$.
Since the right-hand side of Eq. (\ref{phase}) is of the order of unity,
$\tilde{\omega_r}$ for the growing wave
is of the order of unity, too.
In general, $\omega_r$ is much larger than
$\omega_i$.
Therefore, $\tilde{\omega}_i$ is about $\sim 0.1$ at most.
Numerical solutions (see Fig. 1) confirm this estimate.
The growth time $\sim 1/(0.1 \omega_{\rm pp}) \sim 10^{-8}$ s $\ll 1/\Omega$,
$R/c$, where $R=10^7 R_7$ cm is the curvature radius of magnetic fields,
is short enough to bunch particles.
Therefore, the bunched particles emit
coherent radiation just above the polar cap.
The wavelength $\lambda$ of the excited wave is $2 \pi/k
\sim 2 \pi c/\omega_{\rm pp} \sim 300$ cm.
The maximum coherent amplification of curvature radiation
by bunches of pairs is obtained at wavelengths
long compared to the size of bunches $\lambda$.
For wavelengths shorter than $\lambda$ (frequency higher than $\nu_0
\equiv \omega_{\rm pp}/
2 \pi \sim 100$ MHz),
the flux of curvature radiation diminishes with a power law
of some index $\alpha$ as $\propto \nu^{-\alpha}$
\citep[see, e.g.,][]{sag75,ben77,mic82}
extending to the critical frequency $\nu_{\rm c}=3 \gamma_\pm^3 c/4 \pi R
\sim 100 \gamma_{\pm,5}^3 R_7^{-1}$ GHz.
The above frequencies are estimated in the proton rest frame.
Since the proton flow is nonrelativistic,
the redshift of frequencies by the flow is unimportant.
Thus, the coherent radio emission in this model
is well consistent with the observed pulsar radio spectra.
The number of pairs $N$, which can radiate coherently,
may be written as $N \simeq \epsilon M n_{\rm GJ} \lambda^3
\simeq 6 \times 10^{21} \epsilon (M/10^3) (\lambda_3)^3 B_{12} T_{0.3}^{-1}$,
where $\lambda_3=\lambda/300$ cm,
and the factor $\epsilon<1$ is the fraction of particles
that are in a coherent motion.
The cooling time scale
for coherent curvature radiation may be written as
\begin{eqnarray}
t_{\rm cool} \simeq \frac{\gamma_\pm m_{\rm e} c^2}{p N}
\left( \frac{\nu_{\rm c}}{\nu_0} \right)^{4/3}=
\frac{3 R^2 m_{\rm e} c}
{2 e^2 \gamma_\pm^3 N} \left( \frac{\nu_{\rm c}}{\nu_0} \right)^{4/3},
\end{eqnarray}
where $p=2 e^2 c \gamma_\pm^4/3 R^2$ is the emitting power by a single particle.
Here we adopt $\nu_{\rm c}/\nu_0=10^3$.
If $N>3 \times 10^{15}$,
$t_{\rm cool}$ becomes shorter than $R/c \sim 3 \times 10^{-4} R_7$ s.
This is realized for $\epsilon > 5 \times 10^{-7}$ and
gives a bright enough radio luminosity. Since high
radio luminosity can be realized even for a smaller $N$ if the number
of bunches is large enough, this estimate is not unique.
On the other hand, the radio brightness temperature $T_{\rm b}$
may be limited by the self-absorption \citep{che80};
$T_{\rm b}<\gamma_\pm N m_{\rm e} c^2/k_{\rm B}$,
where $k_{\rm B}$ is the Boltzmann constant.
The value $N=3 \times 10^{15}$ gives a limit $\sim 10^{28}$ K,
which is high enough to be consistent with observations.
The above estimate of $N$ and $\epsilon$ appear to be appropriate,
although it is not unique. Thus, a small value of $\epsilon$ suffices
for coherent radio emission, although it is hard to estimate $\epsilon$
from the first principle
because of some nonlinear effects on the bunching process.
\section{WAVE COUNTERACTION ON THE FLOWS}
The excited waves may produce effective frictional force
on the flows.
If the frictional force is too strong, the force
destroys the structure of the two streams.
We have to construct a model that satisfies the two requirements of
wave excitation in a short timescale and
sustainable structure of the flows, which seems incompatible at first glance.
This problem has not been considered seriously so far.
In this section, we obtain a physical requirement
to make the frictional force negligible.
In the quasi-linear theory, the time-averaged distribution
functions evolve according to \citep[see, e.g.,][]{hin78}
\begin{eqnarray}
\frac{\partial f_a}{\partial t}=\frac{\partial}{\partial u}
\Biggl[ D \frac{\partial f_a}{\partial u} \Biggr],
\end{eqnarray}
where
\begin{eqnarray}
D=\frac{q_a^2}{m_a^2 c^2} {\rm Re}
\Biggl[\int dk \frac{E_k^2}
{i (k v-\omega_{r,k})+\omega_{i,k}}
\Biggr],
\end{eqnarray}
and $E_k$ is amplitude of the electric field
with a wavenumber $k$.
Then the change of $u$ due to the friction per unit time
is obtained as
\begin{eqnarray}
\dot{u}=\frac{\partial D}{\partial u}.
\end{eqnarray}
The amplitude $E_k$ is difficult to estimate.
The electric field traps pairs,
if the amplitude of the excited electric field $E$ becomes
larger than a threshold
\begin{eqnarray}
E_{\rm max} &\equiv& \frac{k \gamma_\pm m_{\rm e} c^2}{2 e \gamma_{\rm w}^2}
\simeq \frac{\omega_{\rm pp} \gamma_\pm m_{\rm e} c}{2 e \gamma_{\rm w}^2} \nonumber \\
&\simeq& 10^3
\left( \frac{\gamma_{\rm w}^2}{10} \right)^{-1} \gamma_{\pm,5}
B_{12}^{1/2} T_{0.3}^{-1/2} \quad
\mbox{in esu,}
\label{denba}
\end{eqnarray}
where $\gamma_{\rm w}$ is the Lorentz factor of
the phase velocity of the wave.
We have assumed $\gamma_{\rm w}^2 \gg 1$ in the above estimate.
However, even if $\gamma_{\rm w}^2 \sim 1$,
the correct value differs from the above
at most by a factor of 2.
In the relativistic limit,
$\gamma_{\rm w}^2 \simeq (1+\zeta)/2 \zeta$.
Thus, $\gamma_{\rm w}^2$ is 10 at most.
Assuming the maximum charge density $\rho_{\rm max} \sim E_{\rm max}/\lambda$,
we obtain $\rho_{\rm max} \sim \gamma_\pm m_{\rm e}/(\gamma_w^2 m_{\rm p})
\rho_{\rm GJ}$, where $\rho_{\rm GJ} \equiv \Omega B/(2 \pi c)$ is
the GJ charge density.
Since $\gamma_\pm \sim 10^3$ and $\gamma_{\rm w}^2=1$-$10$,
the maximum charge density turns out to be of the order of
$0.1$-$1$ times the GJ charge density.
Although there may be various nonlinear effects to excite waves,
the maximum amplitude of the electric field may not be much larger
than $E_{\rm max}$.
We approximate the excited electric field
by a monochromatic wave of $E_k=E \delta(k-\omega_{\rm pp}/c)$.
It is apparent that the time scale for the slowdown due to the friction
$t_{\rm fric}$ for the pair flow is longer than that for
the proton flow owing to the large value of $\gamma_\pm$.
Taking into account $\omega_r \simeq \omega_{\rm pp}$ and
$\omega_i \simeq 0.1 \omega_{\rm pp}$,
$t_{\rm fric}$ for the proton flow is obtained as
\begin{eqnarray}
t_{\rm fric}=\frac{1}{|\dot{u}|} \simeq
5 \omega_{\rm pp} \left( \frac{m_{\rm p} c}
{e E} \right)^2.
\end{eqnarray}
We consider that the physical condition remains unchanged
within a scale $R/c$.
In order to make $t_{\rm fric}$ be longer than $R/c$,
$E$ should be smaller than $E_{\rm max}$ by a factor of 3.
Experience has shown that longitudinal waves are frequently
strongly damped by nonlinear processes.
So we expect that $E$ may be smaller than $E_{\rm max}$,
small enough to keep the fictional force small and
strong enough to bunch a small fraction of pair particles.
\section{SUMMARY AND DISCUSSION}
We examined the two-stream instability and coherent curvature
radiation in the proton counterflow model that we have recently proposed.
The existence of proton flows is favorable
not only for screening of the electric field
but also for the bunching of pair plasma by the two-stream instability.
This model predicts a high growth rate
and wavelength of electrostatic waves appropriate
to reproduce observed radio emission by coherent curvature radiation.
The growth rate is basically determined by $\omega_{\rm pp}
\propto \sqrt{B_{12}/T_{0.3}}$.
Since rapidly rotating pulsars tend to have weak magnetic fields,
$\omega_{\rm pp}$ is not so sensitive to the model parameters.
For example, $\omega_{\rm pp}/2 \pi$ becomes about 50 MHz
for $B=10^{9}$ G and $T=1$ ms.
On the other hand, for $B=10^{15}$ G and $T=10$ s, $\omega_{\rm pp}/2 \pi
\sim 500$ MHz.
The resultant growth rate is also insensitive to the model parameters.
It is interesting that the predicted wave length is
comparable to the wave length of the space charge density wave,
which appears outside the screening region in AT.
We noticed the interesting paper of \citet{les98} in which they claimed that
coherent curvature radiation cannot be the source
for the radio emission of pulsars.
However, their treatment is based on several simplifying assumptions:
a full coherence extending up to $\nu_{\rm c}$, a large coherence
volume, and others. Basically, these assumptions lead to
a short cooling time and a lower value for the upper limit of luminosity.
In our case, the coherence volume is smaller and at $\nu_{\rm c}$
only a partial coherence is supposed. Moreover, only a small
fraction of pairs are bunched and the cooling time is
much longer than their estimate. Thus, the limit claimed by \citet{les98}
is irrelevant in our case. Examinations of more general constraints
are beyond the scope of this Letter.
Although the AT model resolves both the screening and radio emission problems,
there remain many ambiguous points:
the frictional force discussed in section 3,
mechanisms to achieve the proton counterflow, and so on.
In the AT model, the proton counterflow comes from the corotating magnetosphere
via the anomalous diffusion \citep{lie85}.
The currents of the primary beam and protons
are most likely to be determined by the global dynamics
in the magnetosphere.
However, we should not persist in the anomalous diffusion,
because there may be other mechanisms to cause the proton counterflow.
Considering that we still do not understand well
the fundamental issues of pulsar physics,
we should be free from any kind of prejudices.
We cannot exclude any possibility at the present stage.
\acknowledgments
This work is supported in part by a Grant-in-Aid for Scientific Research
from the Ministry of Education and Science (14079205 and 16540215; F. T.).
|
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"redpajama_set_name": "RedPajamaArXiv"
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{"url":"https:\/\/www.physicsforums.com\/threads\/forces-on-a-rigid-body.327387\/","text":"# Forces on a rigid body\n\n1. Jul 27, 2009\n\n### FigBug\n\nThis isn't homework, it's for a simple computer program I'm trying to write. It's been a long time since I took a physics class, but I seem to remember getting homework questions like this.\n\nIf I have a 2D rigid body, I know its mass and the location of its CG. The object is being held by two points, how can I find the forces acting on the two points?\n\nI know there are going to be 3 force vectors that must add up to zero. The first one is easy to find, straight down with mass * 9.8. But how do I find the other two? I assume the direction of the vectors is the angle between CG and A and B? If I have one vector and two angles, is that enough to calculate everything I need?\n\nTorque must sum to zero as well, but I don't think I need to worry about that.\n\nAny tips for solving this in the general case? Any tutorials I should look at? I have one physics text, Physics for Scientists & Engineers, but it only covers this topic with 1 or 2 pages.\n\nLast edited by a moderator: May 4, 2017\n2. Jul 27, 2009\n\n### rock.freak667\n\nWell if you split the components of the force at A into x and y, and do the same for B, if the body is in equilibrium as shown, then $\\Sigma F_x= 0$ and $\\Sigma F_y=0$. If you know the two angles, then you'd have two equations with two unknowns.\n\nAlso if you take moments about the CG, then you'd get another equation to use.\n\n3. Jul 27, 2009\n\n### turin\n\nIf this is made to be so, then you can ignore the torque (because there is no applied torque in this case), and then you can solve a system of two equations and two unknowns (or four equations and four unknowns). However, this condition is not guaranteed automatically; you have to additionally require that the forces at A and B satisfy this condition.\n\nIn general, if you allow the forces at A and B to be applied in arbitrary direction, then you will have one free parameter. This simply amounts to what you probably already realize intuitively. If you just barely hold onto the rigid body, so that it does not fall, then the forces will be on the order of mg, and directed mostly upward. Alternatively, you can imagine applying opposing near-horizontal forces at A and B, in which case the forces will need to be very hard (>>mg). You can apply the forces anywhere in between these two extremes as well, giving you one free parameter.\n\nYou could also ask an interesting question: what is the minimum amount of force required at A and B?\n\n4. Jul 28, 2009\n\n### FigBug\n\nI'm getting a bit confused, so I'm going to back up a bit to my actual problem.\n\nI have a speaker array (as shown) that is hanging from two chains and I'm trying to find the forces on the pins labelled A, B, C, D\n\nhttp:\/\/rabien.com\/image\/array.png [Broken]\n\nAm I correct in thinking there won't be any forces in the x direction but only the y?\n\nTo find the forces on A & B, I find the mass of the entire array and the location of the CG. If the CG is left of A or right of B then the array won't be hanging from both chains, one of them will be slack and all the weight will be on the other.\n\nIf Ax < CGx < Bx then the force will be spread between the two chains.\n\nThe force on A with be something like (CGx - Ax) \/ (Bx - Ax) * (Fcg) in the y and 0 in the x?\n\nI'd do something similar for C & D? But it gets more complex if A & B don't have the same y value? Then I would start getting forces in the x direction?\n\nI think the first thing I need to do is figure out the correct way to model my problem before I can solve it.\n\nLast edited by a moderator: May 4, 2017\n5. Jul 28, 2009\n\n### turin\n\nI don't know if I understand your diagram. No doubt you are hoping that we can understand what you \"mean\" because an accurate diagram with all the necessary labels would be tedious. So, here I will tell you what my interpretation is, and if it does not match your intent, then let me know:\n\nThere are six \"blocks\". Each block has a circle drawn roughly in the middle, which represents the CG of that block. All of the blocks are attached consecutively, but you only had the patience to draw one set of connections, C and D, which is your paradigm for connecting the speakers. So, A and B must support the weight of the entire chain (all five speakers and the the platform at the top). There are two connections that hold the 5-speaker chain to the platform (no shown). C and D hold the bottom 4 speakers to the top speaker. Etc. The shape of the chain as you have represented it is static.\n\nOK, so here's my analysis. The way you've drawn the connections suggests that the forces are entirely vertical. That is, A and B experience entirely vertical forces due to tensions in two vertical cables (connected to the ceiling). C and D experience approximately vertical forces due to two approximately vertically alligned brackets. And so on. So, you do need to consider torque, if you want to know how the force is dsitributed between the two connections. As an approximation, you should be able to set the x-components of all forces to zero. Then, you have two conditions to satisfy: the y-components of all forces acting on a body must add up to zero, and the torques acting on a body must add up to zero.\n\n6. Jul 28, 2009\n\n### FigBug\n\nYour interpretation of my diagram is correct. As the array curves backwards, the connectors will become less vertically aligned. Until now, I've been ignoring torque. I'll incorporating torque into my calculations and I'll see where that gets me.\n\nThanks for the help.","date":"2017-08-19 10:27:06","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\": 0.713951826095581, \"perplexity\": 304.3515825850026}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-34\/segments\/1502886105334.20\/warc\/CC-MAIN-20170819085604-20170819105604-00576.warc.gz\"}"}
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Q: Simple JQuery click-and-show doesn't work I'm using this simple bit of JQuery to show/hide a div by clicking on the link, I've used the same code a few times before and it worked perfectly but now all of a sudden it refuses to work.
JQuery is properly included and the page doesn't give a Javascript error (or any other error for that matter).
JQuery:
<script type="text/javascript">
$(function() {
$('#addnew').css('display', 'none');
$('#shownew').click(function() {
$('#addnew').toggle();
return false;
});
});
</script>
HTML (link):
<a href='#' id='shownew'>Add News Item</a>
HTML (div):
<div id="addnew">
<form id="new_news" enctype="multipart/form-data" action="news.php" method="post">
Title:
<br/><input type="text" name="title" id="title" />
<p>Image (optional, will be shown after first paragraph)
<br/><input type="hidden" name="size" value="2000000"><input type="file" name="photo">
<p>Article body:
<br/><textarea cols='40' rows='5' maxlength='5000' name='body' id='body'></textarea>
<p><input type="submit" name="submit" id="submit" value="Submit" />
</form>
</div>
What could I possibly be missing here? As you see from the JQuery, the div is hidden to begin with. When I remove the line that says $('#addnew').css('display', 'none'); the div is displayed correctly, but the link still doesn't toggle it on and off.
A: Is #showNew element present in the DOM before onload? If it is not then your code will not work. If that is the case following code will help you.
$(document).on('click', '#shownew',function() {
$('#addnew').toggle();
return false;
});
A: I reloaded the page a few minutes later and it worked. No idea what was wrong. I know the code was good from the beginning.
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"redpajama_set_name": "RedPajamaStackExchange"
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| 2,884
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\section{Introduction}
A family of generative models known as diffusion models has recently gained a lot of attention with state-of-the-art image generation quality \citep{dhariwal2021diffusion}.
\emph{Guided diffusion} is an approach for controlling the output of a trained diffusion model for conditional generation tasks without retraining its network.
By engineering a task-specific conditional function and modifying only the sampling procedure, guided diffusion models can be used in a variety of applications, such as class-conditional image generation \citep{dhariwal2021diffusion,kawar2022enhancing}, text-to-image generation \citep{nichol2021glide}, image-to-image translation \citep{zhao2022egsde}, inpainting \citep{chung2022improving}, colorization \citep{song2020score}, image composition \citep{sasaki2021unit}, adversarial purification \citep{wang2022guided,wu2022guided} and super-resolution \citep{choi2021ilvr}.
One common drawback of both guided and regular ``unguided'' diffusion models is their slow sampling processes, usually requiring hundreds of iterations to produce a single image.
Recent speed-up attempts include improving the noise schedule \citep{nichol2021improved,watson2021learning}, redefining the diffusion process to be non-Markovian, thereby allowing a deterministic sampling process \cite{song2020denoising}, network distillation that teaches a student model to simulate multiple sampling steps of a teacher model \cite{salimans2022progressive, luhman2021knowledge}, among others. \cite{song2020denoising} show how each sampling step can be expressed as a first-order numerical step of an ordinary differential equation (ODE). Similarly, \cite{song2020score} express the sampling of a score-based model as solving a stochastic differential equation (SDE). By regarding the sampling process as an ODE/SDE, many high-order numerical methods have been suggested, such as \cite{liu2022pseudo}, \cite{zhang2022fast}, and \cite{zhang2022gddim} with impressive results on unguided diffusion models.
However, when applied to guided diffusion models, these methods produce surprisingly poor results (see Figure \ref{fig:class})---given a few number of steps, those high-order numerical methods actually perform worse than low-order methods.
Guided sampling differs from the unguided one by the addition of the gradients of the conditional function to its sampling equation. The observed performance decline thus suggests that classical high-order methods may not be suitable for the conditional function and, consequently, the guided sampling equation as a whole. Our paper tests this hypothesis and presents an approach to accelerating guided diffusion sampling.
The key idea is to use an \emph{operator splitting} method to split the less well-behaved conditional function term from the standard diffusion term and solve them separately.
This approach not only allows re-utilizing the successful high-order methods on the diffusion term but also provides us with options to combine different specialized methods for each term to maximize performance. Splitting method can be used to solve diffusion SDE in \cite{dockhorn2021score}.
Our design process includes comparing different splitting methods and numerical methods for each split term.
When tested on ImageNet, our approach achieves the same level of image quality as a DDIM baseline while reducing the sampling time by approximately 32-58\%.
Compared with other sampling methods using the same sampling time, our approach provides better image quality as measured by LPIPS, FID, and Perception/Recall.
With only minimal modifications to the sampling equation, we also show successful acceleration on various conditional generation tasks.
\begin{figure*}
\centering
\setlength\tabcolsep{1.5pt}
\begin{tabular}{cl}
\shortstack{\small Number \\of steps} & \qquad\: 8 \qquad\qquad\: 16 \qquad\qquad 32 \qquad\qquad 64 \qquad\qquad 128 \qquad\quad 256 \\
\shortstack{DDIM\vspace{0.8cm}} &
\includegraphics[width=0.8\textwidth]{images/class_gen/v4/ddim_p.jpg} \\
\shortstack{PLMS4\vspace{0.8cm}} &
\includegraphics[width=0.8\textwidth]{images/class_gen/v4/plms_p.jpg}\\
\shortstack{\textbf{STSP4}\\(Ours)\vspace{0.5cm}} &
\includegraphics[width=0.8\textwidth]{images/class_gen/v4/bchf_p.jpg} \\
\end{tabular}
\caption{
Generated samples of a classifier-guided diffusion model trained on ImageNet256 using 8-256 sampling steps from different sampling methods.
Our technique, STSP4, produces high-quality results in a fewer number of steps.
}
\label{fig:class}
\end{figure*}
\section{Background}
This section provides a high-level summary of the theoretical foundation of diffusion models as well as numerical methods that have been used for diffusion models.
Here we briefly explain a few that contribute to our method.
\subsection{Diffusion Models}
Assuming that $x_0$ is a random variable from the data distribution we wish to reproduce,
diffusion models define a sequence of Gaussian noise degradation of $x_0$ as random variables $x_1, x_2,...,x_T$, where $x_{t} \sim \mathcal{N}(\sqrt{1-\beta_t} x_{t-1}, \beta_t \mathbf{I})$ and $\beta_t\in[0,1]$ are parameters that control the noise levels.
With a property of Gaussian distribution, we can express $x_t$ directly as a function of $x_0$ and noise $\epsilon \sim \mathcal{N}(0,\mathbf{I})$ by $x_t=\sqrt{\bar{\alpha}_t}x_0 + \sqrt{1-\bar{\alpha}_t}\epsilon$, where $\bar{\alpha}_t=\prod^t_{i=1}(1-\beta_i)$.
By picking a sufficiently large $T$ (e.g., 1,000) and an appropriate set of $\beta_t$, we can assume $x_T$ is a standard Gaussian distribution.
The main idea of diffusion model generation is to sample a Gaussian noise $x_T$ and use it to reversely sample $x_{T-1}$, $x_{T-2},...$ until we obtain $x_0$, which belongs to our data distribution.
\cite{ho2020denoising} propose Denoising Diffusion Probabilistic Model (DDPM) and explain how to employ a neural network $\epsilon_\theta(x_t, t)$ to predict the noise $\epsilon$ that is used to compute $x_t$.
To train the network, we sample a training image $x_0$, $t$, and $\epsilon$ to compute $x_t$ using the above relationship.
Then, we optimize our network $\epsilon_\theta$ to minimize the difference between the predicted and real noise,
i.e., $\|\epsilon - \epsilon_\theta (x_t,t)\|^2$.
\cite{song2020denoising} introduce Denoising Diffusion Implicit Model (DDIM), which uses the network $\epsilon_\theta$ to deterministically obtain $x_{t-1}$ given $x_t$. The DDIM generative process can be written as
\begin{equation} \label{ddim}
x_{t-1} = \sqrt{\frac{\bar{\alpha}_{t-1}}{\bar{\alpha}_{t}} }
\left( x_t - \sqrt{1-\bar{\alpha}_{t}} \epsilon_\theta (x_t,t)\right)
+\sqrt{1-\bar{\alpha}_{t-1}} \epsilon_\theta (x_t,t).
\end{equation}
This formulation could be used to skip many sampling steps and boost sampling speed.
To turn this into an ODE, we rewrite Equation \ref{ddim} as:
\begin{equation}
\frac{x_{t-\Delta t}}{\sqrt{\bar{\alpha}_{t-\Delta t}}} = \frac{x_{t}}{\sqrt{\bar{\alpha}_{t}}}
+ \left(\sqrt{\frac{1-\bar{\alpha}_{t-\Delta t}}{\bar{\alpha}_{t-\Delta t}}} - \sqrt{\frac{1-\bar{\alpha}_{t}}{\bar{\alpha}_{t}}} \right) \epsilon_\theta (x_t,t),
\end{equation}
which is now equivalent to a numerical step in solving an ODE.
To derive the corresponding ODE, we can re-parameterize
$\sigma_t = \sqrt{1-\bar{\alpha}_{t}}/ \sqrt{\bar{\alpha}_{t}}, \: \bar{x}(t) = x_t/\sqrt{\bar{\alpha}_{t}}$ and $\bar{\epsilon}_\sigma(\bar{x}) = \epsilon_\theta (x_t,t)$, yielding $\bar{x}({t-\Delta t}) - \bar{x}({t}) = (\sigma_{t-\Delta t} - \sigma_t) \bar{\epsilon}_\sigma (\bar{x})$.
By letting $(\sigma_{t-\Delta t} - \sigma_t) \rightarrow 0$, the ODE becomes:
\begin{equation} \label{eq:ode}
\frac{d\bar{x}}{d\sigma} = \bar{\epsilon}_\sigma (\bar{x}).
\end{equation}
Note that this change of variables is equivalent to an exponential integrator technique described in both \cite{zhang2022fast} and \cite{lu2022dpm}.
Since $x_t$ and $\bar{x}(t)$ have the same value at $t=0$, our work can focus on solving $\bar{x}(t)$ rather than $x_t$.
Many numerical methods can be applied to the ODE Equation \ref{eq:ode} to accelerate diffusion sampling.
We next discuss some of them that are relevant.
\subsection{Numerical Methods}
\textbf{Euler's Method} is
the most basic numerical method.
A forward Euler step is given by
$ \bar{x}_{n+1} = \bar{x}_n +\Delta \sigma \bar{\epsilon}_\sigma (\bar{x}_n)$.
When we apply the forward Euler step to the ODE Equation \ref{eq:ode}, we get the DDIM formulation \citep{song2020denoising}.
\textbf{Heun's Method}, also known as the trapezoid rule or improved Euler, is given by:
$ \bar{x}_{n+1} = \bar{x}_n +\frac{\Delta \sigma}{2} (e_1 + e_2)$, where $e_1 = \bar{\epsilon}_\sigma (\bar{x}_{n})$ and $ e_2 = \bar{\epsilon}_\sigma (\bar{x}_{n} + \Delta \sigma e_1).$
This method modifies Euler's method into a two-step method to improve accuracy.
Many papers have used this method on diffusion models, including Algorithm 1 in \cite{karras2022elucidating} and DPM-Solver-2 in \cite{lu2022dpm}.
This method is also the simplest case of Predictor-Corrector methods used in \cite{song2020score}.
\textbf{Runge-Kutta Methods} represent a class of numerical methods that integrate information from multiple hidden steps and provide high accuracy results. Heun's method also belongs to a family of 2\textsuperscript{nd}-order Runge-Kutta methods (RK2).
The most well-known
variant
is the 4\textsuperscript{th}-order Runge-Kutta method (RK4), which is written as follows:
$$ e_1 = \bar{\epsilon}_\sigma (\bar{x}_{n}), \quad e_2 = \bar{\epsilon}_\sigma \left(\bar{x}_{n} + \frac{\Delta \sigma}{2} e_1\right),
\quad e_3 = \bar{\epsilon}_\sigma \left(\bar{x}_{n} + \frac{\Delta \sigma}{2} e_2\right), \quad e_4 = \bar{\epsilon}_\sigma \left(\bar{x}_{n} + \Delta \sigma e_3\right),$$
\begin{equation}
\bar{x}_{n+1} = \bar{x}_n +\frac{\Delta \sigma}{6} (e_1 + 2 e_2 + 2 e_3 + e_4).
\end{equation}
This method has been tested on diffusion models in \cite{liu2022pseudo} and \cite{salimans2022progressive}, but it has not been used as the main proposed method in any paper.
\textbf{Linear Multi-Step Method},
similar to the Runge-Kutta methods, aims to combine information from several steps; however, rather than evaluating new hidden steps, this method uses the previous steps to estimate the new step. The 1\textsuperscript{st}-order formulation is the same as Euler's method.
The 2\textsuperscript{nd}-order formulation is given by
\begin{equation}
\bar{x}_{n+1} = \bar{x}_n +\frac{\Delta \sigma}{2} \left(3 e_0 - e_1\right),
\end{equation}
while the 4\textsuperscript{th}-order formulation is given by
\begin{equation}
\bar{x}_{n+1} = \bar{x}_n +\frac{\Delta \sigma}{24} (55 e_0 - 59e_1 + 37 e_2 - 9 e_3),
\end{equation}
where $e_k = \bar{\epsilon}_\sigma (\bar{x}_{n-k})$.
These formulations are designed for a constant $\Delta \sigma$ in each step. However, our experiments and previous work that uses this method (e.g., \cite{liu2022pseudo, zhang2022fast}) still show good results when this assumption is not strictly satisfied, i.e., when $\Delta \sigma$ is not constant.
We will refer to these formulations as PLMS (Pseudo Linear Multi-Step) for the rest of the paper, like in \cite{liu2022pseudo}.
A similar linear multi-step method for non-constant $\Delta \sigma$ can also be derived using a technique used in \cite{zhang2022fast}, which we detail in Appendix \ref{iPLMS}. The method can improve upon PLMS slightly, but it is not as flexible because we have to re-derive the update rule every time the $\sigma$ schedule changes.
\section{Splitting Methods for Guided Diffusion Models}
This section introduces our technique that uses splitting numerical methods to accelerate guided diffusion sampling. We first focus our investigation on \emph{classifier-guided} diffusion models for class-conditional generation and later demonstrate how this technique can be used for other conditional generation tasks in Section \ref{sec:splitting_for_other_tasks}. Like any guided diffusion models, classifier-guided models \citep{dhariwal2021diffusion} share the same training objective with regular unguided models with no modifications to the training procedure; but the sampling process is guided by an additional gradient signal from an external classifier to generate class-specific output images. Specifically, the sampling process is given by
\begin{equation}
\hat{\epsilon} = \epsilon_\theta (x_t) -\sqrt{1-\bar{\alpha}_t} \nabla_x \log p_\phi (c | x_t), \quad
x_{t-1} = \sqrt{\bar{\alpha}_{t-1}}
\left( \frac{x_t - \sqrt{1-\bar{\alpha}_{t}} \hat{\epsilon}}{\sqrt{\bar{\alpha}_{t}}}\right)
+\sqrt{1-\bar{\alpha}_{t-1}} \hat{\epsilon},
\end{equation}
where $p_\phi (c | x_t)$ is a classifier model trained to output the probability of $x_t$ belonging to class $c$.
As discussed in the previous section, we can rewrite this formulation as a ``guided ODE'':
\begin{equation} \label{eq:guide}
\frac{ d \bar{x}}{d \sigma} = \bar{\epsilon}_\sigma (\bar{x}) - \nabla f_\sigma (\bar{x}),
\end{equation}
where $f_\sigma (\bar{x}) = \frac{\sigma}{\sqrt{\sigma^2+1}} \log p_\phi (c | x_t)$. We refer to $f_\sigma$ as the conditional function, which can be substituted with other functions for different tasks. After obtaining the ODE form, any numerical solver mentioned earlier can be readily applied to accelerate the sampling process.
However, we observe that classical high-order numerical methods (e.g., PLMS4, RK4) fail to accelerate this task (see Figure \ref{fig:class}) and even perform worse than the baseline DDIM.
We hypothesize that the two terms in the guided ODE may have different numerical behaviors with the conditional term being less suitable to classical high-order methods. We speculate that the difference could be partly attributed to how they are computed: $\nabla f_\sigma (\bar{x})$ is computed through backpropagation, whereas $\bar{\epsilon}_\sigma (\bar{x})$ is computed directly by evaluating a network.
One possible solution to handle terms with different behaviors is the so-called operator splitting method, which divides the problem into two subproblems:
\begin{equation} \frac{dy}{d\sigma} = \bar{\epsilon}_\sigma (y), \quad \frac{dz}{d\sigma} = - \nabla f_\sigma (z). \end{equation}
We call these the \emph{diffusion} and \emph{condition} subproblems, respectively.
This method allows separating the hard-to-approximate $\nabla f_\sigma (z)$ from $\bar{\epsilon}_\sigma (y)$ and solving them separately in each time step. Importantly, this helps reintroduce the effective use of high-order methods on the diffusion subproblem as well as provides us with options to combine different specialized methods to maximize performance.
We explore two most famous first- and second-order splitting techniques for our task:
\subsection{Lie-Trotter Splitting (LTSP)}
Our first example is the simple first-order Lie-Trotter splitting method \citep{trotter1959product}, which expresses the splitting as
\begin{align}
\frac{dy}{d\sigma} &= \bar{\epsilon}_\sigma (y),&y(\sigma_n) &= \bar{x}_n, & \sigma \in [\sigma_{n+1}, \sigma_{n}] \label{eq:ltts1}\\
\frac{dz}{d\sigma} &= - \nabla f_\sigma (z), &z(\sigma_n) &= y(\sigma_{n+1}), & \sigma \in [\sigma_{n+1}, \sigma_{n}] \label{eq:ltts2}
\end{align}
with the solution of this step being $\bar{x}_{n+1} = z(\sigma_{n+1})$.
Note that $\sigma_n$ is a decreasing sequence in sampling schedule.
Here Equation \ref{eq:ltts1} is the same as Equation \ref{eq:ode}, which can be solved using any high-order numerical method, e.g., PLMS.
For Equation \ref{eq:ltts2}, we can use a forward Euler step:
\begin{equation}z_{n+1}=z_n - \Delta \sigma \nabla f_\sigma (z_n).\end{equation}
This is equivalent to a single iteration of standard gradient descent with a learning rate $\Delta \sigma$.
This splitting scheme is summarized by Algorithm \ref{algo:ltsp}.
We investigate different numerical methods for each subproblem in Section \ref{exp1}.
\begin{table}
\begin{minipage}{0.49\textwidth}
\begin{algorithm}[H]
\label{algo:ltsp}
\SetAlgoLined
sample $\bar{x}_0 \sim \mathcal{N}(0,\sigma^2_{\text{max}}\mathbf{I})$ \;
\For{$n\in\{0,...,N-1\}$}{
$y_{n+1} = \text{PLMS}(\bar{x}_n,\sigma_n,\sigma_{n+1},\bar{\epsilon}_\sigma) $\;
$\bar{x}_{n+1} = y_{n+1} - (\sigma_{n+1}-\sigma_n) \nabla f(y_{n+1})$ \;
}
\KwResult{$\bar{x}_N$}
\caption{Lie-Trotter Splitting (LTSP)}
\end{algorithm}
\end{minipage}
\begin{minipage}{0.47\textwidth}
\begin{algorithm}[H]
\label{algo:stsp}
\SetAlgoLined
sample $\bar{x}_0 \sim \mathcal{N}(0,\sigma^2_{\text{max}}\mathbf{I})$ \;
\For{$n\in\{0,...,N-1\}$}{
$z_{n+1} = \bar{x}_n - \frac{(\sigma_{n+1}-\sigma_n)}{2} \nabla f(\bar{x}_n)$ \;
$y_{n+1} = \text{PLMS}(z_{n+1},\sigma_n,\sigma_{n+1},\bar{\epsilon}_\sigma) $\;
$\bar{x}_{n+1} = y_{n+1} - \frac{(\sigma_{n+1}-\sigma_n)}{2} \nabla f(y_{n+1})$ \;
}
\KwResult{$\bar{x}_N$}
\caption{Strang Splitting (STSP)}
\end{algorithm}
\end{minipage}
\end{table}
\subsection{Strang Splitting (STSP)}
Strang splitting (or Strang-Marchuk)
\citep{strang1968construction} is one of the most famous and widely used operator splitting methods.
This second-order splitting works as follows:
\begin{align}
\frac{dz}{d\sigma} &= - \nabla f_\sigma (z), &z(\sigma_n) = \bar{x}_n,& \quad& \sigma \in \left[ \frac{1}{2}(\sigma_{n}+\sigma_{n+1}), \sigma_n\right] \label{eq:bcpf1} \\
\frac{dy}{d\sigma} &= \bar{\epsilon}_\sigma (y),&y(\sigma_n) = z\left(\frac{1}{2}(\sigma_{n}+\sigma_{n+1})\right),& \quad& \sigma \in [\sigma_{n+1}, \sigma_n] \label{eq:bcpf2}\\
\frac{d \Tilde{z}}{d\sigma} &= - \nabla f_\sigma (\Tilde{z}), &\Tilde{z}\left(\frac{1}{2}(\sigma_{n}+\sigma_{n+1})\right) = y(\sigma_{n+1}),& \:& \sigma \in \left[ \sigma_{n+1}, \frac{1}{2}(\sigma_{n}+\sigma_{n+1})\right] \label{eq:bcpf3}
\end{align}
Instead of solving each subproblem for a full step length, we solve the condition subproblem for half a step before and after solving the diffusion subproblem for a full step. In theory, we can swap the order of operations without affecting convergence, but it is practically cheaper to compute the condition term twice rather than the diffusion term twice because $f_\sigma$ is typically a smaller network compared to $\bar{\epsilon}_\sigma$.
The Strange splitting algorithm is shown in Algorithm \ref{algo:stsp}.
This method can be proved to have better accuracy than the Lie-Trotter method using the Banker-Campbell-Hausdorff formula \citep{mark2001stat}, but it requires evaluating the condition term twice per step in exchange for improved image quality. We assess this trade-off in the experiment section.
\section{Experiments}
Extending on our observation that classical high-order methods failed on guided sampling, we conducted a series of experiments to investigate this problem and evaluate our solution.
Section \ref{exp1} uses a simple splitting method (first-order LTSP) to study the effects that high-order methods have on each subproblem, leading to our key finding that \emph{only} the conditional subproblem is less suited to classical high-order methods.
This section also determines the best combination of numerical methods for the two subproblems under LTSP splitting.
Section \ref{exp2} explores improvements from using a higher-order splitting method and compares our best scheme to previous work.
Finally, Section \ref{sec:splitting_for_other_tasks} applies our approach to a variety of conditional generation tasks with minimal changes.
For our comparison, we use pre-trained state-of-the-art diffusion models and classifiers from \cite{dhariwal2021diffusion}, which were trained on the ImageNet dataset \citep{russakovsky2015imagenet} with 1000 total sampling step. We treat full-path samples from a classifier-guided DDIM at 1,000 steps as reference solutions. Then the performance of each configuration is measured by the image similarity between its generated samples using fewer steps and the reference DDIM samples, both starting from the same initial noise maps. Given the same sampling time, we expect configurations with better performance to better match the full DDIM.
We measure image similarity using Learned Perceptual Image Patch Similarity (LPIPS) \citep{zhang2018unreasonable} (lower is better) and measure sampling time using a single NVIDIA RTX 3090 and a 24-core AMD Threadripper 3960x.
\begin{figure} \vspace{-4mm}
\centering
\shortstack{ \includegraphics[width = 0.49\textwidth]{images/graph_ex1_1.pdf}
\\ \footnotesize (a) Varying the method for the diffusion subproblem}
\shortstack{ \includegraphics[width = 0.49\textwidth]{images/graph_ex1_2.pdf}
\\ \footnotesize (b) Varying the method for the condition subproblem}
\caption{Comparison of different combinations of numerical methods under LTSP splitting for guided diffusion sampling.
We plot LPIPS against the sampling time. [A, B] denotes the use of method A in the diffusion subproblem and method B in the condition subproblem. The red dotted lines indicate a reference DDIM score obtained from 250 sampling steps, which produce images visually close to those from 1,000 steps.
}
\label{fig:exp1}
\end{figure}
\subsection{Finding a suitable numerical method for each subproblem} \label{exp1}
To study the effects of different numerical methods on each subproblem of the guided ODE (Equation \ref{eq:guide}), we use the simplest Lie-Trotter splitting, which itself requires no additional network evaluations. This controlled experiment has two setups: a) we fix the numerical method for the condition subproblem (Equation \ref{eq:ltts2}) to first-order PLMS1 (Euler's method) and vary the numerical method for the diffusion subproblem (Equation \ref{eq:ltts1}), and conversely b) we fix the method for the diffusion subproblem and vary the method for the condition subproblem. The numerical method options are Euler's method (PLMS1), Heun's method (RK2), 4\textsuperscript{th} order Runge-Kutta's method (RK4), and 2\textsuperscript{nd}/4\textsuperscript{th} order pseudo linear multi-step (PLMS2/PLMS4).
We report LPIPS vs. sampling time of various numerical combinations on a diffusion model trained on ImageNet 256$\times$256 in Figure \ref{fig:exp1}. The red dotted lines indicate a reference DDIM score obtained from 250 sampling steps, a common choice that produces good samples that are perceptually close to those from a full 1,000-step DDIM \citep{dhariwal2021diffusion, nichol2021improved}.
Given a long sampling time, non-split PLMS4 performs better than the DDIM baseline.
However, when the sampling time is reduced, the image quality of PLMS4 rapidly decreases and becomes much worse than that of DDIM, especially under 15 seconds in Figure \ref{fig:exp1}.
When we split the ODE and solve both subproblems using first-order PLMS1 (Euler), the performance is close to that of DDIM, which is also considered first-order but without any splitting. This helps verify that merely splitting the ODE does not significantly alter the sampling speed.
In the setup a), when RK2 and RK4 are used for the diffusion subproblem, they also perform worse than the DDIM baseline. This slowdown is caused by the additional evaluations of the network by these methods, which outweigh the improvement gained in each longer diffusion step. Note that if we instead measure the image quality with respect to the number of diffusion steps, RK2 and RK4 can outperform other methods (Appendix \ref{step}); however, this is not our metric of interest. On the other hand, PLMS2 and PLMS4, which require no additional network evaluations, are about 8-10\% faster than DDIM and can achieve the same LPIPS score as the DDIM that uses 250 sampling steps in 20-26 fewer steps.
Importantly, when the sampling time is reduced, their performance does not degrade rapidly like the non-split PLMS4 and remains at the same level as DDIM.
In the setup b) where we vary the numerical method for the condition subproblem, the result reveals an interesting contrast---none of the methods beats DDIM and some even make the sampling diverged [PLMS1, RK4].
These findings suggest that the gradients of conditional functions are less ``compatible'' with classical high-order methods, especially when used with a small number of steps.
This phenomenon may be related to the ``stiffness'' condition of ODEs, which we discuss further in Section \ref{sec:discussion}.
For the remainder of our experiments, we will use the combination [PLMS4, PLMS1] for the diffusion and condition subproblems, respectively.
\subsection{Improved splitting method} \label{exp2}
This experiment investigates improvements from using a high-order \emph{splitting} method, specifically the Strang splitting method, with the numerical combination [PLMS4, PLMS1] and compares our methods to previous work.
Note that besides DDIM \cite{dhariwal2021diffusion}, no previous work is specifically designed for accelerating \emph{guided} sampling, thus the baselines in this comparison are only adaptations of the core numerical methods used in those papers. And to our knowledge, no prior guided-diffusion work uses splitting numerical methods.
Non-split numerical method baselines are PLMS4, which is used in \cite{liu2022pseudo}, RK2, which is used in \cite{karras2022elucidating, lu2022dpm}, and higher-order RK4.
We report the LPIPS scores of these methods with respect to the sampling time in Figure \ref{fig:exp2} and Table \ref{tab:exp2}.
Without any splitting, PLMS4, RK2 and RK4 show significantly poorer image quality when used with short sampling times $<10$ seconds. The best performer is our Strang splitting (STSP4), which can reach the same quality as 250-step DDIM while using 32-58\% less sampling time. STSP4 also obtains the highest LPIPS scores for sample times of 5, 10, 15, and 20 seconds.
More statistical details and comparison with other split combinations are in Appendix \ref{std}, \ref{str_aba}.
\begin{figure}\vspace{-4mm}
\begin{floatrow}
\ffigbox[.45\textwidth]{%
\shortstack{ \includegraphics[width = 0.48\textwidth]{images/graph_ex2.pdf}}%
}{%
\caption{Comparison of different numerical methods for guided diffusion sampling. }%
\label{fig:exp2}
}
\capbtabbox{%
\begin{tabular}{lcccc}
\toprule
&\multicolumn{4}{c}{Sampling time within} \\
& 5 sec. & 10 sec. & 15 sec. & 20 sec. \\
\midrule[0.08em]
DDIM & 0.116 & 0.062 & 0.043 & 0.033 \\
PLMS4 & 0.278 & 0.141 & 0.057 & 0.026 \\
RK2 & 0.193 & 0.059 & 0.036 & 0.028 \\
RK4 & 0.216 & 0.054 & 0.039 & 0.028 \\
\textbf{LTSP4} & 0.121 & 0.058 & 0.037 & 0.028 \\
\textbf{STSP4} & \textbf{0.079} & \textbf{0.035} & \textbf{0.022} & \textbf{0.013} \\
\bottomrule
\end{tabular}
\caption
Average LPIPS when the sampling time is limited to be under 5 - 20 seconds.
}%
\label{tab:exp2}
}{%
}
\end{floatrow}
\end{figure}
In addition, we perform a quantitative evaluation for class-conditional generation by sampling 50,000 images based on uniformly chosen class conditions with a small number of sampling steps and evaluating the Fenchel Inception Distance (FID) \cite{heusel2017gans} (lower is better) and the improved precision/recall \cite{kynkaanniemi2019improved} (higher is better) against an ImageNet test set.
Following \citep{dhariwal2021diffusion}, we use a 25-step DDIM as a baseline, which already produces visually reasonable results.
As PLMS and LTSP require the same number of network evaluations as the DDIM, they are used also with 25 steps. For STSP with a longer network evaluation time, it is only allowed 20 steps, which is the highest number of steps such that its sampling time is within that of the baseline 25-step DDIM.
Here LTSP2 and STSP2 are Lie-Trotter and Strang splitting methods with the combination [PLMS2, PLMS1].
In Table \ref{tab:Sampling}, we report the results of three different ImageNet resolutions and the average sampling time per image in seconds.
Our STSP4 performs best on all measurements except Recall on ImageNet512.
On ImageNet512, PLMS4 has the highest Recall score but a poor FID of 16, indicating that the generated images have good distribution coverage but may poorly represent the real distribution.
On ImageNet256, STSP4 can yield 4.49 FID in 20 steps, compared to 4.59 FID in 250 steps originally reported in the paper \citep{dhariwal2021diffusion}; our STSP4 is about 9.4$\times$ faster when tested on the same machine.
\begin{table}
\begin{minipage}{0.5\columnwidth}
\centering
\resizebox{0.98\columnwidth}{!}{
\begin{tabular}{lccccc}
\toprule
Method & Steps & Time & FID & Prec & Rec \\
\midrule
\multicolumn{4}{l}{\textbf{ImageNet128}} \\
\arrayrulecolor[rgb]{0.7, 0.7, 0.7}\hline
\rule{0pt}{2ex}DDIM & 25 & 0.55 & 6.69 & 0.78 & 0.49 \\
PLMS2 & 25 & 0.57 & 5.71 & 0.80 & 0.51 \\
PLMS4 & 25 & 0.57 & 4.97 & 0.80 & 0.53 \\
\textbf{LTSP2} & 25 & 0.55 & 5.14 & 0.81 & 0.51 \\
\textbf{LTSP4} & 25 & 0.55 & 3.85 &\textbf{0.81} & \textbf{0.54} \\
\textbf{STSP2} & 20 & 0.54 & 5.33 & 0.80 & 0.52 \\
\textbf{STSP4} & 20 & 0.54 &\textbf{3.78}& \textbf{0.81}& \textbf{0.54} \\
[-1.2em]\\
\hdashline[1.2pt/1.2pt]\arrayrulecolor{black}
\rule{0pt}{2ex}\textit{ADM-G} & \textit{250} & \textit{5.59*} & \textit{2.97} & \textit{0.78} & \textit{0.59} \\
\bottomrule
\end{tabular}}
\end{minipage}\hfill
\begin{minipage}{0.5\columnwidth}
\centering
\resizebox{0.98\columnwidth}{!}{
\begin{tabular}{lccccc}
\toprule
Method & Steps & Time & FID & Prec & Rec \\
\midrule
\multicolumn{4}{l}{\textbf{ImageNet256}} \\
\arrayrulecolor[rgb]{0.7, 0.7, 0.7}\hline
\rule{0pt}{2ex}DDIM & 25 & 1.99 & 5.47 & 0.80 & 0.47 \\
PLMS4 & 25 & 2.05 & 4.71 & 0.82 & 0.49 \\
\textbf{STSP4} & 20 & 1.95 &\textbf{4.49}& \textbf{0.83}& \textbf{0.50} \\
[-1.2em]\\
\hdashline[1.2pt/1.2pt]\arrayrulecolor{black}
\rule{0pt}{2ex}\textit{ADM-G} & \textit{250} & \textit{20.9*} & \textit{4.59} & \textit{0.82} & \textit{0.50} \\
\\
\multicolumn{4}{l}{\textbf{ImageNet512}} \\
\arrayrulecolor[rgb]{0.7, 0.7, 0.7}\hline
\rule{0pt}{2ex}DDIM & 25 & 5.56 & 9.07 & {0.81} & 0.42 \\
PLMS4 & 25 & 5.78 & 16.00 & {0.75} & \textbf{0.51} \\
\textbf{STSP4} & 20 & 5.13 &\textbf{8.24}& \textbf{0.83}& {0.45} \\
[-1.2em]\\
\hdashline[1.2pt/1.2pt]\arrayrulecolor{black}
\rule{0pt}{2ex}\textit{ADM-G} & \textit{250} & \textit{56.2*} & \textit{7.72} & \textit{0.87} & \textit{0.42} \\
\bottomrule
\end{tabular}}
\end{minipage}
\caption{Comparison of different numerical methods using a few steps on guided diffusion sampling.
Our methods and the best scores are highlighted in bold.
We provide the reported scores from \cite{dhariwal2021diffusion} using 250 sampling steps, referred to as ADM-G in their paper. *ADM-G's sampling times are measured using our machine.}
\label{tab:Sampling}
\end{table}
\subsection{Splitting methods in other tasks} \label{sec:splitting_for_other_tasks}
Besides class-conditional generation, our approach can also accelerate any conditional image generation as long as the gradient of the conditional function can be defined.
We test our approach on four tasks: text-to-image generation, image inpainting, colorization, and super-resolution.
\textbf{Text-to-image generation:} We use a pre-trained text-to-image Disco-Diffusion \citep{Adam2021disco} based on \cite{crowson2021clip}, which substitutes the classifier output with the dot product of the image and caption encodings from CLIP \citep{radford2021learning}. For more related experiments on Stable-Diffusion \citep{rombach2022high}, please refer to Appendix \ref{dreambooth}, \ref{clip_sd}.
\textbf{Image inpainting \& colorization:} For these two tasks, we follow the techniques proposed in \cite{song2020score} and \cite{chung2022improving}, which improves the conditional functions of both tasks with ``manifold constraints.'' We use the same diffusion model \cite{dhariwal2021diffusion} trained on ImageNet as our earlier Experiments \ref{exp1}, \ref{exp2}.
\textbf{Super-resolution:} We follow the formulation from ILVR \citep{choi2021ilvr} combined with the manifold contraints \cite{chung2022improving}, and also use our earlier ImageNet diffusion model.
\begin{figure}
\centering
\setlength\tabcolsep{1.5pt}
\begin{tabular}{cc|cccc}
\shortstack{\scriptsize ``A beautiful painting of a singular \\
\scriptsize lighthouse, shining its light across \\
\scriptsize a tumultuous sea of blood, \\
\scriptsize trending on artstation.''\vspace{3mm}}
&
\includegraphics[width=0.14\textwidth]{images/painting/01/full.png}&
\includegraphics[width=0.14\textwidth]{images/painting/01/ddim.png}&
\includegraphics[width=0.14\textwidth]{images/painting/01/plms4.png}&
\includegraphics[width=0.14\textwidth]{images/painting/01/ltts4.png}&
\includegraphics[width=0.14\textwidth]{images/painting/01/bchf4.png}
\\
\shortstack{\scriptsize ``A beautiful painting of a starry \\
\scriptsize night, over a sunflower sea,\\
\scriptsize trending on artstation.'' \vspace{5mm}} &
\includegraphics[width=0.14\textwidth]{images/painting/02/full.png} &
\includegraphics[width=0.14\textwidth]{images/painting/02/ddim.png} &
\includegraphics[width=0.14\textwidth]{images/painting/02/plms4.png} &
\includegraphics[width=0.14\textwidth]{images/painting/02/ltts4.png} &
\includegraphics[width=0.14\textwidth]{images/painting/02/bchf4.png}
\\
&Full DDIM & DDIM & PLMS4 & LTSP4 & STSP4 \\
&\small (1,000 steps) & \small (45 steps) & \small (45 steps) & \small (45 steps) & \small (30 steps) \\
& & \multicolumn{4}{c}{ \footnotesize (approximately using the same sampling time) }
\end{tabular}
\caption{ Text-to-image generation using different sampling methods.}
\label{fig_txt2img}
\end{figure}
Figure \ref{fig_txt2img} compares our techniques, LTSP4 and STSP4, with the DDIM baseline and PLMS4 on text-to-image generation.
Each result is produced using a fixed sampling time of about 26 seconds.
STSP4, which uses 30 diffusion steps compared to 45 in the other methods, produces more realistic results with color contrast that is more similar to the full DDIM references'.
Figure \ref{fig_inpaint} shows that our STSP4 produces more convincing results than the DDIM baseline with fewer artifacts on the other three tasks while using the same 5 second sampling time.
Implementation details, quantitative evaluations, and more results are in Appendix \ref{txt2im}, \ref{con_gen}.
\section{Discussion}\label{sec:discussion}
Our findings show that when the sampling ODE consists of multiple terms from different networks, their numerical behaviors can be different and treating them separately can be more optimal.
Another promising direction is to improve the behavior of the gradient of the conditional function / classifier itself and study whether related properties such as adversarial robustness or gradient smoothness can induce the desirable temporal smoothness in the sampling ODE. However, it is not yet clear what specific characteristics of the behavior play an important role. This challenge may be related to a condition called ``stiffness'' in solving ODEs \cite{Hairer2010stiff}, which lacks a clear definition but describes the situation where explicit numerical methods, such as RK or PLMS, require a very small step size \emph{even in} a region with smooth curvature.
As an alternative to the classifier-guided model, \cite{ho2022classifier} propose a classifier-free model that can perform conditional generation without a classifier while remaining a generative model.
This model can utilize high-order methods as no classifier is involved, but it requires evaluating the classifier-free network twice per step, which is typically more expensive than evaluating a normal diffusion model and a classifier. It is important to note that our accelerating technique and classifier-free models are \emph{not} mutually exclusive, and one can still apply a conditional function and our splitting technique to guide a classifier-free model in a direction it has not been trained for.
While our paper only focuses on ODEs derived from the deterministic sampling of DDIM, one can convert SDE-based diffusion models to ODEs \citep{karras2022elucidating} and still use our technique. More broadly, we can accelerate any diffusion model that can be expressed as a differential equation with a summation of two terms. When these terms behave differently, the benefit from splitting can be substantial.
Nevertheless, our findings are based on common, existing models and $\sigma$ schedule from \cite{dhariwal2021diffusion}. Further investigation into the impact of the $\sigma$ schedule or different types and architectures of diffusion models is still required.
\section{Conclusion}
In this paper, we investigate the failure to accelerate guided diffusion sampling of classical high-order numerical methods and propose a solution based on splitting numerical methods.
We found that the gradients of conditional functions are less suitable to classical high-order numerical methods and design a technique based on Strang splitting and a combination of forth- and first-order numerical methods. Our method achieves better LPIPS and FID scores than previous work given the same sampling time and is 32-58\% faster than a 250-step DDIM baseline. Our technique can successfully accelerate a variety of tasks, such as text-to-image generation, inpainting, colorization, and super-resolution.
\section{Appendix}
\addcontentsline{toc}{section}{Appendix}
\part{Appendix}
\parttoc
\section{Implementation}
Our implementation is available her
\footnote{https://github.com/sWizad/split-diffusion}.
The implementation is based on Katherine Crowson's guided-diffusion \footnote{https://github.com/crowsonkb/guided-diffusion}, which is inspired by OpenAI's guided-diffusion\footnote{https://github.com/openai/guided-diffusion}.
All of the pre-trained diffusion and classifier models are available here\footnote{https://github.com/openai/guided-diffusion/blob/main/model-card.md}. For evaluation, we use OpenAI's measurement implementation with their reference image batch, which can be found here\footnote{https://github.com/openai/guided-diffusion/tree/main/evaluations}.
\section{Improving PLMS}
\label{iPLMS}
Initial points are required for using high-order PLMS.
The fourth-order formulation, for example, requires three initial points.
The original paper \citep{liu2022pseudo} employs the Runge-Kutta method to compute the initial points.
However, Runge-Kutta's method has high computational costs and is inconvenient to use when the number of steps is small.
To reduce the computation costs, we compute the starting points of the higher-order PLMS using lower-order PLMS. Our PLMS can be summarized using Algorithm \ref{algo:plms}.
\begin{algorithm
\label{algo:plms}
\SetAlgoLined
\textbf{input:} $\bar{x}_n$ (previous result), $\sigma_{n+1}$, $\sigma_n$, \\
$\{e_i\}_{i<n}$ (evaluation buffer), $r$ (method order) \;
\quad $e_n = \bar{\epsilon}_\sigma(\bar{x}_n)$ \; \quad $c= \min(r, n)$ \;
\quad \textbf{if} $c==1$ \textbf{then} \\ \quad \quad
$\hat{e} = e_n $ \;
\quad \textbf{else if} $c==2$ \textbf{then} \\ \quad \quad
$\hat{e} = (3e_n - e_{n-1})/2 $ \;
\quad \textbf{else if} $c==3$ \textbf{then} \\ \quad\quad
$\hat{e} = (23e_n - 16e_{n-1} + 5 e_{n-2})/12 $ \;
\quad \textbf{else} \\ \quad\quad
$\hat{e} = (55e_n - 59e_{n-1} + 37e_{n-3} - 9e_{n-4})/24 $ \;
\quad \KwResult{ $\bar{x}_n + (\sigma_{n+1} - \sigma_n) \hat{e}$ }
\caption{PLMS}
\end{algorithm}
In Algorithm \ref{algo:plms}, the PLMS formulation is obtained by assuming a constant $\Delta \sigma$ for each step. The results in our experiments and previous work (e.g., \cite{liu2022pseudo, zhang2022fast}) are still reasonable when this assumption is not strictly satisfied, i.e., when $\Delta \sigma$ is not constant.
Inspired by \cite{zhang2022fast}, we also show how to derive another linear multi-step formulation for non-constant $\Delta \sigma$.
Let us first define a dummy variable $\tau$ in which $\Delta \tau$ is a constant in each time step.
To make it simple, let the value $\tau = 0$ when $t=T$ and when $t=0$, $\tau = N$, the total number of steps.
As a result, the discretization of $\tau$ can be defined by $\tau_n = n$ and $\Delta \tau = \tau_n - \tau_{n-1} = 1$ is a constant.
Next, we want to extrapolate the value of $\epsilon_\theta$ using a polynomial $P_\epsilon (\tau)$.
For example, the first order formulation can be produced by integrating a constant polynomial $P_\epsilon (\tau) = e_n$ :
\begin{align*}
\frac{d\bar{x}}{d\sigma} = \bar{\epsilon}(\bar{x}) \approx& P_\epsilon (\tau) = e_n, \\
\int^{\bar{x}_{n+1}}_{\bar{x}_{n}} d\bar{x} = & \int^{\sigma_{n+1}}_{\sigma_{n}} e_n \: d\sigma ,\\
\bar{x}_{n+1} - \bar{x}_{n} = & e_n \Delta \sigma
\end{align*}
which leads us to Euler's formulation.
Rather than using Lagrange's polynomial like \cite{zhang2022fast}, we use Newton's polynomial, which gives a nicer final formulation.
However, both are the same polynomial but have different expressions.
For the 2\textsuperscript{nd} order formulation, we interpolate between $(\tau_n, e_n)$ and $(\tau_{n-1},e_{n-1})$ using a Newton's polynomial $P_\epsilon (\tau) = e_n + (e_n-e_{n-1})(\tau-\tau_n)$.
$$ \int^{\bar{x}_{n+1}}_{\bar{x}_{n}} d\bar{x} = \int^{\sigma_{n+1}}_{\sigma_{n}} e_n + (e_n-e_{n-1})(\tau-\tau_n) d\sigma .$$
Every term is the same as in the 1\textsuperscript{st} order formulation, except for one term that is $\int^{\sigma_{n+1}}_{\sigma_{n}} (\tau-\tau_n) d\sigma $.
Let us use separable integration to approximate this term.
$$ \int^{\sigma_{n+1}}_{\sigma_{n}} (\tau-\tau_n) d\sigma = \int^{\tau_{n+1}}_{\tau_{n}} (\tau-\tau_n) \frac{d\sigma}{d\tau} d\tau \approx \int^{\tau_{n+1}}_{\tau_{n}} (\tau-\tau_n) d\tau\int^{\tau_{n+1}}_{\tau_{n}} \frac{d\sigma}{d\tau} d\tau = \frac{\Delta\sigma}{2} $$
The result is $\bar{x}_{n+1} - \bar{x}_{n} = e_n \Delta \sigma + (e_n - e_{n+1}) \frac{\Delta\sigma}{2}$, which is the PLMS2 formulation.
To compute this term more precisely, we need to know the derivation $d\sigma/d\tau$.
For this example, let us define $\sigma$ by
\begin{equation}
\label{sigma_sch}
\sigma(\tau) = \exp \left(\ln{\sigma_\text{max}} + \frac{\tau}{N} (\ln{\sigma_\text{min}} - \ln{\sigma_\text{max}} ) \right) = \exp(a + \tau b),
\end{equation}
where $ a = \ln{\sigma_\text{max}} $ and $ b = (\ln{\sigma_\text{min}} - \ln{\sigma_\text{max}} ) / N$. Now, we have
$$ \int^{\tau_{n+1}}_{\tau_{n}} (\tau-\tau_n) \frac{d\sigma}{d\tau} d\tau = \Delta \sigma \left( \frac{\exp(b)}{\exp(b)-1} - \frac{1}{b} \right). $$
Consider $\frac{\exp(b)}{\exp(b)-1} - \frac{1}{b}$ when limit $N \rightarrow \infty$ (or $b \rightarrow 0$), this term is equal to $\frac{1}{2}$, which turns the formulation back to PLMS2.
When we set $N=30$ (or $b=-0.33$), the term $\frac{\exp(b)}{\exp(b)-1} - \frac{1}{b}=0.4723$, which is also close to $\frac{1}{2}$ in PLMS2 formulation.
We can continue using higher-order Newton's polynomials to obtain higher-order formulations.
We call this method GLMS (Generalized Linear Multi-Step) and summarize it with Algorithm \ref{algo:glms}.
In our comparison in Figure \ref{fig:exp3}, both PLMS and GLMS produce comparable results.
In the fourth order, GLMS4 performs slightly better than PLMS4.
However, the GLMS formulation is dependent on the $\sigma$ schedule, and the formulation must be revised if the $\sigma$ schedule changes.
As a result, we decided to use PLMS as part of our main algorithm for more flexibility.
\begin{algorithm
\SetAlgoLined
\textbf{input:} $\bar{x}_n$ (previous result), $\sigma_{n+1}$, $\sigma_{n}$, $\{e_i\}_{i<n}$ (evaluation buffer), $r$ (method order) \;
\quad $b = \ln(\sigma_{n+1}) - \ln(\sigma_{n})$ \quad $e_n = \bar{\epsilon}_{\sigma}(\bar{x}_n)$ ; \quad $\{e_i\}$.append($e_n$) ; \quad $c= \min(r, n)$ \;
\quad \textbf{if} $c \geq 1$ \textbf{then} \\ \quad \quad
$\hat{e} = e_n $ \;
\quad \textbf{if} $c\geq 2$ \textbf{then} \\ \quad \quad
$\hat{e} = \hat{e} + (e_{n}-e_{n-1}) \left(\frac{\exp(b)}{\exp(b)-1}-\frac{1}{b}\right) $ \;
\quad \textbf{if} $c \geq 3$ \textbf{then} \\ \quad \quad
$\hat{e} = \hat{e} + (e_{n}-2e_{n-1}+e_{n-2}) \left(\frac{\exp(b)}{\exp(b)-1}(2-\frac{2}{b})-\frac{1}{b} + \frac{2}{b^2}\right) $ \;
\quad \textbf{if} $c \geq 4$ \textbf{then} \\ \quad \quad
$\hat{e} = \hat{e} + (e_{n}-3e_{n-1}+3e_{n-2}-e_{n-3}) \left(\frac{\exp(b)}{\exp(b)-1}(6-\frac{9}{b}+\frac{6}{b^2})-\frac{2}{b} + \frac{6}{b^2} - \frac{6}{b^3}\right) $ \;
\quad \KwResult{ $\bar{x}_n + (\sigma_{n+1} - \sigma_n) \hat{e}$ }
\caption{GLMS}
\label{algo:glms}
\end{algorithm}
\section{Numerical Methods for Unguided Diffusion}
This experiment evaluates the numerical methods used in our paper on \emph{unguided} sampling to see whether they may behave differently.
We perform a similar experiment as in Section \ref{exp1}, \ref{exp2} except on an unguided, unconditional diffusion model and use samples from 1,000-step DDIM as reference images. For each method, we use the same initial noise maps as the DDIM and evaluate the image similarity between its generated images and the reference images based on LPIPS. Figure \ref{fig:exp3} reports LPIPS vs sampling time for ImageNet128 using the $\sigma$ schedule in Equation \ref{sigma_sch}.
We found that RK2 and RK4 perform better than DDIM, but in our main papers these methods perform worse than DDIM when used on the split sub-problems for guided sampling.
Linear multi-step methods continue to be the best performers.
The graph also shows that higher order is generally better, especially when the number of steps is large.
\section{Comparing PLMS and DEIS}
In Tables \ref{tab:deis_2} and \ref{tab:deis_4}, we compare the coefficients $e_n, e_{n-1}, e_{n-2}$, and $e_{n-3}$ of PLMS in Algorithm \ref{algo:plms} and the original implementation DEIS \cite{zhang2022fast} using the default linear schedule and 10 sampling steps. This shows that DEIS and PLMS are two similar methods. DEIS is analogous to PLMS with non-fixed coefficients. The coefficients can change depending on the number of steps and the noise schedule. However, the coefficients from both methods are close, and as previously stated, the DEIS coefficients will converge to the PLMS coefficients. Since DEIS's implementation relies heavily on the noise schedule, if the schedule changes, we must re-implement the method. For these reasons, we prefer PLMS over DEIS for practical purposes.
\begin{table}
\begin{minipage}{0.5\columnwidth}
\centering
\shortstack{
\begin{tabular}{c cccc}
\toprule
&\multicolumn{4}{c}{coefficient of } \\
n\textsuperscript{th} step & $e_n$ & $e_{n-1}$ & $e_{n-2}$ & $e_{n-3}$ \\
\midrule
1 & 1.0 & 0. & 0. & 0. \\
2 & 1.5 & -0.5 & 0. & 0. \\
3 & 1.5 & -0.5 & 0. & 0. \\
4 & 1.5 & -0.5 & 0. & 0. \\
5 & 1.5 & -0.5 & 0. & 0. \\
6 & 1.5 & -0.5 & 0. & 0. \\
7 & 1.5 & -0.5 & 0. & 0. \\
8 & 1.5 & -0.5 & 0. & 0. \\
9 & 1.5 & -0.5 & 0. & 0. \\
10 & 1.5 & -0.5 & 0. & 0. \\
\bottomrule
\end{tabular}
\\ \footnotesize (a) PLMS }
\end{minipage}\hfill
\begin{minipage}{0.5\columnwidth}
\centering
\shortstack{
\begin{tabular}{c cccc}
\toprule
&\multicolumn{4}{c}{coefficient of } \\
n\textsuperscript{th} step & $e_n$ & $e_{n-1}$ & $e_{n-2}$ & $e_{n-3}$ \\
\midrule
1 & 1.00 & 0. & 0. & 0. \\
2 & 1.42 & -0.42 & 0. & 0. \\
3 & 1.43 & -0.43 & 0. & 0. \\
4 & 1.43 & -0.43 & 0. & 0. \\
5 & 1.44 & -0.44 & 0. & 0. \\
6 & 1.45 & -0.45 & 0. & 0. \\
7 & 1.46 & -0.46 & 0. & 0. \\
8 & 1.47 & -0.47 & 0. & 0. \\
9 & 1.48 & -0.48 & 0. & 0. \\
10 & 1.50 & -0.50 & 0. & 0. \\
\bottomrule
\end{tabular}
\\ \footnotesize (b) DEIS }
\end{minipage}
\caption{Comparison of DEIS and PLMS on second order }
\label{tab:deis_2}
\end{table}
\begin{table}
\begin{minipage}{0.5\columnwidth}
\centering
\shortstack{
\begin{tabular}{c cccc}
\toprule
&\multicolumn{4}{c}{coefficient of } \\
n\textsuperscript{th} step & $e_n$ & $e_{n-1}$ & $e_{n-2}$ & $e_{n-3}$ \\
\midrule
1 & 1.0 & 0. & 0. & 0. \\
2 & 1.5 & -0.5 & 0. & 0. \\
3 & 1.92 & -1.33 & 0.41 & 0. \\
4 & 2.29 & -2.46 & 1.54 & -0.38 \\
5 & 2.29 & -2.46 & 1.54 & -0.38 \\
6 & 2.29 & -2.46 & 1.54 & -0.38 \\
7 & 2.29 & -2.46 & 1.54 & -0.38 \\
8 & 2.29 & -2.46 & 1.54 & -0.38 \\
9 & 2.29 & -2.46 & 1.54 & -0.38 \\
10 & 2.29 & -2.46 & 1.54 & -0.38 \\
\bottomrule
\end{tabular}
\\ \footnotesize (a) PLMS }
\end{minipage}\hfill
\begin{minipage}{0.5\columnwidth}
\centering
\shortstack{
\begin{tabular}{c cccc}
\toprule
&\multicolumn{4}{c}{coefficient of } \\
n\textsuperscript{th} step & $e_n$ & $e_{n-1}$ & $e_{n-2}$ & $e_{n-3}$ \\
\midrule
1 & 1.0 & 0. & 0. & 0. \\
2 & 1.42 & -0.42 & 0. & 0. \\
3 & 1.77 & -1.12 & 0.34 & 0. \\
4 & 2.09 & -2.07 & 1.28 & -0.34 \\
5 & 2.11 & -2.11 & 1.31 & -0.32 \\
6 & 2.14 & -2.16 & 1.35 & -0.33 \\
7 & 2.16 & -2.22 & 1.38 & -0.34 \\
8 & 2.20 & -2.28 & 1.42 & -0.35 \\
9 & 2.23 & -2.35 & 1.47 & -0.35 \\
10 & 2.23 & -2.28 & 1.55 & -0.38 \\
\bottomrule
\end{tabular}
\\ \footnotesize (b) DEIS }
\end{minipage}
\caption{Comparison of DEIS and PLMS on forth order }
\label{tab:deis_4}
\end{table}
\begin{figure}
\centering
\shortstack{ \includegraphics[width = 0.5\textwidth]{images/graph_ex3.pdf}}
\caption{Comparison of different numerical methods on an unguided diffusion model. Using samples from a 1000-step DDIM as reference solutions, we measure average LPIPS scores and plot them against the average sampling time.}
\label{fig:exp3}
\end{figure}
\section{LPIPS vs. the number of sampling step} \label{step}
We report additional LPIPS results of the experiment in Section \ref{exp1} but with respect to the number of sampling steps.
The result shows that methods in the RK family can outperform other methods given the same number of sampling steps. However, once taken into account the slower evaluation time per step, these methods are overall slower to reach the same level of LPIPS of other methods.
\begin{figure}
\centering
\shortstack{ \includegraphics[width = 0.48\textwidth]{images/graph_ex1_step1.pdf}
\\ \footnotesize (a) Vary method for diffusion subproblem }
\shortstack{ \includegraphics[width = 0.48\textwidth]{images/graph_ex1_step2.pdf}
\\ \footnotesize (b) Vary method for condition subproblem}
\caption{In addition to Figure \ref{exp1}, we plot LPIPS against their \textbf{sampling steps}. RK family can outperform other methods in many situations. However, methods in RK family took a longer time per diffusion step.}
\label{fig:exp1_step}
\end{figure}
\section{More Statistics for Experiement \ref{exp2}} \label{std}
We report the mean and standard deviation of each LPIPS score of the experiment in Section \ref{exp2} in Table \ref{tab:std}.
In Table \ref{tab:p-value}, we report the $p$-value for the null hypothesis that our STSP4 performs worse than other methods.
\begin{table}
\centering
\begin{tabular}{lcccc}
\toprule
&\multicolumn{4}{c}{Sampling time within} \\
& 5 sec. & 10 sec. & 15 sec. & 20 sec. \\
\midrule[0.08em]
DDIM & 0.111 $\pm$ .078 & 0.062 $\pm$ .065 & 0.042 $\pm$ .056 & 0.031 $\pm$ .048 \\
PLMS4 & 0.240 $\pm$ .131 & 0.085 $\pm$ .112 & 0.039 $\pm$ .072 & 0.018 $\pm$ .040 \\
RK2 & 0.152 $\pm$ .090 & 0.048 $\pm$ .051 & 0.030 $\pm$ .037 & 0.026 $\pm$ .037 \\
RK4 & 0.190 $\pm$ .106 & 0.044 $\pm$ .022 & 0.033 $\pm$ .038 & 0.019 $\pm$ .032 \\
\textbf{LTSP4} & 0.111 $\pm$ .092 & 0.056 $\pm$ .060 & 0.040 $\pm$ .054 & 0.028 $\pm$ .046 \\
\textbf{STSP4} & \textbf{0.072} $\pm$ .065 & \textbf{0.033} $\pm$ .044 & \textbf{0.018} $\pm$ .028 & \textbf{0.012} $\pm$ .022 \\
\bottomrule
\caption{Our STSP4 has low average LPIPS scores and low standard deviations of LPIPS (N=120 samples).}
\label{tab:std}
\end{tabular}
\end{table}
\begin{table}
\centering
\begin{tabular}{lcccc}
\toprule
&\multicolumn{4}{c}{Sampling time within} \\
& 5 sec. & 10 sec. & 15 sec. & 20 sec. \\
\midrule[0.08em]
DDIM & $9.1\times10^{-11}$ & $9.0\times10^{-10}$ & $7.1\times10^{-9}$ & $9.2\times10^{-8}$ \\
PLMS4 & $3.3\times10^{-41}$ & $2.1\times10^{-13}$ & $8.1\times10^{-4}$ & $3.7\times10^{-2}$ \\
RK2 & $1.2\times10^{-30}$ & $6.4\times10^{-5}$ & $6.1\times10^{-5}$ & $2.5\times10^{-7}$ \\
RK4 & $5.0\times10^{-31}$ & $6.2\times10^{-3}$ & $6.1\times10^{-5}$ & $1.6\times10^{-3}$ \\
LTSP4 & $5.6\times10^{-11}$ & $9.1\times10^{-11}$ & $2.8\times10^{-10}$ & $1.7\times10^{-7}$ \\
\bottomrule
\caption{$p$-value for STSP4 has lower average LPIPS scores compare to other methods at approximately the same sampling time.}
\label{tab:p-value}
\end{tabular}
\end{table}
\section{STSP4 vs. More Numerical Methods Combination}\label{str_aba}
We extend the experiment from Section \ref{exp2} and compare our STSP4 and DDIM baselines with more numerical method combinations.
Here we report LPIPS vs sampling time in Figure \ref{fig:exp_stsp}.
The results show that Strang splitting method with [PLMS4, PLMS1] (our STSP4) is still the best combination, similar to the finding in Section \ref{exp2}.
\begin{figure}
\centering
\shortstack{ \includegraphics[width = 0.48\textwidth]{images/graph_stsp_aba.pdf}}
\shortstack{ \includegraphics[width = 0.48\textwidth]{images/graph_stsp_aba1.pdf}}
\caption{We compare using Strang splitting with different numerical methods on the diffusion subproblem.}
\label{fig:exp_stsp}
\end{figure}
\section{Comparison with DEIS and DPM-solver}
We compare our splitting method to DPM-solver \cite{lu2022dpm} and DEIS \cite{zhang2022fast}. Since both methods have different implementation details, such as using different noise schedules, which affect the ODE solution, these methods do not converge to the same exact solution. Thus, it is not sensible to directly compare them, and we instead implement our method in their official implementations of DPM-solver \cite{lu2022dpm} and DEIS \cite{zhang2022fast}. We then compare the results with LPIPS on classifier-guided diffusion pretrained on ImageNet256 similar to Table \ref{tab:exp2} in Section \ref{fig:exp2}.
The results are shown in Table \ref{tab:dpm} and \ref{tab:deis}.
Our splitting methods can perform better than both DPM-solver \cite{lu2022dpm} and DEIS \cite{zhang2022fast}.
\begin{table}
\centering
\begin{tabular}{lcccc}
\toprule
&\multicolumn{4}{c}{Sampling time within} \\
& 5 sec. & 10 sec. & 15 sec. & 20 sec. \\
\midrule[0.08em]
DPM-Solver-1 (DDIM) & 0.333 & 0.125 & 0.080 & 0.045 \\
DPM-Solver-2 & 0.565 & 0.188 & 0.078 & 0.045 \\
DPM-Solver-3 & 0.540 & 0.233 & 0.087 & 0.043 \\
\textbf{LTSP4} & 0.185 & 0.105 & 0.071 & 0.048 \\
\textbf{STSP4} & \textbf{0.169} & \textbf{0.062} & \textbf{0.061} & \textbf{0.037} \\
\bottomrule
\caption{The comparison with DPM-solver \cite{lu2022dpm}. Average LPIPS when the sampling time is limited to be under 5-20 seconds.}
\label{tab:dpm}
\end{tabular}
\end{table}
\begin{table}
\centering
\begin{tabular}{lcccc}
\toprule
&\multicolumn{4}{c}{Sampling time within} \\
& 3 sec. & 6 sec. & 9 sec. & 12 sec. \\
\midrule[0.08em]
0-DEIS (DDIM) & 0.333 & 0.125 & 0.080 & 0.045 \\
1-DEIS & 0.466 & 0.193 & 0.092 & 0.044 \\
3-DEIS & 0.625 & 0.511 & 0.433 & 0.345 \\
\textbf{LTSP4}& 0.321 & 0.120 & 0.080 & 0.048 \\
\textbf{STSP4}& \textbf{0.212} & \textbf{0.080} & \textbf{0.046} & \textbf{0.031} \\
\bottomrule
\caption{Comparison with DEIS \cite{zhang2022fast}. We report the average LPIPS scores when the sampling time is limited to be under 3-12 seconds.}
\label{tab:deis}
\end{tabular}
\end{table}
\section{Experiment on FID vs. Sampling Time}
In this section, we demonstrate how splitting methods can accelerate guided diffusion sampling using FID scores. We vary the number of sampling steps, generate 20k samples, and compare the FID of the splitting methods (LTSP4 and STSP4) to many non-splitting methods, including DDIM, PLMS4, RK2, and RK4. Figure \ref{fig:fid_time} shows a comparison of FID vs. sampling time for each method. This experiment uses a classifier-guided diffusion model that was pretrained on the ImageNet128 dataset by \cite{dhariwal2021diffusion}.
Our method can generate good sample quality, especially when the average sampling is limited to under 0.3 seconds (or about 50 steps of DDIM for 128$\times$128 resolution), while other methods show large FID scores at lower sampling steps or require more time to generate similarly high-quality samples.
\begin{figure}
\centering
\shortstack{ \includegraphics[width = 0.48\textwidth]{images/FID/FID.pdf}}
\caption{FID vs. Sampling time measured on ImageNet128}
\label{fig:fid_time}
\end{figure}
\section{Text-guided image generation} \label{txt2im}
For text-to-image generation or text-guided image generation, our implementation is based on Disco-Diffusion v3.1\footnote{https://colab.research.google.com/drive/1bItz4NdhAPHg5-u87KcH-MmJZjK-XqHN}, which also relies on \cite{crowson2021clip}.
We use v3.1 that does not contain unrelated features; however, our method can be applied to any of the versions.
We use the fine-tuned 512x512 diffusion model from Katherine Crowson \footnote{http://batbot.tv/ai/models/guided-diffusion/512x512\_diffusion\_uncond\_finetune\_008100.pt} and use pre-trained OpenAI's CLIP models \footnote{https://github.com/openai/CLIP} including RN50, ViTB32, and ViTB16.
For other model and conditional function configurations, we use Disco-Diffusion v3.1's default settings.
\section{Controllable generation}
\label{con_gen}
We provide implementation details of our sampling algorithm for other conditional generation tasks.
\textbf{Image inpainting}:
Given a target masked image, $y_0$, and a mask $P$ which is a matrix of $0,1$ values, we want to sample $x_0$ so that $y_0 = Px_0$. The key concept from \cite{song2020score} is to use reverse diffusion in the unmasked area and forward diffusion in the masked area through an additional step called the impose step.
Let $x'_{t-1}$ be an unconditional diffusion sample from $x_t$ and $y_{t-1}$ be a forward diffusion sample from $y_0$. The impose step can be summarized as follows:
\begin{equation}
x_{t-1} = (I-P^TP)x'_{t-1} + P^T y_{t-1}.
\end{equation}
To sample a corrupted target image $y_{t-1}$, we use the sampling formulation from \cite{song2020denoising} to sample from $y_0$ by
\begin{equation} \label{impu_forward}
y_t \sim \mathcal{N}(\sqrt{\bar{\alpha}_t}y_0 + \sqrt{1-\bar{\alpha}_t-\eta^2_t} \epsilon_\theta(x_t, t), \eta^2_t I )
\end{equation}
where $\eta_t = \sqrt{(1-\bar{\alpha}_{t-1})/(1-\bar{\alpha}_t}) \sqrt{1-\bar{\alpha}_{t}/\bar{\alpha}_{t-1}}$.
This formulation works more effectively with numerical methods than the original sampling formulation from \cite{song2020score}, which is $y_t \sim \mathcal{N}(\sqrt{\bar{\alpha}_t}y_0, (1-\bar{\alpha}_t) I )$.
Rather than sampling $x'_{t-1}$ unconditionally, we follow \cite{chung2022improving} and use guided diffusion sampling with the conditional function defined by:
\begin{equation} \label{impu_condi}
f(x_t) = \frac{1}{2\gamma} || y_0 - P \hat{x}_0(x_t) ||^2_2, \quad \hat{x}_0(x_t) = \frac{x_t - \sqrt{ 1 - \bar{\alpha}_t} \epsilon_\theta (x_t, t)}{\sqrt{\bar{\alpha}_t}},
\end{equation}
where $\gamma$ is a control parameter.
Since directly computing $\epsilon_\theta (x_t, t)$ with the diffusion network in Equation \ref{impu_forward} and \ref{impu_condi} is time consuming, we use a secondary-model method from Katherine Crowson\footnote{https://colab.research.google.com/drive/1mpkrhOjoyzPeSWy2r7T8EYRaU7amYOOi} to speed it up.
\textbf{Image colorization}: The idea behind colorization is very similar to inpainting.
We convert images from the RGB format to the HSV format, with the grayscale value in the first channel, using an orthogonal matrix:
$$C = \begin{bmatrix}
0.577 & -0.816 & 0\\
0.577 & 0.408 & 0.707 \\
0.577 & 0.408 & -0.707 \\
\end{bmatrix}.$$
To mask out other channels and keep only the first grayscale channel, we define the mask matrix $P$ as 1 in the grayscale channel and 0 in the other two channels.
The impose step and conditional function can be defined as
$$ x_{t-1} = (I-C^TP^TPC)x'_{t-1} + C^TP^T PC y_{t-1}, \quad f(x_t) = \frac{1}{2\gamma} || y_0 - PC \hat{x}_0 (x_t) ||^2. $$
\textbf{Image super-resolution}: Let us denote $D$ as a down-sampling matrix.
The impose step and conditional function is given by
$$ x_{t-1} = (I-D^TD)x'_{t-1} + D^T y_{t-1}, \quad f(x_t) = \frac{1}{2\gamma} || y_0 - D \hat{x}_0 (x_t) ||^2. $$
In our implementation, we replace the $D$ and $D^T$ operations with the ILVR \citep{choi2021ilvr} down-sampling and up-sampling functions.
Figure \ref{apx_fig_inpaint}, \ref{apx_fig_color}, and \ref{apx_fig_supres} show additional qualitative results on the three tasks.
We evaluate LPIPS and PSNR between the generated images and their original images for the three tasks in Table \ref{tab:imputation}. Our test set consists of 200 input images, and each test image will be used to produce 6 samples for each task for the evaluation.
Note that LPIPS and PSNR are not the ideal measurements for this evaluation, but they are a de facto standard for benchmarking. Our goal here is to demonstrate how our technique can generalize to other conditional generation tasks.
Non-diffusion techniques can not be compared the acceleration effect with ours since they are based on completely different things. Some comparison of the diffusion technique to other techniques can also be found in \cite{chung2022improving}.
To achieve state-of-the-art performance on these tasks in terms of quality and speed, other recent techniques may be more suitable, such as improved initialization \citep{chung2022come} and forward-backward repetition \citep{meng2021sdedit}. However, our contributions are orthogonal to these investigations.
\begin{table}[h]
\centering
\begin{tabular}{l|cc|cc|cc}
\toprule
&\multicolumn{2}{c|}{Inpainting} & \multicolumn{2}{c|}{Colorization} & \multicolumn{2}{c}{Super-resolution}\\
Methods & LPIPS & PSNR & LPIPS & PSNR & LPIPS & PSNR \\
\midrule
DDIM & 0.17 & 19.52 & 0.28 & 20.40 & 0.46 & 17.88 \\
PLMS4 & 0.25 & 15.01 & 0.47 & 13.50 & 0.73 & 7.85 \\
\textbf{LTSP4} & 0.17 & 19.61 & 0.31 & 19.40 & 0.51 & 16.07 \\
\textbf{STSP4} & \textbf{0.16} & \textbf{20.03} & \textbf{0.26} & \textbf{21.27} & \textbf{0.42} & \textbf{19.34} \\
\bottomrule
\end{tabular}
\caption{Average LPIPS and PSNR scores from different methods on three different tasks.}
\label{tab:imputation}
\end{table}
\begin{figure*}
\centering
\setlength\tabcolsep{1.5pt}
\begin{tabular}{c|c|c@{}c@{}c|c@{}c@{}c}
Original & Input & &STSP4 & & & DDIM \\
\includegraphics[width=0.1\textwidth]{images/inpainting/task15/gt.png} &
\includegraphics[width=0.1\textwidth]{images/inpainting/task15/input.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task15/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task15/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task15/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task15/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task15/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task15/ddim3.png}\\
\includegraphics[width=0.1\textwidth]{images/inpainting/task11/gt.png} &
\includegraphics[width=0.1\textwidth]{images/inpainting/task11/input.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task11/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task11/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task11/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task11/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task11/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task11/ddim3.png}\\
\includegraphics[width=0.1\textwidth]{images/inpainting/task3/gt.png} &
\includegraphics[width=0.1\textwidth]{images/inpainting/task3/input.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task3/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task3/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task3/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task3/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task3/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task3/ddim3.png}\\
\includegraphics[width=0.1\textwidth]{images/inpainting/task4/gt.png} &
\includegraphics[width=0.1\textwidth]{images/inpainting/task4/input.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task4/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task4/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task4/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task4/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task4/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task4/ddim3.png}\\
\includegraphics[width=0.1\textwidth]{images/inpainting/task7/gt.png} &
\includegraphics[width=0.1\textwidth]{images/inpainting/task7/input.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task7/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task7/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task7/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task7/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task7/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task7/ddim3.png}\\
\includegraphics[width=0.1\textwidth]{images/inpainting/task8/gt.png} &
\includegraphics[width=0.1\textwidth]{images/inpainting/task8/input.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task8/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task8/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task8/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task8/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task8/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/inpainting/task8/ddim3.png}
\end{tabular}
\caption{Additional inpainting results on ImageNet256.
We show three different results generated by each method for each input. All results are generated using the same 5 second sampling time.
}
\label{apx_fig_inpaint}
\vspace{-3.5mm}
\end{figure*}
\begin{figure*}
\centering
\setlength\tabcolsep{1.5pt}
\begin{tabular}{c|c|c@{}c@{}c|c@{}c@{}c}
Original & Input & &STSP4 & & & DDIM \\
\includegraphics[width=0.1\textwidth]{images/colorization/task5/gt.png} &
\includegraphics[width=0.1\textwidth]{images/colorization/task5/input.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task5/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task5/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task5/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task5/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task5/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task5/ddim3.png}\\
\includegraphics[width=0.1\textwidth]{images/colorization/task9/gt.png} &
\includegraphics[width=0.1\textwidth]{images/colorization/task9/input.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task9/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task9/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task9/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task9/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task9/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task9/ddim3.png}\\
\includegraphics[width=0.1\textwidth]{images/colorization/task11/gt.png} &
\includegraphics[width=0.1\textwidth]{images/colorization/task11/input.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task11/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task11/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task11/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task11/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task11/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task11/ddim3.png}\\
\includegraphics[width=0.1\textwidth]{images/colorization/task7/gt.png} &
\includegraphics[width=0.1\textwidth]{images/colorization/task7/input.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task7/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task7/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task7/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task7/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task7/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task7/ddim3.png}\\
\includegraphics[width=0.1\textwidth]{images/colorization/task8/gt.png} &
\includegraphics[width=0.1\textwidth]{images/colorization/task8/input.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task8/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task8/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task8/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task8/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task8/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task8/ddim3.png}\\
\includegraphics[width=0.1\textwidth]{images/colorization/task10/gt.png} &
\includegraphics[width=0.1\textwidth]{images/colorization/task10/input.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task10/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task10/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task10/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task10/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task10/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/colorization/task10/ddim3.png}
\end{tabular}
\caption{Additional colorization results on ImageNet256.
We show three different results generated by each method for each input. All results are generated using the same 5 second sampling time.
}
\label{apx_fig_color}
\vspace{-2.5mm}
\end{figure*}
\begin{figure*}
\centering
\setlength\tabcolsep{1.5pt}
\begin{tabular}{c|c|c@{}c@{}c|c@{}c@{}c}
Original & Input & &STSP4 & & & DDIM \\
\includegraphics[width=0.1\textwidth]{images/super/task5/gt.png} &
\includegraphics[width=0.1\textwidth]{images/super/task5/input.png}&
\includegraphics[width=0.1\textwidth]{images/super/task5/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/super/task5/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/super/task5/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/super/task5/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/super/task5/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/super/task5/ddim3.png}\\
\includegraphics[width=0.1\textwidth]{images/super/task15/gt.png} &
\includegraphics[width=0.1\textwidth]{images/super/task15/input.png}&
\includegraphics[width=0.1\textwidth]{images/super/task15/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/super/task15/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/super/task15/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/super/task15/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/super/task15/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/super/task15/ddim3.png}\\
\includegraphics[width=0.1\textwidth]{images/super/task11/gt.png} &
\includegraphics[width=0.1\textwidth]{images/super/task11/input.png}&
\includegraphics[width=0.1\textwidth]{images/super/task11/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/super/task11/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/super/task11/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/super/task11/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/super/task11/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/super/task11/ddim3.png}\\
\includegraphics[width=0.1\textwidth]{images/super/task7/gt.png} &
\includegraphics[width=0.1\textwidth]{images/super/task7/input.png}&
\includegraphics[width=0.1\textwidth]{images/super/task7/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/super/task7/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/super/task7/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/super/task7/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/super/task7/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/super/task7/ddim3.png}\\
\includegraphics[width=0.1\textwidth]{images/super/task8/gt.png} &
\includegraphics[width=0.1\textwidth]{images/super/task8/input.png}&
\includegraphics[width=0.1\textwidth]{images/super/task8/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/super/task8/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/super/task8/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/super/task8/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/super/task8/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/super/task8/ddim3.png}\\
\includegraphics[width=0.1\textwidth]{images/super/task10/gt.png} &
\includegraphics[width=0.1\textwidth]{images/super/task10/input.png}&
\includegraphics[width=0.1\textwidth]{images/super/task10/bchf1.png}&
\includegraphics[width=0.1\textwidth]{images/super/task10/bchf2.png}&
\includegraphics[width=0.1\textwidth]{images/super/task10/bchf3.png}&
\includegraphics[width=0.1\textwidth]{images/super/task10/ddim1.png}&
\includegraphics[width=0.1\textwidth]{images/super/task10/ddim2.png}&
\includegraphics[width=0.1\textwidth]{images/super/task10/ddim3.png}
\end{tabular}
\caption{
Additional 8x super-resolution results on ImageNet256. We show three different results generated by each method for each input. All results are generated using the same 5 second sampling time.
}
\label{apx_fig_supres}
\vspace{-2.5mm}
\end{figure*}
\section{Dreambooth Stable Diffusion}
\label{dreambooth}
Dreambooth \citep{ruiz2022dreambooth} is a technique for fine-tuning a pretrained text-to-image diffusion model on a given set of images.
We discover that, similar to guided diffusion models, Dreambooth on Stable Diffusion (a pretrained text-guided latent-space diffusion) sometimes cannot be used with high-order methods but can be accelerated by our proposed method.
This example demonstrates that our splitting method is effective not only on classifier-guided models but also classifier-free diffusion models.
The guided ODE of a classifier-free model is given by
\begin{equation} \label{eq:dream_guide}
\frac{ d \bar{x}}{d \sigma} = \bar{\epsilon}_\sigma (\bar{x}|\phi) + s (\bar{\epsilon}_\sigma (\bar{x}|c) - \bar{\epsilon}_\sigma (\bar{x}|\phi) ),
\end{equation}
where $c$ is the input prompt, $\bar{\epsilon}_\sigma (\bar{x}|c)$ is the network output conditioned on the input prompt, and $\bar{\epsilon}_\sigma (\bar{x}|\phi)$ is the network output conditioned on a null label $\phi$.
We can split the guided ODE into two subproblems as follows:
\begin{equation}
\frac{dy}{d\sigma} = \bar{\epsilon}_\sigma (y|\phi), \quad
\frac{dz}{d\sigma} = s (\bar{\epsilon}_\sigma (z|c) - \bar{\epsilon}_\sigma (z|\phi) ).
\end{equation}
We test on ``mo-di-diffusion\footnote{https://huggingface.co/nitrosocke/mo-di-diffusion}'', a Dreambooth Stable Diffusion model that was fine-tuned on a dataset of screenshots from Disney studio. We use the prompt `` a girl face in modern Disney style.'' The result is shown in Figure \ref{fig:sd}.
However, we believe that Dreambooth diffusion models may have different problems from classifier-guided diffusion models and deserve their own in-depth study.
\begin{figure*}
\centering
\setlength\tabcolsep{1.5pt}
\begin{tabular}{cl}
\shortstack{\small Number \\of steps} & \qquad\quad\: 20 \qquad\qquad\qquad\: 40 \qquad\qquad\qquad\quad 80 \qquad\qquad\qquad 160 \\
\shortstack{PLMS4\\\citep{liu2022pseudo}\vspace{0.8cm}} &
\includegraphics[width=0.8\textwidth]{images/SD/plms4.jpg} \\
\shortstack{\textbf{LTSP4}\\(Ours)\vspace{0.8cm}} &
\includegraphics[width=0.8\textwidth]{images/SD/ltsp4.jpg}\\
\shortstack{\textbf{STSP4}\\(Ours)\vspace{0.8cm}} &
\includegraphics[width=0.8\textwidth]{images/SD/stsp4.jpg} \\
\end{tabular}
\caption{
Generated samples from a text-guided Stable Diffusion model fine-tuned on a dataset of screenshots from Disney studio using 20-160 sampling steps. Our splitting technique produces high-quality results in fewer sampling steps. prompt: ``a girl face in modern Disney style''
}
\label{fig:sd}
\end{figure*}
\section{CLIP-Guided Stable Diffusion}
\label{clip_sd}
UPainting \citep{li2022upainting} suggest that text-to-image Stable Diffusion quality can be improve using gradient from CLIP model.
This is an example of combining classifier-free and gradient-guided technique to obtain better result.
As we have demonstrated in our paper, adding a gradient term to the diffusion model can cause high-order methods fail to accelerate sampling.
The guided ODE \ref{eq:guide} can be modified as follows:
\begin{equation} \label{eq:clip_guide}
\frac{ d \bar{x}}{d \sigma} = \bar{\epsilon}_\sigma (\bar{x}|\phi) + s (\bar{\epsilon}_\sigma (\bar{x}|c) - \bar{\epsilon}_\sigma (\bar{x}|\phi) ) - \lambda \nabla_{\bar{x}} (f_\text{img} (\bar{x}) \cdot f_\text{txt} (a)),
\end{equation}
where $f_\text{img} (\bar{x})$ is CLIP's image encoder output and $f_\text{txt} (a)$ is the output of CLIP's text encoder.
We can apply our method by splitting the Equation \ref{eq:clip_guide} into two subproblems by
\begin{equation}
\frac{dy}{d\sigma} = \bar{\epsilon}_\sigma (y|\phi) + s (\bar{\epsilon}_\sigma (y|c) - \bar{\epsilon}_\sigma (y|\phi) ), \quad
\frac{dz}{d\sigma} = - \lambda \nabla_{z} (f_\text{img} (z) \cdot f_\text{txt} (a)).
\end{equation}
We show sample images using different numerical methods in Figure \ref{fig:clip_sd}. Our method produces high-quality results in fewer sampling steps.
\begin{figure}
\centering
\setlength\tabcolsep{1.5pt}
\begin{tabular}{c|ccc}
\shortstack{\small Stable Diffusion's prompt: ``a ball'' \\
\small CLIP's prompt: ``a metal sphere'' \vspace{1cm}}
&
\includegraphics[width=0.2\textwidth]{images/CLIP_SD/2_plms4.jpg}&
\includegraphics[width=0.2\textwidth]{images/CLIP_SD/2_ltsp4.jpg}&
\includegraphics[width=0.2\textwidth]{images/CLIP_SD/2_stsp4.jpg}
\\
\shortstack{\small Stable Diffusion's prompt: ``a ball'' \\
\small CLIP's prompt: ``a red apple'' \vspace{1cm}}
&
\includegraphics[width=0.2\textwidth]{images/CLIP_SD/1_plms4.jpg}&
\includegraphics[width=0.2\textwidth]{images/CLIP_SD/1_ltsp4.jpg}&
\includegraphics[width=0.2\textwidth]{images/CLIP_SD/1_stsp4.jpg}
\\
& PLMS4 & \textbf{LTSP4} & \textbf{STSP4} \\
& \citep{liu2022pseudo} & (Ours) & (Ours)\\
&\small (100 steps) & \small (100 steps) & \small (55 steps) \\
\end{tabular}
\caption{ Text-to-image generation using CLIP-guided Stable Diffusion from different high-order sampling methods with approximately the same sampling time.}
\label{fig:clip_sd}
\end{figure}
\section{Convergence Orders of Methods}
In this section, we show the convergence order of Lie-Trotter and Strang splitting methods. Suppose the differential equation we want to solve is defined by
\begin{align}
\frac{dx}{dt} = f_0 (x) = f_1 (x) + f_2(x),
\end{align}
where $f_1, f_2$ are assumed to be differentiable.
We define $\Phi_{\Delta t,f_i}$ as a mapping solution of an ODE $\frac{dx}{dt} = f_i (x,t)$ in an interval $[t_0, t_0 + \Delta t]$.
Noting that $\Phi_{0,f_i}(x) = x$ and $\frac{d}{dt} \Phi_{\Delta t,f_i}(x) = f_i(x)$.
By perform a Taylor expansion, we have
\begin{align} \label{expan}
\Phi_{\Delta t,f_i}(x) = x + \Delta t f_i (x) + \frac{(\Delta t)^2}{2} f'_i(x) f_i(x) + \mathcal{O}(\Delta t^3).
\end{align}
\textbf{Lie-Trotter splitting}
A single step of the Lie-Trotter splitting method can be expressed as $\Phi_{\Delta t,f_2}(\Phi_{\Delta t,f_1}(x))$. Applying the expansion of Equation \ref{expan} to this formulation gives:
\begin{align}
\Phi_{\Delta t,f_2}(\Phi_{\Delta t,f_1}(x)) &= [x + \Delta t f_1 (x) + \mathcal{O}(\Delta t^2)] + \Delta t f_2 [x + \Delta t f_1 (x) + \mathcal{O}(\Delta t^2)] + \mathcal{O}(\Delta t^2) \nonumber\\
&= x + \Delta t f_1 (x) + \Delta t f_2 (x) + \mathcal{O}(\Delta t^2) \nonumber\\
&= \Phi_{\Delta t,f_0}(x) + \mathcal{O}(\Delta t^2).
\end{align}
Hence, the Lie-Trotter splitting method is of first-order.
\textbf{Strang splitting}
Consider a single step of the Strang splitting, which is $\Phi_{\Delta t/2,f_2}(\Phi_{\Delta t,f_1}(\Phi_{\Delta t/2,f_2}(x)))$. To show the second-order accuracy of the Strange splitting, we first expand the two inner operators.
\begin{align}
\Phi_{\Delta t,f_1}(\Phi_{\Delta t/2,f_2}(x)) &= [x + \frac{\Delta t}{2} f_2 (x) + \frac{(\Delta t)^2}{2^2 2!} f'_2(x) f_2(x) + \mathcal{O}(\Delta t^3)] \nonumber \\
&+ (\Delta t) f_1 [x + \frac{\Delta t}{2} f_2 (x) + \mathcal{O}(\Delta t^2)] \nonumber \\
&+ \frac{(\Delta t)^2}{2} f'_1 [x + \mathcal{O}(\Delta t)] f_1 [x + \mathcal{O}(\Delta t)] + \mathcal{O}(\Delta t^3) \\
&=x + \frac{\Delta t}{2} f_2 (x) + \frac{(\Delta t)^2}{2^2 2!}f'_2(x)f_2(x) \nonumber \\
&+ (\Delta t) f_1(x) + \frac{(\Delta t)^2}{2} f'_1 (x)f_2(x) \nonumber \\
& + \frac{(\Delta t)^2}{2} f'_1(x) f_1(x) +\mathcal{O}(\Delta t^3)
\end{align}
Consequently,
\begin{align}
\Phi_{\frac{\Delta t}{2},f_2}(\Phi_{\Delta t,f_1}(\Phi_{\frac{\Delta t}{2},f_2}(x)))
&= x + (\Delta t) f_1 (x) + \frac{\Delta t}{2}f_2(x) \nonumber \\
&+ \frac{(\Delta t)^2}{2^2 2!} f'_2(x)f_2(x) + \frac{(\Delta t)^2}{2} f'_1(x)f_2(x) + \frac{(\Delta t)^2}{2!}f'_1(x)f_1(x) \nonumber \\
& + \frac{\Delta t}{2} f_2 [x + (\Delta t) f_1 (x) + \frac{\Delta t}{2}f_2(x) + \mathcal{O}(\Delta t^2)] \nonumber \\
& + \frac{(\Delta t)^2}{2^2 2!}f'_2[x+\mathcal{O}(\Delta t)]f_2[x+\mathcal{O}(\Delta t)] + \mathcal{O}(\Delta t^3)
\end{align}
\begin{align}
\Phi_{\frac{\Delta t}{2},f_2}(\Phi_{\Delta t,f_1}(\Phi_{\frac{\Delta t}{2},f_2}(x)))
&= x + (\Delta t) f_1 (x) + (\Delta t) f_2 (x) \nonumber \\
&+ \frac{(\Delta t)^2}{2!}[f'_1(x)f_1(x) + f'_1(x)f_2(x)+f'_2(x)f_1(x)+f'_2(x)f_2(x)] \nonumber \\
&+ \mathcal{O}(\Delta t^3) \\
&=x + (\Delta t) f_0(x) +\frac{(\Delta t)^2}{2!} f'_0(x) f_0(x) + \mathcal{O}(\Delta t^3) \\
&= \Phi_{\Delta t, f_0}(x) + \mathcal{O}(\Delta t^3)
\end{align}
Therefore, the Strang splitting method's convergence rate is of second-order.
\section{Toy Example}
In this section, we create a toy example to demonstrate how high-order numerical methods can become unstable on a certain class of ODE problems (Stiff equation) despite involving no neural networks. Let us define the following ODE:
\begin{align} \label{eq:toy_ode}
\frac{dx}{dt} = \epsilon(x) + s \cdot g(x), \qquad x(0) = \begin{bmatrix} 1 \\ 0\end{bmatrix},
\end{align}
where $s$ is a scaling parameter and
\begin{align}
\epsilon \left( \begin{bmatrix} x_1 \\ x_2\end{bmatrix} \right) = \begin{bmatrix} 0 & 1 \\ -1 & -2\end{bmatrix}\begin{bmatrix} x_1 \\ x_2\end{bmatrix}, \quad
g \left( \begin{bmatrix} x_1 \\ x_2\end{bmatrix} \right) = \begin{bmatrix} 0 & 0 \\ -1 & -1\end{bmatrix}\begin{bmatrix} x_1 \\ x_2\end{bmatrix}.
\end{align}
Figure \ref{fig:toy} depicts solution trajectories of various numerical methods
We can observe that the PLMS4's trajectory can run far from the exact solution than the Euler's method or the splitting methods, LSTP4 and STSP4. The exact solution of Equation \ref{eq:toy_ode} is
\begin{align}
x(t) = \frac{1}{s}\begin{bmatrix} -1 \\ s+1 \end{bmatrix} e^{-(s+1)t} + \frac{1}{s}\begin{bmatrix} s+1 \\ -s-1 \end{bmatrix} e^{-t}.
\end{align}
When $s$ increases, the term $e^{-(s+1)t}$ decays to zero more rapidly than the term $e^{-t}$. When the two terms behave differently, classical high-order numerical methods tend to perform poorly unless they employ a very small step size.
\begin{figure}
\centering
\setlength\tabcolsep{1.5pt}
\begin{tabular}{cccc}
\shortstack{$s=3$\vspace{1.8cm}}
&
\includegraphics[width=0.30\textwidth]{images/toy/3_10.pdf}&
\includegraphics[width=0.30\textwidth]{images/toy/3_15.pdf}&
\includegraphics[width=0.30\textwidth]{images/toy/3_20.pdf}
\\
\shortstack{$s=5$\vspace{1.8cm}}
&
\includegraphics[width=0.30\textwidth]{images/toy/5_10.pdf}&
\includegraphics[width=0.30\textwidth]{images/toy/5_15.pdf}&
\includegraphics[width=0.30\textwidth]{images/toy/5_20.pdf}
\\
& 10 steps & 15 steps & 20 steps \\
\end{tabular}
\caption{
Solution trajectories of different numerical methods on a toy ODE problem using different numbers of steps. Non-splitting methods especially PLMS4 are more likely to fail to converge to the exact solution when the number of steps is reduced.
}
\label{fig:toy}
\end{figure}
\section{Stability Analysis}
In this section, we further analyze numerical solutions using stability analysis. We compute the lowest number of steps before the numerical solution is guaranteed to diverge by theory and visualize the solution trajectories using different numbers of steps to empirically support the theory.
We only focus on Euler and other second-order numerical methods in this part.
One way to analyze numerical methods that solve Equation \ref{eq:toy_ode} is to evaluate them with a test equation that leads to the solution $y(t)=e^{-(s+1)t}$, such as
\begin{equation} \label{test_eq}
y'=-(s+1)y.
\end{equation}
Note that the solution $y(t) \rightarrow 0$ as $t \rightarrow \infty$.
\textbf{Euler's Method:} Applying the Euler's method to Equation \ref{test_eq} yields:
\begin{align*}
y_{n+1} = y_n - \Delta t (s+1) y_n = (1-\Delta t (s+1))y_n.
\end{align*}
After solving this recurrence relation, we have $y_n = (1-\Delta t (s+1))^n y_0$. The condition for the numerical solution $y_n \rightarrow 0$ as $n \rightarrow \infty$ is equivalent to $|1-\Delta t (s+1) |< 1$ or
\begin{align*}
-1 < 1 - &\Delta t (s+1) < 1 ,\\
2 > \Delta t& (s+1) > 0 .
\end{align*}
Let us substitute $\Delta t = 1/N$, where $N$ is the number of steps. Now, we can conclude that if $N$ is lower than $\frac{s+1}{2}$, the solution of Euler's method in Equation \ref{test_eq} diverges from the exact solution.
\textbf{PLMS2:} Consider a second-order linear multistep method on the same test Equation \ref{test_eq}:
\begin{align}
y_{n+1} &= y_n +\Delta t \left(-\frac{3}{2}(s+1)y_n + \frac{1}{2}y_{n-1}(s+1)\right) \\
&= \left(1-\Delta t \frac{3}{2} (s+1)\right)y_n +\Delta t\frac{1}{2} (s+1).
\end{align}
After solving the linear recurrence relation, we obtain
\begin{gather}
y_{n} = a_1 r_1^n + a_2 r_2^n,\\
\text{where } r_1 = \frac{1}{2}\left(1-\frac{3}{2}\Delta t (s+1) + \sqrt{1 - \Delta t (s+1) + \frac{9}{4}(\Delta t)^2 (s+1)^2} \right),\\ \text{and } r_2 = \frac{1}{2}\left(1-\frac{3}{2}\Delta t (s+1) - \sqrt{1 - \Delta t (s+1) + \frac{9}{4}(\Delta t)^2 (s+1)^2} \right).
\end{gather}
The numerical solution $y_n \rightarrow 0$ as $n \rightarrow \infty$ when both $|r_1|<1$ and $|r_2|<1$, which is equivalent to
\begin{align} \label{condi_plms2}
\left|\frac{1}{2}\left(1-\frac{3}{2} \frac{(s+1)}{N} \pm \sqrt{1 - \frac{(s+1)}{N} + \frac{9}{4}\left(\frac{(s+1)}{N}\right)^2 } \right)\right| < 1.
\end{align}
In Table \ref{tab:theory}, we report the lowest number $N$ for each $s$ before Inequality \ref{condi_plms2} is not satisfied. In other words, if the number of steps is below the lowest number $N$ in the table, the solution of the method in Equation \ref{test_eq} is guaranteed to diverge from the exact solution. The analysis of the higher-order methods can be done in a similar fashion.
\textbf{LTSP2:} We analyze the Lie-Trotter splitting method similarly. In this case, the test Equation \ref{test_eq} needs to also be split into
\begin{align}
\hat{y}' =& - \hat{y}, \label{test_sp1} \\
\tilde{y}' =& - s \tilde{y}. \label{test_sp2}
\end{align}
Let us apply the second order linear multistep method (PLMS2) in Equaiton \ref{test_sp1} and Euler's method (PLMS1) on Equation \ref{test_sp2}. We have
\begin{align}
\hat{y}_{n+1} = \hat{y}_n -\Delta t \left( \frac{3}{2}\hat{y}_n - \frac{1}{2} \hat{y}_{n-1}\right), \qquad \tilde{y}_{n+1} = \tilde{y}_n -\Delta t s \tilde{y}_n.
\end{align}
Thus, a single combining step of LTSP2 can be formulated by
\begin{align}
y_{n+1} = (1-s\Delta t) \left(\left(1-\frac{3}{2}\Delta t\right)y_n + \frac{\Delta t}{2} y_{n-1}\right).
\end{align}
Similar to the above, we solve the linear recurrence relation and obtain the following condition
{\small
\begin{align} \label{condi_ltsp2}
\left|\frac{1}{2}\left( \left(1-\frac{s}{N}\right) \left(1-\frac{3}{2}\frac{s}{N}\right) \pm \sqrt{\left(1-\frac{s}{N}\right)^2 \left(1-\frac{3}{2}\frac{s}{N}\right)^2 + \frac{2}{N}\left(1-\frac{s}{N}\right) } \right)\right| < 1.
\end{align}
}%
We report the lowest integer number $N$ for each $s$ before Inequality \ref{condi_ltsp2} is not satisfied in Table \ref{tab:theory}.
\textbf{STSP2:} We analyze the Strang splitting method by splitting the test Equation \ref{test_eq} into
\begin{align}
\bar{y}' =& - s \bar{y} \label{test_st1} \\
\hat{y}' =& - \hat{y} \label{test_st2} \\
\tilde{y}' =& - s \tilde{y} \label{test_st3}
\end{align}
We apply the second-order linear multistep method (PLMS2) in Equaiton \ref{test_st2} and Euler's method on Equation \ref{test_st1} and \ref{test_st3}.
\begin{align}
\bar{y}_{n+1} =& \left(1 - \frac{\Delta t}{2} s\right) \bar{y}_n \label{numer_st1}\\
\hat{y}_{n+1} =& \left(1 - \frac{3}{2} \Delta t \right) \hat{y}_n + \frac{\Delta t}{2} \hat{y}_{n-1} \label{numer_st2}\\
\tilde{y}_{n+1} =& \left(1 - \frac{\Delta t}{2} s\right) \tilde{y}_n \label{numer_st3}
\end{align}
We combine Equation \ref{numer_st1}-\ref{numer_st3} into
\begin{align}
y_{n+1} = \left(1 - \frac{s}{2N}\right)^2\left(1 - \frac{3}{2N}\right)y_n + \frac{1}{2N}\left(1 - \frac{s}{2N}\right)^2y_{n-1}.
\end{align}
After solving the linear recurrence relation, we obtain the following condition
\begin{align} \label{condi_stsp2}
\left|\frac{1}{2} \left(b \pm \sqrt{b^2 + \frac{2}{N}c}\right)\right| < 1,
\end{align}
where $b=\left(1-\frac{s}{2N}\right)^2\left(1-\frac{3}{2N}\right)$ and $c = \left(1-\frac{s}{2N}\right)^2$. In Table \ref{tab:theory}, we report the lowest number of steps $N$ for each $s$ before Inequality \ref{condi_stsp2} is not satisfied.
In Table \ref{tab:theory}, we compare the lowest number of steps $N$ before each method is guaranteed to diverge from our analysis. We also show numerical solutions of our toy example in Figure \ref{fig:toy2} to compare to our analysis. It is important to note that if the number of steps exceeds Table \ref{tab:theory}, we cannot presume that the numerical solution will function properly.
\begin{table}
\centering
\begin{tabular}{l ccc ccc cc}
\toprule
& $s=5$ & $s=10$ & $s=15$ & $s=20$ & $s=30$ & $s=40$ & $s=60$ & $s=80$\\
\midrule[0.08em]
Euler & 4 & 6 & 9 & 11 & 16 & 21 & 31 & 41\\
PLMS2 & 6 & 11 & 16 & 22 & 32 & 42 & 63 & 83\\
\textbf{LTSP2} & 2 & 3 & 7 & 9 & 14 & 19 & 29 & 39\\
\textbf{STSP2} & 2 & 3 & 4 & 5 & 8 & 10 & 15 & 20\\
\bottomrule
\caption{The lowest number of steps before we can guarantee by theory that each numerical method will fail to solve Equation \ref{test_eq}. Notice that LTSP2 and STSP2 are having lower number which mean they are also harder to fail when the number of step are reduced than Euler and PLMS2.}
\label{tab:theory}
\end{tabular}
\end{table}
\begin{figure}
\centering
\setlength\tabcolsep{1.5pt}
\begin{tabular}{cccc}
\shortstack{$s=10$\vspace{1.8cm}}
&
\includegraphics[width=0.30\textwidth]{images/toy2/s10_10.pdf}&
\includegraphics[width=0.30\textwidth]{images/toy2/s10_15.pdf}&
\includegraphics[width=0.30\textwidth]{images/toy2/s10_20.pdf} \\
\shortstack{$s=15$\vspace{1.8cm}}
&
\includegraphics[width=0.30\textwidth]{images/toy2/s15_10.pdf}&
\includegraphics[width=0.30\textwidth]{images/toy2/s15_15.pdf}&
\includegraphics[width=0.30\textwidth]{images/toy2/s15_20.pdf} \\
\shortstack{$s=20$\vspace{1.8cm}}
&
\includegraphics[width=0.30\textwidth]{images/toy2/s20_10.pdf}&
\includegraphics[width=0.30\textwidth]{images/toy2/s20_15.pdf}&
\includegraphics[width=0.30\textwidth]{images/toy2/s20_20.pdf}
\\
& 10 steps & 15 steps & 20 steps \\
\end{tabular}
\caption{This figure show how numerical solutions look like when the number of steps are close to the number in Table \ref{tab:theory}}.
\label{fig:toy2}
\end{figure}
\section{Submission of conference papers to ICLR 2022}
ICLR requires electronic submissions, processed by
\url{https://openreview.net/}. See ICLR's website for more instructions.
If your paper is ultimately accepted, the statement {\tt
{\textbackslash}iclrfinalcopy} should be inserted to adjust the
format to the camera ready requirements.
The format for the submissions is a variant of the NeurIPS format.
Please read carefully the instructions below, and follow them
faithfully.
\subsection{Style}
Papers to be submitted to ICLR 2022 must be prepared according to the
instructions presented here.
Authors are required to use the ICLR \LaTeX{} style files obtainable at the
ICLR website. Please make sure you use the current files and
not previous versions. Tweaking the style files may be grounds for rejection.
\subsection{Retrieval of style files}
The style files for ICLR and other conference information are available online at:
\begin{center}
\url{http://www.iclr.cc/}
\end{center}
The file \verb+iclr2022_conference.pdf+ contains these
instructions and illustrates the
various formatting requirements your ICLR paper must satisfy.
Submissions must be made using \LaTeX{} and the style files
\verb+iclr2022_conference.sty+ and \verb+iclr2022_conference.bst+ (to be used with \LaTeX{}2e). The file
\verb+iclr2022_conference.tex+ may be used as a ``shell'' for writing your paper. All you
have to do is replace the author, title, abstract, and text of the paper with
your own.
The formatting instructions contained in these style files are summarized in
sections \ref{gen_inst}, \ref{headings}, and \ref{others} below.
\section{General formatting instructions}
\label{gen_inst}
The text must be confined within a rectangle 5.5~inches (33~picas) wide and
9~inches (54~picas) long. The left margin is 1.5~inch (9~picas).
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\section{Headings: first level}
\label{headings}
First level headings are in small caps,
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\subsection{Headings: second level}
Second level headings are in small caps,
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Third level headings are in small caps,
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\section{Citations, figures, tables, references}
\label{others}
These instructions apply to everyone, regardless of the formatter being used.
\subsection{Citations within the text}
Citations within the text should be based on the \texttt{natbib} package
and include the authors' last names and year (with the ``et~al.'' construct
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\subsection{Footnotes}
Indicate footnotes with a number\footnote{Sample of the first footnote} in the
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Precede the footnote with a horizontal rule of 2~inches
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\subsection{Figures}
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enough for purposes of reproduction; art work should not be
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figure. Place one line space before the figure caption, and one line
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However, it is best for the
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\begin{figure}[h]
\begin{center}
\fbox{\rule[-.5cm]{0cm}{4cm} \rule[-.5cm]{4cm}{0cm}}
\end{center}
\caption{Sample figure caption.}
\end{figure}
\subsection{Tables}
All tables must be centered, neat, clean and legible. Do not use hand-drawn
tables. The table number and title always appear before the table. See
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Place one line space before the table title, one line space after the table
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(except for first word and proper nouns); tables are numbered consecutively.
\begin{table}[t]
\caption{Sample table title}
\label{sample-table}
\begin{center}
\begin{tabular}{ll}
\multicolumn{1}{c}{\bf PART} &\multicolumn{1}{c}{\bf DESCRIPTION}
\\ \hline \\
Dendrite &Input terminal \\
Axon &Output terminal \\
Soma &Cell body (contains cell nucleus) \\
\end{tabular}
\end{center}
\end{table}
\section{Default Notation}
In an attempt to encourage standardized notation, we have included the
notation file from the textbook, \textit{Deep Learning}
\cite{goodfellow2016deep} available at
\url{https://github.com/goodfeli/dlbook_notation/}. Use of this style
is not required and can be disabled by commenting out
\texttt{math\_commands.tex}.
\centerline{\bf Numbers and Arrays}
\bgroup
\def1.5{1.5}
\begin{tabular}{p{1in}p{3.25in}}
$\displaystyle a$ & A scalar (integer or real)\\
$\displaystyle {\bm{a}}$ & A vector\\
$\displaystyle {\bm{A}}$ & A matrix\\
$\displaystyle {\tens{A}}$ & A tensor\\
$\displaystyle {\bm{I}}_n$ & Identity matrix with $n$ rows and $n$ columns\\
$\displaystyle {\bm{I}}$ & Identity matrix with dimensionality implied by context\\
$\displaystyle {\bm{e}}^{(i)}$ & Standard basis vector $[0,\dots,0,1,0,\dots,0]$ with a 1 at position $i$\\
$\displaystyle \text{diag}({\bm{a}})$ & A square, diagonal matrix with diagonal entries given by ${\bm{a}}$\\
$\displaystyle {\textnormal{a}}$ & A scalar random variable\\
$\displaystyle {\mathbf{a}}$ & A vector-valued random variable\\
$\displaystyle {\mathbf{A}}$ & A matrix-valued random variable\\
\end{tabular}
\egroup
\vspace{0.25cm}
\centerline{\bf Sets and Graphs}
\bgroup
\def1.5{1.5}
\begin{tabular}{p{1.25in}p{3.25in}}
$\displaystyle {\mathbb{A}}$ & A set\\
$\displaystyle \mathbb{R}$ & The set of real numbers \\
$\displaystyle \{0, 1\}$ & The set containing 0 and 1 \\
$\displaystyle \{0, 1, \dots, n \}$ & The set of all integers between $0$ and $n$\\
$\displaystyle [a, b]$ & The real interval including $a$ and $b$\\
$\displaystyle (a, b]$ & The real interval excluding $a$ but including $b$\\
$\displaystyle {\mathbb{A}} \backslash {\mathbb{B}}$ & Set subtraction, i.e., the set containing the elements of ${\mathbb{A}}$ that are not in ${\mathbb{B}}$\\
$\displaystyle {\mathcal{G}}$ & A graph\\
$\displaystyle \parents_{\mathcal{G}}({\textnormal{x}}_i)$ & The parents of ${\textnormal{x}}_i$ in ${\mathcal{G}}$
\end{tabular}
\vspace{0.25cm}
\centerline{\bf Indexing}
\bgroup
\def1.5{1.5}
\begin{tabular}{p{1.25in}p{3.25in}}
$\displaystyle {a}_i$ & Element $i$ of vector ${\bm{a}}$, with indexing starting at 1 \\
$\displaystyle {a}_{-i}$ & All elements of vector ${\bm{a}}$ except for element $i$ \\
$\displaystyle {A}_{i,j}$ & Element $i, j$ of matrix ${\bm{A}}$ \\
$\displaystyle {\bm{A}}_{i, :}$ & Row $i$ of matrix ${\bm{A}}$ \\
$\displaystyle {\bm{A}}_{:, i}$ & Column $i$ of matrix ${\bm{A}}$ \\
$\displaystyle {\etens{A}}_{i, j, k}$ & Element $(i, j, k)$ of a 3-D tensor ${\tens{A}}$\\
$\displaystyle {\tens{A}}_{:, :, i}$ & 2-D slice of a 3-D tensor\\
$\displaystyle {\textnormal{a}}_i$ & Element $i$ of the random vector ${\mathbf{a}}$ \\
\end{tabular}
\egroup
\vspace{0.25cm}
\centerline{\bf Calculus}
\bgroup
\def1.5{1.5}
\begin{tabular}{p{1.25in}p{3.25in}}
$\displaystyle\frac{d y} {d x}$ & Derivative of $y$ with respect to $x$\\ [2ex]
$\displaystyle \frac{\partial y} {\partial x} $ & Partial derivative of $y$ with respect to $x$ \\
$\displaystyle \nabla_{\bm{x}} y $ & Gradient of $y$ with respect to ${\bm{x}}$ \\
$\displaystyle \nabla_{\bm{X}} y $ & Matrix derivatives of $y$ with respect to ${\bm{X}}$ \\
$\displaystyle \nabla_{\tens{X}} y $ & Tensor containing derivatives of $y$ with respect to ${\tens{X}}$ \\
$\displaystyle \frac{\partial f}{\partial {\bm{x}}} $ & Jacobian matrix ${\bm{J}} \in \mathbb{R}^{m\times n}$ of $f: \mathbb{R}^n \rightarrow \mathbb{R}^m$\\
$\displaystyle \nabla_{\bm{x}}^2 f({\bm{x}})\text{ or }{\bm{H}}( f)({\bm{x}})$ & The Hessian matrix of $f$ at input point ${\bm{x}}$\\
$\displaystyle \int f({\bm{x}}) d{\bm{x}} $ & Definite integral over the entire domain of ${\bm{x}}$ \\
$\displaystyle \int_{\mathbb{S}} f({\bm{x}}) d{\bm{x}}$ & Definite integral with respect to ${\bm{x}}$ over the set ${\mathbb{S}}$ \\
\end{tabular}
\egroup
\vspace{0.25cm}
\centerline{\bf Probability and Information Theory}
\bgroup
\def1.5{1.5}
\begin{tabular}{p{1.25in}p{3.25in}}
$\displaystyle P({\textnormal{a}})$ & A probability distribution over a discrete variable\\
$\displaystyle p({\textnormal{a}})$ & A probability distribution over a continuous variable, or over
a variable whose type has not been specified\\
$\displaystyle {\textnormal{a}} \sim P$ & Random variable ${\textnormal{a}}$ has distribution $P$\\% so thing on left of \sim should always be a random variable, with name beginning with \r
$\displaystyle \mathbb{E}_{{\textnormal{x}}\sim P} [ f(x) ]\text{ or } \mathbb{E} f(x)$ & Expectation of $f(x)$ with respect to $P({\textnormal{x}})$ \\
$\displaystyle \mathrm{Var}(f(x)) $ & Variance of $f(x)$ under $P({\textnormal{x}})$ \\
$\displaystyle \mathrm{Cov}(f(x),g(x)) $ & Covariance of $f(x)$ and $g(x)$ under $P({\textnormal{x}})$\\
$\displaystyle H({\textnormal{x}}) $ & Shannon entropy of the random variable ${\textnormal{x}}$\\
$\displaystyle D_{\mathrm{KL}} ( P \Vert Q ) $ & Kullback-Leibler divergence of P and Q \\
$\displaystyle \mathcal{N} ( {\bm{x}} ; {\bm{\mu}} , {\bm{\Sigma}})$ & Gaussian distribution %
over ${\bm{x}}$ with mean ${\bm{\mu}}$ and covariance ${\bm{\Sigma}}$ \\
\end{tabular}
\egroup
\vspace{0.25cm}
\centerline{\bf Functions}
\bgroup
\def1.5{1.5}
\begin{tabular}{p{1.25in}p{3.25in}}
$\displaystyle f: {\mathbb{A}} \rightarrow {\mathbb{B}}$ & The function $f$ with domain ${\mathbb{A}}$ and range ${\mathbb{B}}$\\
$\displaystyle f \circ g $ & Composition of the functions $f$ and $g$ \\
$\displaystyle f({\bm{x}} ; {\bm{\theta}}) $ & A function of ${\bm{x}}$ parametrized by ${\bm{\theta}}$.
(Sometimes we write $f({\bm{x}})$ and omit the argument ${\bm{\theta}}$ to lighten notation) \\
$\displaystyle \log x$ & Natural logarithm of $x$ \\
$\displaystyle \sigma(x)$ & Logistic sigmoid, $\displaystyle \frac{1} {1 + \exp(-x)}$ \\
$\displaystyle \zeta(x)$ & Softplus, $\log(1 + \exp(x))$ \\
$\displaystyle || {\bm{x}} ||_p $ & $L^p$ norm of ${\bm{x}}$ \\
$\displaystyle || {\bm{x}} || $ & $L^2$ norm of ${\bm{x}}$ \\
$\displaystyle x^+$ & Positive part of $x$, i.e., $\max(0,x)$\\
$\displaystyle \bm{1}_\mathrm{condition}$ & is 1 if the condition is true, 0 otherwise\\
\end{tabular}
\egroup
\vspace{0.25cm}
\section{Final instructions}
Do not change any aspects of the formatting parameters in the style files.
In particular, do not modify the width or length of the rectangle the text
should fit into, and do not change font sizes (except perhaps in the
\textsc{References} section; see below). Please note that pages should be
numbered.
\section{Preparing PostScript or PDF files}
Please prepare PostScript or PDF files with paper size ``US Letter'', and
not, for example, ``A4''. The -t
letter option on dvips will produce US Letter files.
Consider directly generating PDF files using \verb+pdflatex+
(especially if you are a MiKTeX user).
PDF figures must be substituted for EPS figures, however.
Otherwise, please generate your PostScript and PDF files with the following commands:
\begin{verbatim}
dvips mypaper.dvi -t letter -Ppdf -G0 -o mypaper.ps
ps2pdf mypaper.ps mypaper.pdf
\end{verbatim}
\subsection{Margins in LaTeX}
Most of the margin problems come from figures positioned by hand using
\verb+\special+ or other commands. We suggest using the command
\verb+\includegraphics+
from the graphicx package. Always specify the figure width as a multiple of
the line width as in the example below using .eps graphics
\begin{verbatim}
\usepackage[dvips]{graphicx} ...
\includegraphics[width=0.8\linewidth]{myfile.eps}
\end{verbatim}
or
\begin{verbatim}
\usepackage[pdftex]{graphicx} ...
\includegraphics[width=0.8\linewidth]{myfile.pdf}
\end{verbatim}
for .pdf graphics.
See section~4.4 in the graphics bundle documentation (\url{http://www.ctan.org/tex-archive/macros/latex/required/graphics/grfguide.ps})
A number of width problems arise when LaTeX cannot properly hyphenate a
line. Please give LaTeX hyphenation hints using the \verb+\-+ command.
\subsubsection*{Author Contributions}
If you'd like to, you may include a section for author contributions as is done
in many journals. This is optional and at the discretion of the authors.
\subsubsection*{Acknowledgments}
Use unnumbered third level headings for the acknowledgments. All
acknowledgments, including those to funding agencies, go at the end of the paper.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 2,072
|
Q: MySQL: How to calculate weeks out from a specific date? I need to calculate the weeks out from a date in my MySQL select statement. There is a date column in one of the tables, and I need to calculate how many weeks away the date is.
SELECT EventDate, (calculation) AS WeeksOut FROM Events;
Example:
*
*6 days away, weeks out = 0
*7 days away, weeks out = 1
*13 days away, weeks out = 1
*14 days away, weeks out = 2
A: In order to get past the whole "New Year" issue and you still want to use WEEK(), I found the following method quite effective.
SELECT
YEAR(end_date)*52+WEEK(end_date)
- YEAR(start_date)*52 - WEEK(start_date) as weeks_out
FROM
events;
The difference with this method (as opposed to the DATEDIFF method) is that it is aligned with the week. So today (which is Monday) and last Friday would return 1 using this method, but would return 0 with the DATEDIFF method
A: Use the DATEDIFF function:
ROUND(DATEDIFF(end_date, start_date)/7, 0) AS weeksout
The problem with WEEKS is that it won't return correct results for dates that cross over January 1st.
The 0 is the number of decimal places to use in the ROUND function.
A: Here's a simple way to do it:
SELECT EventDate, (week(EventDate) - week(curdate())) AS WeeksOut FROM Events;
Example:
mysql> select week('2010-11-18') - week ('2010-10-18');
+------------------------------------------+
| week('2010-11-18') - week ('2010-10-18') |
+------------------------------------------+
| 4 |
+------------------------------------------+
1 row in set (0.00 sec)
Another option is calculate the interval in days and divide by 7:
SELECT EventDate, datediff(EventDate,curdate())/7 AS WeeksOut FROM Events;
Example:
mysql> select datediff('2010-11-18' , '2010-10-18') / 7;
+-------------------------------------------+
| datediff('2010-11-18' , '2010-10-18') / 7 |
+-------------------------------------------+
| 4.4286 |
+-------------------------------------------+
1 row in set (0.00 sec)
A: In newer versions of MYSQL if you use the timestamp as column type, you can use TIMESTAMPDIFF:
SELECT TIMESTAMPDIFF(WEEK, '2020-06-09 08:59:36', '2020-09-09 08:58:25');
|-----------------------------------------------------------------------|
| 13 |
So in your example it would be:
SELECT TIMESTAMPDIFF(WEEK, NOW(), EventDate) AS WeeksOut FROM Events;
A: Try TIMESTAMPDIFF
TIMESTAMPDIFF(WEEK, curdate(), EventDate) AS WEEKS_DIFFERENCE
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 4,534
|
Q: Hyperparameter selection for Deep Reinforcement Learning I am trying to learn machine learning from Andrew NG's Machine learning specilization on Coursera. In the chapter about reinforcement learning Andrew NG said that if you do not selecet correct hyperparameters your model can take a long time to train. Are there any guidelines on picking hyperparameters for Deep Reinforcement Learning? Lets say I have an agent who has 10000 states, how many layers and units my neural network should have? If I am using mini-batches how big should each batch be? If the states are continious states, how far back the agent should look before taking a decision?
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 487
|
Quax (auch Quaks, † 16. Februar 2012 in Mannheim) war eine frei lebendes Rosapelikan-Weibchen, das seit September 2008 Mitteleuropa bereiste. Benannt wurde sie von bayerischen Ornithologen nach der Hauptfigur des Films Quax, der Bruchpilot mit Heinz Rühmann.
Viel Zeit verbrachte sie im Rhein-Neckar-Raum und der angrenzenden Pfalz, wo sie den Mannheimer Luisenpark sowie den Vogelpark in Bobenheim-Roxheim als Stützpunkte wählte. Durch ein deutlich sichtbares Geschwür am rechten Fuß konnte sie leicht identifiziert werden. Am 16. Februar wurde sie schwer verletzt mit inneren Blutungen und einem Leberriss in der Nähe des pfälzischen Bobenheim-Roxheim aufgefunden und in den Luisenpark Mannheim gebracht, wo sie trotz tierärztlicher Versorgung verstarb.
Ornithologen betrachteten Quax mit großem Interesse, da sie Weißstörche auf ihrem Vogelzug begleitete und auch mit ihnen in Spanien überwinterte. Der Grund für dieses außergewöhnliche Verhalten ist unbekannt.
Weblinks
deutsches "Quax-Tagebuch", Landesbund für Vogelschutz in Bayern
französische Berichterstattung über Quax' Reisen mit Weißstörchen, ornithomedia.com (englisch / französisch)
Fotocommunity mit Fotos zur Pelikandame Quax
Einzelnachweise
Individueller Vogel
Vogelzug
Geschichte (Mannheim)
Pelikan in der Kultur
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 5,688
|
Le genre Platyperigea regroupe des lépidoptères (papillons) de la famille des Noctuidae.
Espèces rencontrées en Europe
Platyperigea albina (Eversmann 1848)
Platyperigea aspersa (Rambur 1834)
Platyperigea germainii (Duponchel 1835)
Platyperigea grisea (Eversmann 1848)
Platyperigea ingrata (Staudinger 1897)
Platyperigea kadenii (Freyer 1836)
Platyperigea montana (Bremer 1861)
Platyperigea proxima (Rambur 1837)
Platyperigea syriaca (Staudinger 1892)
Platyperigea terrea (Freyer 1840)
Liens externes
Genre de Lépidoptères (nom scientifique)
Noctuidae
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 2,968
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\section*{Program summary}
\begin{list}{}{\setlength{\leftmargin}{0pt}}
\item\emph{Program title:} EPCGP
\item\emph{Catalogue identifier:} \verb|EPCGP_v1_0|
\item\emph{Program summary URL:}
\url{http://cpc.cs.qub.ac.uk/summaries/EPCGP_v1_0.html}
\item\emph{Program obtainable from:} CPC Program Library, Queen's
University, Belfast, N. Ireland
\item\emph{Licensing provisions:} Standard CPC licence,
\url{http://cpc.cs.qub.ac.uk/licence/licence.html}
\item\emph{No. of lines in distributed program, including test data,
etc.:} 18748
\item\emph{No. of bytes in distributed program, including test data,
etc.:} 200342
\item\emph{Distribution format:} ZIP
\item\emph{Programming language:} C++ with OpenMP extensions (main
numerical program), Python (helper scripts)
\item\emph{Computer:} modern PC (tested on AMD and Intel processors),
HP BL2x220
\item\emph{Operating system:} Unix/Linux and Windows
\item\emph{Has the code been vectorized or parallelized?:} yes
(OpenMP)
\item\emph{RAM:} 200 MB for single run
\item\emph{Running time:} 6h for $100\kern.25em\mathrm{ps}$ evolution,
depending on the values of parameters.
\item\emph{Classification:} 7. Condensed Matter and Surface Science; 7.7 Other Condensed Matter inc. Simulation of Liquids and Solids.
\item\emph{Nature of problem:} An exciton-polariton superfluid is a novel, interesting physical system allowing investigation of high temperature Bose--Einstein condensation of exciton-polaritons---quasiparticles carrying spin. They have brought a lot of attention due to their unique properties and potential applications in polariton-based optoelectronic integrated circuits. This is an out-of-equilibrium quantum system confined within a semiconductor microcavity. It is described by a set of nonlinear differential equations similar in spirit to the Gross--Pitaevskii (GP) equation, but their unique properties do not allow standard GP solving frameworks to be utilized. Finding an accurate and efficient numerical algorithm as well as development of optimized numerical software is necessary for effective theoretical investigation of exciton-polaritons.
\item\emph{Solution method:} A Runge--Kutta method of 4th order was employed to solve the set of differential equations describing exciton-polariton superfluids. The method was fitted for the exciton-polariton equations and further optimized. The C++ programs utilize OpenMP extensions and vector operations in order to fully utilize the computer hardware.
\end{list}
\section{Introduction}
\begin{figure}[ht]\centering
\includegraphics[height=5cm]{Voronych_1.eps}
\caption{Structure of a GaAs semiconductor microcavity. Multiple
layers of GaAs and AlGaAs form disributed Bragg reflectors (DBRs),
which confine light inside quantum wells (QWs).}
\label{fig:microcavity}
\end{figure}
In this paper we propose a novel, optimized numerical method of modeling exciton-polariton superfluid in a semiconductor microcavity. Excitons are electron-hole pairs, bound by the Coulomb force, behaving as a single electrically-neutral particle~\cite{Wannier1937,Mott1938}. Microcavities pumped by laser beams confine light in the form of a standing wave between highly reflective Bragg mirrors, which are made from multiple layers of different refractive index, see Fig.~\ref{fig:microcavity}. Between the reflectors there are located semiconductor quantum wells where the excitons are formed and can freely move in the X--Y plane. If the wells are located in the anti-nodes of the standing wave, they strongly couple to photons and thus, they form new quasiparticles---the exciton-polaritons.
\begin{figure}[ht]\centering
\includegraphics[height=3cm]{Voronych_2.eps}
\caption{Dispersion relation for exciton-polaritons in a semiconductor
microcavity displaying upper (UP, red) and lower (LP, blue)
polariton branches.}
\label{fig:dispersion}
\end{figure}
Fig.~\ref{fig:dispersion} depicts the dispersion relation for photons, excitons and exciton-polaritons in a microcavity. It reveals two anti-crossing branches, called upper (UP) and lower polaritons (LP). Exciton-polaritons are an out-of-equilibrium quantum system due to the interplay between their lifetime, up to $200\kern.25em\mathrm{ps}$, and laser pumping sustaining their number in the cavity. The compound nature of polaritons results in the fact that their effective mass is lower than the mass of a free electron, and in the regime of their low density they can be described as bosons with a spin degree of freedom~\cite{Hopfield1958,Agranovich1957,Kavokin2007}. Thus, in specific conditions, they form a quasi-particle counterpart of an atomic Bose-Einstein condensate (BEC)~\cite{Deng2010,Byrnes2014} and reveal superfluidity~\cite{Amo2009} in relatively high temperatures~\cite{Deveaud2007}.
Except for their amazing physical properties being a subject of the fundamental research, recently exciton-polaritons have brought a lot of attention due to their potential applications in optoelectronic integrated circuits, consisting of transistors~\cite{Liew2010}, spin-switches~\cite{Amo2010} and logic gates~\cite{Franson2007,Menon2010,Espinosa-Ortega2013}. Additionally, they can form localized nondiffracting X-waves~\cite{Voronych2016,Sedov2015} which could be used for transferring a classical signal between elements in the circuits. Thus, polaritonics is regarded as a future of new photonic-electronic devices, which will be capable of processing information at a rate of terabits per second and frequencies in the range~$100\kern.25em\mathrm{GHz}$--$10\kern.25em\mathrm{THz}$~\cite{Feurer2007}.
The simplest physical model of the exciton-polariton superfluid is given by the Gross--Pitaevski equation (GPE). This is a nonlinear Schr\"odinger equation, which omits the quasi-particle nature of polaritons and which was primarily used for studying an akin discipline -- the physics of ultracold quantum bosonic gases (of atoms) and their BECs.
For this reason, over the years, a variety of numerical methods of solving GPEs were developed and implemented in software. They range from the most general, suitable for broad investigation of the gases, to specially fitted to specific systems and problems. Most papers devoted to numerical investigation of GPEs focused on their stationary solutions~\cite{Muruganandama2009}. Various condensate geometries~\cite{Chang2009}, simplifications and special cases~\cite{Chang2007} were taken into account. Numerical methods involved finite-difference approach~\cite{Chang2009,Chang2008,Zeng2009}, bi-$k$-Lagrange elements~\cite{Li2009}, spectral collocation methods with Chebyshev
polynomials of the first and second kind~\cite{Jeng2013} as well as basis set expansion technique~\cite{Tiwari2006}. Time-dependent equations were solved with implicit and semi-implicit Crank--Nicolson methods~\cite{Wang2010,Xu2012,Muruganandama2009,Madarassy2013,Mohammadi2014}, Euler scheme~\cite{Zeng2009}, third and fourth-order adaptive Runge--Kutta methods~\cite{Balac2013}, split-step finite difference method~\cite{Zeng2009} and time-splitting sine and Fourier pseudospectral methods~\cite{Wang2011,Vudragovic2012}. In the latter case, space was discretized with second- and fourth-order finite differences, exponential splines~\cite{Mohammadi2014} or with Chebyshev--Tau spectral discretization method~\cite{Wang2010}.
As a result, several mature software packages were developed. The OCTBEC utilizes optimal quantum control theory to model various BECs in Matlab~\cite{Hohenester2014}. Similar libraries were prepared in Fortran~\cite{Muruganandama2009} and C programming languages~\cite{Vudragovic2012}. The most advanced toolkit is the GPELab, implemented in Matlab~\cite{Antoine2014,Antoine2015}. It combines various listed methods in order to solve both stationary and time-dependent GPEs and enables tackling sets of equations. The hardware utilized for computations involved diverse platforms: OpenMP and MPI-based computer clusters~\cite{Satiric2016}, NVIDIA's CUDA parallel architecture~\cite{Dziubak2012,Loncar2016} as well as Sony PlayStation 3 Cell Broadband parallel systems~\cite{Edwards2009}.
Deeper insight into the physics of polaritons requires however taking into account their compound character and solving a GPE for a spinor polariton wave function, consisting of two independent components: the excitonic $\psi_x$ and photonic $\psi_c$ one. This turns the GPE into a system of two coupled equations of different kind, of which neither is a GPE itself and thus, methods developed for solving GPEs cannot be directly applied. Further including of the spin degree of freedom for polaritons results in the system of four equations.
Here we present the EPCGP program suite which we have developed in order to support research on exciton-polaritons in semiconductor microcavities. The suite utilizes our novel algorithm based on the Runge--Kutta method of fourth order, optimized for the equations describing exciton-polariton superfluid. Moreover, program routines are able to gain from the parallel computing environment and vector operations, which significantly speeds up the computations. It allows investigation of one- and two-dimensional systems. We believe that use of EPCGP suite goes beyond the basic theoretical work and will also find applications in preparation of experiments and engineering of polaritonic circuits.
The paper is structured as follows. Section~\ref{sec:theory} introduces the Reader to the equations describing the exciton-polariton superfluid. Section~\ref{sec:numerics} goes into details of numerical computations, presenting the choice of algorithms, data structures and properties of the methods, such as their stability, computational complexity and error estimation. Next, Section~\ref{sec:applications} presents a selection of interesting results obtained with our software. Finally, Section~\ref{sec:suite} describes the actual suite code and goes through the process of preparation of input parameters, compilation and running the programs.
\section{Theoretical description of exciton-polariton superfluid}
\label{sec:theory}
\subsection{Polaritonic wave functions and the Gross--Pitaevskii equation}
Exciton-polariton superfluid is described by a composite wave function $\psi$, which consists of the photonic ($\psi_c$) and excitonic ($\psi_x$) parts~\cite{Sanvitto2012}. In the spinor notation,
\begin{equation}
\psi(\mathbf{x}, t) = \begin{pmatrix}
\psi_c(\mathbf{x},t)\\
\psi_x(\mathbf{x},t).
\end{pmatrix}.
\end{equation}
$\psi_{c,x}$ are complex functions of space coordinate $\mathbf{x}$ and time $t$ such that $\lvert\psi_{c,x}(\mathbf{x}, t)\rvert^2$ is the distribution of quasiparticles in a space and $\int \lvert\psi_{c,x}(\mathbf{x}, t)\rvert^2\,d\mathbf{x}$ gives the number of quasiparticles in the system at given time instant.
Formulation of equations describing the dynamics of polaritons requires solving a GPE, derived originally for an atomic BEC, for $\psi$
\begin{equation}
i\hbar \dfrac{d\psi}{dt}
=
\left( -\dfrac{\hbar^2}{2m}\nabla^2 + V_{\text{ext}} +
g\lvert\psi\rvert^2\right) \psi.
\label{eq:basic_GP}
\end{equation}
Here $m$ is the mass of quasiparticles or atoms in the condensate, $V_{\text{ext}}$ is an external potential and $g$ quantifies strength of nonlinear interactions. Symbols $\hbar$, $i$ and $\nabla^2$ denote the reduced Planck constant, imaginary unit and the nabla operator $\nabla^2=\sum_{i=1}^n\tfrac{\partial^2}{\partial x_i^2}$, respectively.
It is worth remembering that the GPE is a semi-classical equation, derived under assumption that a light beam pumping a microcavity is classical, and it describes correctly the exciton-polaritons in the regime of their low density, where to a good approximation polaritons behave as bosons. There are two kinds of solutions of the GPE: the stationary, which describes the state of minimized energy, and the time-dependent, which allows to observe the dynamics of the system. Their derivations are included in the graduate courses of physics and there is a lot of literature devoted to this topic~\cite{Rogel-Salazar2013}. Since we are interested in the evolution of the exciton-polarion superfluid, from now on we will focus solely on the time-dependent solutions.
In case of a semiconductor microcavity pumped by a laser pump
\begin{equation}
F(\mathbf{x},t)=F_p\,e^{i\,(\mathbf{k}_p\cdot\mathbf{x}-\omega_p\,t)}\,e^{-\frac{(\mathbf{x}-\mathbf{x}_0)^2}{2w_x^2}},
\end{equation}
where $F_p$ is the field amplitude, $\mathbf{k}_p$ its momentum (plane profile), $\omega_p$ is the frequency, $\mathbf{x}_0$ is the coordinate of center of Gaussian laser spot on the sample and $w_x$ is its spread, Eq.~(\ref{eq:basic_GP}) takes the following matrix form~\cite{Kavokin2007}
\begin{multline}
\label{eq:gp_matrix1}
i\hbar\,\dfrac{d}{dt}\begin{pmatrix}
\psi_c(\mathbf{x},t)\\
\psi_x(\mathbf{x},t)
\end{pmatrix}
=
\begin{pmatrix}
F(\mathbf{x},t)\\
0
\end{pmatrix}
+{}\\
{}+\left[
h^0+\begin{pmatrix}
V_c(\mathbf{x})-i\hbar\,\frac{\gamma_c}{2}& 0\\
0& V_x(\mathbf{x})-i\hbar\,\frac{\gamma_x}{2}
+g\,\lvert\psi_x(\mathbf{x},t)\rvert^2
\end{pmatrix}
\right
\begin{pmatrix}
\psi_c(\mathbf{x},t)\\
\psi_x(\mathbf{x},t)
\end{pmatrix}.
\end{multline}
The microcavity is characterized by the following parameters: $\gamma_c$ and $\gamma_x$--- the decay rates (loss rates) for photons and excitons, $g$---the strength of nonlinear exciton interaction, $V_c(\mathbf{x})$, $V_x(\mathbf{x})$---the single particle potentials acting on photons and excitons, and $\Omega_R$---the Rabi frequency. The single-particle Hamiltonian $h^0$ is given by
\begin{align}
h^0={}&\begin{pmatrix}
\omega_c(-i\nabla)& \Omega_R\\
\Omega_R& \omega_x(-i\nabla)
\end{pmatrix},\\
\omega_c(-i\nabla)={}&\omega_c^0-\frac{\hbar^2\nabla^2}{2m_c},\\
\omega_x(-i\nabla)={}&\omega_x^0-\frac{\hbar^2\nabla^2}{2m_x},
\end{align}
where $\omega_c(-i\nabla)$ is the cavity mode energy dispersion, $\omega_c^0$ is the cavity mode energy, $m_c$ is the effective mass of a polariton (usually of the order of $m_c=10^{-5}\cdot m_0$, $m_0$ being the mass of a free electron), $\omega_x(-i\nabla)$ is the exciton dispersion, $\omega_x^0$ is the exciton energy and $m_x$ is the effective mass of an exciton.
Although Eq.~(\ref{eq:gp_matrix1}) fully describes the evolution of exciton-polaritons, it includes a number of parameters which are usually unnecessary for investigation of the system in practice. For example, the single particle potentials $V_c(\mathbf{x})$, $V_x(\mathbf{x})$ may be neglected in some situations and the exciton mass $m_x$ is regarded as infinite compared to the mass of a polariton. We can also replace $\omega_p$, $\omega_c^0$ and $\omega_x^0$ with two parameters representing detuning of the pump field $\delta_{\omega}$ and detuning of polaritons $\delta$ from the cavity mode frequency $\omega_c^0$. Additionally, we assume that $\mathbf{x}=0$ lies in the center of the laser spot $\mathbf{x}_0$. Summarizing, in our further discussion we take
\begin{align*}
V_x=V_c={}&0,\\
\omega_p\to{}&\omega_p+\omega_c^0=\delta_{\omega},\\
\omega_c^0\to{}&\omega_c^0-\omega_c^0=0,\\
\omega_x^0\to{}&\omega_x^0-\omega_c^0=\delta,\\
\omega_c(-i\nabla)={}&-\frac{\hbar^2\nabla^2}{2m_c},\\
\omega_x(-i\nabla)={}&\delta,\\
\mathbf{x}_0={}&0.
\end{align*}
Under these assumptions Eq.~(\ref{eq:gp_matrix1}) is simplified to
\begin{multline}
\label{eq:gp_matrix2}
i\hbar\,\frac{d}{d t}\begin{pmatrix}
\psi_c(\mathbf{x},t)\\
\psi_x(\mathbf{x},t)
\end{pmatrix}
=
\begin{pmatrix}
F(\mathbf{x},t)\\
0
\end{pmatrix}
+{}\\
{}+\left[
h^0+\begin{pmatrix}
-i\hbar\,\frac{\gamma_c}{2}& 0\\
0& -i\hbar\,\frac{\gamma_x}{2}
+g\,\lvert\psi_x(\mathbf{x},t)\rvert^2
\end{pmatrix}
\right]\begin{pmatrix}
\psi_c(\mathbf{x},t)\\
\psi_x(\mathbf{x},t)
\end{pmatrix},
\end{multline}
where
\begin{align}
F(\mathbf{x},t)={}&F_p\,e^{i\,(\mathbf{k}_p\cdot\mathbf{x}-\delta_{\omega}\,t)}\,e^{-\frac{\mathbf{x}^2}{2w_x^2}},\\
h^0={}&\begin{pmatrix}
-\tfrac{\hbar^2\nabla^2}{2m_c}& \Omega_R\\
\Omega_R& \delta
\end{pmatrix}.
\end{align}
Next, we rewrite Eq.~(\ref{eq:gp_matrix2}) into a more convenient form
\begin{align}
\label{eq:gp_linear_psic1}
i\hbar\,\frac{d}{dt}\,\psi_c(\mathbf{x},t)={}&
F(\mathbf{x}, t)+\Omega_R\,\psi_x(\mathbf{x},t)
+\left(-i\hbar\,\frac{\gamma_c}{2}-\frac{\hbar^2\nabla^2}{2m_c}\right)\,
\psi_c(\mathbf{x},t),\\
\label{eq:gp_linear_psix1}
i\hbar\,\frac{d}{dt}\,\psi_x(\mathbf{x},t)={}&
\Omega_R\,\psi_c(\mathbf{x},t)
+\left(-i\hbar\,\frac{\gamma_x}{2}+g\,\lvert\psi_x(\mathbf{x},t)\rvert^2+\delta\right)\,
\psi_x(\mathbf{x},t).
\end{align}
This is the set of equations governing the dynamics of exciton-polaritons that we numerically solve.
\subsection{Spin effects}
Important feature of exciton-polaritons is their spin, which allows to investigate their applications in spintronics~\cite{Sanvitto2012}. In order to include spin in Eq.~(\ref{eq:gp_matrix2}), excitonic and photonic wave functions $\psi_{x,c}$ have to be computed separately for spin $\sigma=+1$ and $\sigma=-1$. The coupling
constant $g$ is now replaced with two constants, $g_1$---quantifying coupling between excitons of the same spin and $g_2$---coupling between excitons of different spin. This leads to following matrix equation
\begin{multline}
\label{eq:gp_matrix2spin}
i\hbar\,\dfrac{d}{dt}\begin{pmatrix}
\psi_{c,-1}(\mathbf{x},t)\\
\psi_{x,-1}(\mathbf{x},t)\\
\psi_{c,+1}(\mathbf{x},t)\\
\psi_{x,+1}(\mathbf{x},t)
\end{pmatrix}
=
\begin{pmatrix}
F_{-1}(\mathbf{x},t)\\
0\\
F_{+1}(\mathbf{x},t)\\
0
\end{pmatrix}
+{}\\
{}+\left[
h^0+\begin{pmatrix}
-i\hbar\,\frac{\gamma_c}{2}& 0& 0& 0\\
0& -i\hbar\,\frac{\gamma_x}{2}
+g_1\,\lvert\psi_{x,-1}(\mathbf{x},t)\rvert^2& 0& g_2\,\lvert\psi_{x,+1}(\mathbf{x},t)\rvert^2\\
0& 0& -i\hbar\,\frac{\gamma_c}{2}& 0\\
0& g_2\,\lvert\psi_{x,-1}(\mathbf{x},t)\rvert^2& 0& -i\hbar\,\frac{\gamma_x}{2} +g_1\,\lvert\psi_{x,+1}(\mathbf{x},t)\rvert^2
\end{pmatrix}
\right]\times{}\\
{}\times\begin{pmatrix}
\psi_{c,-1}(\mathbf{x},t)\\
\psi_{x,-1}(\mathbf{x},t)\\
\psi_{c,+1}(\mathbf{x},t)\\
\psi_{x,+1}(\mathbf{x},t)
\end{pmatrix},
\end{multline}
where $-1$ and $+1$ denote the spin $\sigma$ and
\begin{align} F_{+1}(\mathbf{x},t)={}&F_{p_{+1}}\,e^{i\,(\mathbf{k}_{p_{+1}}\cdot\mathbf{x}-\delta_{\omega_{+1}}\,t)}\,e^{-\frac{\mathbf{x}^2}{2w_{x_{+1}}^2}},\\ F_{-1}(\mathbf{x},t)={}&F_{p_{-1}}\,e^{i\,(\mathbf{k}_{p_{-1}}\cdot\mathbf{x}-\delta_{\omega_{-1}}\,t)}\,e^{-\frac{\mathbf{x}^2}{2w_{x_{-1}}^2}},\\
h^0={}&\begin{pmatrix}
-\tfrac{\hbar^2\nabla^2}{2m_c}& \Omega_R& 0& 0\\
\Omega_R& \delta& 0& 0\\
0& 0& -\tfrac{\hbar^2\nabla^2}{2m_c}& \Omega_R\\
0& 0& \Omega_R& \delta
\end{pmatrix}.
\end{align}
The set of differential equations resulting from (\ref{eq:gp_matrix2spin}) obtains the following form
\begin{align}
\label{eq:gp_linear_psic1spinM}
i\hbar\,\frac{d}{dt}\,\psi_{c,-1}(\mathbf{x},t)={}&
F_{-1}(\mathbf{x}, t)+\Omega_R\,\psi_{x,-1}(\mathbf{x},t)
+\left(-i\hbar\,\frac{\gamma_c}{2}-\frac{\hbar^2\nabla^2}{2m_c}\right)\,
\psi_{c,-1}(\mathbf{x},t),\\
\label{eq:gp_linear_psic1spinP}
i\hbar\,\frac{d}{dt}\,\psi_{c,+1}(\mathbf{x},t)={}&
F_{+1}(\mathbf{x}, t)+\Omega_R\,\psi_{x,+1}(\mathbf{x},t)
+\left(-i\hbar\,\frac{\gamma_c}{2}-\frac{\hbar^2\nabla^2}{2m_c}\right)\,
\psi_{c,+1}(\mathbf{x},t),\\
\label{eq:gp_linear_psix1spinM}
i\hbar\,\frac{d}{dt}\,\psi_{x,-1}(\mathbf{x},t)={}&
\Omega_R\,\psi_{c,-1}(\mathbf{x},t) +\left(-i\hbar\,\frac{\gamma_x}{2}+g_1\,\lvert\psi_{x,-1}(\mathbf{x},t)\rvert^2+g_2\,\lvert\psi_{x,+1}(\mathbf{x},t)\rvert^2+\delta\right)\,
\psi_{x,-1}(\mathbf{x},t),\\
\label{eq:gp_linear_psix1spinP}
i\hbar\,\frac{d}{dt}\,\psi_{x,+1}(\mathbf{x},t)={}&
\Omega_R\,\psi_{c,+1}(\mathbf{x},t) +\left(-i\hbar\,\frac{\gamma_x}{2}+g_1\,\lvert\psi_{x,+1}(\mathbf{x},t)\rvert^2+g_2\,\lvert\psi_{x,-1}(\mathbf{x},t)\rvert^2+\delta\right)\,
\psi_{x,+1}(\mathbf{x},t).
\end{align}
This is the second set of polaritonic equations that we solve numerically using the EPCGP suite.
\subsection{Boundary conditions}
\label{ssec:boundary}
In order to solve the set of differential equations (\ref{eq:gp_linear_psic1})--(\ref{eq:gp_linear_psix1}) and (\ref{eq:gp_linear_psic1spinM})--(\ref{eq:gp_linear_psix1spinP}), it is necessary to set boundary conditions. For initial time $t=0$ no quasiparticles are present in the microcavity thus, all wave functions are equal zero. Additionally, $\psi_{c,x}$ vanish at the boundaries of the cavity. This leads to the following set of conditions used in computations
\begin{align*}
\psi_c(\mathbf{x},t=0)={}&0,\\
\psi_x(\mathbf{x},t=0)={}&0,\\
\psi_c(\lVert\mathbf{x}\lVert\geq L/2,t)={}&0,\\
\psi_x(\lVert\mathbf{x}\lVert\geq L/2,t)={}&0,
\end{align*}
where $L$ denotes the radius of the microcavity and $\mathbf{x}_0$ lies in the center of the mesh. Similar boundary conditions apply for the set of equations with spin.
\subsection{Parameters of the exciton-polariton equations}
Since the typical size of microcavities is of the order of micrometers and the lifetime of exciton-polaritons does not exceed $0.1\kern.25em\mathrm{ns}$, the most common units encountered in the literature in the description of exciton-polariton superfluids~\cite{Kavokin2007} are micrometers ($\mathrm{\mu m}$) and picoseconds ($\mathrm{ps}$). They are complemented with a convenient unit of energy -- millielectronvolt ($\mathrm{meV}$). This allows to express the wave functions in $\mathrm{\mu m}^{-1/2}$ for 1D condensate ($\mathrm{\mu m}^{-1}$ in the 2D case), frequency in $\mathrm{meV}$, decay rates in $\mathrm{ps}^{-1}$ and the interaction coefficient $g$ in $\mathrm{meV}\cdot\mathrm{\mu m}$($\mathrm{meV}\cdot\mathrm{\mu m}^2$ in the 2D case). Pumping laser field $F_p$ is given in $\mathrm{meV}\cdot\mathrm{\mu m}^{-1/2}$ ($\mathrm{meV}\cdot\mathrm{\mu m}^{-1}$ in the 2D case) with momentum $k_p$ in $\mathrm{\mu m}^{-1}$ and detuning $\delta$ in $\mathrm{ps}^{-1}$. Finally, physical constants expressed with these units equal to: reduced Planck constant $\hbar=0.6582\kern.25em\mathrm{meV}\cdot\mathrm{ps}$ and mass of afree electron $m_e=5.677\times10^3\kern.25em\mathrm{meV}\cdot\mathrm{\mu m}^{-2}\cdot\mathrm{ps}^2$.
The typical values of the parameters of equations (\ref{eq:gp_matrix2}) and (\ref{eq:gp_matrix2spin}) are gathered in Table~\ref{tab:parameters}. In case of 1D and 2D systems, the interaction coefficient may be converted with the following formula
\begin{equation}
g^{\text{1D}}=\frac{g^{\text{2D}}}{\sqrt{2\pi d^2}},
\end{equation}
where $d$ is a width of a 1D microcavity.
\begin{table}[ht]
\begin{align*}
\hbar={}&0.6582\,[\mathrm{meV}\cdot\mathrm{ps}]&&\text{-- reduced Planck constant,}\\
\psi_c(x,t)={}&[1/\mu\mathrm{m}]&&\text{-- wave function for photons,}\\
\psi_x(x,t)={}&[1/\mu\mathrm{m}]&&\text{-- wave function for polaritons,}\\
F_p={}&[\mathrm{meV}/(\mu\mathrm{m})]&&\text{-- amplitude of the pump field,}\\
k_p={}&[1/(\mu\mathrm{m})]&&\text{-- momentum of the pump field,}\\
\delta_{\omega}={}&[1/(\mathrm{ps})]&&\text{-- detuning of the pump field,}\\
w_x={}&[\mu\mathrm{m}]&&\text{-- spread of the pump,}\\
g={}&0.01\,[\mathrm{meV}\cdot(\mu\mathrm{m})^2]&&\text{-- interaction coefficient,}\\
\Omega_R={}&4.4\,[\mathrm{meV}]&&\text{-- Rabi frequancy,}\\
\gamma_x={}&0.01\,[1/(\mathrm{ps})]&&\text{-- decay rate of an exciton,}\\
\gamma_c={}&0.1\,[1/(\mathrm{ps})]&&\text{-- decay rate of a photon,}\\
m_0={}&5.677\times 10^{3}\,[\mathrm{meV}/(\mu\mathrm{m}/(\mathrm{ps}))^2]&&\text{-- mass of a free electron},\\
m_c={}&m_0\cdot 2\times 10^{-5}\,[\mathrm{meV}/(\mu\mathrm{m}/(\mathrm{ps}))^2]&&\text{-- effective mass of polaritons.}
\end{align*}
\caption{The parameters of the exciton-polariton equations (\ref{eq:gp_matrix2}) and (\ref{eq:gp_matrix2spin}) in the 2D case.}
\label{tab:parameters}
\end{table}
\section{Numerical methods}
\label{sec:numerics}
\subsection{Equations governing the dynamics of exciton-polaritons}
The two sets of equations presented in Section~\ref{sec:theory}, Eqs.~(\ref{eq:gp_linear_psic1})--(\ref{eq:gp_linear_psix1}) and (\ref{eq:gp_linear_psic1spinM})--(\ref{eq:gp_linear_psix1spinP}), share a similar structure. Left-hand side of these equations is the first derivative of the individual wave function with respect to time. The form of the right-hand side depends on the computed wave function. In case of $\psi_c$ (as well as $\psi_{c,\sigma=\pm1}$) the terms include functions of time, linear functions of $\psi_x$ and $\psi_c$ and second order partial derivatives of the computed wave function $\psi_c$. Equations defining $\psi_x$ ($\psi_{x,\sigma=\pm1}$) depend on the linear function of $\psi_c$ and both linear and nonlinear expressions involving $\psi_x$. The main problem in solving these equations lies in a unique combination of complex-valued terms, nonlinearities and second order partial derivatives at their right-hand sides. Implicit (backward) methods, although usually stable, require solving algebraic equations, which make them unusable in the case of exciton-polariton equations. In case of explicit (forward) methods it is more difficult to keep errors negligible. Taking into account that our goal is to observe detailed evolution of the system with a finite time step, we compared the most important numerical methods of solving nonlinear differential equations, which could find appplication in computing the evolution of an exciton-polariton superfluid.
The most basic method is the Euler one. It is simple and fast, but produces inaccurate results---an error introduced in the single step is of the order of $O(h^2)$, where $h$ is the step length. The Runge--Kutta methods require additional stages of computation and therefore are slower, but much more accurate---the errors are of the order of $O(h^{n+1})$, where $n$ is the order of the method. The methods based on the Richardson extrapolation (e.g.\ Bulirsch--Stoer algorithm) or predictor-corector algorithms are not suited to this task due to strong nonlinearities occurring in the exciton-polariton condensates. They cause huge errors which must be compensated by small step size and computation time. Comparison of the above explicit methods is shown in Table~\ref{tab:ode_methods}. The best performance for a given precision was achieved by the adaptive Runge--Kutta algorithm. However, the standard Runga--Kutta method of 4th order performed similarly well (only $25\%$ slower compared to the adaptive method) and its advantage lies in the constant step size, which makes solving of the evolution of the exciton-polaritons easier. The other algorithms, although led to the same results, required more computing time. Especially, advanced Bulirsch--Stoer and predictor-corector methods occurred to be slower than a relatively simple Runge--Kutta algorithm.
\begin{table}
\begin{tabular}{lccc}
\textit{Method}& \textit{Number of steps}& \textit{Relative error}& \textit{Computation time}\\\hline
Euler& $1.0\times10^6$& $10^{-5}$& $120\kern.25em\mathrm{s}$\\
Runge--Kutta (2nd order) & $2.0\times10^5$& $10^{-5}$& $50\kern.25em\mathrm{s}$\\
Runge--Kutta (4nd order) & $2.0\times10^3$& $10^{-5}$& $10\kern.25em\mathrm{s}$\\
Adaptive Runge--Kutta& $1.5\times10^3$& $10^{-5}$& $8\kern.25em\mathrm{s}$\\
Bulirsch--Stoer & $1.2\times10^5$& $10^{-5}$& $60\kern.25em\mathrm{s}$\\
Predictor-corector & $2.5\times10^5$& $10^{-5}$& $80\kern.25em\mathrm{s}$\\
\end{tabular}
\caption{The comparison of results of solving GPE for exciton-polariton superfluids with different numerical methods. The test was based on a simulation of $1\kern.25em\mathrm{ps}$ evolution of a 1D condensate without spin. All the programs were required to achieve relative accuracy of computations equal to $10^{-5}$. The parameters used for computations are: $d=5$, $F_p=0.5$, $k_p=0$, $\delta=0$, $\delta_{\omega}=0$, $w_x=10$, $g=0.1$, $\Omega_R=4.4$, $\gamma_x=0.01$, $\gamma_c=0.1$. The cavity size was set to $100\kern.25em\mathrm{\mu m}$ with $N=1000$ mesh nodes.}
\label{tab:ode_methods}
\end{table}
\subsection{The Runge--Kutta algorithm}
\label{ssec:RK}
The Runge--Kutta (RK) algorithm of the 4th order belongs to the family of the RK methods. This approach evolved from the Euler method, where a differential equation $\tfrac{d}{dt} y(t) = f(t, y)$ is solved by substituting $\tfrac{d}{dt} y(t) \approx [y(t + h) - y(t)]/h$, where $h$ is a time step. This leads to an approximation $y(t + h)\approx y(t) + hf(t, y)$. In the Euler method the smaller the time step $h$ is, the more accurate is the solution but, at the same time, the computer program is more time-consuming and prone to errors resulting from finite-precision mathematical operations. When $h>1$, the Euler method becomes unstable.
The 4th-order RK method stems from the Euler algorithm but introduces additional steps which improve accuracy and stability of computation. These steps are denoted $k_1,\ldots,k_4$ and are computed in the following way
\begin{align}
k_1={}& h\,f(y, t),\\
k_2={}& h\,f(y+\tfrac{1}{2}\,k_1, t+\tfrac{1}{2}\,h),\\
k_3={}& h\,f(y+\tfrac{1}{2}\,k_2, t+\tfrac{1}{2}\,h),\\
k_4={}& h\,f(y+k_3, t+h).
\end{align}
Then,
\begin{equation}
y(t+h)= y(t)+\tfrac{1}{6}\,(k_1+2\,k_2+2\,k_3+k_4).
\end{equation}
Within this approach, $k_1$ corresponds to the Euler method, $k_2$ and $k_3$ keep the corrections computed at the half-time step $t+\tfrac{1}{2}h$ and $k_4$ is the final correction calculated for the full step. This method requires four computations of right-hand side of the equation, but due to better accuracy allows to use larger time steps and therefore performs better than the Euler algorithm.
In order to apply the RK method to Eqs.~(\ref{eq:gp_linear_psic1})--(\ref{eq:gp_linear_psix1}), both complex wave functions $\psi_{x,c}$ must be computed parallely in every step of the algorithm. This is expressed in the following sequence of computations
\begin{align*}
k_1^c={}& h\,f^c(\psi_x, \psi_c, t),\\
k_1^x={}& h\,f^x(\psi_x, \psi_c, t),\\
k_2^c={}& h\,f^c(\psi_x+\tfrac{1}{2}\,k^x_1, \psi_c+\tfrac{1}{2}\,k^c_1, t+\tfrac{1}{2}\,h),\\
k_2^x={}& h\,f^x(\psi_x+\tfrac{1}{2}\,k^x_1, \psi_c+\tfrac{1}{2}\,k^c_1, t+\tfrac{1}{2}\,h),\\
k_3^c={}& h\,f^c(\psi_x+\tfrac{1}{2}\,k^x_2, \psi_c+\tfrac{1}{2}\,k^c_2, t+\tfrac{1}{2}\,h),\\
k_3^x={}& h\,f^x(\psi_x+\tfrac{1}{2}\,k^x_2, \psi_c+\tfrac{1}{2}\,k^c_2, t+\tfrac{1}{2}\,h),\\
k_4^c={}& h\,f^c(\psi_x+k^c_3, \psi_c+k^c_3, t+h),\\
k_4^x={}& h\,f^x(\psi_x+k^x_3, \psi_c+k^c_3, t+h),\\
\psi_c(t+h)={}& \psi_c(t)+\tfrac{1}{6}\,(k_1^c+2\,k_2^c+2\,k_3^c+k_4^c),\\
\psi_x(t+h)={}& \psi_x(t)+\tfrac{1}{6}\,(k_1^x+2\,k_2^x+2\,k_3^x+k_4^x),
\end{align*}
where $f^c(\psi_x, \psi_c, t)$ represents the right-hand side of Eq.~(\ref{eq:gp_linear_psic1}) and $f^x(\psi_x, \psi_c, t)$---of Eq.~(\ref{eq:gp_linear_psix1}). Similarly, RK method applied to Eqs.~(\ref{eq:gp_linear_psic1spinM})--(\ref{eq:gp_linear_psix1spinP}) requires parallel computation of four sets of corrections ($k_n^{c,-1}$, $k_n^{c,+1}$, $k_n^{x,-1}$ and $k_n^{x,+1}$) related to four wave functions. This makes the algoritm twice as long as in the case of spinless equations.
In order to represent the wave functions $\psi_{x,c}$ in a limited computer memory, the X-Y plane must be discretized in order to introduce a finite set of space coordinates. Taking into account the form of equations describing exciton-polariton superfluid and the boundary conditions listed in Subsection~\ref{ssec:boundary}, a natural choice is to use a uniform mesh of $N$ nodes in a 1D case and a square mesh of $N\times N$ nodes for 2D superfluid. The mesh should be centered in $\mathbf{x}=0$ and the distance between the consecutive nodes should be $\Delta_x$ and $\Delta_y$. Hence, the effective size of the microcavity equals to $N\Delta_x$ for 1D system and $N\Delta_x\times N\Delta_y$ for a 2D microcavity.
Let us now focus on the right-hand side of the Eq.~(\ref{eq:gp_linear_psic1}). It contains the nabla operator acting on the photonic wave function, $\nabla^2\psi_c(\mathbf{x},t)$. In case of 1D condensate, this translates into $\nabla^2\psi_c(\mathbf{x},t)=\tfrac{d^2}{dx^2}\psi_c(x,t)$ which can be approximated for a uniform mesh by the following central finite difference formula
\begin{equation}
\dfrac{d^2}{dx^2}\psi_c(x,t) = \dfrac{\psi_c(x-\Delta_x,t)-2\psi_c(x,t)+\psi_c(x+\Delta_x,t)}{\Delta_x^2},
\end{equation}
where $\Delta_x$ is the distance between mesh nodes. Similarly, in two dimensions,
\begin{align}
\nabla^2\psi_c(x,y,t)
={}& \left(\dfrac{d^2}{dx^2}+\dfrac{d^2}{dy^2}\right)\psi_c(x,y,t)\nonumber\\
={}& \dfrac{\psi_c(x-\Delta_x,y,t)-2\psi_c(x,y,t)+\psi_c(x+\Delta_x,y,t)}{\Delta_x^2}\nonumber\\
&\qquad{}+\dfrac{\psi_c(x,y-\Delta_y,t)-2\psi_c(x,y,t)+\psi_c(x,y+\Delta_y,t)}{\Delta_y^2},
\end{align}
where $\Delta_x$ and $\Delta_y$ denote the distances between mesh nodes in the X and Y directions, respectively.
The total error accumulated in a single time step of the 4th order RK method is of the order of $O(h^5)$~\cite{NR}. Errors resulting from discretization of the space are of the order of $O(\Delta_x^2)$ (1D system) and $O(\Delta_x^2\Delta_y^2)$ (2D system). Summarizing, the smaller time step and the distance between mesh nodes, the more accurate result is obtained.
Stability of the presented Runge--Kutta method is imposed by the Courant--Friedrichs--Lewy (CFL) condition, which sets relation between the time step and mesh density. In case of the 1D system the CFL condition amounts to
\begin{equation}
\dfrac{\hbar}{m_c}\dfrac{h}{\Delta^2_x} \leq 1
\end{equation}
and for 2D one to
\begin{equation}
\dfrac{\hbar}{m_c}\dfrac{h}{\Delta^2_x} + \dfrac{\hbar}{m_c}\dfrac{h}{\Delta^2_y} \leq 1.
\end{equation}
\subsection{Data structures}
The wave functions, $\psi_{x,c}$ take complex values, represented in the computer memory by a pair of double-precision IEE754 floating-point numbers. The discrete mesh is stored as a 1D or 2D array of values of the nodes. In this way, a single memory allocation of $16N$ bytes in 1D case ($16N^2$ in 2D case) is sufficient to store the results.
Data structures used by the 4th order RK numerical integration method are also 1D and 2D arrays of complex numbers. Since the algorithm requires computing coefficients $k_1,\ldots,k_4$ for each mesh node, the total memory requirement is $16\cdot 6N$ bytes for 1D mesh ($16\cdot 6N^2$ for 2D mesh). In case of typical value of $N=1000$ the amount of memory required by the program to run is of the order of several hundred megabytes.
\subsection{Optimization}
The computational complexity of the RK algorithm presented in the Subsection~\ref{ssec:RK} is of the order of $O(N\cdot M)$, where $N$ is the number of mesh nodes and $M$ is the number of computed time steps. In case of 2D superfluid, this value grows to $O(N^2\cdot M)$.
The main advantage of EPCGP suite lies in the specially developed optimization of the RK method used for solving the equations describing exciton-polariton superfluid. Up to date, most optimization methods have been based on dividing the mesh into subsets (tiles) of equal sizes and performing the RK steps for all these subsets in parallel. Synchronization points lie between algorithm steps and at each iteration of the main loop of the program. This allows to reduce the required time $T$ times, where $T$ is the number of computing cores involved.
Our method takes into account the specific form of the right-hand-sides of the equations describing exciton-polaritons. We noticed that the terms may be put in groups of different properties: (a) expressions not depending on $\psi_{c,x}$, e.g.\ $F(\mathbf{x},t)$, (b) terms proportional to the computed wave functions, e.g.\ $\Omega_R\psi_{c,x}$, (c) terms proportional to the square of the functions, and (d) terms proportional to $\lvert\psi_x\rvert^2 \psi_x$. Therefore, the EPCGP performs the individual steps of the RK algorithm, denoted as $k_1,\ldots,k_n$, in the order (a)--(d). In each substep, the corresponding power of $\psi_{x,c}$ is computed and stored for the next substep. Additionally, the whole set of terms for all mesh nodes is computed in a single step with the help of vector commands, available for the contemporary computing platforms. In this way, when $N$ is sufficiently small, the computation time is reduced to $O(M)$ for both 1D and 2D systems. In case of larger values of $N$, all operations are divided into sets of $64$--$512$ nodes, which are suitable for hardware vector operations. This allows to set the computation time of the order of $O(N\cdot M / V)$ or $O(N^2\cdot M / V)$, where $V$ is the maximal target of the vector operation.
The EPCGP suite utilizes OpenMP parallel framework~\cite{OpenMP,OpenMP_book} as well as MPI (Message Passing Interface)~\cite{MPI,MPICH} in order to split the computational task. This solution fits well to the typical environment of computer clusters. The main process/thread is responsible for gathering the data and saving results to disk files.
Both OpenMP and MPI technologies are optional and the suite gives the same results regardless they are used or not. They can be turned on or off by setting compiler directives in the source code of the program.
\subsection{Discrete Fourier transform}
The algorithms involved in solving the equations describing the exciton-polariton superfluid in the EPCGP suite compute the evolution in the configuration space. However, the suite has been additionally equipped with procedures calculating discrete Fourier transforms (DFTs) and the inverse DFTs of the wave functions $\psi_{x,c,\sigma=\pm1}$. The goal of including these procedures is to ease presentation of results in the frequency space, which is often encountered in the literature devoted to exciton-polaritons.
The DFT of a 1D wave function $\psi(x)$ over the mesh of $N$ nodes and distance $\Delta_x$ between the nodes where $x=x_0 + k\Delta_x$ is given by
\begin{align}
\tilde{\psi}(k_x)
= \dfrac{1}{\sqrt{N}}\sum_{k=0}^{N} \psi(x_0 + k\Delta_x) e^{-i[k_x\,(x_0 + k\Delta_x)]},
\end{align}
with inverse transform defined as
\begin{equation}
\psi(x)
= \dfrac{1}{\sqrt{N}}\sum_{k=0}^{N} \tilde{\psi}(k_{x_0} + k\Delta_{k_x}) e^{i[x\,(k_{x_0} + k\Delta_{k_x})]},
\end{equation}
where, under assumption that $x=0$ lies in the middle of the mesh,
\begin{align}
k_{x_0}={}& -\dfrac{\pi}{\Delta_x},\\
\Delta_{k_x} ={}& \dfrac{2\pi}{N\Delta_x}.
\end{align}
There are numerous known algorithms of computing DFTs. The EPCGP suite utilizes the Cooley--Tukey Fast Fourier Transform (FFT) algorithm~\cite{Smith2007} in order to achieve the best possible performance. The procedure is further optimized for use with OpenMP library. The inverse DFT shares the same code due to the similarity of FFT and inverse FFT algorithms. Two-dimensional case is computed with two passes of a 1D FFT procedure.
\section{Examples and Applications}
\label{sec:applications}
The EPCGP suite was utilized to obtain numerous results for different input parameters. Both 1D and 2D exciton-polariton superfluids were investigated and spin effects were optionally taken into account. Stability of results was ensured by the proper relation between mesh density and size of the time step, found with help of the Courant--Friedrichs--Lewy condition, presented in Subsection~\ref{ssec:RK}.
Here we present several plots showing the evolution of a 1D condensate. Fig.~\ref{fig:example1} presents typical simulation where spin is neglected. Two wave functions are depicted as particle number densities $\lvert\psi_{x,c}\rvert^2$ changing in time. The investigated system arrives at a stationary solution after $t=15\kern.25em\mathrm{ps}$. Fig.~\ref{fig:example2} presents simulation for similar parameters as for Fig.~\ref{fig:example1}, but this time spin is taken into account. In this case, the condensate reveals instabilities after a long evolution time $t>250\kern.25em\text{ps}$. Fig.~\ref{fig:example3} displays similar case but for $g_1\not=g_2$. The solution reveals oscillations, which vanish for $t>20\kern.25em\text{ps}$. Finally, Fig.~\ref{fig:example2D} depicts an evolution of a 2D system for a given initial state.
\begin{figure*}\centering
\includegraphics[width=10cm]{Voronych_3.eps}
\caption{Time evolution of 1D exciton-polariton superfluid without spin effects. The red plot depicts the evolution of the polaritonic wave function $\lvert\psi_x\rvert$ whereas blue---photonic wave function $\lvert\psi_c\rvert$. The computations were performed for a condensate of width $d=5\kern.25em\mu\text{m}$, pump amplitude $F_p=0.5\kern.25em\text{meV}\cdot\sqrt{\mu\text{m}}$, detuning of the pump $\delta_{\omega}=5\kern.25em 1/\text{ps}$, Rabi frequency $\Omega_R = 4.4\kern.25em\text{meV}$, interaction coefficient $g=-50\kern.25em\text{meV}\cdot(\mu\text{m})^2$ and decay rates $\gamma_c=0.5\kern.25em 1/\text{ps}$, $\gamma_x=0.05\kern.25em 1/\text{ps}$. After $t=15\kern.25em\text{ps}$ the system arrives at a stationary solution.}
\label{fig:example1}
\end{figure*}
\begin{figure*}\centering
\includegraphics[width=10cm]{Voronych_4.eps}
\caption{Time evolution of 1D exciton-polariton superfluid with spin effects. The red plots depict the evolution of the polaritonic wave functions $\lvert\psi_{x,\sigma=\pm1}\rvert$ whereas blue -- photonic wave functions $\lvert\psi_{x,\sigma=\pm1}\rvert$ for spins $\sigma\in\{-1,1\}$. The computations were performed for a condensate of width $d=5\kern.25em\mu\text{m}$, pump amplitude $F_p=0.5\kern.25em\text{meV}\cdot\sqrt{\mu\text{m}}$, detuning of the pump $\delta_{\omega}=5\kern.25em 1/\text{ps}$, Rabi frequency $\Omega_R = 4.4\kern.25em\text{meV}$, interaction coefficients $g_1=50\kern.25em\text{meV}\cdot(\mu\text{m})^2$, $g_2=-10\kern.25em\text{meV}\cdot(\mu\text{m})^2$ and decay rates $\gamma_c=0.5\kern.25em 1/\text{ps}$, $\gamma_x=0.05\kern.25em 1/\text{ps}$. After $t=20\kern.25em\text{ps}$ the system arrives at a stationary solution, but long evolution times $t>250\kern.25em\text{ps}$ reveal instabilities.}
\label{fig:example2}
\end{figure*}
\begin{figure*}\centering
\includegraphics[width=10cm]{Voronych_5.eps}
\caption{Time evolution of 1-dimensional polaritonic BEC with spin effects, modeled with the set of G--P equations. The red plots depict the evolution of the polaritonic wave functions $\lvert\psi_{x,\sigma=\pm1}\rvert$ whereas blue -- photonic wave functions $\lvert\psi_{x,\sigma=\pm1}\rvert$ for spins $\sigma\in\{-1,1\}$. The computations were performed for a condensate of width $d=5\kern.25em\mu\text{m}$, pump amplitude $F_p=0.5\kern.25em\text{meV}\cdot\sqrt{\mu\text{m}}$, detuning of the pump $\delta_{\omega}=5\kern.25em 1/\text{ps}$, Rabi frequency $\Omega_R = 4.4\kern.25em\text{meV}$, interaction coefficients $g_1=50\kern.25em\text{meV}\cdot(\mu\text{m})^2$, $g_1=-2\kern.25em\text{meV}\cdot(\mu\text{m})^2$ and decay rates $\gamma_c=0.5\kern.25em 1/\text{ps}$, $\gamma_x=0.05\kern.25em 1/\text{ps}$. The solution reveals oscillations, which vanish for $t>20\kern.25em\text{ps}$.}
\label{fig:example3}
\end{figure*}
\begin{figure}[p]
\begin{center}
\raisebox{3.5cm}{a)}
\includegraphics[height=3.5cm]{Voronych_6a.eps}
\includegraphics[height=3.5cm]{Voronych_6b.eps}\\
\raisebox{3.5cm}{b)}
\includegraphics[height=3.5cm]{Voronych_6c.eps}
\includegraphics[height=3.5cm]{Voronych_6d.eps}\\
\raisebox{3.5cm}{c)}
\includegraphics[height=3.5cm]{Voronych_6e.eps}
\includegraphics[height=3.5cm]{Voronych_6f.eps}
\end{center}
\caption{The evolution of $\psi_c(x, y)$ (left column) and
$\psi_x(x, y)$ (right column), being the solution of
Eqs.~(\ref{eq:gp_linear_psic1})-(\ref{eq:gp_linear_psix1}) for a
specially constructed initial state, computed for a) $t=0$, b)
$t=1ps$, c) $t=5ps$. The results were obtained for the following
parameters: $F_p=0$, detuning of the pump $\delta_{\omega}=0$,
Rabi frequency $\Omega_R = 1\kern.25em\text{meV}$, interaction
coefficient $g=0$ and decay rates $\gamma_c=\gamma_x=0$.}
\label{fig:example2D}
\end{figure}
\section{EPCGP Program Suite}
\label{sec:suite}
The EPCGP is a program suite developed for numerical modeling of evolution of an exciton-polariton superfluid in four different scenarios:
\begin{itemize}
\item 1-dimensional exciton-polariton superfluid, neglected spin effects,
\item 2-dimensional exciton-polariton superfluid, neglected spin effects,
\item 1-dimensional exciton-polariton superfluid, spin effects included,
\item 2-dimensional exciton-polariton superfluid, spin effects included.
\end{itemize}
This allows to perform numerical simulations in most of typical cases.
\subsection{Compilation of the Programs}
In order to compile and test EPCGP program suite for Linux/Unix operating systems with GNU utilities (GNU make, GNU compiler collection) it is enough to run the following commands in a directory containing unpacked source code
\begin{verbatim}
make
make check
\end{verbatim}
In case of Linux/Unix with GNU make and Intel C Compiler, one has to modify \verb|Makefile|, replacing \verb|gcc| with \verb|icc| and \verb|-fopenmp| option with \verb|-openmp|.
For other platforms and compilers: one should compile all the program files with a standard C/C++ compiler and OpenMP extensions turned on. If compiler does not offer OpenMP extensions, the program will still work but will not utilize multiple cores or processors.
\subsection{Description of the Program Suite}
Program computes time evolution of distribution of photons and polaritons in the polaritonic semiconductor microcavity. The results are saved to a disk file in a format suitable for further processing, e.g.\ visualization. At each step it also prints some indicators, used for validation of the computations, namely: norms of wave functions, current evolution time and the amount of time spent in computations.
Program parameters are set in the source code, by assigning values to the predefined variables.
\begin{verbatim}
// Parameters of the setup.
const double wkx = 4.0; // Spread of the initial Gaussian along k_x.
const double wky = 0.25; // Spread of the initial Gaussian along k_y.
const double A = 0.5; // Amplitude of the initial Gaussian.
const double m = 1.0; // Boson mass [meV].
const double me = 1.0; // Effective mass of polaritons [meV].
const double wb = 10; // The width of the "safe" window [µm].
const double cavsizex = 12; // Cavity size along X axis [µm].
const double cavsizey = 12; // Cavity size along Y axis [µm].
const double h = 0.0001; // Time step [ps].
// Parameters of the simulation.
const int xsize = 121; // Number of mesh nodes along X axis.
const int ysize = 121; // Number of mesh nodes along Y axis.
const double sx = cavsizex / (xsize - 1); // Spatial step along X axis.
const double sy = cavsizey / (ysize - 1); // Spatial step along Y axis.
const double xmin = -(cavsizex / 2); // Lower boundary of X coordinate.
const double xmax = (cavsizex / 2); // Upper boundary of X coordinate.
const double ymin = -(cavsizey / 2); // Lower boundary of Y coordinate.
const double ymax = (cavsizey / 2); // Upper boundary of Y coordinate.
const double kxmin = -pi / sx; // Lower boundary of k_x coordinate.
const double kxmax = pi / sx; // Upper boundary of k_x coordinate.
const double kymin = -pi / sy; // Lower boundary of k_y coordinate.
const double kymax = pi / sy; // Upper boundary of k_y coordinate.
const double ksx = 2 * pi / cavsizex; // Frequency step along k_x axis.
const double ksy = 2 * pi / cavsizey; // Frequency step along k_y axis.
const int nsteps = 200000; // Number of simulation iterations.
const int print_tstep = 1000; // Print every nth time step.
const int print_xstep = 1; // Print every nth spatial point along X axis.
const int print_ystep = 1; // Print every nth spatial point along Y axis.
\end{verbatim}
After setting the parameters, program has to be recompiled in order to achieve best optimization of the machine code. Running of the program is not interactive and therefore allows for execution in the environment of computer clusters. In order to set the maximal number of cores or processors utilized by the program one could use \verb|OMP_NUM_THREADS| environment variable. If not set, this value is obtained from the operating system and all computing cores are utilized.
\section{Conclusions}
In this paper we presented the EPCGP program suite developed for numerical modeling of an exciton-polariton superfluid in a semiconductor microcavity. It solves sets of nonlinear differential equations describing exciton-polaritons in one and two dimensions. They are based on the Gross--Pitaevskii equation, but describe separate excitonic and photonic wave functions. We listed and briefly described the parameters of the modeled system.
Numerical procedures included in the EPCGP suite utilize the Runge--Kutta method of the 4th order. The choice of the numerical algorithm was preceded by the analysis of applicability and performance of several numerical routines in solving the exciton-polariton equations for typical values of experimental parameters. We optimized the Runge--Kutta algorithm for this task by rearranging algebraic operations in order to avoid unnecessary intermediate steps. Furthermore, the suite code utilizes parallel OpenMP and MPI compiler extensions as well as efficient vector operations built into modern processors. This makes the EPCGP suite a fast and convenient tool for reliable numerical modeling of exciton-polariton superfluids. It may find applications in theoretical investigation of properties and phenomena observed in exciton-polariton systems.
\section*{Acknowledgments}
MS, OV, AB were supported by the EU 7FP Marie Curie Career Integration
Grant No. 322150 ``QCAT'', NCN grant No. 2012/04/M/ST2/00789, MNiSW
co-financed international project No. 2586/7.PR/2012/2 and MNiSW
Iuventus Plus project No. IP 2014 044873.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 1,224
|
using AspectInjector.Broker;
using System;
using System.Linq;
using Xunit;
namespace AspectInjector.Tests.General
{
public class InjectionDataTests
{
[Fact]
public void Injection_Parameters_Are_Correct()
{
var a = new TestClass();
Checker.Passed = false;
a.Do();
Assert.True(Checker.Passed);
Checker.Passed = false;
a.Do2();
Assert.True(Checker.Passed);
}
private class TestClass
{
[TestInjection(true, byte.MaxValue, sbyte.MinValue, char.MaxValue, short.MinValue, ushort.MaxValue, int.MinValue, uint.MaxValue, float.MinValue, long.MinValue, ulong.MaxValue, double.MinValue)]
public void Do() { }
[TestInjection2(new ulong[] { ulong.MinValue, ulong.MaxValue }, 2, new object[] { new object[] { 0.5f, true }, 1, typeof(TestInjection2) }, new double[] { 12d, -0.777d }, new float[] { }, new bool[] { true }, typeof(TestClass), StringComparison.InvariantCulture)]
public void Do2() { }
}
[Injection(typeof(TestAspect))]
private class TestInjection2 : Attribute
{
public TestInjection2(object[] oa)
{
}
public TestInjection2(ulong[] ul, object o, object[] oa, double[] da, float[] fa, bool[] ba, Type type, StringComparison e)
{
Ul = ul;
O = o;
Oa = oa;
Da = da;
Fa = fa;
Ba = ba;
Type = type;
E = e;
}
public ulong[] Ul { get; }
public object O { get; }
public object[] Oa { get; }
public double[] Da { get; }
public float[] Fa { get; }
public bool[] Ba { get; }
public Type Type { get; }
public StringComparison E { get; }
}
[Injection(typeof(TestAspect))]
private class TestInjection : Attribute
{
public TestInjection(bool bo, byte b, sbyte sb, char c, short s, ushort us, int i, uint ui, float f, long l, ulong ul, double d)
{
Bo = bo;
B = b;
Sb = sb;
C = c;
S = s;
Us = us;
I = i;
Ui = ui;
F = f;
L = l;
Ul = ul;
D = d;
}
public bool Bo { get; }
public byte B { get; }
public sbyte Sb { get; }
public char C { get; }
public short S { get; }
public ushort Us { get; }
public int I { get; }
public uint Ui { get; }
public float F { get; }
public long L { get; }
public ulong Ul { get; }
public double D { get; }
}
[Aspect(Scope.Global)]
public class TestAspect
{
[Advice(Kind.Before)]
public void Before2([Argument(Source.Triggers)] Attribute[] data)
{
var a = data.OfType<TestInjection2>().FirstOrDefault();
if (a == null) return;
Checker.Passed = a.Ul[0]==ulong.MinValue && a.Ul[1] == ulong.MaxValue && (int)a.O == 2 && (float)((object[])a.Oa[0])[0] == 0.5f && (bool)((object[])a.Oa[0])[1] == true
&& (int)a.Oa[1] == 1 && (Type)a.Oa[2] == typeof(TestInjection2) && a.Da[0] == 12d && a.Da[1] == -0.777d
&& a.Fa.Length == 0 && a.Ba[0] == true && a.Type == typeof(TestClass) && a.E == StringComparison.InvariantCulture;
}
[Advice(Kind.Before)]
public void Before([Argument(Source.Triggers)] Attribute[] data)
{
var a = data.OfType<TestInjection>().FirstOrDefault();
if (a == null) return;
Checker.Passed = a.Bo && a.B == byte.MaxValue && a.Sb == sbyte.MinValue && a.C == char.MaxValue &&
a.S == short.MinValue && a.Us == ushort.MaxValue && a.I == int.MinValue && a.Ui == uint.MaxValue &&
a.F == float.MinValue && a.L == long.MinValue && a.Ul == ulong.MaxValue && a.D == double.MinValue;
}
}
}
public class CustomAttributesTests
{
[Fact]
public void General_CustomAttributes_PassRoutableValues()
{
Checker.Passed = false;
var a = new CustomAttributesTests_Target();
a.Do();
Assert.True(Checker.Passed);
var b = new CustomAttributesTestsAttribute("111") { Value = "olo" };
}
[Fact]
public void General_CustomAttributes_Multiple()
{
Checker.Passed = false;
var a = new CustomAttributesTests_MultipleTarget();
a.Do123();
Assert.True(Checker.Passed);
}
}
[CustomAttributesTests("TestHeader", Value = "ololo", data = 43)]
internal class CustomAttributesTests_Target
{
public void Do()
{
}
}
[CustomAttributesTests_Multiple1]
internal class CustomAttributesTests_MultipleTarget
{
[CustomAttributesTests_Multiple2]
public void Do123()
{
}
}
[Injection(typeof(CustomAttributesTests_Aspect))]
internal class CustomAttributesTestsAttribute : Attribute
{
public string Header { get; private set; }
public string Value { get; set; }
public int data = 42;
public CustomAttributesTestsAttribute(string header)
{
Header = header;
}
}
[Aspect(Scope.Global)]
public class CustomAttributesTests_Aspect
{
[Advice(Kind.After)]
public void AfterMethod([Argument(Source.Triggers)] Attribute[] data)
{
var a = (data[0] as CustomAttributesTestsAttribute);
Checker.Passed = a.Header == "TestHeader" && a.Value == "ololo" && a.data == 43;
}
}
[Injection(typeof(CustomAttributesTests_MultipleAspect))]
public class CustomAttributesTests_Multiple1Attribute : Attribute
{
}
[Injection(typeof(CustomAttributesTests_MultipleAspect))]
public class CustomAttributesTests_Multiple2Attribute : Attribute
{
}
[Aspect(Scope.Global)]
public class CustomAttributesTests_MultipleAspect
{
[Advice(Kind.After)]
public void AfterMethod([Argument(Source.Triggers)] Attribute[] data)
{
Checker.Passed = data.Length == 2
&& data[0] is CustomAttributesTests_Multiple1Attribute
&& data[1] is CustomAttributesTests_Multiple2Attribute;
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 107
|
SPORTS 2/4/18 7:21pm
Women's basketball ends James Madison's 11-game winning streak with a 50-43 win
By Sienna Catherine Standfield
James Madison University's 11-game winning streak ended today after the Elon University women's basketball team won 50-43. Though the game started off with several turnovers from both teams, Elon managed to end with 16 points in the first period— a 10 point lead over James Madison. It was an important game for the Phoenix as they lost their first match against the Dukes, so there was no room for anything but a strong start and an even stronger finish.
SPORTS 2/3/18 11:53pm
Elon uses hot start to cruise past Delaware
By Jack Haley
In the past, the Elon University men's basketball team has had no trouble containing the University of Delaware. Tonight's contest was no different. The Phoenix handled the visiting Blue Hens 89-76 to extend their all-time record to 7-1 against the University of Delaware.
SPORTS 1/21/18 5:37pm
Johnson scores her 1000th point in Phoenix win against the Blue Hens
With an abundance of turnovers in the first half, a win didn't look possible for the Phoenix. But when the final buzzer sounded, the Elon University women's basketball team pulled out a 64-51 win against the University of Delaware.
SPORTS 1/21/18 12:00am
Elon loses back-to-back games for the first time this season
Elon (12-9, 4-4) tried to get back on track after a devastating loss on the road to James Madison University Thursday, Jan. 18, hosting the Colonial Athletic Association (CAA) leading Tribe of William and Mary (13-6, 6-2). The Phoenix were unable to get back to the winning way, falling 80-73 at home.
Women's soccer coach steps down
By Erik Webb
The Elon University women's soccer program will be without a leader following an announcement this morning. Head coach Chris Neal is stepping down from the helm of the program after 10 years to take a coaching job at the University of Arkansas, Director of Athletics Dave Blank announced this morning.
Fairways and family: How one set of brothers is keeping a trend alive on the men's golf team
One is left-handed and the other is right-handed. One is a redshirt-senior and the other is a freshman. Both play for the Elon University men's golf team representing the same last name. Hailing from Westwood, Massachusetts, brothers Patrick and Will Frodigh ended up together at Elon by chance. Patrick transferred twice, spending two years at the University of Denver, a year at the University of Louisville, and then entering Elon for his final two years.
SPORTS 1/13/18 10:33pm
Elon gets decisive win over CAA rival Charleston
The Elon University men's basketball team (12-7, 4-2) beat league-favorite College of Charleston (12-6, 3-3) in Alumni Gym 63-58 Saturday night as they continued Colonial Athletic Association (CAA) action. The Phoenix came into the contest having won just one of their last eight matchups against the Cougars.
Elon men drop OT thriller to UNCW
"A stinging loss." That is how Elon University men's basketball head coach Matt Matheny described Thursday's game as his team fell on their home hardwood for the first time this season, dropping an OT thriller to the defending conference champion University of North Carolina at Wilmington, 80-78.
Welcome to the club: Seibring and Thompson score 1,000 career points at Elon
By Emmanuel Morgan
Final push lifts Elon over Northeastern
It was a cold day outside, but the Elon University women's basketball team remained hot inside Alumni Gym during its matchup against the Northeastern University Huskies earlier today. After moving past Northeastern 78-71, the Phoenix remains undefeated at home on the year and moves to 10-4 (2-1 in conference) this season.
Elon narrowly edges visiting Towson Tigers
After Towson University senior guard Brian Starr missed a game-tying three pointer as the clock expired, the Elon University men's basketball team escaped with a narrow win to start the 2018 calendar year. Trailing for most of the game, the Phoenix offense didn't come alive until the second half, where it was able to secure the 75-72 victory.
SPORTS 12/7/17 12:09pm
Swoope's scorching start
He doesn't have to be tall to make a big impact. In fact, he's the shortest starter on the Elon University men's basketball team, but when Dainan Swoope steps onto the court, he makes his presence known. The 6-foot, 185-pound junior guard has had a stellar start to the 2017-2018 season. Through the first nine games of the season, Swoope is averaging 17.1 points per game, which is ninth in the Colonial Athletic Association. The next closest Phoenix is redshirt senior forward Brian Dawkins, who averages 13.4 points per game and is 18th on the list.
Phoenix outlasts Peacocks in double overtime
The Elon University mens basketball team outlasted the Peacocks of Saint Peter's University in double overtime on Saturday night in Alumni Gym. Despite the Phoenix's offense being held stagnant at multiple points during the game, Elon was able to secure the 71-65 victory.
SPORTS 11/30/17 11:05pm
Men's basketball edges South Florida in overtime thriller
By Roman Costa
The Elon University men's basketball team secured its third home victory of the season on Thursday night, defeating the University of South Florida in overtime thriller, 79-78. In a string of fate, this marks the third consecutive year in which the Phoenix has played (and won) a home overtime game on November 30th.
SPORTS 11/28/17 8:38pm
Inside the revival of Elon's football program
How Elon changed its trajectory after nearly a decade of constant losing seasons
SPORTS 11/28/17 10:41am
Phoenix golf squads study abroad in Scotland
The Elon University golf teams became the most recent Phoenix teams to study abroad, following Elon's quest to create better global citizens in its students. According to Elonphoenix.com, the Elon athletics department "organizes and funds team global study courses, combining learning experiences with competition in countries around the world. Since 2011, Phoenix student-athletes have studied abroad in Europe, Asia and Central America." Earlier this year, the football team traveled to Costa Rica while the tennis teams traveled to Hawaii.
Elon falls to Furman in first round of FCS playoffs
A blocked extra point was the deciding factor Saturday as the Elon University football team fell in the first round of the Football Championship Subdivision (FCS) to Furman University, 28-27. In a game that witnessed three lead changes and eight touchdowns, No. 15 Phoenix was upset by the No. 22 Paladins in Rhodes Stadium.
PREVIEW: Elon takes on Furman in FCS playoffs
With the Elon University football team set to make its first postseason appearance since 2009, the No. 15 Phoenix prepares to host tomorrow's playoff game against No. 22 Furman University.
Elon football is playoffs bound
Following an 8-3 (6-2 in conference) season, the Elon University football team is playoffs bound. The Phoenix will play host to the Furman University Paladins on Saturday, Nov. 25, the Football Championship Subdivision (FCS) playoffs committee announced during the selection show on ESPNU this morning.
Top ranked James Madison defeats Elon, wins CAA title
After losing to James Madison University 31-3 Saturday, the Phoenix walked to its locker room with lowered heads in its final regular season game. And now, with the Football Championship Subdivision playoffs looming in the near future, instead of asking, "Why not us," Elon (8-3, 6-2) is wondering what will happen next. With Elon losing 31-3 to the reigning national champions, Elon now must look to the postseason.
Latest ELN
ENN: Elon Local News Full Broadcast | May 13, 2019
ELN Morning | May 9, 2019
The Online Exclusive | May 7, 2019
Latest Pendulum
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Q: Replace column value based on value in other column, for all rows in a pandas dataframe I am having trouble thinking pythonically about something, and would love some guidance.
I have a dataframe that contains columns with dates of events at which certain files should be uploaded, and a column with the names of those events. So events can be X, Y, Z, and files can be 1, 2, 3.
Not all files need to be uploaded at all events, i.e. if it's Event X, then files 1, 2, and 3 need to be uploaded, but if it's Event Y, then only file 3 needs to be uploaded. The date columns either have a date in them, or are blank.
What I want to do is, for all the files for events that are not needed, replace blank with "Not Needed".
Initial:
File1 File2 File3
X Aug 1 Sept 1
X Aug 3 Aug 4 Sept 9
Y Sept 10
Z Aug 12
X Aug 13 Aug 15
Z Aug 1
Goal
File1 File2 File3
X Aug 1 Sept 1
X Aug 3 Aug 4 Sept 9
Y NN NN Sept 10
Z Aug 12 NN NN
X Aug 13 Aug 15
Z Aug 1 NN NN
So in other words, for the blanks that SHOULD be blank because a file is not expected, replace that value with "Not Needed", while leaving the other blanks alone.
I have tried doing this with .replace(), .apply() with functions, and I am not having any success.
The code below sort of works, but it works not only when there is a match, but even when there is not a match.
Fill in descriptive text for scales not collected at certain visits (where upload dates would be blank)
df_combined['FAQ-Audio-upDate'] = np.where(df_combined['VisitName'] == "Screening", "FAQ Not Expected", "")
df_combined['FAQ-Form-upDate'] = np.where(df_combined['VisitName'] == "Screening", "FAQ Not Expected", "")
How can I change the value in one column based on the value in another column, across the entire dataframe? What I want is basically this:
For every row in the dataframe
If the value in the VisitName column == X
Change the value in ColumnA to "Not Expected"
Thank you!!
A: So, I can answer your base question pretty easily, but there's a couple of style things I think you might want to change that I'd like to get into. I'm fairly certain this question has been addressed in other threads, but you've got a couple of problems wrapped up in 1 so I'm just going to address them here
For every row in the dataframe If the value in the VisitName column == X Change the value in ColumnA to "Not Expected"
You want to be using index slices to set values. Get a boolean mask of the dataframe based on the logic you want, use that to create a new dataframe containing only the rows that you want to update, get the index of this new dataframe, and use this index with the original dataframe to change the values over.
import pandas as pd
df = pd.DataFrame(data=None, index=["X", "Y", "Z"], columns=["VisitName",
"ColumnA", "ColumnB"])
not_expected_index = df[df.loc[:, "VisitName"] == "X"].index
df.loc[not_expected_index, "ColumnA"] = "Not Expected"
This is the preferred way in pandas to change values in a DataFrame based on other values in another column.
Now, there's a couple of things about the original DataFrame you posted that I'd like to mention.
First, if you already have Null values in the dataframe cells, then you can use the pandas dataframe fillna method to populate these values.
df.fillna("Not Expected")
Second, why do you want to use the string "NN" or "Not Needed" over the default Null value? For any operations within pandas, I prefer to stick with the actual null values, so that you can use aggregation functions like sum or count freely on dataframes with null values.
Second, the index contains repeated values:
df.index = ["X", "X", "Y", "Z", "X", "Z"]
Dataframes will allow duplicate index values, but they can behave in funny ways that you need to be aware of.
For example:
print(df)
returns
VisitName ColumnA ColumnB
X NaN NaN NaN
X NaN NaN NaN
Y NaN NaN NaN
Z NaN NaN NaN
X NaN NaN NaN
Z NaN NaN NaN
setting a value in VisitName for X
df.loc["X", "VisitName"] = "test"
returns
VisitName ColumnA ColumnB
X "test" NaN NaN
X "test" NaN NaN
Y NaN NaN NaN
Z NaN NaN NaN
X "test" NaN NaN
Z NaN NaN NaN
If I were tackling this problem, I'd either use the date as the index, with a True or False value in a file's column depending on whether it needs to be sent or not on that date,
index File1 File2 File3
8/01/17 True False True
8/08/17 False True True
8/15/17 True True False
8/24/17 False True False
9/01/17 False False False
9/12/17 True False True
or I'd just use an integer index, with a column for the date and a column for what file is being sent.
index date file
0 8/01/17 1
1 8/01/17 2
2 8/08/17 2
3 8/15/17 1
4 8/15/17 2
5 8/15/17 3
I mean, if you're locked into using the other setup, that's fine, but I think these would be easier dataframe setups to work with, since they'd support groupby methods more easily.
Also, keep in mind that if you're using a for loop, then you might as well not be using pandas. The whole point of pandas is that it uses C to speed up index operations. Never use
for row in df.index:
df.loc[row, 'columna'] += 2.
Always use
df.loc[:, 'columna'] += 2.
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A DAVID FICKLING BOOK
This is a work of fiction. Names, characters, places, and incidents either are the product of the author's imagination or are used fictitiously. Any resemblance to actual persons, living or dead, events, or locales is entirely coincidental.
Text copyright © 2010 by Andrew Mulligan
All rights reserved. Published in the United States by David Fickling Books, an imprint of Random House Children's Books, a division of Random House, Inc., New York.
David Fickling Books and the colophon are trademarks of David Fickling.
Visit us on the Web
Educators and librarians, for a variety of teaching tools, visit us at www.randomhouse.com/teachers
_Library of Congress Cataloging-in-Publication Data_
Mulligan, Andy.
Trash / Andy Mulligan. — 1st American ed.
p. cm.
Summary: Fourteen-year-olds Raphael and Gardo team up with a younger boy, Rat, to figure out the mysteries surrounding a bag Raphael finds during their daily life of sorting through trash in a third-world country's dump.
eISBN: 978-0-375-89843-3
[1. Mystery and detective stories. 2. Poverty—Fiction. 3. Refuse and refuse disposal—Fiction. 4. Developing countries—Fiction. 5. Political corruption—Fiction.] I. Title.
PZ7.M918454Tr 2010
[Fic]—dc22
2010015940
Random House Children's Books supports the First Amendment and celebrates the right to read.
v3.1_r2
# Contents
_Cover_
_Title Page_
_Copyright_
Part One
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Part Two
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Part Three
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Part Four
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Part Five
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Appendix
A Note from the Author: What is a book-code?
_Acknowledgements_
_About the Author_
# PART ONE
# 1
My name is Raphael Fernández and I am a dumpsite boy.
People say to me, 'I guess you just never know what you'll find, sifting through rubbish! Today could be your lucky day.' I say to them, 'Friend, I think I know what I find.' And I know what everyone finds, because I know what we've been finding for all the years I've been working, which is eleven years. It's the one word: _stuppa_ , which means – and I'm sorry if I offend – it's our word for human muck. I don't want to upset anyone, that's not my business here. But there's a lot of things hard to come by in our sweet city, and one of the things too many people don't have is toilets and running water. So when they have to go, they do it where they can. Most of those people live in boxes, and the boxes are stacked up tall and high. So, when you use the toilet, you do it on a piece of paper, and you wrap it up and put it in the trash. The trash bags come together. All over the city, trash bags get loaded onto carts, and from carts onto trucks or even trains – you'd be amazed at how much trash this city makes. Piles and piles of it, and it all ends up here with us. The trucks and trains never stop, and nor do we. Crawl and crawl, and sort and sort.
It's a place they call Behala, and it's rubbish-town. Three years ago it was Smoky Mountain, but Smoky Mountain got so bad they closed it down and shifted us along the road. The piles stack up – and I mean Himalayas: you could climb for ever, and many people do... up and down, into the valleys. The mountains go right from the docks to the marshes, one whole long world of steaming trash. I am one of the rubbish boys, picking through the stuff this city throws away.
'But you must find interesting things?' someone said to me. 'Sometimes, no?'
We get visitors, you see. It's mainly foreigners visiting the Mission School, which they set up years ago and just about stays open. I always smile, and I say, 'Sometimes, sir! Sometimes, ma'am!'
What I really mean is, _No, never – because what we mainly find is stupp_.
'What you got there?' I say to Gardo.
'What d'you think, boy?' says Gardo.
And I know. The interesting parcel that looked like something nice wrapped up? What a surprise! It's stupp, and Gardo's picking his way on, wiping his hands on his shirt and hoping to find something we can sell. All day, sun or rain, over the hills we go.
You want to come see? Well, you can smell Behala long before you see it. It must be about two hundred football pitches big, or maybe a thousand basketball courts – I don't know: it seems to go on for ever. Nor do I know how much of it is stupp, but on a bad day it seems like most of it, and to spend your life wading through it, breathing it, sleeping beside it – well... maybe one day you'll find 'something nice'. Oh yes.
Then one day I did.
I was a trash boy since I was old enough to move without help and pick things up. That was what? – three years old, and I was sorting.
Let me tell you what we're looking for.
Plastic, because plastic can be turned into cash, fast – by the kilo. White plastic is best, and that goes in one pile; blue in the next.
Paper, if it's white and clean – that means if we can clean it and dry it. Cardboard also.
Tin cans – anything metal. Glass, if it's a bottle. Cloth or rags of any kind – that means the occasional T-shirt, a pair of pants, a bit of sack that wrapped something up. The kids round here, half the stuff we wear is what we found, but most we pile up, weigh and sell. You should see me, dressed to kill. I wear a pair of hacked-off jeans and a too-big T-shirt that I can roll up onto my head when the sun gets bad. I don't wear shoes – one, because I don't have any, and two, because you need to feel with your feet. The Mission School had a big push on getting us boots, but most of the kids sold them on. The trash is soft, and our feet are hard as hooves.
Rubber is good. Just last week we got a freak delivery of old tyres from somewhere. Snapped up in minutes, they were, the men getting in first and driving us off. A half-good tyre can fetch half a dollar, and a dead tyre holds down the roof of your house. We get the fast food too, and that's a little business in itself. It doesn't come near me and Gardo, it goes down the far end, and about a hundred kids sort out the straws, the cups and the chicken bones. Everything turned, cleaned and bagged up – cycled down to the weighers, weighed and sold. Onto the trucks that take it back to the city, round it goes. On a good day I'll make two hundred pesos. On a bad, maybe fifty? So you live day to day and hope you don't get sick. Your life is the hook you carry, there in your hand, turning the trash.
'What's that you got, Gardo?'
'Stupp. What about you?'
Turn over the paper. 'Stupp.'
I have to say, though: I'm a trash boy with style. I work with Gardo most of the time, and between us we move fast. Some of the little kids and the old people just poke and poke, like everything's got to be turned over – but among the stupp, I can pull out the paper and plastic fast, so I don't do so bad. Gardo's my partner, and we always work together. He looks after me.
# 2
So where do we start?
My unlucky-lucky day, the day the world turned upside down? That was a Thursday. Me and Gardo were up by one of the crane-belts. These things are huge, on twelve big wheels that go up and down the hills. They take in the trash and push it up so high you can hardly see it, then tip it out again. They handle the new stuff, and you're not supposed to work there because it's dangerous. You're working under the trash as it's raining down, and the guards try to get you away. But if you want to be first in line – if you can't get right inside the truck, and that is _very_ dangerous: I knew a boy lost an arm that way – then it's worth going up by the belt. The trucks unload, the bulldozers roll it all to the belts, and up it comes to you, sitting at the top of the mountain.
That's where we are, with a view of the sea.
Gardo's fourteen, same as me. He's thin as a whip, with long arms. He was born seven hours ahead of me, onto the same sheet, so people say. He's not my brother but he might as well be, because he always knows what I'm thinking, feeling – even what I'm about to say. The fact that he's older means he pushes me around now and then, tells me what to do, and most of the time I let him. People say he's too serious, a boy without a smile, and he says, 'So show me something to smile at.' He can be mean, it's true – but then again he's taken more beatings than me so maybe he's grown up faster. One thing I know is I'd want him on my side, always.
We were working together, and the bags were coming down – some of them already torn, some of them not – and that's when I found a 'special'. A special is a bag of trash, unsplit, from a rich area, and you always keep your eyes wide for one of them. I can remember even now what we got. Cigarette carton, with a cigarette inside – that's a bonus. A zucchini that was fresh enough for stew, and then a load of beaten-up tin cans. A pen, probably no good, and pens are easy to come by, and some dry papers I could stick straight in my sack – then trash and trash, like old food and a broken mirror or something, and then, falling into my hand... I know I said you don't find interesting things, but, OK – once in your life...
It fell into my hand: a small leather bag, zipped up tight and covered in coffee-grounds. Unzipping it, I found a wallet. Next to that, a folded-up map – and inside the map, a key. Gardo came right over, and we squatted there together, up on the hill. My fingers were trembling, because the wallet was fat. There were eleven hundred pesos inside, and that – let me tell you – is good money. A chicken costs one-eighty, a beer is fifteen. One hour in the video hall, twenty-five.
I sat there laughing and saying a prayer. Gardo was punching me, and I don't mind telling you, we almost danced. I gave him five hundred, which was fair because I was the one who found it. Six hundred left for me. We looked to see what else there was, but it was just a few old papers, photos, and – interesting... an ID card. A little battered and creased, but you could make him out easy enough. A man, staring up at us, right into the camera, with those frightened eyes you always have when the camera flashes. Name? José Angelico. Age? Thirty-three years old, employed as a houseboy. Unmarried and living out somewhere called Green Hills – not a rich man, and that makes you sad. But what do you do? Find him in the city and say, 'Mr Angelico, sir – we'd like to return your property'?
Two little photos of a girl in school dress. Hard to say how old, but I reckoned seven or eight, with long dark hair and beautiful eyes. Serious face, like Gardo's – as if no one had told her to smile.
We looked at the key then. It had a little tag made of yellow plastic. There was a number on both sides: 101.
The map was just a map of the city.
I took it all away and slipped it down my shorts – then we kept on sorting. You don't want to draw attention to yourself, or you can lose what you find. But I was excited. We were both excited, and we were right to be, because that bag changed everything. A long time later I would think to myself: _Everyone needs a key_.
With the right key, you can bust the door wide open. Because nobody's going to open it for you.
# 3
Raphael still!
I'll hand on to Gardo after this – after the evening.
You see, just after dark I realized I had something very, very, very important, because the police arrived and asked for it back.
You don't see many police in Behala, because in a shanty you sort out your own problems. There's not a lot to steal, and we don't usually steal from each other – though it happens. We had a murder a few months ago, and the police came then. An old man killed his wife – slit her throat and left her bleeding down the walls to the shack underneath. By the time they came he'd run and we never heard whether they got him. We had four police cars come on an election visit, surrounding a man who wanted to be mayor – lights flashing and radios crackling away, because they all love a show, these police. Otherwise, they have better things to do.
This time it was five men, one of them looking very important, like a senior officer – older man, fatter man. More of a boxer, with a smashed-up nose, no hair, and a mean look.
The sun had gone down. There was a cooking fire, where my auntie was boiling up the rice, and tonight – on account of the money I'd found – we were having that precious one-eighty chicken. About thirty of us were gathered – not all to eat one chicken! That was just for the family. But it's hot in the evenings, so people are out squatting, standing, roaming.
I think Gardo had a ball and we'd been fooling around under the hoop. Now we all stood still in the headlights of this big black four-wheel-drive, and the men got out.
The boxer cop had a quick chat with Thomas, who's the main man in our little patch, and then he was talking to all of us.
'A friend of ours has a problem,' he said. Voice like a megaphone. 'It's a pretty big problem, and we're hoping you can help. Fact is, he's lost something important. We're giving good money to anyone who finds it. Another fact is, if anyone here finds it, we're going to give a thousand pesos to every family in Behala, you understand? That is how important it is to our friend. And we're giving ten thou to you – to the one who actually puts it in my hand.'
'What have you lost?' said a man.
'We've lost... a bag,' said the policeman, and my skin went dry and cold, but I managed not to show it. He turned and took something from the man behind him, and held it up. It was a handbag made of black plastic, big as my hand. 'It probably looks like this,' he said. 'Bit bigger, bit smaller – not exactly the same, but similar. We think this bag might have something important in it that's going to help us solve a crime.'
'When did you lose it?' said someone.
'Last night,' said the policeman. 'It was put in the trash by mistake. Out on McKinley Hill, somewhere round there. And the truck picked up all the McKinley trash this morning. That means it's either here right now, or coming in tomorrow.' He watched us, and we watched him.
'Has anyone found a bag?'
I could feel Gardo's eyes fixed on me.
I so nearly raised my hand. I so nearly spoke up then and there, because ten thousand is good money. And a thousand to every family? That's what they were promising, and if they gave it, oh my! I'd be the most popular boy in the neighbourhood. But I didn't, because I was also thinking fast, thinking that I could as well give it up in the morning as now. I better be clear: I'd never had any trouble with the police before then, so it wasn't that I didn't like them or didn't want to be helpful. But everyone knows not to trust too far. What if they just took it and drove off laughing? What was I going to do to stop them? I needed time to think, so I stood there, dumb. Maybe there was a bit of calculation going on as well. If they had money to give away, then they could be raised up over ten, and we could get it all up front. If it was precious enough for them to come all this way out to see us, then perhaps ten thousand would turn into twenty?
My auntie said, 'Raphael found something, sir.'
She nodded, and all the police were looking straight at me.
'What did you find?' said the boss.
'I didn't find a bag, sir,' I said.
'What did you find?'
'I found a... shoe.'
Somebody laughed.
'What kind of shoe? One shoe? When was this?'
'One shoe, sir – just a lady's shoe. I can get it – it's in my house.'
'What makes you think we're going to be interested in that? You playing games?'
He was looking back at my auntie, and her eyes were back on the rice, then on me, then on the rice.
'He said he found something,' she said. 'He never said what he found. Just trying to be helpful, sir.'
The cop in charge spoke loudly. 'Listen. We're going to be back here in the morning,' he said. 'We are going to pay anyone who wants work. One day, one week – however long it takes. We need to find that bag, and we'll pay to find it.'
One of the other policemen walked over to me, quite a young man. Gardo was right next to me then, and the policeman put his hand under my chin and tilted my head up. I looked into his eyes, trying so hard not to look scared. He was smiling, but I was glad to feel Gardo right up against me, and I smiled back as best I could.
'What's your name?' he said.
I told him.
'Brothers? Sisters? This your brother?'
'My best friend, sir. This is Gardo.'
'Where do you live, son?'
I told him everything, fast and happy, smiling hard – and I watched him fix our house in his mind, and then fix my face. He rubbed my ear gently, like I was a kid. He said: 'You gonna help us tomorrow, Raphael? How old are you?'
'Fourteen, sir.' I know I look younger.
'Where's your father?'
'No father, sir.'
'That was your ma?'
'Auntie.'
'You want work, Raphael? You gonna help?'
'Sure,' I said. 'How much are you paying? I'll work for ever!' I made my smile bigger and my eyes wider, trying just to be an excited, harmless, cute little trash boy.
'One hundred,' he said. 'One hundred for the day, but if you find that bag...'
'I wanna help too,' said Gardo, pretending to be eight years old and showing his teeth. 'What's in the bag, sir? More money?'
'Bits and pieces. Nothing valuable, but—'
'What kind of crime?' I said. 'How's it gonna help you solve a crime? Is it a murder?'
The policeman smiled at me some more. He looked at Gardo too. 'I don't even think it will,' he said. 'But we got to give it our best shot.' He was looking at me hard again, and Gardo's arm was right round me. 'I'll see you tomorrow.'
Then the policemen climbed back into their car and drove on, and we made sure we stood right up close to show we weren't afraid, and we made sure we ran with the car and waved. Now, Behala's full of little neighbourhoods just like ours. The shacks we live in grow up out of the trash piles, bamboo and string, piled upwards – it's like little villages in amongst the hills. We watched the car, rocking over the ruts and holes, the lights going up and down. If they wanted to talk to everyone, they'd have to make the same speech ten times.
Later on, my auntie came close and said, 'Why are you telling lies, Raphael Fernández?'
'I found a wallet,' I said. 'I gave you what I found – why did you say that to them?'
She came close and she spoke quietly. 'You found the bag, didn't you? You tell me now.'
'No,' I said. 'I found money.'
'Why did you say a shoe? Why did you not tell the truth?'
I shrugged, and tried to be sly. 'Ma, I thought they might want the wallet back,' I said.
'Money in a wallet? Where's the wallet now?'
'I'm going to get it! I just didn't want to speak up in front of everyone, everyone looking right at me, and—'
'You found the wallet in a bag? You can't lie to me.'
'No!' I said. 'No.'
She looked at me hard again, and shook her head. 'You gonna get us into a lot of trouble, I think. Whose wallet was it? People always have a name, and if you—'
'I just took the money,' I said. 'I'll throw the damn thing away right now.'
'You give it to the police.'
'Why? It's not what they're looking for, Ma. I didn't find a bag.'
'Oh, boy,' she said. 'Raphael. What I'm thinking is, if they're throwing money around to get that something back, you don't want to be caught messing about with it. I am serious, Raphael. If you found anything like the thing they're wanting, you need to give it up – first thing in the morning, when they're back.'
Gardo ate with us. He often did, just as I often ate with him and his uncle. I spent the night at his, just as he spent the night at ours – I'd wake up forgetting which place I was in and who was under the blanket with me. Anyway, just as we finished, the police car came back, big and black, and drove right out of the gates.
We watched it go.
I couldn't believe Auntie had said what she said. I knew she'd had problems with the police before, on account of my father, and I guess she had some feeling, even then, that things were going to get complicated. I think she wanted to stop it all there, all at once – but I still say she was wrong. It was one of the things that made leaving easier.
I went up to my house, Gardo following. We live high, compared to many. Two rooms built out of truck pallets, with plastic and canvas holding it fast, and it's stacked over three families below. You go up three stepladders to get to it. First, the bit where Auntie and my half-sister sleep, and beyond that's another little box, about the size of a sheet. That's where me and my cousins go, and Gardo too when he's with us. My cousins were in there now, snoring away, and all around was the noise of neighbours' chatter and laughter, and radios, and someone calling.
I moved one of the cousins along, and we got close in to the side, where I store my things. It's a crate that beer came in, and it's up on one side. I've got a spare pair of shorts, another two T-shirts and a pair of slippers. I've also got my little spread of treasures, like all the boys do. With me it's a penknife I found, with a broken blade – still a good little tool. I've got a cup with a picture of the Virgin Mary. I've got a watch that doesn't go. I've got a little plastic duck, which the cousins play with, and I've got one pair of jeans. The jeans were wrapping up the precious bag, and it felt dangerous just to be unwrapping it.
Gardo held a candle close and sat hunched, watching me. We were both bending over it. When I glanced up at him, his lips were thin. The whites of his eyes stood out like a pair of eggs.
'We gotta move it,' he said. 'You can't leave it here, boy.'
'I think you're right,' I said. 'Where to?'
He paused.
I pulled out the ID and looked at the man. José Angelico, looking back at me sadly. And his little girl, more serious. 'What do you think he's done?' I said.
'Something bad,' said Gardo. 'And when they come back, I think they going to talk to you again... You see the way that guy was looking at you?'
I nodded.
'You see the way he was touching you? He's got you fixed.'
'I know,' I said. 'You too, maybe.' I laughed. 'You think he wants to be our special friend?'
'This isn't funny,' said Gardo. 'We need Rat.'
'Why Rat?'
'I'm thinking it's about the only place they're not gonna look.'
'You think he'll take it, though? Rat's not stupid.'
'Give him ten, he'll take it. Break his arms if he doesn't.' Gardo took the ID and put it away. 'They won't go down there, the police – they won't even see him.'
I knew it was a good plan. I knew it was the only plan as well, because we had to get it out of the house.
'Do it now?' I said.
Gardo nodded.
'Don't threaten him, though,' I said. 'He'll do it for me.'
# 4
Still Raphael.
So sorry, but I want to tell about Rat, and then I will hand over.
Rat is a boy – three or four years younger than me. His real name is Jun-Jun. Nobody called him that, though, because he lived with the rats and had come to look like one. He was the only kid in Behala that I knew of who had no family at all, and at that time I didn't know too much about his past. There were plenty of boys without fathers, and a lot like me without mothers either. But if you had no parents, you had aunties or uncles, or older brothers, or cousins, and so there was always somebody who would take care of you and give you a bit of the mat to sleep on, and a plate of rice. The thing about Rat was, he had nobody, because he'd come from some place way out of the city – and if it hadn't been for the Mission School he'd have been dead.
Gardo and I went back down the ladders with the candles. I'd put the bag under my T-shirt, and tried to hold my arms so it wasn't too obvious – but it was as if people didn't want to see me anyway. Auntie especially was looking away, and shifted so she had her back to us both. We crossed the roadway and were soon deep in amongst the trash.
I better say, the trash is alive at night: that's when the rats come out strong. During the day you don't see so many, and they stay out of your path. You get a surprise now and then when one jumps up, and sometimes you get a good kick and send one spinning. Not often, though. They're quick, and they can dive, jump, fly and squirm their way out of anywhere.
I followed Gardo, and on either side I was aware of the little grey movements. There is light over Behala, because some of the trucks come at night – they've rigged up big floodlights, and they're usually on. We'd gone left, right, over the little canal that just about gets through, stinking of the dead – and then off we went into a lane only the trash people use – no trucks, and not even many people. It was dead trash underfoot, and it was damp – you were up to your knees. Soon we came to one of the old belt-machines, but this one was disused and rotting. The belt itself had been stripped out, and the wooden panels had been taken. It was just a huge metal frame, rusting away. The arm that held the belt pointed up into the sky like a big finger, and now and then kids would climb it and sit in the breeze. At ground level, its legs were sunk into concrete piles, and underneath the legs was a hole.
I suppose machinery must have been down there at one time, because there were steps down, and they were slimy. Trash is often wet, and the juices are always running. Maybe the ground here was a bit lower, I don't know – but it was always muddy.
We stopped at the top of the steps, and I called out: 'Rat!'
I called quite soft – I didn't want anyone to know what we were doing, or where we were. The problem was, the kid couldn't hear me if he was down there, and I was pretty sure he would be. Where else would he be?
'Hey, Rat!' I called again. I could hear the little cheeps and squeaks. Gardo was following me now, because even though he's braver than me and stronger, he's not easy with rats. I'll kill one with my foot, but Gardo got bitten badly a while ago, and his whole hand went bad. He'll kill them, but he'd rather stay away from them. I was halfway down the steps, and a little one streaked up past me, then another.
'Rat!' I called, and my voice echoed in the machine-chamber. I got down low with the candle, trying not to breathe too deep because of the stink – and I heard him turn in his bed.
'What?' he said. He's got a high little voice. 'Who is that?'
'Raphael and Gardo. We got a favour to ask you. Can we come in?'
'Yes.'
It might seem crazy asking a kid if you can come into his hole, but this hole was about the only thing Rat had, apart from what he wore. I would not have lived there – anywhere would have been better. For a start it was damp and dark. For another thing, I would have been scared that the trash above would fall and pile up down the stairs, trapping me, like it did on Smoky Mountain. These mountains do move. It's not us climbing about on them that makes them fall, it's usually just their own weight as the belts pile more and more stuff on. You can get caught in a fall, and it's heavy stuff. I've never known anyone killed, but one kid broke bones, falling badly. When Smoky went down, there were nearly a hundred killed, and everyone knows some of those poor souls are still down there, down with the trash, turned into trash, rotting with the trash.
Anyway, I got to the last step, trying not to think of all that, and put my candle low. There was a sudden flicker of black, and another rat – this one big as they come – shot past me, right over my shoulder.
The kid was sitting up, just in his shorts, gazing at me with frightened eyes and his big broken teeth sticking out of his mouth.
'Raphael?' he said. 'What do you want?'
I thought, I should have brought him a bit of food. He goes hungrier than most, and his face is pinched. Kids used to call him Monkey Boy before Rat, because his face does have that wide-eyed, staring look that little monkeys have. He was sitting on some layers of cardboard, and around him there were piles of rubbish that he must have been sorting. The walls and ceiling were damp brick, and there were cracks everywhere. That was where the rats came in and out, and I guessed there were nests just the other side. He had arms skinny as pencils, and Gardo's crack about breaking them had made me smile. You could break Jun's arms with your finger and thumb. He was a spider, not a rat.
'We need your help,' I said.
'That's OK.'
'You don't know what we want,' said Gardo. 'How's it OK already?'
'It's OK.' The boy smiled, and his teeth gleamed out crookedly. He blinked. He has a twitch, and when he's scared, his whole head starts to shake. He wasn't scared right now, though – he was more interested. Also, I know he liked me. I wouldn't say he and I were friends, not at all. But I didn't mind working next to him, which meant we'd talk a bit, and I'd listen to his chit-chat-singing. A lot of kids would just throw things at him and laugh.
I sat down, but Gardo stayed on the step, squatting. 'You gotta hide something,' I said. I put the bag on the cardboard, and put my candle next to it. He found another and lit it, and all three of us sat in silence.
'OK,' he said. 'What's in it? Who's it belong to?' He had a thin, breathy little voice like he was six years old.
I opened the flap and unzipped it. I took out the items and laid them down. The wallet. The key. The map.
'You happy to hide it? You didn't hear the police come, did you?'
'I didn't see any police,' said Rat. 'But I can hide it if you want. See that brick? That comes right out, and the next one too. Won't last long, though – it's gonna get eaten, OK?'
'Wait,' said Gardo. 'I'm thinking about this. It's not the bag they want, is it? It's what's in the bag.'
'We've still got to hide it,' I said.
'Why don't we just sling it?'
'If we sling it,' I said, 'and they find it... then they'll know someone's got what's inside, maybe. If they know what they're looking for.'
'Who's looking?' said Rat. 'What did the police want?'
I told him quickly, and his eyes widened. 'Ten thousand, Raphael!' he said. 'You're crazy! Give it in and get the cash.'
'Oh yes,' said Gardo, sneering. 'You really think they'll give it? You taken in by that? And if they do, boy – you think he'll hold onto ten thousand?'
Rat looked from me to Gardo and back again.
'Look,' I said. 'We've got to hide it. They come back tomorrow – they say they're going to pay everyone to work. We all get a few days' work, maybe – give it up next week.'
'Everyone's happy,' said Rat. 'That's a good idea, maybe. But you got to ask, why do they want it so bad, OK? How much was in this?' His thin fingers opened the wallet and pulled out the ID card.
'Eleven hundred,' I said.
He smiled right at me. 'Anything for using my house?'
'I'll give you fifty,' I said, and he grinned even wider and touched my arm.
'You promise, OK? That's a promise?'
'Promise.'
His hands went to the map. 'We ought to find out what they want,' he said. 'What is this – buried treasure?'
'There's nothing on it,' I said. 'It's just a city map.'
He looked harder at the ID then, staring at the photograph. 'Who is this?'
'José Angelico,' I said.
I knew Rat couldn't read. He turned the paper over and over, looking at the face.
'José Angelico,' he said slowly. 'You think the police want him? You think he's a wanted man? He looks nice enough. This his little girl?'
He was looking at the child, putting the faces next to each other.
'Maybe,' I said. 'I don't know.'
'He's rich enough to send her to school,' said Rat. 'That's a school dress.'
'What if he's been murdered?' said Gardo. 'Maybe they're looking for his body – looking for the murderers too. This could be part of something bad.'
'Who lost the bag, though?' I said. 'How do you lose a bag in the trash?'
'Not by accident,' said Rat. He was staring at the photos again. 'We ought to find out who he is, OK? He might give more than the police.'
'And what's the key?' said Gardo, pointing to it. 'That's his house key, maybe. Maybe he's locked out of his house? Find out where he lives—'
'Oh no, that's not a house key,' said Rat, staring. He hadn't noticed the key in the darkness. Now he picked it up and put it next to my candle. He looked up at me again. 'Oh my. You don't know what that is, do you?'
'Could be to a safe,' I said. 'What is it, a padlock key? What's the one-oh-one?'
'You don't know what that is!' said Rat slowly. He was teasing us. 'I do. I'll raise you to a hundred.'
'What?'
He was smiling wider than I'd ever seen him smile, and his broken teeth stuck out like straws. 'I've seen these so many times, OK – I can tell you exactly what it is and where it is. You give me that fifty? Now? Make it a hundred, or you get no further.'
'You know what it is? Really?'
Rat nodded.
I pulled out some notes, and counted them out on the cardboard. There was a skittering of feet behind the wall, and I heard something running right round the little room, surrounding us. There were squeakings again: the place was alive. Gardo and I sat on, looking at Rat, waiting for his great piece of information.
'Central Station,' he said softly. 'I lived there nearly a year, when I came in first of all. I can tell you for sure: this is a locker key for the left luggage. Just outside platform four, last block on the right. One-oh-one's small, up at the top – the cheapest they do. This man's left something there.'
He smiled again and we sat there, just looking at each other. Gardo whistled, and I felt my heart beat faster and faster.
'You wanna go there?' said Rat. 'We go there now if you want.'
# 5
Gardo here, and I take the story on from Raphael.
We agreed to split the story because some things he forgets – like he wanted to go to the station that night, right then, and then the next day, like a little kid. He got so excited thinking about what he might find, I had to say no about ten times, because one thing I knew was that we had to be there, in Behala, for the big search – especially if the policemen who talked to us were there.
I had to get a hold of his hair and I said, 'How is it going to look when everyone is there to earn money, and the boy they know found something – maybe a shoe, or maybe something else – doesn't show?'
Raphael is my best friend but he's like a kid, always laughing, playing, thinking everything's fun, thinking it's a game – so I said they have to see us working and looking, and that way maybe they leave us alone: and so we waited.
Next morning, like I said, the whole of Behala turns out, early and ready, before dawn. Like Raphael said, we get money for what we can sell, hand to mouth, so getting paid for the day is like a dream, and there were way too many pickers – I guess people had told people, and there were crowds of us, all piling in. Then the police arrived early also, and even as the sun came up, everyone was way up on the trash – men, women and every damn kid, even the tiny ones – earning their precious hundred, some without even hooks, just using hands – in fact, there were so many of us, it was dangerous, and you could feel the trash sliding about, and there was no room to throw the stuff you'd sorted.
I was hooking stuff up, scratching other people almost, and it was more and more dangerous, so after one hour all us kids were ordered off, and just the men stayed on, and the trash was being gone through again – right by where we'd been the previous day. The managers were there, talking to the police, shouting up to the men – and it was all being picked over and over, again and again. But nothing was coming up.
All the while, more cars – police car, then another police car, then a police truck, motorbikes, more police cars, and then big cars like government cars – and men in suits as well as police, getting out and their nice shoes getting wet and filthy. And it's still not seven o'clock and you can't move for the cars and people, like it's a festival.
No belts were working, as they turned them all off.
Things get worse.
Soon we can see the line of trucks coming in is stretching right back through the gates and down the road, waiting to unload: after just one hour I'd counted twenty-six. The drivers didn't even care at first – they squatted in the shade, and some boys went off to get them tea and cigarettes. There were kids jumping into the trucks then, and picking there, on the roadside, but me and Raphael stayed down, listening around for more 'information', me wondering all the time where this was going to end – knowing, because I knew, that people were going to be angry soon, and it would be these police losing patience first. When the police get mean, you don't want to be around. On the other hand, I did not want Raphael hiding and drawing attention that way, so that was why I kept him right in the middle of it.
One man had a box with a great wad of notes in it, and he'd shown it around to prove we'd all be paid. I overheard another one talking, and I worked out what was happening – they were using their brains. Somehow they knew the bag had been lost in this place called McKinley – which is a rich area – so it wasn't hard to trace the trucks that look after that neighbourhood. Now, the McKinley trucks had made one visit yesterday, which is how we found what we found – and more were coming in again today. So, for today's trucks, all the police had to do was get them to drop the loads on a clear patch of ground, and we could pick over it easy, in an hour.
Sure enough, just before noon they brought up the three special McKinley trucks and they dropped their loads, and they kept us all back, so we were all just looking at it. I said to Raphael then, turning him round so no one saw: 'Are you still sure, friend?'
He was looking scared because I think he was just beginning to realize how big this must be.
He said, very soft, 'I'm more sure than ever, Gardo,' so I stayed close.
We tried to look just happy and excited then, because the last thing I wanted was for anyone to think we were suspicious or scared or worried or hiding something – but I was frightened too, and I grabbed Raphael and made sure we joined in the pushing and shoving, like we hadn't a care in the world. When we saw Rat, we waved: he was squatting close by, smoking, and he would look over at me sometimes, but nobody looked at him, because Rat is grey as trash, and he has only the clothes he wears, which are so filthy he can move around and no one sees him.
After a while the police gathered all us kids together and got us working – they'd got extra hooks from somewhere, and as we were on level ground it wasn't a hard job: we just ripped and ripped, and spread it all out.
There were about a hundred of us.
The people in McKinley have toilets, so there wasn't any stupp – McKinley trash is good-quality trash: food, newspaper, a lot of plastic and glass, but the police wouldn't let us take anything, because as far as they were concerned, we were looking for just one thing.
Then someone found a handbag, and there was real excitement, lots of shouting: it was blue, and old, with one stringy little handle, so it was thrown back, everyone very disappointed, and the police just watched us work, looking grim and their patience running out.
By mid-afternoon, I guess, we'd finished, and I don't think a pile of rubbish had ever got a better looking at: the men on the trash piles had finished as well, and everyone was ordered down. Of course, we all would have worked for the rest of the day, and the rest of the week – we were hoping to string it out and get five hundred out of it – but the police were smart, and could see that even in a mountain of rubbish, you can pick through what's up top pretty fast, and you can see what's new and what isn't.
I saw the boxer policeman was back – the big guy who'd made the speech yesterday – and he was talking it all over with the site managers and two men in suits by one of the big black cars. There was a lot of arguing going on, a lot of calls being made, and I could see the managers weren't happy – I think because the line of loaded trucks was getting longer and longer, and the drivers were finally getting itchy, drinking tea all day and not knowing when they were going home. And you could see what the problem was: if the police allowed these trucks to unload new, fresh trash, the precious bag was going to be buried even further down, if it was there. But on the other hand, this was the city dumpsite, and how long can you close down a dump when all these millions of people are sending stuff to it? How long before the city stops?
But what must have been burning them up was that no one could be sure the bag had ever got here. After all, kids go through the trash straight out of the bins, in McKinley same as everywhere. Sometimes you see them in the street, sorting on the pavements. Also, like I said, kids get up inside the carts before they've even reached the dump – so they could not know the bag had even got to the dumpsite. It was strange to think there were just three boys in the world who knew exactly where it was.
We all sat around.
Money got paid out at last, and everyone was one hundred pesos richer. It was getting dark, the sky red all over, and the police finally gave up and started leaving, me and Raphael smiling. Then all the belts started with a sound that splits your ears, and the trucks started crawling through again, and they brought out more lights and worked on and on, right through until the morning.
In our little neighbourhood there were more cooking fires than usual, and a few cases of beer. There was music and singing, and everyone was happy – most of all Raphael, who thinks the job is done and he's been so smart.
But inside Raphael's house, right by me – because I was staying close now – after the food, his auntie says to both of us: 'Are we safe?'
I knew she wasn't, and I also knew she'd brought it on herself. Opening her mouth had not been smart – in fact, I hate to say it, but we talked about it since: if she had kept her mouth shut, things would have been so much easier. 'Are we safe?' she said again.
I said, 'We are completely safe. Don't worry,' which was a lie.
'I was spoken to,' she said to me. 'They wanted to know why I said he found something. A policeman asked me about it again, and I shouldn't have spoken, but I did. Now they're wondering about both of you. They got both your names.'
'Yes, but we told them,' said Raphael, doing his smile and pushing back his hair, 'it was just a shoe, and they know nothing.'
She was quiet, but only for a moment.
'I saw you go out last night,' she said, very soft like you could hardly hear, so we were huddling close. 'I don't want to know where, I don't want to know why, but I just want to know we're safe. There's nothing in the house, is there?'
We both said: 'No.'
'You promise me that? Because they will take these houses apart—'
'I promise,' said Raphael, so light and bright. All I could think about was the lies, stacking up now, and how I hoped it was worth it. The bag was safe, down with Rat – I wanted to get away and check it.
Raphael's auntie kept at him, though: 'They're talking about searching here,' she said. 'That's what people say. Ours will be the first, you can bet on that. If they take it apart again—'
Raphael took her hand then: 'There's nothing in the house,' he said.
'Ten thousand is a lot of money!' she said, and her voice rose up. 'Have you thought what we could do with that?'
I interrupted then. 'You think they'd give it?' I said. 'You really think they'd give it?'
'I think they would!' she said.
Raphael shook her hand gently. 'Ma,' he said. 'Ma. If someone here – one of us – if one of us got all that money, you think we'd be allowed to keep it for long?'
She reached out to me then, and took hold of my arm, so we were all three linked together. 'You're smart,' she said to me. 'Gardo, you're smarter than this boy, and I know you can run fast and get clear – and maybe I shouldn't have spoken, and I'm sorry I did. But I'm too old to move again, and the two little ones...'
Her eyes were all full of tears, glittering wet – and I got scared because she was scared, and I know Raphael was most scared of all, though he won't ever say so. 'I don't want us getting caught up with the police,' she said, gripping us hard. 'Everyone knows what things they do.'
I couldn't meet her eye.
For one thing, I was mad she'd spoken up – it was still the dumbest thing she could have done. For another, I had a feeling things were going to get bad. Sure, I wanted to be smart, like she said I was, and I knew I had to lead this, because Raphael needs to be led. I needed to keep a hold of him.
I was planning it fast, and that's why I said nothing.
We just had to get to the railway station – that's what I thought. We had to find out what was in the locker, and do it fast. Then, maybe, in a few days' time, we could give up the wallet with the key inside it and get everyone off our backs.
If that was too suspicious, I could get Rat to give it up – nobody would suspect him, because he worked alone, he didn't talk to people. So I thought, _Let Rat be the little hero and bring them what they wanted in a few days' time_.
But if even that was too dangerous, I was thinking – then we could just throw the wallet and key up into the trash, and wait till somebody – anybody – found it, if they ever did.
There was nothing in the house, that was true – and nobody could prove anything, and we were _not_ in danger, and we could still make money – that is what I told myself, and Raphael was thinking just the same kind of thing, and we talked it through all night, thinking we were being smart and so not knowing what we were getting into. Not dealing with the fact that if the police think you've got something, they won't stop till they've got it from you.
# 6
Raphael again.
The next day Gardo let us go to the station. I told him me and Rat would go alone if he didn't.
He said, what if we were being watched? I couldn't see how they could watch us with us not seeing them, and I said we'd be moving so fast they'd never know.
He said, what if they come back to the dumpsite, looking for us? I said, what if they don't?
He said, what if they've got the station staked out? And I said, what if we just do nothing for ever and forget the whole thing? Is that what he wanted? He kind of snarled at me then, but I'd got my way.
So, early morning we went down to the tracks. The trains cut through the south side of Behala, very close to the docks. If you want to get to Central, you can pick one up ten minutes from my house.
People have built their homes right up to the line, because the ground is flat and clear. Every now and again the homes get torn down and the people get shipped out. Over time, they come back, and the game starts again. It's not as dangerous as you might think, because the trains are only four a day just there, and they go slow. They're long and heavy, and you can hear them coming a mile away. The only person I ever heard of getting run over by a train was a woman about two years ago, and she did it on purpose, walking up as the train came and laying her head right on the rail.
Gardo, me and Rat waited for the six o'clock. It came by pretty much on time, and we ran alongside the last coach. It's a passenger train, and it goes for nine hours, way down to a town called Diamond Harbour. It starts at the docks, but not many people get on there. Then it goes to Central, where it gets so full you can't breathe. We swung up and in through the windows – there's no glass and no bars – and the only people were an old couple at one end, so we spread ourselves over the benches, and looked out and waved like we were on holiday.
'What if they're watching?' said Gardo again. When he gets something on his mind, you can't ever get it off again.
'How can they be?' said Rat.
'They'd be looking for people doing anything suspicious. How many times have we been on a train, Raphael?'
'I don't know, not often—'
'They're police, yes? They're gonna be looking out to see what we're doing. What if they know there was a locker key – they just don't know the number?'
'No, listen,' I said. 'That's crazy. If they know the bag had a locker key, they'd have broken into every locker in the station. They cannot know what's in the bag.'
'Maybe they're at the station now, opening every locker. Waiting for us.'
'If they are, we just walk away. We're just three boys out roaming.'
Rat said nothing. He just looked from me to Gardo and back again, and when I caught his eye, he smiled and we both laughed.
Gardo told us to shut up. 'Twenty thousand now,' he said. 'That's the prize money they're offering, I heard – they just doubled it.'
'You know they won't pay it.'
'What I'm saying is, whatever they're looking for is getting more important. If this José Angelico killed someone – what if he killed an important man – a politician, maybe: someone rich – and we've got the clues to catch the guy? What are we going to do then? We end up stopping the police catching a killer—'
I said, 'Gardo, why don't we just see what's in the locker?' And I smiled right at him and lay back on the bench. 'We decide what to do then, OK?' I told him to rest his brain.
'I do the locker,' said Rat.
We both looked at him, and Gardo asked him what he meant.
'I best do the locker,' he said. 'OK? I best square it with the station boys too – say we're just doing an errand for someone, give them something. Also, in case anyone's looking... I know where it is. I'll go in fast, grab what's there – meet you back by the tracks. Anyone sees me, I just run. Three of us run, they'll get one of us. If it's me, I'll lose them. OK?'
'How much to the station boys?' I said. 'They going to want how much?'
'I don't know. I'll try twenty and make it look like a small thing. Give me a hundred, though.'
I gave Rat the notes, and he was twitching a little, getting scared. Gardo was shaking his head, thinking deep. He said: 'It's a good idea, Rat. I can see where you're coming from. But I say stick together. We ought to stay together in this.' He looked at me and said, 'You better stay close to me!'
Minutes later, the train was slowing for the station, and we stood out on the sides. I could see the platform coming up, so I jumped and ended up rolling on the grass. Gardo nearly fell on me, but Rat stayed on his feet. I hadn't seen before just how quick Rat could be, and he was so thin it was like he was just straws and paper, like he could blow off in the wind like a little kite. He didn't even look round, he just skipped along, and we hurried after him. We ran up onto the platforms, and a couple of kids looked at us with a kind of mean-eyed suspicion, like this was their territory – which it was.
They followed us up, at a distance.
We jumped early because you don't ever want to be seen getting off the train. If guards or even porters see you, you can get a real thrashing. The station boys are different. As long as they don't steal or get in the way, nobody cares too much. They keep the station clean, and go through a train in about two minutes. If they beg or sell, they know to do it off at the sides – that's why people let them alone.
So now we were all making our way up the platform, just a straggling bunch of three barefoot boys; we might have been invisible. I knew the dangerous bit was going to be the locker, because that was something you did not usually see. Boys like us opening luggage lockers? It wouldn't have to be police. It would be anyone who noticed. They'd assume right away that we were thieving, and thieving boys get no mercy from anyone.
Just off the platform we were met by more station boys and these ones were bigger. We got kind of herded over to the side and I could feel Gardo getting ready, feeling for his hook, which he always carries somewhere. Rat did the talking, though, since he used to live there and knew some of them, and I saw him pass over the twenty – then another fifty, then a twenty. Everyone shook hands, and they let us go. I guess Rat had paid for them not to follow us, because we went on alone to the main station square.
'They give us five minutes,' he said.
It's a giant station, and that time in the morning it's just getting crazy – a good time for us, but scary as hell. You got porters, you got travelling families, you got trucks delivering stuff, horns blasting, train whistles, loud speakers. Everyone's cutting in and out of everyone else, and the noise is so loud you have to shout. Rat kept moving fast, and I was beginning to get frightened again. I hadn't liked the look of the station boys, but now – everywhere I looked I could see mean-looking railway guards – and we were getting stared at. I had to keep saying to myself, 'We're not breaking the law' – but it felt like we were, and everyone knows stories about what happens to kids if they get caught breaking the law. I don't mean what I said about just riding in a train and being thrashed. We've got prisons in this city, and the prisons take kids quicker than they take men. You also hear stories of boys not even making it to prison, but I don't know how much truth there is in any of it – everyone's out to scare you with a story. I was told once about runaways, and it made me sick. How if a new kid shows up with nowhere to go, and the police get him – they wait till night, break his legs and put him on the tracks. They're stories, and they may not be true, but I couldn't stop thinking of them as I walked across that station, feeling small – nearly losing Rat, but Gardo by my side, up close. Both of us just waiting to be caught.
Rat kept going. Somehow he'd shaken off that twitch he gets, and was walking fast, looking happy as a kid. He stayed a little bit ahead of us. He had something in his hand, and I saw it was the key, so I guessed we must be near. We went under a bridge into some kind of hall with a low ceiling and lines of tube-lights. We kept walking, like we knew where we were going, and there they were: two long aisles of grey metal lockers – lines and lines of doors.
We kept on walking.
Some doors were big enough to take suitcases, and some, up above, were small enough for just a handbag. There were no police, no guards – no station boys – and Rat knew exactly where he was going, and he hung back for a moment so we drew level, and he said, 'You keep moving, OK? Walk.'
There were two women opening one locker, and we went straight past them. They were far too busy with whatever it was they were putting in to notice us. A tall man at the far end was locking a door, and his back was to us. I could see the numbers: 110, 109, 108 – none of them were smashed, everything was neat and quite new, and there were still no police. Then, suddenly, Rat had turned and he had the key in the lock. We walked straight past him, and we heard the sound of metal. Nobody shouted, nobody even noticed. I was ten paces on when I heard the sound of a door closing, and then Rat was next to us again, and I could see he had something under his arm.
'Don't run,' he said. 'Slow down, OK?'
We did as he said but my heart was pounding. Gardo was smart enough to stop and play with a drinks machine, checking the slot for money. I was thinking, _Look like nothing's wrong!_ – three station kids making their way. Rat had the package under his shirt now. We went out onto platform four, and right along to the end, weaving through the people. We did start to run then, out of relief. We got down on the tracks, and we started to run fast. Five minutes later, we got among bushes and bramble, and there was a small pile of concrete sleepers to sit on, and we were out of breath.
Rat was grinning and laughing, and I was as well. He held the package in both hands, and offered it up like a present. It was a brown envelope, sealed up with tape, and it took me some time to get it open.
Inside was a letter, with a stamp in the corner, waiting to be posted.
There was writing in a thick pen: _If found, please deliver_. Then the address: _Gabriel Olondriz_ was the name. Underneath that: _Prisoner 746229, Cell Block 34K, South Wing, Colva Prison_.
I felt myself go cold again, but I grinned up at Gardo and he looked hard, right at me.
I opened the letter and read it out loud. One page, and a little slip stuck to it, with just a line of numbers, making no sense. Then again, the letter made no sense: we understood none of it. All we were sure of was that we were in something deep, getting deeper.
# PART TWO
# 1
My name is Father Juilliard, and I am the one pulling these accounts together – all names changed, for obvious reasons. You will understand the importance of this at the end: but it's a story that had to be told. The next set of events is best left to me, and to one of my former staff.
I will just tell you that I have been running the Pascal Aguila Mission School on the Behala dumpsite for seven years. It was going to be a one-year job: my task was to set it back on its feet after some financial mismanagement. It was to be my final posting – I'm sixty-three. But I fell in love with the place, and have been here ever since. Unfortunately I am being retired this year – partly because of this story. The school has already appointed its new head, and my final official task is the handover.
I hope to stay in the country, but I'm not sure I can.
I should say, by the way, that our school does need new energy, as we've been getting smaller rather than larger. It's hard to keep the children attending class: we have to bribe them with food. Our income's going down, and the food resources are never regular. It's also so hot, and around the dry season it gets stifling. The school is made of large metal boxes – the iron containers you see on ships and trucks. Ten were donated to start the Mission. They were bolted together, and windows and doors were hacked out – there it was, an instant metal school. Six more crates were bought, and they made the upstairs. Two form a chapel. Three have been knocked together for a babies' room, with a little play area in one corner. Half of one is a rest area, and the other half is my office.
I only knew Raphael and Gardo by sight, as they rarely came to classes. Few children do after the age of ten. Their families want them picking trash, and it's hard to argue that education's ever going to be helpful – so we lose them. Little Jun – the boy they call 'Rat' – I knew better. He would visit me in my office, sneaking up when the other children had gone, climbing the outside like a monkey. I'd let him in through a window, I'd give him the ointments and plasters he needed, and – if he wanted one – I'd let him take a bath. I would have to give him food too, because he was evidently starving. We had a rule that food was only provided at lunch time and for half an hour after classes. I broke that rule for Jun, and a handful of others like him, because I have always said that you have to break the rules. I set rules up; then I break them. Sister Olivia broke the rules as well, as you shall hear.
_Don't put your feet on the chairs, don't take more food than food for you – don't take food out to your family. Stay in line, say the prayer quietly, wear a shirt when you're indoors, wash your feet before chapel_ – I have to laugh myself, but rules are what we live by even though we all know they're sometimes foolish. One rule that I like a lot, though, is an unusual one: _on the stairs up to chapel, nobody must speak_.
Why can't you speak on the chapel stairs? Let me tell you – somewhere it is relevant.
The steps and the chapel are dedicated to the man whose name we bear – Pascal Aguila – one of the country's lesser-known freedom fighters. The Aguila family donates a large sum of money every year, and they bought those last six containers for our upstairs. They ask that we honour Pascal's memory – which is a pleasure as well as a duty. He was a man who fought corruption and was shot to death for his pains, so we honour him several times a day, just by being quiet on the stairs. I find that the children never need reminding. Just now and then, if there's a boy or girl who's new, they might be chattering; then you hear a great gust of ' _Shhhhhh_ ', like a breeze, and everyone is silent. We tell them about Pascal, of course, and his picture hangs over the altar. He was a man determined to build things and make life better. He spoke a dozen languages, yet he was from a poor family. He became a lawyer, but he continued to live in a poor quarter of the city. He took on impossible cases, and won them. When squatters had their houses bulldozed, Pascal Aguila forced the government to find them land. When a building project hired a thousand men and failed to supply them with boots, gloves or hats, Pascal Aguila sued, and forced a change in the law that made the construction industry a whole lot safer. When cholera hit the swamps, just up from the docks, Pascal Aguila forced the local hospital – a private concern, for the paying rich – to set up a special unit for the poor. His final act – the one that killed him – was to expose three senators who'd been siphoning off public taxes and stowing them off-shore. They all resigned, and the prosecution rumbles on. Pascal Aguila was shot to pieces in a taxi, on his way to testify. Twenty-six bullets – the same calibre as a policeman's gun, and his murderers were never found.
I sometimes sit on the stairs, under the plaque we had made, and I think about this brave man. It is by such small things – small as a silent staircase – that the dead live on and help us. In this country, the dead are very important.
You want to know how I was part of Raphael's tale, of course, and what I did. I was on the edge, only. Sister Olivia, our temporary house-mother, was more crucial, and perhaps more foolish – but I got involved because of the school computer, which was donated by the RCBC bank. We score these little successes! We get our foot in the door. You won't think me uncharitable, I hope, when I confess that the computer was old and out of date, and if they hadn't given it to us, it would have ended on one of the trash heaps. Who cares? They gave with a good heart, I think, and we have had much use out of it. It connects to the Internet, and the children play games on it when I let them.
It was a Thursday afternoon when Jun came by, with the two boys I hardly knew.
'Sir po,' he said. 'Sir po?'
He's got a high-pitched, musical little voice, and I recognized it instantly.
I turned and smiled, and he was leaning on my office door. He's thin as a match, and the colour of ash. He has a smile that makes me smile too, and I'm always pleased to see him. 'We are looking for something, po.' 'Po', by the way, is the word of respect people use here for their elders. 'Can we use the computer, sir po?'
I told him it was late. Then I looked beyond him, and saw he had two friends with him – slight, skinny boys. One looked shy and the other looked watchful – you could see at once who the leader was. His head was shaved and his eyes didn't blink. He had long arms and, even with the poor diet he had, the poise – the grace – of an athlete. The other one had long hair over his face, and another enchanting smile.
'Po, sir po. This is Gardo.' He pointed at the boy with the shaved head. 'This is Raphael – d'you know them?'
I told him I didn't but was pleased to – and we all shook hands.
'They're taking part in a quiz,' said Jun. 'It's a newspaper thing, sir. They have to research, sir. They said they don't come to school here so why would you help them, so I said I'd come. They can give money for the computer time, OK? I said maybe you would, po.'
I told them to come in, and they came over to my desk. Shorts and T-shirts, bare feet black right up to their knees – their smell filled the room. The one called Raphael looked at me, pushing his hair back, too shy to make eye contact. He held a twenty-peso note in both his hands, for computer time. Gardo stayed behind him, and I could feel him staring right at me, as if he might have to fight.
'I'm afraid the connection's slow today,' I said.
I put a second chair by the computer, and waved away the boy's money. They slid onto the chairs, and Raphael got straight down to work. Children always know how to use computers – it never fails to amaze me. Children who'd never stepped inside a classroom could work a keyboard faster than me. It was the games shops where they learned, of course. For ten pesos you could get fifteen minutes of shooting and chasing.
I saw him go straight to a search engine, and the bald boy opened a piece of paper. Raphael tapped in a name, and we all watched as the computer thought long and hard.
I said: 'What have you eaten today, Jun?'
He smiled up at me and held my arm. 'Nothing!' he said proudly.
I went down to the kitchen and made some sandwiches. I got three glasses too, and filled them with lemonade. By the time I got back, the boys were chattering in low, excited voices, scrolling down the screen and pointing. They'd called up a local news site, and were reading carefully.
'What's the question?' I said. They looked blank, so I said, 'For your quiz? What question are you answering?'
Raphael said, 'It's about history, sir.' Then he was talking in his own language, which I am ashamed to say I hardly speak, despite the length of time I've been out here. The second boy, Gardo, was shaking his head. Whatever they were looking at seemed to be a serious business.
Jun, meanwhile, took a sandwich in a hand that was so dirty it made me wince. The boy bites his nails right down to the quick, and his fingers remind me of skeletons. He promises and promises to come to class, but he so rarely does – he must have the strangest mix of ideas from the ones he's attended! It's become a joke between us. I always say, 'So – you'll be in school tomorrow?' He assures me that he will, and I know he won't. I will never forget the sight of him the first time he took a shower here. He had a towel wrapped round himself, and was dancing with the cold and the excitement of the spurting water – and maybe the amazement of seeing his own flesh looking clean. I gave him one of our school uniforms, but I never saw him wear it.
Sister Olivia fell in love with him too, and asked me about adoption. A twenty-two-year-old girl from England, wanting to adopt! I told her not to think of it. The machinery for adoption out here is slow, for one thing. In six years I've known one successful case for a foreigner. No government is going to give away its children, I understand that – and yet you look around at the thousands who cannot be taken care of and it breaks your heart. You look at the mountains of garbage, and the children on them, like so much more garbage, and it's easy to think what you do in a school like this is of absolutely no consequence or good to anyone. More and more children. When I walk around the shanties, I see the babies, and I am always asked to hold them. And while we're smiling and laughing, I am thinking, in the back of my mind: _This tiny child – as soon as it can crawl, it will be crawling through trash_.
The boys finished on the computer soon after I came back with the tray, and they turned and had a sandwich, and drank their lemonade. They were polite, as the children here always are, but they wanted to go.
I said, 'So. School tomorrow? All three of you?'
Jun laughed. 'Definitely!'
Raphael said, 'I want to come, po. But I'm working.' He pushed his hair back and smiled his dazzling smile.
I reminded him that he could work and also do a morning class. I reminded him that the school was set up for exactly that purpose: to let the children work while providing education. If they attend five days, they get two kilos of rice and a few bits and pieces extra, depending on what's been donated – that is the incentive. Raphael looked at me, and I wondered if he was thinking that obvious thought: _And what use is an education to me?_
He said, 'I will come, po.'
Then Jun took the plate and glasses into my kitchen. He insisted on washing them, and setting them in the drying rack. Then he gave me a hug and I slipped him fifty pesos.
The other boys were waiting for him outside, and they ran away together – I never saw them again. It was a few weeks later that I discovered they'd been lying. There had been no quiz, of course. They were finding out everything they could about Mr José Angelico, the man whose ID they'd found. They'd also been researching Gabriel Olondriz, who at that time was serving his twenty-third year in the city's biggest prison.
Rat had been up to something too, which he will reveal in due course. They had all got what they wanted, and had deceived me beautifully.
# 2
This is Raphael again, and now it gets serious.
The police came that night, just like Gardo said they would, and searched our house. I was arrested.
Four van-loads came, and everyone in the block was ordered out. They had flashlights and batons, and they moved through fast while more and more people gathered, up from the other neighbourhoods. The police said nothing to anyone. They showed some bit of paper to Thomas – our senior man – and they didn't wait for him to say anything. Then it took them less than an hour, and we all stood listening as they shouted to each other and threw things. Some of the little kids were crying, but most people were calm, just watching.
What could anyone do?
Then they got back in the vans, having found nothing.
I had not thought they would take me, because nobody had said anything to me. I saw the young policeman again, and I saw him nod in my direction, and I realized they were talking about me. It still came as a surprise – I don't know why – when two police came over and took hold of my arms.
This is going to be very difficult to write about, the next part, but it's only me that can.
I did not know what to do. I did not make a sound, and I did not move – I was too scared to breathe and I didn't know which man to look up at. Gardo was right with me at once, and he was talking fast, saying, 'What are you doing? What's he done?' over and over, touching me. My auntie started to scream, and then she fell down on the ground. Immediately there was a great commotion, and I saw how important it was that I was not taken. People were shouting; some were pleading with the policemen, and getting between me and the car. One of the vans had stopped, and some police were coming back, but before I could take in any more, I was walked to the car that had its door open, my arms held hard. Gardo got his arm round me, but someone pushed him off, and I heard him shouting over the top of everyone else, but one of his uncles had hold of him. I got to the car and I tried to back off, but I was dragged and pushed. I was between two big men, and whatever I said, nobody heard me – I twisted, but I was just picked up, and I was in the back seat. Doors slammed, and I saw Gardo again. He was screaming at me, trying to get to me, and a policeman grabbed him by the neck and threw him off. Then the car was moving and I was crying. I saw faces through the window, staring at me, shouting at me, but I couldn't see anyone I knew, and Gardo was gone.
I was so frightened I felt sick and I couldn't stop crying.
We were bumping and rocking because the road is so rutted and the driver was going as fast as he could. There was still a crowd around me, and someone was banging on the roof – and then we were through the gates, and on the road. They put their siren on, and we whipped through. Red lights didn't matter, the traffic police waved us on. For some reason it didn't feel quite so bad when we were going past stores, and the roads were full of people, and everything was lit up. But when we turned off into smaller roads, there were no people, and soon there were no lights.
I have never felt so lost and lonely, and I still could not stop crying. I said, 'Where are we going?'
One man said, 'Where do you think we're going?'
I said, 'I haven't done anything, sir.'
The man said, 'Keep still, boy – we know that.'
'I haven't done anything, sir,' I said again. I kept saying it through my sobs.
I tried to keep still, like the man had told me to, but I couldn't. I was rocking backwards and forwards. All you can think about is how alone you are, and how anything can happen now. A little while ago, things had felt safe and ordinary – my auntie, Gardo, the cousins, the fire – and people, all around me. Now! It is like falling through a trapdoor. In a second, every single thing had changed, and you are falling – your friends cannot get to you, nobody knows where you are, and you think, _So when do I stop falling?_ You think, _What plan do they have for me that I can do nothing about?_
Rat had the envelope. Rat had the ID. I would not give either of them up because we knew more now. We knew about José Angelico, and there was a fight beginning.
The streets and buildings were all grey-cement coloured, and we drove left, right, up, down, and came round fast into a car park, up close to a heavy-looking gate. A policeman with a dog opened it, and we drove through, and down a ramp. To be going down, underground, was more frightening still, and I started to cry harder. I called for my auntie as well, and that is when – I will be honest – I wet myself.
We stopped in bright lights, and I was taken out of the car. I could hardly move by myself, and a policeman had to pull me – not because I was resisting, but because I was so frightened my legs wouldn't work. He spoke quite softly and put his arm round me, half carrying me. We went down some steps and through metal doors. We came to a corridor, and there were cells on either side of it, all with numbers. A policeman opened one of the doors, and I was put inside. The door closed and I stood there, not knowing what to do, feeling so sick I thought I would fall over and die. Seconds later, the door opened again with lots of noise, and a policeman came in and told me to sit down.
I sat on the floor, and I was sick. I hadn't eaten much, but up it came and went all over my knees, and I started crying again, and I had never before heard the sounds that I was making – I had never cried like I was crying then.
The policeman sat on the bench, and he didn't close the door this time. I think he realized that I was too frightened to be left alone and that somebody should be with me. The policeman gave me a little towel, and I tried to clean myself, but my hands would not work.
Time passed.
There was nothing in the cell but the bench, which was concrete. The policeman said a few things to me, just casual questions about who I was. I found that I couldn't speak, much as I tried to. After a while, a man in a light grey suit came in and looked at me. He asked me my name. I managed to say it, but my voice wasn't my voice.
'Six,' he said. 'We'll use six.'
He went out, and two policemen came and lifted me to my feet. They had to almost carry me. I was taken back along the corridor, and this time up some steps instead of down. We climbed high and then passed some offices, with policemen working in them. Nobody looked up. We turned some corners, and I remember a sign board with pictures of a beach, and there was a list of names. I saw a clock, and it said two-twenty. Then we went into a room with a number six chalked on the door, and there was a metal table with the man in the suit sitting at it, having got there ahead of us. Behind him, standing, was the important police officer who had first come to Behala – the rough guy with the smashed nose. Behind him was a window, and next to him was a third man in shirt sleeves, bald and sweaty and angry and tired-looking.
I was put in a chair.
'Raphael,' said the tired man. 'Raphael Fernández? You know where you are?'
I shook my head.
'You're in Ermita Police Station. You know why you're here?'
I shook my head again, and tried to speak. Nothing came out.
'We need the bag you found,' said the policeman.
There was silence then, and my throat was so dry I had no idea what my voice would sound like if I managed to say something. But I tried and tried, and the words came from somewhere. 'I didn't find a bag, sir,' I said. Still I didn't recognize this voice that was coming out of me.
'This isn't going to end, Raphael, until you give us the bag.'
'I didn't find a bag, sir,' I said. I had to make myself a child – just a terrified, foolish child. 'I promise, sir. I swear.'
A cup of water was put next to me, and when I tried to pick it up, I spilled it. I started to cry again, and I wanted to go to the toilet. The tired man waited while someone mopped up the water.
'All you have to do,' he said, 'is take us back to your house. Give us the bag – wherever you put it. We give you money, like we said we would. Everyone's happy.'
I managed to look at him.
'I swear to God, sir. I swear on my mother's soul: I did not find a bag. I found money. I found eleven hundred pesos, and that's all—'
'You found money.'
'Yes, sir.'
'So you _did_ lie? You _did_ find something?'
'Yes, sir, I did.'
'Where did you find it? When?'
'By belt number four. Thursday afternoon.' I was lying. I didn't want them to know where I'd been. The problem is, your own lies can trap you. The man in the grey suit was writing things down.
'Who were you with? Who saw you?'
'Nobody, sir. I was—'
'That's a lie,' said the policeman, and he came at me from the side. I don't know where he hit me or what with, but I was knocked to the floor. My chair turned over and the side of my face was split. I fell badly, and my wrist was bent under me, and I saw him standing over me and I thought he was going to start kicking. I screamed, 'No! No! No!' over and over again, and tried to get under the table. The policeman didn't kick me. He reached down, grabbed me, and he and the man in the suit lifted me up by the hair and an arm, and I was put back in the chair. Someone had me by the hair still.
'I was with Gardo,' I shouted. There was blood in my mouth. 'Just my friend! But I didn't give him money! He didn't see me find it. I'm sorry, I'm sorry! I was with Gardo, and I found some money – I did not...' I started to sob. 'I did not find a bag!'
'And the shoe?' said the policeman behind me. He was the one holding my hair. 'What about the shoe?'
'I didn't find a shoe, I was lying!' I cried. I tried to wipe my face, but it was all blood and snot, and I was slapped again, hard, so that lights were flashing. 'I found the money!' I shouted. 'I didn't want to...' I was panting for breath, and I started to sob. The policeman was leaning over me, one big hand on the table, one hand twisting my hair.
'What was the money in?' said the suit man. 'Leave him alone.'
'It was wrapped up in paper,' I said. 'I think it was a bill.'
'Eleven hundred pesos, wrapped in a bill?'
'It was an electricity bill, sir. I think. It was orange, and I think they're the electrical bills.' I was thinking so fast, just fighting for my life.
'You can read, can you?' said the man in the suit. 'This piece of shit can read?'
'Yes, sir, I can read!'
'How's that? Huh?' He stood opposite me, leaned in and lifted my face. I could smell his cigarettes and his sweat. 'Who taught trash like you to read? What's your name?'
'Raphael, sir—'
'Who taught you to read?'
'Gardo, and my auntie.'
'What kind of bill? What address?'
'I didn't see, I didn't look.'
'How much money?'
'Eleven hundred.'
'Exactly eleven hundred? How many notes?'
'One five, six ones.'
'Where are they now?'
'I gave them to my auntie. I kept one for myself.'
'What about the bag?'
'No bag, sir.'
'I'm going to kill you, you liar!' He lunged at me, and I was falling backwards, but the policeman lifted me and the suit man had my throat. I was up against the wall, and that is when I lost control and simply... all down my legs, I lost control – I was so frightened – and I was stinking, and I was shouting, 'I didn't find a bag, sir!'
'Get him out – get rid of him!'
I was lifted up and they were carrying me to the window. The man in the suit was opening it, I was held by the policeman by my ankle and my arm, and I was going towards it sideways – it was coming at me, this big open window. I remember warm air. I remember suddenly I was out, and the hand holding my arm let go, and I was upside down, held by just one ankle – I could see the filthy wall: it was like a pit – and a long way down below me I could see a stone floor with what looked like trash cans. I was screaming so much now, and when I looked up they were all looking down at me.
'Where's the bag?' shouted one of them. 'Did you find it?'
All I could shout was no. Gardo has asked me – Rat too – did I come close to giving in? And the truth is, no, I did not. It sounds crazy, but there was a part of me sure I'd never found it, and some other part of me begging me not to give it up – maybe for José Angelico, because we knew more about him now. The hand on my ankle was tight, and I knew any second it could let me go and I would fall. I would fall on my head and be broken. The man was shaking me, and everything was spinning, and there was blood, sweat, my own mess, and the walls turning, but I would not say anything other than no, and they would believe me or it would just be over.
I was suddenly dragged up.
They hauled me in over the edge so all my chest was cut, but I hardly knew it at the time. I was stood up and slapped again, and then they all waited.
I fell on my knees, and they let me.
I managed to take hold of somebody's leg, and held it – I put my head on my hands. I was down there, kneeling, and I said, 'I swear on my mother's soul I did not find a bag. I am telling the truth, sir – please don't kill me. I cannot help you, I am speaking the truth.'
Where did I find the strength? I know that it was José Angelico's strength.
'I am sorry,' I said, and I was fighting for my life, and knew it. 'I should have told you I found money, but I should have given it to my friend also, and I didn't so I lied to you. Please don't kill me, please.'
'What belt were you under?' said the policeman.
'Four, sir, honestly – I promise.'
'Where's the bill the money was wrapped in?'
'I put it in the paper sack. I put the money in my pocket.'
'Raphael, listen to me.'
This was the man in the suit, I think. He knelt down next to me, but my head was throbbing so badly I cannot really remember.
'You're the breadwinner, aren't you, for your stinking little family?'
I nodded, but I didn't look up. 'Yes, sir.'
'If anything happened to you, your family would have big, big problems. What would your auntie do?'
'I don't know, sir.'
'Two little cousins – what would happen to them? Can you hear me?'
'Yes – I don't know, sir. I didn't find a bag, sir, please believe me.'
'We can drop you out of that window. Or we can take you out the back. We can do it right now – we have a special place, you know? Perfect for little scum like you. Where no one hears anything. And we will – if we want to – break every bone in your body.' He took me by the arm, and was squeezing it and lifting it. ' We will break this first. You understand that, don't you?'
I was nodding still, and shivering, and stinking. My twisted arm was in the air, me on my knees, and I waited for the snap, the pain so great I was silent, open-mouthed, unable to make a sound, just waiting.
'We could put you in the trash and nobody would care. Nobody would even come looking – you understand me? You'd end up in a sack.'
I nodded. I could not speak.
'So I'm going to ask you one last time...' He hoisted me and bent me over the window so I was staring down, and I felt someone take my ankles so all they had to do was tip me out. Again, I was looking at the ground as they balanced me. 'Where is the bag you found?'
I tried to look up, but my arm was so bent and my back was so twisted. I tried to speak, and couldn't, and tried again. I said, 'On my mother's soul, sir—'
The man shouted: 'What? I can't hear you!'
I was tipped out more, and I screamed for help. 'I promise, I promise!' I shouted. 'I found money only. I found no bag. If I had found it... if I knew anything about it, I swear you would have it now. I would give it to you! I would – please, listen...' I could hardly breathe but I found the words. 'I would take you back to my house and give it to you. But how can I, sir, when I did not find it?'
I started sobbing, because I knew that this was my last chance. I felt the hands on my ankles shift, and then – after some silence – I was lifted back into the room and dropped onto the floor.
When I looked up, I could see the men talking together in low voices. I was shaking all over, and I could not move. After more time, one of them looked over and told me to stand up.
'You've shat yourself, haven't you?' he said.
I nodded, and I clawed my way up the wall so I was half standing.
The man shook his head. 'You stink of it. And of garbage.' He turned away from me. 'We're wasting our time,' he said. 'Boy, that's all you are, that's what all of you are. You are a piece of garbage. What are you?'
'Sorry, sir, garbage, sir.' I whispered it.
'Eleven hundred pesos, wasting our time with crap. Look at you.'
I managed to meet his eyes again, waiting to be struck as he came over.
'What is the point of you, eh?' He turned to the other men. 'Look at him – why do these people keep breeding? Put your hands behind your back.'
I did so, and waited to be hit.
He sighed more heavily, and I could see that he hadn't slept for a long time – he was frightened and tired. I prayed in my head – I could see he was weighing me, looking me over, wondering what, if anything, I was worth. Valuable or trash? To be kept here and beaten and beaten... or thrown away? What if they brought Gardo? What if they brought my aunt, and beat three different stories out of us?
I think I held my breath.
At last he decided. He looked at the policeman behind me and said, 'Get him out. We're wasting time.'
I felt a hand on the back of my neck. I was taken out of the door. I was taken down the stairs, and a guard took me down a passage and down more steps. A few minutes later, I was on the street, and I found myself running on legs that bent like I was drunk, and wouldn't do as I wanted. But at least I was running, crazily, down a long, empty road. At least I was free, and at least – unlike poor José Angelico – I was alive.
My legs got stronger. I knew then that I could run for ever.
# 3
It was raining and cool.
I just kept running steadily. I had no idea where I was and I didn't care – I felt like I could run for ever. I ran through the streets, heading for any lights that I saw. I had no money at all, and I didn't care. The world felt so big, the rain was so fresh, and I remember thinking, _Why is it raining in the dry season? How can it be so cool?_ The sky was so high. Time had slowed right down, but it can't have been more than three hours, and as I ran I realized more and more how stuck the police were, if I was the only clue they had. Again it was clear how important the things we'd found must be, and then I began to think how lucky I was and how close death had been.
The hand could have opened and dropped me. I could have been thrown away, I could be – now, right now – slowly dying on a stone floor.
I closed my eyes and ran faster with my arms stretched out.
My auntie had said, 'Raphael found something,' and that was the only clue they had. Just those words had led to the whole neighbour hood being searched, me being taken. Taken, but free now.
At last I slowed to a walk, and at the far end of the street I saw a landmark I knew. I didn't know its name, but I knew it was in the city business district. The landmark was the statue of a soldier, raised up high. He had a drawn sword, ready for some charge in some war. I had passed him before, yelling something to his comrades, fighting for freedom! I walked right up to him and looked up, and I said, 'They let me go. I did not give it up.'
I could not believe they had let me go, and the statue just carried on yelling.
There was a surge of rain and the kind of breeze I'd felt up on the dumpsite, in from the sea – a typhoon breeze, though this was not the typhoon season. I looked at the soldier and thought, _So, am I garbage?_ And I laughed, because it occurred to me – there and then – that the garbage boy had just lied his way out from under the noses of those clever men. A little garbage boy had sat there shaking, saying, 'I don't have the bag,' when all the time I knew exactly where it was and what had been in it. We'd caught the train and we'd found the locker. We had the letter – and OK, we did not know what it all meant yet. But the garbage boys were way ahead of the garbage police, and I had said nothing to those men.
I walked on.
It would take two or three hours to reach Behala, and I was so happy walking – I knew which direction to take. I passed an old man and two little kids with a cart. They were night sweepers, shovelling trash. I asked the man if he had a cigarette, and he looked at me strangely. I had forgotten that my face was covered in blood.
He gave me a little bit of a cigarette, and I sat and smoked with him. The kids stood and looked at me, and I was stinking, but nobody seemed to care much. The little girl was about five, and the other – maybe a girl, maybe a boy – looked about seven. The seven-year-old got a bottle of water out of the cart, and I splashed some over my nose and mouth. Then I said goodbye and started running again.
Let me tell you something else – I think I will tell it now.
On that computer we had found out about José – the man whose bag it was. José Angelico, God rest his poor soul, was a dead man. His name had been in the news. Gardo had said, 'What if he's a killer?' – but it turned out the poor man had been killed.
Guess where he had died?
He had died in a police station. The newspaper said that he had died while police were interrogating him. In the same police station as me? I wondered. In the same room?
Had they dropped him from the window on purpose? By mistake?
I was passing a little park, and I ducked into it for a moment and sat on the grass. The rain was so light and cool. I guess I was in deep shock, so I just sat for a while, and I thought more about poor José Angelico.
He had been arrested on suspicion of a major, major crime – it had made all the papers. After the computer, we had gone to the papers – one thing there's a lot of on the dumpsite is old news papers. It didn't take us long to find the right ones, and we sat there like three little old men, me reading it all out to Rat, who nodded and stared. The police had arrested José Angelico for robbery.
Six million dollars.
We sat back and tried to imagine what even a thousand dollars looks like. Gardo tried to translate it into pesos and got a headache so bad he had to lie down. We were laughing, trying to imagine how you walk with all those million dollars in your pocket, and then we stopped laughing.
José Angelico had died in a police station, they said, and that's why I stuck to the lie, even as they held me out of that window – for the sake of José Angelico and his serious-faced little girl. I also think José was with me, because I know the dead come back.
The crime he was accused of was robbing a government man – the vice-president – of six million dollars, and maybe he'd done it and the money was waiting somewhere. He must have put that bag in the trash before they got him – I think perhaps they made him confess to it, and that's when they came looking.
One newspaper told us a little bit about him. It said that he had been an orphan, but had been adopted by a man called Dante Jerome Olondriz, son of Gabriel Olondriz. That was the name on the letter we'd found – Gabriel Olondriz, the man in Colva Prison. José Angelico, it said, had worked as a houseboy for the vice-president for eighteen years. It said that José Angelico had an eight-year-old daughter and no other family. That was why he was writing to Gabriel Olondriz.
I sat shaking in the rain, and I knew for sure now that we would have to go to Colva Prison and deliver the letter.
# 4
My name is Grace and you will hear only one thing from me.
Father Juilliard has asked me to say what kind of a man José Angelico was, as I worked closely with him. I am a maid to Senator Zapanta – the vice-president who was robbed. I have been his maid for four years, so I knew the senior houseboy well. I can say that José was kind, gentle, trustworthy and honest. He had a very quiet voice. He didn't smoke. He took a little brandy at the weekend, but not so much. His wife had died before I knew him, and he was paying for his daughter to go to school. Her name was Pia Dante, but she could not live with her father. José was live-in staff, and the senator's house is a long way from schools. He boarded her with a family near to her school, and they saw each other once a week. He had also had a son, but the little boy had died very young.
I don't know what else to say.
I was very, very upset when I heard about it, and like everyone, I said it was impossible. José Angelico was the most trustworthy man, and he did not seem brave. As soon as I could – after he had been taken – I went to find his daughter. But when I found the house, I was told she had gone. I asked where, I asked when, and I honestly tried to find a way of looking for her – but the family that had boarded her were not helpful. I don't know what happened to the little girl. There are many boys and girls on the streets, as everybody knows.
José Angelico was a good man, whatever he did – and I won't forget him.
# PART THREE
# 1
I'm Olivia Weston, and I was what they call a 'temporary house-mother' at Behala's Mission School. I also have one part of the story. The boys and Father Juilliard have asked that I write it down carefully, so that is what I will do.
I'm twenty-two, and I was taking time after university to see some of the world. I came to the city intending to stay in it for a few days, get over my jet-lag, and then fly on to meet up with friends for a month or so of swimming and surfing.
I visited the Behala dumpsite, though, and my plans changed.
I did go swimming and surfing – I did have a holiday. But I found lying on the beach was good for a week, and then I started to feel restless and useless. Behala had hit me hard, and I couldn't get it out of my mind. I'd gone there to deliver some sponsorship money for my parents, who had a friend who'd worked there. My father works in the Foreign Office, and had paid my airfare (and a bit more) in the hope I'd get something educational out of the trip. Sure enough, before I knew it, Father Juilliard had suggested I teach reading and writing to the little ones. Then I got involved in a water-sanitation project they have going. Then I was doing very basic first aid, because the kids are always getting scratched or bitten, and things go septic fast – and then I got the title 'temporary house-mother' – which means you agree to do daytime shifts helping out wherever you can.
I fell in love.
I fell in love with the eyes looking at me, and the smiles. I think charity work is the most seductive thing in the world, and I'd never done it before. For the first time in your life you're surrounded by people who tell you you're making a difference. The Behala children are beautiful, and to see them on the rubbish tips all day can break your heart. If you come to this country, do the tourist things. But come to Behala too and see the mountains of trash, and the children who pick over them. It is a thing to change your life.
I knew Jun – the little boy they called Rat. Jun would not call me Olivia – it was always 'Sister', and then it became 'Mother'. I am stupidly soft-hearted – I will drip tears over a stray cat back in England. Little Jun had me wrapped round his finger in about two days, and I was forever giving him little bits of food, and little bits of money. I don't know how else a boy like that survives.
We have a rest room in the school, where people can go when it all gets too much, and just lie down under a fan. We've got a small fridge in there too – and the housemothers use it as a base. Jun got into the habit of visiting me and trying to make things tidy, and I got into the habit of giving him things. So when he brought his two friends to see me, it was a nice surprise but I had no idea what I was getting involved in.
They asked if we could talk, and I assumed it was about what had happened the night before. Father Juilliard was resting, and I didn't want to disturb him – he'd been up most of the night trying to find out where Raphael had been taken, and I think he was still badly shaken – the police had not been helpful. Then, of course, the child had simply come walking back to Behala, walking in as the sun rose. I wasn't there, but I'd heard all about it – and I could see how badly he'd been beaten. His auntie had held him and held him, and wouldn't let him go. The whole neighbourhood came out, apparently. Father Juilliard says the people here are like that. When one of their number is hurt, everyone feels the wound.
Now he smiled shyly at me, pulling back his hair. The bruising was terrible, and I remember wondering how an adult could possibly strike such a child. He saw me staring, and moved behind his friend. Gardo – the bald boy – put his hand very gently on his arm before turning back to me.
Jun said, 'We don't know what to do, Mother. We've got a big problem. You know Gardo, yes?'
Gardo sat down, looking at his knees. I could see that he had tried to dress up clean – he looked scrubbed and his T-shirt was fresh. He tried to smile, but he just looked nervous. I was jumping to the conclusion, of course, that he was about to ask for money – and I was bracing myself to refuse. One of Father Juilliard's rules was that we did not give money away as gifts. The odd ten or twenty, yes – everyone did a little bit of that now and then. But I knew Gardo was building up to ask for a big sum. I was surprised, then – and a bit ashamed – when he said, 'My grandfather's in prison, ma'am, and I want to go and see him.'
I said, 'I'm so sorry. Which prison?'
He told me the name, and as I knew nothing about the city's prisons it didn't mean much and I wondered why I'd asked the question.
'Why is he in prison?' I said.
Gardo looked away, and the bruised boy – Raphael – put his arm round his shoulders and said something in his own language. I realized I had touched on something personal, but I could hardly back-track now – and in any case, it was one of the logical questions.
'They say he beat up someone,' said Jun softly, 'but it's not true. It's all corruption because there's some men who want his house.'
Gardo, I saw, had started to cry. He wiped his eyes and said: 'They're trying to get him out of his house! They file a charge. They pay the police, the police arrest him. Now they've got his house.'
Gardo wiped tears away again. Raphael hugged him harder, and said something again – something reassuring, I assumed – in his own language.
Then he said to me: 'Gardo needs to see him, Sister.' The boy's mouth was swollen, and his speech was awkward. 'Can you help us get to the prison?'
I took a gulp of water, and Jun topped up my glass.
It was dawning on me that I had been right: this was going to be a request for money. They needed bus fares, or bribe money. I was surprised again, therefore, when Gardo said: 'We need you to go with me, Sister. Please?'
'Me?'
They all nodded.
'You want me to go and see your grandfather?' I said.
Gardo nodded.
'How?' I said. I was completely bewildered. 'Why do I need to see him?'
'We've got to get some information to him,' said Gardo. 'The police were asking questions about him – that's why they beat my friend. Maybe they come for me next time!'
'I don't understand.'
'It's a difficult situation, Mother,' said Jun. I'd never seen him so grave. 'The old man needs to know what is going on here. We need some information too, to help him. Or he loses the house.'
'But your family, perhaps – your mother...'
Gardo shook his head. 'No mother.'
'Your grandfather must have sons,' I said. 'And there must be visiting times – why can't somebody just... visit? I'm not sure what good I can do, that's the problem.'
Gardo said, 'You don't understand.'
'You're right,' I said. 'I don't.'
'The prisons here,' said Jun. 'A visit once a month. Mother, they're going to lose their house – that's everything here. You lose your house, you've got nothing. And you – you're a social worker...'
Gardo said: 'You take your passport. You sign your name. They let you inside.'
I was silent. At last we'd got to the bottom of it.
The boy said something I didn't hear, and put his head in his hands. Jun put his hand on mine and said, 'We ask you because it is so important and no one else can help.'
'You're the only foreigner we know,' said Raphael. 'And the prisons out here... they do what they want.'
'You say you're a social worker,' said Jun. 'You say you just want to see him for half an hour. They may keep you waiting, OK? They may say no at first. But in the end, if you just sit there... There's a chance, yes?'
Gardo looked at me, and his eyes were still full of tears.
Jun said, 'You're the nicest, kindest mother we ever had here. He's only asking because, without this, they maybe gonna lose the house.'
'They beat me,' said Raphael. 'They think I got some papers, but I don't have them.'
'Please, Mother?'
* * *
That was how I found myself in a taxi heading for Colva Prison.
Vanity and stupidity, and the fact that three little boys could break my heart one minute and flatter me the next, all the time lying and lying. I took just Gardo with me, and the first thing we did was stop at a big store to get him some new clothes. He'd cleaned himself up, as I said, but his shorts and shirt were ingrained with so many months' dirt they were stiff on his body.
The looks I got walking him into the boys' clothing department were something I'll never forget. And the time it took him to choose was also something I remember. I'd asked the taxi to wait, thinking, _Shorts and a shirt – five minutes of shopping_. Unfortunately it wasn't like that. Gardo wanted to take his time, and he was the most intent, careful shopper I'd ever seen. He wanted jeans, and he wanted the most expensive kind. I could not pay western prices for something that I knew was probably made for peanuts in this very city, so I managed to talk him down to a cheaper pair. Then he wanted a long basketball shirt, which I thought was totally wrong for the impression we were hoping to create. I took him to a rack with formal shirts on it, and he turned his nose up at all of them. I was beginning to get flustered by now, so again we compromised. We chose a T-shirt, which he insisted must be too big. Then we chose a more formal shirt with a collar, to wear over the top.
He tried it all on, and we went to the checkout – or I thought we were heading that way, but suddenly I was in the shoe section, and he was looking at trainers. Again, the prices stunned me, but I had to admit that a smartly dressed boy with bare feet – dirty bare feet – is not going to be convincing.
We chose a medium-priced pair, and when we got to the checkout I put it all on my credit card. The reward, of course, was that I had never seen a boy so happy in my life, and – I have to say – so handsome. He emerged from the changing room, and he was simply no longer a Behala dumpsite boy! He was taller, he was bursting with confidence and smiles... he was even walking differently. I could not resist kissing him, which made the shop assistants howl with laughter.
We got to the taxi. I gulped when I saw the meter. And on we went.
# 2
Father Juilliard.
I feel I ought to say that had I known what Olivia had agreed to do, I would have intervened and prevented it. I would have seen it for the scam that it was. The problem is, you never see them coming, and six years here in Behala have taught me that some of our children are the best liars in the world. I guess it is survival. It's awful to say it, but... trust. You just shouldn't put yourself in a position where trust could be betrayed.
I am the worst, though. While they were working on Olivia, they had very special plans for me.
Raphael and Gardo were smart. But little Jun... Rat. What he did took my breath away.
Things were about to get very dangerous indeed.
# 3
Olivia. And yes, I know. It was stupid.
The taxi took me into a part of the city that was more squalid than I'd ever seen. You may say that's strange, coming from someone who works in Behala, but it's not. Behala is a huge, monstrous, filthy, steaming rubbish dump and you cannot believe human beings are allowed to work there, let alone live there. Rubbish and shacks – it's extreme, it's horrible and I will never forget the stink.
Behala also makes you want to weep, because it looks so like an awful punishment that will never end – and if you have any imagination, you can see the child and what he is doomed to do for the rest of his life. When you see the old man, too weak to work, propped in a chair outside his shack, you think, _That is Raphael in forty years. What could possibly change?_ These children are doomed to breathe the stink all day, all night, sifting the effluent of the city. Rats and children, children and rats, and you sometimes think they have pretty much the same life.
Colva, however, was something else again.
We drove on cracked roads. The pavements were broken, and it looked as if there'd recently been an earthquake. We drove between low-rise flats, strewn with washing and electricity cables. There were people everywhere, mainly sitting as if they had nothing ever to do. The taxi's air-con wasn't working, and it was getting hotter and hotter. This was the dry season, but there was talk of a freak typhoon coming in from the sea. There was real heat in the breeze.
We turned, and on our right was a high concrete wall. Gardo said, 'Prison,' and pointed, but you did not need to be told. There were coils of barbed wire at the top, some of it straggling down where it had come loose from its moorings. There were guard towers every fifty paces, open to the sun and rain. We turned right and followed the next wall. On the left were huts of bamboo and straw, and more people – many of them tiny children. I always notice the tiny children, sitting in the dirt, playing with stones and sticks. I learned later that many of the families in these shacks had relatives as inmates on the other side of the wall. They had to live there and get food in, or the prisoner would starve.
We came round to the entrance and I paid off the taxi. Then I walked up to the guardhouse. It was a concrete box with a large window. Several guards sat inside. Beside it was a red and white barrier to stop vehicles, and a man with a machine gun. I showed my passport and delivered the speech I had prepared.
They made a phone call. I noticed that Gardo was holding my hand, and I too was scared. We were kept waiting for no more than two minutes, and another officer came to the window and asked me to repeat what it was I wanted. I told the story twice because another person arrived, and then my passport was taken away. I was given a register to sign, and a visitor badge. Gardo got one too. Then we were led round the barrier and across a yard.
To walk into a prison is a very frightening thing, because you cannot help but think, _What if something goes wrong and they won't let me out?_ I was also thinking about that line – the line there has to be, and you have to cross – that separates freedom from complete incarceration. What door would it be that would swing open and shut again behind us?
We were taken past an office, and to what looked like a large waiting room. There were benches all the way round it, and we were invited to sit. Seconds later, a guard came to escort us out of the waiting room, down a corridor. At the end of the corridor was an iron gate made of bars. It was unlocked for us, and we all walked through, and it closed with that dreadful, clanging, ringing slam of metal on metal. We were shown to a smaller waiting room and asked to sit. We sat there for nearly an hour.
You don't get anywhere in this country by showing impatience – I learned that very quickly here. It is so much better to wait, and smile, and nod. Gardo said almost nothing. I could see his lips moving, as if he was saying a prayer.
Out of the blue, he said to me, 'What is _in memoriam_?'
I said, 'I think it's Latin. When somebody dies, you write that and it means, "in memory of".' I asked him why he wanted to know.
He smiled at me and said, 'Video game.' Then he started muttering again, as if he was reciting the same long prayer.
Eventually the door opened and a man in a short-sleeved shirt came in. He had a very warm smile, and he shook my hand and introduced himself as Mr Oliva. I told him my name was Olivia, and it seemed to break the ice instantly. He assured me that Mr Oliva would help Miss Olivia if he possibly could. He had a photocopy of my passport in his hand, and he sat opposite me.
He was quietly spoken and so polite, and apologized for keeping me waiting.
'I'm the social welfare officer,' he said. 'The governor is busy with some problems at the moment, or he would see you himself – we always try to accommodate these requests. The inmate you wish to see, he does get these requests quite often. You've given us his number, but it's not the right number. Are you quite sure it's Mr Olondriz that you want to see?'
'I think so,' I said.
'Yes, please, sir,' said Gardo. 'Gabriel Olondriz.'
'Like I say, he does get visitors and is always keen to see them. You know he's a very sick man?'
Gardo nodded at me, and I said: 'Yes.'
There was a silence.
'It's one of the reasons we're here,' I said.
'It is not out of the question,' said Mr Oliva. 'There are some formalities, however. Usually we can set these things up all the better if we have some notice, you see. You could come next week, maybe?'
I shook my head. 'I'm very sorry,' I said. I could feel Gardo's panic – he could sense we were close to success. 'I'm embarrassed, in fact. This is my friend Gardo, and he only told me about the problems yesterday, and he says it's urgent. I think it's incredibly kind of you to even consider seeing us.'
Mr Oliva smiled. 'You are very patient and very educated. You're a social worker, yes? In Behala?'
'I'm an unpaid worker – it's completely voluntary.'
Mr Oliva extended his hands and shook mine firmly. 'Thank you,' he said. 'Without people coming to help like this, things would be worse than they are. This city has many problems. Every city has problems – but maybe this city has more than most, I don't know. You are looking after this boy?'
I said, 'He was very upset yesterday. I didn't understand everything, but he told me I might be able to do something.'
'Is he a good boy?'
'Yes.'
'He goes to your school?'
'Not as often as I would like,' I said, and Mr Oliva laughed.
He exchanged a few words with Gardo and patted his arm. 'You know the man you wish to see is in the hospital at the moment?'
'I don't know very much about him,' I said, 'except what Gardo told me.'
'He's not a well man. I think you might be upset. Also, the conditions – the meeting area. You've been in a prison before?'
I shook my head.
Mr Oliva smiled. 'You see, our government has many pressing problems. It does not put money into its prisons – I think the same was true in your country a hundred years ago. I think you will be upset by what you see. Perhaps just the boy should come – if it's between him and Mr Olondriz?'
'I think I ought to be with him,' I said.
I didn't know why. I was getting frightened again – but having come this far, would I really sit in the waiting room? This was my year of seeing the world, and it occurred to me that to see the world of Behala, and now a jail – perhaps it would teach me more than I'd ever found at university.
Mr Oliva said, 'The problem is the fees. To organize visits like this – to "fast-track", so to speak. They told you at the gate?'
'They didn't,' I said.
'They were embarrassed,' he replied. 'It is a question of getting security clearance – we have to send somebody very fast for approval. We could get a waiver if you gave us some time.' He looked so honest. 'Is it really so urgent?' he said.
I nodded.
'I can check in a moment,' he said. 'But I think it will be ten thousand. And a receipt – with the governor so busy...'
'I don't need a receipt,' I said. I must admit, I felt slightly sick. The day was costing me a fortune. 'The problem is, I'm not sure I'm carrying as much as that.'
Gardo was looking away.
'I'll get the forms and check,' Mr Oliva said. 'I want very much to help you, but... I don't set the fees, they are set by the government.' He smiled. 'I think the government must be very rich!'
Ten minutes later he was back. He had a form in his hand. 'You will have to be photographed also, I'm afraid. And I was right: it is ten thousand.'
I was carrying eleven thousand. I had been to the bank that morning and had withdrawn extra because I was meeting friends for dinner in a very expensive restaurant that night. In half an hour they'd made a security pass for me, with my photograph and a number of signatures. Mr Oliva shook my hand again.
As he left, he called out loudly, and in a moment there were four guards in the corridor. One said something to Gardo, and he said, 'Come.'
I remember their echoing boots.
We were led to another room with lockers. We were asked to take everything out of our pockets – we had to take off our shoes and shake them. They put everything inside and slammed the locker doors, and we set off down another passageway, and I could hear people in the distance, shouting – I knew the dividing line was close now, and my heart was beating fast. Sure enough, the corridor took us into a long hall, bisected by floor-to-ceiling bars, and the shouting of men was louder still, as if we were coming to some kind of market place. We were led to a gate in the centre, and as the guards opened it, I became aware of the constant banging of metal on metal. Everywhere, doors were slamming, and I could hear the ratcheting of keys in locks. Suddenly we were in a strange no-man's-land, like a decompression chamber – a space in which the door behind us locked before the door in front was opened. Under all the shouting there was laughter, and – I have to say it – it was like animal noise, with a dreadful echo. It was also, if it were possible, getting hotter, as if something was breathing on us. Orders were shouted: everyone was suddenly in a hurry. That final door was unlocked, and we were beckoned through.
'Welcome!' cried the guard receiving us.
He smiled at me. A smile of genuine interest and warmth, which seemed so wrong for the hell we were walking into.
# 4
I had expected cells, but all I saw was cages.
They were on my left and right, and they were the type of cages you might put lions and tigers in, in an old-fashioned zoo. They were just high enough for a short man to stand up in, and they were about four metres long, maybe two metres deep. I looked up and saw that these cages were stacked three high, with ladders up the sides. They continued in long rows, and I could see that there were alleyways between them. It was so terribly hot. As we passed the alleyways, I saw that they led you deep into more cages. It was like a warehouse, but every cage held people.
As I walked among them, I was being stared at from left and right, and from above. Also, because many people were lying down or sitting, I was being stared at from below.
The noise was impossible – everyone seemed to be shouting. Gardo put his hand in mine again and it steadied me.
'Hello, ma'am!' was being shouted, again and again. Cheerful cries – friendly cries, and so much laughter. There were hands stretching out between the bars, and there were solemn faces as well as the laughing faces. 'Can you spare something, ma'am? Ma'am! Ma'am! How are you? How are you?'
I looked to the right and stopped dead.
I was looking at a boy who could not have been more than eight years old, wearing only shorts. He was smiling at me. In his lap sat a younger boy, sleeping.
I think I said, 'No,' and just looked at him, unable to move – stuck for a moment.
Gardo eased me forward gently, but the eight-year-old started calling eagerly, and he stood up and came to the front of the cage so that he was holding the bars with both hands. 'Hello, ma'am!' he said. 'Hello, ma'am – twenty pesos, ma'am.'
I turned round in a full circle. I was in the centre of the place by now, and to turn was to lose yourself, because all the cages were identical, and though there were big signs with numbers, they meant nothing to me. I had no sense of direction any more: all I could see was faces and hands waving. Man then child. Young man, then older man, then child again – thin bodies, glistening with sweat. Almost everyone in shorts only, and a smell of old food, sweat and urine.
'It's OK,' said Gardo, keeping his hand over mine.
The guard who was escorting us had not noticed that we'd stopped. Now he did, and waited. I was being asked questions. 'Where are you going? Where are you going, Sister?'
'What's your name?'
'What country?'
'American? American? Hi there!'
'I love you! I love you, Joe!'
The guard came back. Gardo had my hand and my arm, and was trying to get me moving. It was oven-hot, and the smell was getting worse. I knew that if I didn't move, I would fall. I had a water bottle with me, thank goodness – and I drank deep and long, and there were people cheering. People were shouting out for water. I lost my balance and staggered against bars – Gardo was there, but he couldn't hold me. I felt hands on my arm and on my hair, and voices whispering close:
'Help me, ma'am...'
'Nobody here, ma'am – nobody coming, ma'am...'
There was a young boy with dyed hair lying back in the arms of an older man; there was a child in a pair of torn pants curled up on a piece of newspaper. They were living in a furnace.
Gardo disentangled the hands – they were stroking me. Anxious eyes, still so well-mannered – even in despair, to keep your manners – I could feel tears, useless tears rising in my stupid eyes.
I managed to walk on. It was like going uphill – I managed to take one step, then another, and as if I was on stepping stones, I continued up the corridor. I looked ahead, at the guard's blue-shirted back, and followed him, and we came to a metal door and went through it. When it shut behind me, I leaned against the wall and closed my eyes and cried.
There was a staircase, and when I had recovered, I went up it. The noise and the smell gradually faded from me.
The guard said, 'He is in the hospital now.'
He said something to a second guard, and another door was unlocked for us. We moved out of the bright light, and I was aware of a breeze from a wall fan. My eyes took time to adjust, because the light was dim. I was led along a narrow corridor – I think there was a wheelchair. Then I was taken to the right, into an empty room, and there was a table, and several folding chairs. I sat in one and put my head low down, because I still felt that I might pass out. I think Gardo disappeared for a moment – I think I was left alone. I drank more water, and after some time I felt better.
Gardo reappeared and sat next to me.
I said, 'There were children in there.'
Gardo just looked at me.
'What have they done?'
He shrugged. 'They're poor. They do many things.'
'But... you can't lock people up like that. What have they done?'
Gardo said nothing. 'They steal,' he said, after some time. 'Maybe fighting.' He smiled his thin smile, as if to encourage me. 'They get some food. It's not so bad.'
We waited for... I don't know – time had changed. Maybe not long. And then we heard voices, and two guards arrived. They were helping a very old man towards us. They had to be slow and patient with him, because he could not walk very well. He was wearing dark, loose-fitting trousers and a white shirt, buttoned at the neck. The guards supported him, but I saw that he had a stick as well, and he made his way painfully along the passage. He was staring at me, and I was struck by his burning white eyes – short-sighted, but hungry – peering, as if he had been waiting for me.
# 5
Olivia still. They asked me to write all of this but maybe Gardo needs to say things as well. I noticed that he – Gardo, I mean – had stood up and moved behind me. I stood up too. Nobody seemed quite sure what to do.
'Miss Olivia?' said the man.
'Yes,' I said.
He blinked. 'Sit. Please, sit.' Then he said something in his own language, and the guards helped him to the chair. He was perspiring heavily – I could see moisture all over his forehead, and he found a handkerchief and mopped first his brow, and then his face, and then his neck.
At last he sat back and smiled. 'They told me your name,' he said. 'Thank you so much for visiting me. I hope it hasn't been too... dreadful for you.'
It was clearly an effort for him to speak. He seemed very sick to me – far too sick to be in prison. I couldn't think of anything to say.
'I do not _recognize_ your name,' he continued. 'And nobody would tell me the reason for... paying me this honour. Please... forgive me, I'm... As you can see, you've come when I'm extremely weak. But I never say no. I never say no.'
The man was not simply weak: he was dying. I don't know how I knew, but I was certain of it. His skin was drawn tight, and breathing was so hard. There was a large growth under his jaw, and he seemed to be in pain. Everything was an effort. Sitting still was an effort, and lifting his head was an effort – I saw him wince as he adjusted his position. He smiled at me again, and I saw his skull clearly through the skin. This was Gardo's... grandfather? But something didn't seem right. The man had not even greeted him.
'I'm pleased to meet you,' he said. 'I will tell you anything you want to know. What is your brief?'
I still hadn't spoken, and I wasn't sure that I could. I wasn't sure what my voice would sound like if I did. I moistened my lips and said: 'I'm so sorry to have...' I couldn't think what to say. 'To have... disturbed you. But Gardo...'
I looked round and Gardo was standing there, still as a post. He had not greeted the man, and the man had still not greeted him.
'Believe me,' said the old man, 'a visitor is always welcome. Without visitors I would have gone mad, and they come in fits and starts. I can go several weeks with nobody. Then it is as if I am back in fashion: I have two in a day. You, my dear, are the first face for some time. And your boy, this is... ?'
'This is Gardo,' I said. 'You know each other, don't you?'
The old man looked at me and then at Gardo. He seemed puzzled, and he smiled.
'You do know each other,' I said. 'It's actually Gardo who wants to see you. About your house.'
The man said something in his own language, and Gardo replied softly. The man spoke again, and Gardo said nothing.
'Miss Olivia,' said the old man, smiling. He closed his eyes and waited. 'I'm sure your boy is a good boy, and I am delighted that he's brought you here. But to answer your question...' He paused again, this time for breath. 'To answer your question: no. I am not acquainted with him and I have never seen him before. As for a house... I have no house. I have almost nothing. It was all taken from me a long time ago.'
'Gardo, you said this was your grandfather,' I said.
Gardo was looking away.
'I don't understand,' I said. 'You told me... Sir, I'm a bit confused.'
'Yes. So am I.'
'The reason I came was... I just said it: Gardo wanted to see you about your house.'
I was going over Gardo's story in my mind, and the confusion was getting worse and making me panic. Was it the wrong prisoner? There had been confusion over the number. Were we sitting with the wrong man?
'Olivia, you don't know who I am, do you? You don't know anything about me.'
'No,' I said. 'I have no idea.'
He said something to Gardo in his own language, and Gardo answered softly.
The man drew breath sharply, and closed his eyes. 'He says you paid ten thousand pesos to get to me. He is very generous with your money, I think. The going rate, Miss Olivia, is fifteen hundred. They got five thousand from a journalist once, but they kept him waiting three days and it was coming up to the Zapanta election.'
'I don't understand,' I said. 'Do you know Gardo or not?'
'No.'
'Then...'
'He has used you to bribe his way to me. The money you paid bribes the administration here. The guards will bring people to me, and – like I said – there are often people wanting to see me, and I thought you must be one of them. The prison authorities make a good living from me, I think.'
'But I don't... I still don't understand. Why do people come to see you?'
'Gardo, you're not going to explain this?'
Gardo said something in his own language, and there was a short, abrupt exchange. Gardo seemed to be pleading, but the old man interrupted. 'No,' he said. 'No. We speak in English with Miss Olivia. Miss Olivia has paid for this interview. We will say everything in English.' He looked at me. 'Your boy is playing a game and he wants to ask me questions on his own. He wants to speak to me privately, and I have said no. I can see you are bewildered, and – I am also very surprised... please.'
He bent forward in his chair, and I thought for a terrible moment he was going to be sick. He leaned on his stick, and seemed to be waiting for the pain to pass. He said something to Gardo in his own language again. Gardo took a cup from the table and filled it from my water bottle. He handed it to the old man, but the old man was shaking. He got a hand to the cup, but Gardo had to keep hold of it and feed it gently up to his mouth. The man clutched the boy's arm.
'I'm sorry,' he said. He drank again. 'I was saying... If I tell you who I am, Miss Olivia, and how I come to be here, things may become clearer. I am very near death now, as you can see. Do you know they still will not let me out? As if I could harm a fly.' He smiled at me. 'You know my name, but it means nothing to you. There's no reason why it should.'
The pain had passed, and he was relaxing.
'The reason I am in this jail is that I brought corruption charges against Senator Regis Zapanta thirty-five years ago. Do you know Senator Zapanta?'
'No,' I said.
'He's a big man in this country – our trusted vice-president. He is always in the papers for one thing or another. You are a tourist and you're passing through – you would not know these names. Gardo here will know the name and even the face – is that true, Gardo?'
Gardo was nodding. 'Everyone knows him.'
'In this city he is a very big man. You don't read the papers?'
I shook my head.
'Nor do I any more. Once a month if I am lucky – they starve me of the news, and perhaps it's for the best. Waiting for change has exhausted me: it's probably best I hear so little! I was never important, Olivia – I served as a small officer only, in the east quarter of the city – humble ranks. You won't know the system, so I won't... Oh, it doesn't even matter. What matters is that forty years ago I came upon information that Senator Zapanta had spirited away thirty million dollars of international aid money. It was a package of grants, with the United Nations leading, and it was to build hospitals and schools. They called it "seed-corn" money. Now, "seed-corn" money is very important in the way these things work. When a country receives such money, it is a condition that a proportion of the money is matched by the government, and by other donor countries too. In this case, that thirty million was going to be added to, by our government here and by, oh... private investment – the big banks were involved. So that thirty would, we hoped, turn to sixty or seventy. Seventy million would have changed the city, Miss Olivia – at that time. But no schools or hospitals were ever built, and the city stayed poor. Senator Zapanta stole it, and I tried to prove he stole it. It never went to court, because the senator quickly counter-sued. It seemed he had many more friends than I, and infinitely more power. I ended up charged and prosecuted. I was convicted – my appeals were laughed at. Life imprisonment, I got, and...'
He paused again, and winced with pain.
'I think the sentence is nearly over.'
# 6
Gardo again – just something short from me. Just to say to Sister Olivia that I am so sorry for what I did. We talked about it, the three of us, and we decided it was the only way – Rat said maybe we could tell you part of it, but I said no. I was the one who said we should trust nobody but ourselves.
I am sorry for that.
You must remember, please, that it was I who read the letter from José Angelico, over and over and over. We all knew – all of us – that we were so close, and what Raphael went through in the police station... Sister, I do not know how he went through that. I thought he was soft before that, just a little boy who would break, but I was wrong. Please understand, we could not tell you. It was just the three of us: Raphael, Rat and me, and already we knew that soon we would be leaving – that it was not possible to stay much longer in Behala. So we did not want anyone to know anything.
Please forgive me for that, and I hope I see you again sometime. I am sorry how it ended for you.
# 7
Gabriel Olondriz smiled at me.
This is Olivia again.
'I will tell you a little more,' he said. 'It will make sense, in time, and then this boy will tell us what he wants.'
I said, 'How can a man steal thirty million dollars?'
'How?'
'Yes.'
'It is done so often. It is done so easily – not in a suitcase: it is not like robbing a bank. In the government's case it is usually done through bogus contracts: everybody siphons a little bit here, a little bit there. It is done through clever accounting and paying off the people who should be watching. In the case of Mr Zapanta, I know many men were involved, and some probably thought they were doing our country a service. It took me the best part of two years, but I assembled the paperwork. Like you, Miss Olivia, for some time I worked unsalaried, because this was volunteer work I deemed to be of very great importance. We got copies of false contracts, and the bank transfers to invented accounts. We got copies of trans actions, always cash withdrawals, because this man always loved to handle cash. Huge sums in dollars! Dollars were the currency, never our own – and where were they going? Olivia, forgive me. I have told this tale so often it no longer has any... freshness.'
'What happened?' I said.
'He was stock-piling dollars in a vault in his home.'
'But you... you couldn't prove it?'
'I had so much evidence. Unfortunately for me, I was naïve. My office was raided. The same night there was a terrible fire at my house. I was away, but both my maid and my driver were killed in it. And every scrap of evidence went up in smoke. Then, Olivia – this was the clever part. He had been planning my downfall, and charges were ready to be laid against me – for financial malpractice. It was suggested that I had defrauded the government of half a million dollars, and it was proved that I had organized the murder of a well-known banker. Miss Olivia... to learn about the crimes I had committed while... sleeping! At first I thought it was all so crazy, and all so obvious, that I need not be afraid. I had lawyers who were relaxed also, and sure of success. But the lawyers – I realized this way too late – had been bought, and they fed all my defence straight back to Mr Zapanta. It is enough to make you laugh, almost. The senator was smart. I was stupid. In this country you pay for being stupid, just as you pay for being poor. After a few months, just as the case was going well and I was certain to win it... I was arrested. Like I said, I was convicted.' He paused. 'I have been in jail ever since.'
Gardo stood up and pressed a cloth to the old man's forehead. I saw the old man hold Gardo's hand again.
'Please, sir,' said Gardo suddenly. 'Who is Dante Jerome?'
The old man looked at Gardo, and then at me.
'I think this boy has many questions,' he said. 'He has come to ask me questions, and I will answer them. Dante Jerome was my son.'
'What is the harvest?' said Gardo. 'Also – sir – there are some words: _It is accomplished_. What does this mean?'
The old man said: 'What is accomplished? What do you mean?' He was speaking quietly.
' _It is accomplished_ ,' said Gardo. ' _Go to the house now, and your soul would sing_.'
The old man worked his lips, and stared. 'I need you to tell me what is accomplished,' he said. 'You have to explain yourself, I think.'
'I don't know,' said Gardo. 'I don't know what it means. But I am told that if you could visit Senator Zapanta's house right now, your soul would sing because it is accomplished.'
The old man opened his mouth, but he said nothing. He looked at me, and then at Gardo. His eyes had become luminous again, and he was leaning forward in his chair. He took hold of Gardo's wrist and said – very softly: 'Who are you, boy? Please stop playing games now. You know things that are very important.'
'I am from Behala dumpsite.'
'Yes. A street boy, I knew it.'
He held Gardo tight. 'And that is one of the... darkest streets, I think. I worked for many years with street children, my son also. You will think I am being cruel, Olivia, but under these new clothes I can smell the street. It never, ever goes away. Why are you here, boy? Please tell me.'
Gardo said: 'Because I have found a letter from Mr José Angelico, sir. We found it in a station locker. It is a letter that the police are looking for, and it is addressed to you, and it says that you must rejoice because it is accomplished.'
'Give me the letter.'
'I did not dare to bring it, sir.'
'Why not?'
'For fear it would be taken, sir.'
'José writes to me each year. Why would you have a letter he wrote to me?'
'We think he wrote it just before the police took him. We found it, and—'
'Why did the police take him? Where is he?'
'The police killed him, sir. He was killed when they were questioning him.'
Gardo spoke softly, but the last words still fell like a blow. I saw the old man wince again and buckle, and Gardo stood back from him. He talked softly to the old man in his own language, and the man seemed to take yet more blows – I watched his old hands clench into fists. When the gentleman looked up, his face was wet and all I could see was pain.
We watched the old man shake. Something deep inside was shaking him, and there was nothing we could do but watch.
# 8
This is me, Raphael.
Sister Olivia was a good friend to us that day, and – for reasons that will be clear soon enough – we did not see her again to say thank-you. Writing this is a way to say thank-you, and one day maybe we will meet again and say it the way we need to say it.
I am so sorry for deceiving you, Sister.
I must talk about what we did while Gardo was in the jail – which was important. Then I will hand over to Rat, and write for him. You see, he and I decided to do something too, because it was hard sitting waiting and waiting all day, and I have not felt right since the police station – I cannot stay still, and everyone is looking at me always. We took the letter again, and stole off by the canal to a place nobody goes – a place I felt safe in, where you could see people coming. We squatted down and went over the newspaper cuttings again, me reading them out, all the way through. I read the letter too, which was coming apart in my hands by now. We both knew it almost by heart, since we'd been helping Gardo remember it – even the jumble of numbers stuck on at the end. Those names again, coming at us: José Angelico, the man killed in a police station. He felt like a brother to me now and I was dreaming about him. Gabriel Olondriz, his friend in Colva Prison. And now the fat senator, Zapanta... When I read the line about Senator Zapanta, Rat stopped me and made me re-read it: ' _If only you could go to Zapanta's house now: it would make your soul sing_.'
'What's that mean?' said Rat.
I didn't know. We'd all been saying that every time we read it: _I don't know, don't know, don't know_.
'Where's his house, though? Maybe we should visit.'
'Green Hills,' I said. 'Everyone knows that. Same place as José Angelico.'
The senator was a famous man, and everyone knew he had a place out there, just beyond the city, big as a town. Everyone knew he was rich and old, and I'd seen his fat face in the papers I hooked up, oh, so often – papers that more often than not wrapped up the stupp. Everyone knew he owned big pieces of the city – there are only five or six families who do out here, and his name was on streets, on a shopping mall in the fancy part of town, and in rising skyscrapers... He was a big man in every way. Vice-president for two years and his smiling face everywhere.
It was Rat's idea to pay him a visit, and I liked the idea, if only to get me out of Behala.
'Why would seeing the place make your soul sing?' said Rat. We wondered and wondered, and agreed that taking a trip might tell us.
It seemed to me the problem would be the usual one. Money – for the bus. I'd given everything to my auntie, so I was broke again.
Rat said to me, 'It's OK. I got enough.'
I have to say I didn't believe him. I said, 'How have you got anything?' I didn't say it to be mean – it's just that he's about the poorest-looking boy on the dumpsite, so the idea he had more than a peso made me smile.
He smiled right back at me and shook his head. 'I've got more than you think,' he said slowly. 'Come with me, and let's see who's poor.'
And that was when I came to learn a few things about Rat that I had never known and never asked about.
We cut back to the trail that takes you to the disused belt – belt number fourteen – checking the whole way that nobody was watching. I was still feeling scared whatever I did now – I could not shake it off, and I was always watching behind me, so when we went down the steps, and the rats flew up, I cried out and he had to hold me like a little kid.
'How do you live down here?' I said. It was the most disgusting place on the whole dumpsite.
He just laughed. 'It's the best house I ever had,' he said. 'You don't like it because you're lucky. You always had a house.'
'I don't know how you stand it, boy.'
'They don't bother me, I'm telling you. You get some that are friendly.'
'And what about at night?' I said. 'They never take a bite out of you?'
Rat laughed at me. 'They have a sniff, OK – maybe, when I'm sleeping. But what they gonna bite? There's no meat on me.'
He lit a couple of candles. I could hear scufflings in the wall, and mewling yelps.
'There's a nest somewhere,' I said. 'I wouldn't sleep down here if you paid me.'
'There's always nests everywhere. That's a big one, though, OK? They kept me awake last night – must be hundreds of them. Oh, and by the way – that bag...'
'What about it?'
Just the thought of the bag and I froze up.
'You can tell the police to come down here and look, because that bag's gone, Raphael. Two nights, and they'd eaten it. The wallet too: chewed up and disappeared.'
He was rocking a brick backwards and forwards gently. Then he turned and looked at me, suddenly serious.
'By the way,' he said, 'I better trust you. I just better trust you, and you better be good to trust. I know you're going to tell Gardo, but you tell nobody else!'
'Tell what?' I said. I had no idea what he was saying.
'I'm just thinking, here you are – here's me, showing you all my secrets. You could rob me blind now, you and Gardo – what would I do then?'
He was fierce, but all I could do was laugh at him. Not to be mean – but the idea of robbing Rat was crazy.
'What is there to rob?' I said. 'A little pair of shorts, and you're wearing them.'
Rat started to laugh right back at me. It was a high-pitched squeak of a laugh. The brick was on the floor now, and he was reaching into the space behind. Carefully, with his thin fingers – with the rats going crazy all around us – he removed a small metal box, not much bigger than a cigarette carton, and closed up tight. He set it between his feet and opened it.
He grinned up at me. 'Not much to rob, huh? You want to see what I've got? I've got more than you think.'
'What's in there?'
'Buried treasure, boy. Two thousand, three hundred and twenty-six pesos. My going-away fund.'
Sure enough, he showed it to me, counting it out. I think the amazement must have shown in my face, because he started laughing again, and rocking on his heels. 'I got one more box for just day-to-day stuff,' he said. 'One more tin box, that is, so the rats don't eat it. Two hundred and sixty in that one. I figure, today we're on a kind of holiday – so I'm gonna borrow out of this one, the travelling box.'
'But how do you get so much?' I said. I was totally amazed. Two thousand was a fortune for boys like us.
'I get it slow, and I keep it. Everyone gives me a little. The little piles up, and I don't eat much, or I get given food. Sister Olivia, for instance – she gave me fifty just yesterday, and then I went back for a sandwich.'
'And what are you saving for?'
Rat put his head down and seemed to be thinking hard. Then he crept to the steps and took a long look up them, like he really thought there might be someone listening. He came back and squatted – put a banknote in his pocket and closed the lid of the box. Then he put his hands up on my shoulders and looked right in my eyes.
'You and me are friends now,' he said, 'right?'
I nodded.
'Real friends?' he said.
'Of course,' I said.
'OK, I'm going to tell you something I never told any other boy. I told Olivia, made her promise to tell no one, just because I was so tired of never telling.' He dropped his voice to a whisper. A rat ran over his foot in the darkness, right between us; I had to force myself to keep still. 'I'm not from round here,' he said. 'You know that, don't you? Like, most of you are Behala boys, but I come from the south. I was at Central Station for nearly a year, and I heard about the Mission School, so this is where I came.'
I nodded again, and he was quiet. Like the secret inside was so big he couldn't say it.
'I want to go home, Raphael,' he said. He was so quiet I could hardly hear. 'I came off the islands when I had to. I want to go back.'
'Where's your home?'
'Sampalo. That's where I was born.'
'Go home then,' I said. 'You can go home with two thousand, can't you? The ferries cost... I don't know—'
He snorted, and I shut up.
'I can go home on the ferry, sure – go tomorrow if I want. And then what, when I get there? It's cost a thou just for the ticket. What happens then? You think people in Sampalo live on sand? That's why everybody comes _here_ , man – that's why I came here. That's why I got sent here! I've gotta make a stake. Fifty thousand is what I need. Then I buy a boat, and I go home and fish for ever.'
'You can fish?' I said.
'Course I can fish! I was fishing before I could talk! I could swim before I could crawl! I will buy a boat, and I'm going to fish and fish and fish.'
I looked at Rat then, because he sounded so fierce – and that wide-eyed, old little face looked back at me. I tried to imagine him back on his island, Sampalo, steering his fishing boat, throwing out the lines. I'd heard of the place, of course – and never known it was Rat's home. It was a place people talked about, and I knew it was a long, long way away. Tourists went there, and it was supposed to be beautiful as paradise. You cried when you got there, you cried when you left – that's what people said.
'With a boat I can fish,' he said. 'That's got to be better than what we do here, hasn't it? Huh? Little house on the beach?' He was looking at me hard. 'Fishing boat out on the sand? None of this stink – none of this... crazy way to make a living. You, me. Gardo too – all of us maybe. Sun comes up, we're already out. Been out all night, maybe – you think about it.'
'I can't fish,' I said.
'So what?' he said. 'I teach you. Cook what you need, sell the rest at the market – grow flowers. I had a sister grew flowers right out of the sand. You like the thought of that?'
'We'd need more money,' I said. 'We'd need to buy three boats, not one.'
'Yes,' said Rat. 'Maybe so. But...'
He was quiet a moment, thinking hard. 'Whatever happens, we can't stay here much longer, can we?'
I felt him touch my face very softly.
'I don't know,' I said. 'I guess we've got to wait and see what happens.'
'You can't stay here, Raphael. You'll always be thinking they're coming back for you.'
I was still swollen up and bruised, but the cuts were healing. My ribs were aching from when they hauled me in back through the window, and every time I touched them I felt sick again. So, yes – I did know what he meant, but how he knew it I don't know. That time with the police had changed everything, and people seemed different now too – people were looking at me strangely, like I'd brought bad luck. They'd all been pleased to see me back safe – but... my auntie was scared, and I was scared. There was something else too that I never told Rat, because I was ashamed.
It was sleep.
I was finding sleeping hard. I was having nightmares and waking up crying. I'll tell the truth – I said I would – I was wetting myself too. I would wake up with Gardo holding me like I was a baby and the cousins waking up scared, crying out, and the neighbours banging the walls because I was screaming so loud.
I think Auntie wanted me out, and I didn't know what to do about it.
# 9
This is Rat, also known as Jun-Jun – I tell my story and it's written down!
We took a bus from the dumpsite, took it right into the city to the big crazy bus station, Raphael going first and doing the talking. OK, he was bruised up, so he still looked a state – but when you look like me, you can't even get a ride very often, not when you're alone: you get kicked off like you're a curse. So he led the way but I was steering, hiding my ugly face till we were squeezed on up the back.
Of course, when we got to the stand we found out that buses to Zapanta's land went from a different place, so we jogged a couple of miles and caught a big red one. Under bridges, over bridges, me by the window looking out over the freeway past some shopping mall the size of a town with a great big sports stadium where they were going to have some great big boxing match, pictures of the fighters on scaffolds, grinning down like giants. People getting up and people getting down, running for the bus, and the ticket boy banging the side, screaming – then in two hours we were free and running out into the fruit fields in the sun. We went high up a hill and then came down into a valley, and it felt good to be getting so far away, and I could feel Raphael relaxing too, and we were humming to the music and playing with some sweet little kid on the seat in front of us. We even got a nice view of the sea, because Green Hills is right by a very pretty stretch. The rich all love a bit of the sea, don't they? – and it sure smells nicer than the sludge and stupp we call Behala.
Then the driver stopped by a huge set of gates and whistled to us.
People watched us getting down, and I said goodbye to them all, shaking hands for fun – them thinking I was a mad kid being taken out by a friend so smiling back. I was laughing when we hit the ground, and I took care that we moved on straight away, though I took a big look at the gatehouse – I wasn't going to let Raphael keep still, because I knew he was scared of everything, and if I let anything happen, Gardo would probably just cut my head off with his hook.
Two guards by the gate looked right at us, and I felt him tense up, but we were gone, me first, him right behind, holding my hand. I saw a guard with a dog just inside, and there were two with machine guns. There was a big pole to stop traffic getting through up the drive, and spikes up off the road in case anyone tried it. The road stretched off into the distance, and all the trees and grass were like a park – like paradise, like Mr Vice-President had bought up paradise and got his boys on the door in case anyone came wanting a piece of it. We ran, me laughing like we were just kids out having fun – little kids that nobody gets suspicious of – and we kept going, following the walls. We came to another gatehouse soon, just as grand, with big metal gates tight shut – and we kept on going. I guessed there'd be cameras somewhere, but the only ones I'd seen so far were at those gates, so I was more hopeful. I was pretty sure we could get into the grounds if we wanted to, just by hopping up a tree. How close we'd get to the house was another thing.
And why would our souls be singing? Maybe it was on fire, and the fat man's ass was roasting like a pig? That would be a thing to see. Anyway, that's when Raphael stopped, out of breath and sick suddenly. He pulled me back and said: 'Is this such a good idea?'
'What?' I just pretended not to understand, trying to get him on again.
'Is this a good idea? Rat, if anyone sees me...'
I put my arm right round him and pushed him to the side. 'Who's going to see you?' I said. 'You're asking this now? Spending my money, and all you want to do is go home?'
'I'm just thinking...' He was trying to be calm, but he was sweating bad. 'What are we going to find out? All we're gonna do is get ourselves chased and maybe even thrashed—'
'We've been chased before, Raphael. They don't catch us.'
'This is someone big, though. You saw the size of that dog!'
'They're for show. They're all lazy as hell—'
'We've _seen_ the place,' he said. 'We can see what kind of place it is!'
I trotted on to a tree. I felt I had to keep him moving, so I pulled him towards it.
'Just follow,' I said. 'You're braver than me. We can do this!'
I got up the trunk and hauled myself higher. Raphael followed, thank goodness, and soon we were up in the leaves looking way over the fence into the promised land – I did Bible study at the Mission School and it was helping me now: I felt like little Moses. We eased out onto the thinnest, longest stem that could take our weight, and dropped easily onto the grass, rolling up onto our feet. Then we were running again, towards a little cluster of trees. Coming through them, past a little pond, we found ourselves on what I knew was a golf course, with nice little lawns and a flag, and a little sandpit for the kids. There was nobody around, but water sprinklers sprinkling, to keep the grass looking so fresh and green you wanted to roll in it. We kept low, and we tried always to be in the cover of rising ground if we could – but we saw nobody.
Soon we got to a line of huge trees, whose branches came down low. They were brushing the grass, and it was a good place to be – it was cool, and we were hidden. We were squeezing through to the other side and looking out – that's when we saw it.
Raphael said, 'Boy.'
I just looked at it, lost for words.
'How many people live there?' he said.
I laughed. I laughed for some time, and finally said, 'Do you know, I bet it's just him! I bet it's just one big man, walking around all day, looking at his money, scared to death someone's coming to get it.'
'How rich do you have to be?' said Raphael. 'Just look at it...'
'Look at the towers, man – it thinks it's a castle. It thinks it's in a fairy tale.'
I was drinking it in, too amazed, because I had never seen anything like it. The man had chosen his spot, I'll say that for him. He'd bought up the prettiest bit of woods in the land, and just where the grass ran down nice and flat, he'd built himself a palace, for the king he thought he was. It was all black and white wood, like stripes and crosses, with so many windows you wouldn't want to count them, let alone clean them. It was all stacked up in layers, and there was a golden dome in the middle, catching the sun – like halfway through, the builders had said they ought to try making a cathedral, just for the fun of it. At each end stood a tower with battlements, and our country's flags were waving proudly, and everywhere else were fussy little spires and statues. There was a great big fountain too, jetting up right in the front, shooting up even now, in the dry season, with nobody to look at it except us.
As we watched, coming up the drive we saw a police car. Then, just behind us – just as we drank it in and wondered – a low voice very close said: 'What are you wanting, boys?'
I cried out and swung round – but poor old Raphael was just running. He ran straight out onto the grass, then stood, not knowing what to do, like some kind of stranded cat. I held my ground and shouted: 'Stop! It's OK!' Sometimes you just know there's no danger, in a split second, and I knew the main danger was Raphael getting seen in the open.
The man's voice was calm.
The man who'd spoken wasn't angry with us. He was under a nearby tree, just back from ours, and we simply hadn't seen him – he hadn't even meant to scare us, I was sure of that. He was crouching so low and still that we'd gone right past. I could see a pair of grass-cutters in his hands, and a wide hat to keep off the sun, and it was obvious he was just a lowly old gardener, one of the hundreds they must need to keep the place so neat.
Raphael sidled back and got behind me, shaking and panting.
'You looking for anything in particular?' said the man.
'No, sir,' I said.
'Oh, just passing through. Maybe you just came to laugh?'
'What's there to laugh about?' I said.
The man smiled at us both. He could see Raph was in a state. 'I thought you must have heard, and that's why you're here. Sit a moment,' he said. 'Have a smoke. The boys at the gatehouse say we're getting a lot of people coming by, asking if the papers are true.'
'We're just roaming,' I said. 'What's in the papers?'
The man smiled again, and took off his hat. His face was so creased it looked like an old fruit – he was totally sunburned, and all I knew was, he was old as hell. A laugh came from deep down in his guts and rattled on until he was coughing, so he pulled a cigarette from somewhere and lit up, offering the pack.
'It's only been in some of the papers,' he said. 'But no one knows for sure. They don't want to admit it, that's what I think – but what are all the police cars for? That's what we're asking.'
'What _are_ they for?' I said, taking a cigarette.
'You counted them? How many today?'
'Seven,' I said, shading my eyes. There were seven cars round the fountain.
'Yesterday there were twelve. Day before that... sixteen, and the president was here. Dropped in by helicopter.'
He started to laugh again. I passed a cigarette to Raphael, and we huddled back in the shade.
'Those police down there, fooling about. Walking in the big man's house, I don't know why. It's all over, as far as I can see – the show's over, so what's there to do? I guess they're standing around, all asking the same questions. You know who lives here, don't you? You know who you're visiting?'
'Yes,' I said. 'The senator.'
The gardener was smiling at us wider than ever, with his head on one side. 'I worked here twenty-two years,' he said. 'Spoken to him twice. First time I said, "Yes, sir," and the second time I said, "Thank you, sir." He's the fattest man I ever saw too – they had to get a car sent back and made bigger for him. I'd get sick on the food he throws away!' He coughed, and smoked deeper. 'You know, I wish I could go inside. I want to go in there and hear what they're saying. I can guess, though! It's not hard to guess, maybe.'
'About what?' I said again. 'What happened there, sir?'
'He must be working hard, covering it all up, trying to save his face. He'll spend anything not to look a fool.'
I said nothing then. _Let him tell it_ , I thought – _he's getting to it_. Raphael was right behind me, listening close, and the smoke was calming him.
The old man closed his eyes and sucked on his cigarette. 'It does me good,' he said, 'just to think about it. I think all those policemen are standing around, all very polite, and saying, "Sir? Tell us again. How did you let your houseboy walk out of the door with six million dollars?" ' He laughed loud and long, and Raphael started to smile too. So did I.
'Six million dollars,' the man said at last. 'Picked them up and took them out of the door. You know how he did it?'
We both shook our heads, smiling wider. It felt good just to see the old man having such a fine time, remembering it.
'Everyone here knows,' he said, 'but the papers don't have everything – they don't have the whole story yet. It was the boy they trusted.'
'What did he do?' I said. I could feel Raphael holding onto me tight, because it sounded like the pieces were fitting together. Once again, we knew we were close to whatever it was we were chasing.
'The word is, he did it with a fridge.'
'What?' I said. 'Did what with a fridge? You saying six million dollars... what—'
'It's what the guards say,' he said. 'One of the maids as well. The name's in the papers, but they won't say what he did. They won't say why they killed him, either.' The old man spat on the grass. 'Well – he was the houseboy here. Worked here – I don't know – not as long as me, but long. I knew him to talk to, smoke away with, and he was a nice enough boy. What I hear is that a little while back he gets told to buy a new fridge. The old one's dead, and the man needs a fridge for all that food! So – the boy orders one, and men deliver it. The boy says, "Take the old one with you, please?" Fair enough, it's got to go, it's just junk to the senator. These delivery men, they have no objections – there'll be parts they can sell. So they load it up, and our boy rides with them in the truck, with the gate pass. Chats with the guards, laughs – cool as cool. All on camera, so they say – the fridge, all roped up in sheets. But he doesn't get down. He stays on the truck to show them a short cut. Then he stays all the way. Says he wants the fridge for himself, because he knows he can make something on it. So he gives them two thousand pesos to set it down just where he wants it – and that's good money: nobody's making problems with that kind of money. Some graveyard, they say – not even a house. And that's the end of the trail. He's never seen again.'
'He'd put the money in the fridge?' I said.
The gardener was laughing again. 'That's what everybody thinks. Six million dollars in a broken fridge!'
He nodded at the house and the police cars.
'And they're just standing around, I bet. No idea where it's gone. What a boy! I just wish I'd got to shake his hand.'
He stopped smiling.
'How did they get him?' I said.
'I don't know. The papers don't say.' He threw his cigarette into the grass. 'I know he had a little girl, so they could have traced her, maybe.'
Raphael spoke for the first time. 'His name was José Angelico, wasn't it?' he said.
The old man looked up and stared. Then he nodded. 'You read about it, huh? You know they found the fridge? I guess they're asking where he put the cash – that's what they want. I tell you, boys, I hope he gave it away before they killed him, because I believe that son of a bitch in there's been stealing for years. Stealing even from me and you – can you believe that?'
He was shaking his head.
'Vice-president,' he said, and he spat on the grass. 'I hope he never gets it back – not a cent of it. And I hope the shock kills him.'
# 10
Olivia's story – last section.
'José Angelico was my grandson,' said the old man.
Gardo held the cup to his mouth again. The old man drank and wiped his eyes.
He laughed briefly. 'I have many grandchildren,' he said. 'Shall I tell you why? Because Dante – you asked about him, Dante Jerome – that's my son: he adopted thirteen boys and nineteen girls.' He smiled, but it was a tired smile. 'I know that sounds impossible, but it was some government programme. You could adopt children then as easily as... hail a taxi. Dante started a school, you see – probably like the one you work in, Miss Olivia. And he had four children of his own, and he found that it was safest to adopt the children in his care. Every time I saw him, I'd say...' His voice trailed off. 'Oh my.' He scratched his head. 'Little José, little José... What a way to end.'
Gardo spoke again in his own language.
The old man groaned, and then he coughed and fought for breath. We waited.
'José was a favourite. One should not, I know, have favourites. But José Angelico... He was the sweetest boy. He was clever too, and he did not sleep – he was always working! "I will be a doctor," he would say – so many of them say that. But... Oh my, we thought for a while it would come true. Olivia, is this making sense to you?'
I nodded. 'Yes,' I said. It was a lie, because I was totally confused.
'Oh, Gardo... you didn't bring the letter,' he said. He looked at the boy. 'Is there something in it that... is dangerous, perhaps?'
'We think so,' said Gardo. 'I thought the police might take it away. My friend was arrested, so we know they're looking.'
'What about his daughter? Where is Pia Dante?'
'We don't know, sir.'
'She will have nobody.' He was lost in thought for a moment, and then he said to me: 'He wrote to me every year, José. On my birthday and at Christmas. Once he wanted to be a doctor, then a lawyer. Dante would have found the money – he had ways of getting money! So many deals, the boys he put into college – if they were clever, I mean. But little José...' He winced and wiped his eyes. 'Not so little any more. I saw him last year – he was a man, of course. He wanted me to see his daughter – she also is my god-daughter. Oh...' He wiped his eyes. 'He gave up his studies years ago – he was just a houseboy, you know. Better than many jobs, I have no doubt of that, but we had hoped for better things... I think he lost patience.'
'Patience with what?' I said.
The old man paused. 'You cannot wait for ever. How long they keep us waiting: for ever. We knock on the door for ever? José lost patience, lost ambition, dropped out of the school. He didn't tell me where he was working. Boy,' he said, turning to Gardo. 'Please – we had better do this business. I am so tired.'
'Sir,' said Gardo.
'You asked me what _It is accomplished_ meant – that was in the letter. Speak truthfully.'
'Yes,' said Gardo.
'Can you remember exactly what he said? Is this why you're here?'
'Sir,' said Gardo, 'I memorized all of the letter. If you like...' He looked at the door. 'I can say it to you.'
We both looked at him. 'You memorized the whole letter?' said the old man. 'By heart?'
Gardo nodded his head. 'It is not so long,' he said, smiling.
The old man sat back, and Gardo licked his lips.
'Speak.'
Gardo stood up straight. He put his hands behind his back, and I had a vision of him in a classroom, reciting.
' _To Prisoner 746229_ ,' he said. ' _Cell Block 34K, South Wing_ , _Colva Prison_.' He took a deep breath. ' _Dear Grandfather. It is a long time since I have written to you but you have always been in my thoughts, particularly of late, and you will perhaps be happy to know that on your birthday many glasses were raised in your honour. Not a day goes by without me thinking of you, even though getting to you is so hard now, especially as duties take me away from the city_.'
Gardo paused.
' _I think also of Dante Jerome, your dear son_ – in memoriam. _I bring up my daughter to honour his memory and your own. Sir: I am to tell you something important, and it may be that I never see your face again. I tell you that the seed-corn has been planted, but not in the way you expected. Soon the harvest, I hope and pray, soon the harvest because it is accomplished, it is accomplished, it is accomplished. I say it three times, but if I could make a banner – if I could write it in the sky for you to look out on, I would do so. My friend, it is accomplished. I am writing in haste, because nothing is for certain, and I have many reasons to be cautious always, as you said to me so many times. I know they will find me. This letter will lie in a private place, with instructions. If it comes to your hand, then you know I am taken. Ask after my daughter, please – use any influence you have, for I am afraid for Pia Dante now. But the seeds are safe, sir – and the veil of the temple is rent in the midst. If only you could go to Zapanta's house now: it would make your soul sing_.
' _Your loving godson, José Angelico, bless you, your wife, all your many children and their memories, and all of us so lucky as to be born in your light_.'
Gardo stopped, and I could see that the old man had gone pale. His eyes were closed and he was very still. His mouth was open, and I thought for a dreadful moment that he was having a heart attack, or was about to. I could see his chest rising and falling. Gardo took up the glass of water.
'No,' said the old man. 'What he says is impossible.'
'That is the letter, sir.'
'There was something else,' whispered the man. 'He said there were instructions.'
'Sir?'
He managed to open his eyes, and all at once his face was changing colour. His face was damp again with sweat, and he turned to Gardo and reached for him. He held the boy's arm. 'Was there something else? A slip of paper?'
'Yes, sir.'
'Of course there was. There always was. Did you bring that?'
'No. I memorized... some of it.'
'Why only some of it?'
'Because it...'
'Because it was too long? Because it made no sense?'
Gardo was nodding.
'It was just numbers and slashes, wasn't it? Boy, you are chosen.'
'Yes, sir. It was just numbers, starting 940.4.18.13.14. Then I think 5.3.6.4 – I can't remember any more.'
Gardo paused, and the old man whispered, 'You don't know what it means. You've got the instructions, Gardo – you're holding a key... The numbers are a code.' He spoke in his own language; he was fidgeting in his chair, trying to stand.
'You did right not to bring the letter,' he hissed. 'Oh, my boy, you are – you are an angel. You are a young, sainted angel. It's a code that we used, José and I – other boys too. It's what you call a book-code, simple when you have the book. We played games with it, but it was also for special things. Those numbers... they correspond to letters on certain pages – I must get my Bible. If you know where to look – if you know the rules... the code is so simple.' He spoke in his own tongue again. He was standing now, leaning on the table.
'What's he saying, Gardo?'
'I need my Bible. My Bible is the book we used.'
'I don't understand,' I said. The door had opened: a guard was standing there, watching us.
'Of course you don't. How could you? I'm explaining nothing, Olivia – the boy must have my Bible, and I think it will... oh God. I can't... It might reveal where the seeds have been placed. If he is serious, and he must be serious! He would not... trifle – he wouldn't write in that way unless it was true.' The guard walked towards us. The old man didn't notice. ' _It is accomplished_ was the phrase we used – it's the words of Christ, yes? – the best translation. You read your Bible? In St John, at the crucifixion: _It is finished – accomplished_ – and we used it, flippantly perhaps, referring to the finding of... the restoration of all that had been stolen. That is what we spent our lives hoping to accomplish. Do you see now?'
A light was dawning, even on me. I said: 'Are you saying that José found some money—?'
He cut me off and turned to the guard. 'I need my Bible, sir. It's by my bed.'
The guard said, 'It is the end of the visit, sir.'
'I need my Bible, though,' he repeated.
The guard nodded, but did not move. He said something in his own language again.
The old man said, 'Please, I have to give my friends something. They have come all this way.' He spoke in his own language, and the guard looked at him steadily. When the guard spoke again, it was brief and terse.
The old man looked at me. 'He cannot help us now,' he said. 'He says that the visit is over, and nothing must leave the prison. But he says that he will help us. His name is Marco, and he says you have to go.'
'Can't we take the Bible?' I said to the guard. 'Where is it?'
'He says he will give it to you later. His name is Marco, and I have told him that it's important. He has promised. You have promised, haven't you?'
The guard nodded, and ten minutes later I was outside the prison gate, with Gardo by my side. We waited, but nobody appeared with a Bible, and the guard had gone. He had spoken in a low voice to Gardo, and Gardo had spoken earnestly back, and they had shaken hands.
'He said it is impossible to give it now,' Gardo told me as we looked for a taxi. 'But he says he will bring it to Behala.'
'When?'
'I don't know.'
'You didn't ask? What did you say to him? Is this... I don't understand what's going on. Will he bring it?'
'He will want money,' said Gardo softly. 'I think he will want a lot of money, but he will bring it. This is very dangerous now, for you also. He could betray us.'
The following morning, many things happened, and this is the end of my story.
Gabriel Olondriz died peacefully in the prison hospital. His death was reported in many newspapers. I assume the prison guard – the one who had the old man's Bible – realized at once that he had in his possession a precious relic of a famous old political soldier. That meant the price of the Bible could only go up. Perhaps he had overheard the old man, and understood part of the story. Perhaps he had simply seen the light in the gentleman's eyes, and knew by instinct that there was a fortune to be made.
I never saw the guard again, because I finish here – things moved fast and I have never been so frightened.
When I got home, I went out to dinner as planned, and despite everything I'd seen, I slept well. In the early morning, however, three policemen came to my hostel, and I was asked to accompany them to a police station. My friend Mr Oliva had faxed everything to his security chief, and someone efficient put Gardo and me into some computer. I had given our Behala address, and that address must have tripped the alarm. Of course, Behala was under surveillance, and any activity from the dumpsite – anything strange – was going to ring bells and alert people.
They were there on my doorstep, three of them. I was terrified – I had no idea what to do. I got a message to Father Juilliard and he came straight away, thank God, and contacted my father. The police warned me that they would find out everything: I protected the boys as best I could, hoping to God they wouldn't be taken again. I guess I was lucky that I had understood so little. I did not mention a Bible, and I said that Gardo and the old man had spoken in their own language – that as far as I knew, they'd been talking about a house, grandson to grandfather.
Because of my father, somebody from the British Embassy arrived, and argued very strongly that I was naïve and innocent. I had also broken no law. No charges could be brought – the official kept repeating that, gently, persuasively.
After some time I was released and my passport was returned. I took advice and I was on a plane out of the country the same day.
* * *
And that is my story, and thank you for letting me tell it. I left part of my heart in your country, boys, and now I can never go back. I say to myself, so what did you learn? What did you learn from the Behala dumpsite, and how has it changed you?
I learned perhaps more than any university could ever teach me. I learned that the world revolves around money. There are values and virtues and morals; there are relationships and trust and love – and all of that is important. Money, however, is more important, and it is dripping all the time, like precious water. Some drink deep; others thirst. Without money, you shrivel and die. The absence of money is drought in which nothing can grow. Nobody knows the value of water until they've lived in a dry, dry place – like Behala. So many people, waiting for the rain.
I said goodbye to so few and I can never go back. That is a pity, and it feels so wrong, because in Gardo, Raphael – and maybe most of all Rat – I left part of my heart, and writing this only makes me long to see you again, and this page is wet with my tears, boys.
Goodbye, and thank you so much for using me.
# PART FOUR
# 1
This is Rat once again, aka Jun-Jun, and I tell the part where I was the leader. Where it gets bad, bloody and oh so dangerous!
It was soon after Gardo got back, with me and Raphael waiting for him by the canal, the sun going down. He got back, and the police came in. Almost before we had time to talk, we heard the siren, and oh my God, it was a river of blue! If they'd come slow and quiet, OK – maybe they'd have got us, but oh God, thank you again that they love to make a noise and have to show up like some carnival, sirens blasting out over the town. We just did the obvious thing: soon as we saw them, we made off, no time to say goodbye, just a half-minute to grab my money, and out we went. Behala's a mile wide, and there are so many ways, so I led them down to the docks, we got a garbage barge across the bay, and then walked.
Gardo has a friend of an uncle or someone who has a store selling dry goods, and we slunk in there and slept over, wondering what on earth we should do, now we were really on the run.
That's what it was for us: _on the run_ , wanted men with no place to go! We had the letter still, and the map – and Gardo told us all about the Bible-code, or what he understood of it. We told him about the fridge of money and Zapanta's house, and we sat there thinking and thinking, wondering how we'd do what we needed to do – everyone sure we needed that Bible, and nobody knowing what the next step could be.
I had the idea right then, because it was clear to me we had to stay safe. I said we should lie low in one of the big tourist areas where so many street kids work and beg. There's a great gang of them there, and I'd spent some time in it after my station days. So that's what we did: we went up to the strip joints around Buendía and found a spot by a cheap hotel. We put ourselves on the edge of the crowd and tried not to draw attention. I cut off Raphael's hair, just in case anyone came looking – made him look like a little madman, though he's cute enough still – cute enough to beg from foreigners, though he wouldn't do it.
I said you got to, he said no. I said my money wouldn't last, and Gardo told me to shut up. So I sewed the cash into my shorts, and looked after us all with it, eating on the street and smoking to look rough as we could. We stuck together and stayed in the dark – stayed with the street boys for a night in the ruin of a place they used, but none of us felt safe. They weren't mean like the station boys, mainly because there's so many coming and going, but I think we were just so used to being a three. The crowd made Raphael nervous. We found a tiny room instead, high up in a stack of old shacks over a laundry. It wasn't much bigger than a coffin, but it was better than no doors, no windows, and the rent was low. We could just about sit up straight, so there we went and whispered our plans.
I made one little change, which Gardo laughed at me for – but wasn't I the hero in the end? I have never liked being nailed up inside a house, and I did it for Raphael too, who still wasn't sleeping good: I got an old tyre lever, and loosened part of the roof. Emergency exit, just in case – because we knew things were getting hotter and hotter. We knew this was real, scary heat, all around us – even in the weather there was a wind, and the freak typhoon hovering over the sea, and we all felt something big was coming. There was no way back from it now, and for the boys it meant they couldn't even see their people again – I heard them whispering and wondering, and Raphael cried at night for his auntie and his cousins.
They could never go back to the dumpsite: they had lost their homes, I guess.
We knew most of all that everything depended on that damn Bible, and the little bit of paper we had, with the lines of numbers. We had to get that Bible, and set those two things together.
So Gardo risked it, and one day borrowed my dirty clothes and walked all the way to Colva Prison.
He sat and sat, working out where the guards came out, and he spent another two days watching the different shifts, pretending to be deaf and dumb. When he spotted the guard he was looking for, he followed him.
He followed him away from the prison, then he let the guard see him and followed some more. The guard – Marco – he just kept going and going, then found some little tea-house in the Chinese quarter. Just the two of them. That was so brave of Gardo, because we'd all worked out how the guard must know there was a price on Gardo's head. We'd gone over it and over it: the prison must have got wise to his connection to the dump, and talked to the police. They would have given anything to know what the old man and he had talked about.
The big question, therefore, was if we could trust Marco.
When Gardo came back, he told us bad news.
'The man wants twenty,' he said.
He meant twenty thousand, of course. That was the price of the Bible.
Raphael cursed and said: 'You sure he's got it? You sure he'll give it?'
Gardo thought he had, but what was dangerous was whether he'd really hand it over. He could so easily take a bit of money, say half – and then hand us in. How big a reward would they be offering for news of Gardo? The one thing none of us talked about was what would happen to us if we got arrested. We all knew that if we got taken again, we'd never get out, we'd be dead. I was getting nightmares too by this stage, waking up crying, all three of us like little boys.
But we stuck together like a gang.
'You think he'll give it?' said Raphael for the hundredth time. 'Even if we get that kind of money – you think it's safe?'
Gardo shrugged. 'We either forget it,' he said, 'and live here for ever. Or we give it a go.'
Twenty thousand pesos, though, and I had a little under two. My going-home money, squandering it on sitting around. Like I said, we all knew we were near something huge, but the thing we were near had fences all around it. Raphael read papers to me, and every day there was an update on the Zapanta robbery, with more little hints about how it happened. _Police following leads and hoping to arrest someone soon_. The fat man saying nothing, but the old scandal of what he did or didn't steal himself was being raked over again, and his big face looking dirty and not smiling any more. The stories would finish the same way every time: _Nothing ever proved against him_. Gardo told us again and again what the old man in prison had said, and we all knew who we believed.
I wanted that fat pig's money so bad I was aching, and all I could think about was fridges, and that brave houseboy on a truck, stopping at a graveyard. How he got the key and his wallet into the trash: we always wondered whether he slung it when they were chasing him, or put it there for someone special to find. We talked it through, but never found an answer – I think it must have been some last-minute desperate thing, and then they must have beaten it out of him at the police station, just before they killed him. If I get to heaven, it's the first thing I'm going to ask him. I have no doubt he's up there. None.
Anyway, to return to the story. After a week of this and getting nowhere, I decided to make my move, and get the twenty for Marco. I'd been turning it over in my head, not sharing it – but the more I thought about it, the more it seemed the only way.
I told Raphael and Gardo I was going back to Behala dumpsite, 'just to fetch something', and I thought they weren't going to let me. They said I was crazy and it was way too dangerous. They told me if anyone saw me I could be grabbed and handed over – there was bound to be a reward offered now for any one of us.
They couldn't imagine what it was I wanted to get, of course, and I didn't want to tell them for fear of bad luck. I'm just so used to keeping what I do private, I could not share what I was going to do – nor the fact I had to do it before the end of the month, which was coming up fast. All Souls' Night on its way – that's the Day of the Dead. I had to get it done before that.
I just said, 'I'm going,' again and again. Midnight came, and I slipped out through the roof while the boys were sleeping.
I did say, I think, when you look like the devil's child you can't even ride a bus?
You can hold out your money, but you still get swatted off like a fly – that time I rode with Raphael was luck, and the fact that he has a nice smile and I hid behind him. So I walked some of the way, and jumped trucks some of the way. My luck held, and got better: I found a garbage truck by the city zoo, and guess where it was going? It was going to Behala, so I got inside it. Closer to my old home, I had to be on the lookout. Other kids might jump up too, and if I was seen, the boys were right – I had no family, so I might have been sold like a dog.
We got inside the gates all right. There was a police car parked up, doors open, and that gave me a turn. But the police were just chatting to the guards, all scratching their arses, and the dogs didn't notice anything.
The truck took me past the Mission School, slowing down like it was my personal taxi. I was out fast, dropping and rolling, and I dived in under the building. The school is a big set of metal boxes, all bolted up together. The lower ones stand on legs, so there's a little bit of space beneath. I curled up here and waited for my heart to slow down. Nobody was out, it seemed, so I uncurled and moved to the back.
There's a guard at the front, but he dozes away, because who's going to break in? Who's going to steal storybooks? It would be robbing from your own people, which is why I felt so low. I was about to thieve not just from the Behala people, where I'd lived, but from Father Juilliard, who had been about the closest thing to a father I'd had so far, never knowing my real father. He was a bit slow and a bit too trusting, of course – everyone knew that. But he was a good old boy and I loved him.
I started to climb the corner.
The windows downstairs all had shutters, which were locked up at night. The upstairs windows had bars and no shutters, and I'd always made sure of an entry point. The truth was that just now and then it was nice to sleep in a big room, but I didn't make a habit of it. The other bit of truth is that I was in the bad, very bad habit of lifting money from the school safe – I did it once a month, just a little. So there were two bars I'd managed to bend so nobody would notice but my head would fit through. I was through now like a shadow, and down on the old man's bit of carpet.
How did I steal from the safe?
OK. The safe is on a table, fastened to the wall. It's not big, and it doesn't need to be because it doesn't hold much. I guess all the big money goes through banks, and they just keep a bit of cash for day-to-day stuff – a bit of cash for emergencies, I suppose – but we're still talking twenty or twenty-five thousand, so I hoped. I would never take much, just a hundred or so, hoping Father Juilliard would never miss it, and if he did, he'd think he'd miscounted. Once, twice a month at most – and that was how my little stash got to grow, which is what I didn't tell Raphael, who's more honest than me. But it's coming out now.
You're thinking, _How does a boy like a dumb rat get into a safe?_ And the answer is so simple you could laugh. Father Juilliard, my friend, you must have a bad memory, because you write the lock combination in your diary. You change it every month, sir – at the end of the month – and write the new code down. I would always see it, open on your desk. I'd remember it. This month it was 20861 – I saw it when we were on the computer and you brought us that lemonade... but it wouldn't be the same after All Souls' Night – and that was why I'd had to make my mind up to come.
I put in that code, and the door clicked open. Inside I found twenty-three thousand and a bit more. So that was our Bible money for Mr Marco.
It went into my shorts, and I got ready to leave.
On a thought, because – please don't think the worse of me – the shame was making me ache, I stopped again. The old man's desk was full of paper, and there was a pen in the drawer. I hadn't meant to, and I knew it was a risk, but I hated the thought of you never knowing, and wondering who had so betrayed you, so I drew you a picture. I could spell Jun-Jun, so I put the words over me and a big arrow. I tried to draw me like I was hugging Father Juilliard, who I gave a big crucifix to in case the likeness was no good. I put lots of 'x's, because I knew people used them as kisses – and I put it in the safe. I had tears in my eyes. This was a goodbye, and though Behala dump could go up in flames and I'd just dance – the Mission School had been a good, safe, warm, friendly, happy, fun place. Sister Olivia had been one of the best, and the volunteers before her. Father Juilliard had told me stories, given me food, given me money. He'd even kissed me once, which nobody before or since ever has done.
When I thought of this, climbing down the wall was hard, but I thought about Raphael and Gardo and what we had to do. I thought about José Angelico too, smashed apart by police, and I carried on.
I waited for a garbage truck to come by. I waited for it to slow. I was up on the back and inside, and we sailed out of the gates onto the street. I reached our little house well before dawn, and slunk in next to the boys so they didn't hear me. One of the nice things about Raphael is – because he slept with his little cousins, I guess – he's in the habit of sleeping up close. I crawled in under the blanket, and at once felt an arm go round me, holding me tight – and I felt less like a mean, sly, traitorous, ungrateful thief.
And he had no nightmares that night – he slept easy till sunrise, breathing soft, right on my neck.
# 2
Gardo again.
Rat wouldn't tell us where he got the money for two days, and when he finally did, it didn't seem like such a big deal to me, but I could see he was feeling bad so we said that if we got the Bible, and if the Bible gave away the great José Angelico mystery – and if we got to that pile of money – we would put the twenty thou back in the Mission School, with some added as a gift.
Rat was happy again, and we made some careful treks out over the city to find the guard – which we did, and we fixed up for the handover, and I knew this was the most dangerous thing yet, because he knew I was desperate for that book, which meant first it was valuable, and second – he must know something very strange was going on.
I kept thinking of being in that prison with Sister Olivia, and how they had my picture taken, and I was thinking all the time, _What if, what if, what if?_ – till I couldn't sleep.
_What if they stake out the tea-house?_
_What if they get me?_
_What if they just shoot me?_
_What if they have the whole place surrounded?_
_What if they're all there in plainclothes, waiting for me, and I don't see them till it's way too late?_
They would break every bone in all our bodies, slow and mean and loving it.
Raphael had told me all about the window in the police room, and I knew if we were taken, none of us would come out of there. I knew I would die before I let them take me or the others: I would fight until they had to kill me, because what Raphael told me scared the life out of me, and I know I could not have done what he did.
It was Tuesday afternoon we were to meet, just after Marco's shift – same place: the tea-house in Chinatown. I washed the good clothes Sister Olivia bought me, because you don't get so many street boys round that area and I wanted to blend in more. Raphael and Rat shadowed me all the way, but separated up and keeping a distance – we didn't want to be a threesome in case policemen were waiting.
I used a fifty to buy a baseball cap, and with the trainers on I didn't look like a street boy at all, and I just walked quickly through everyone and everything – but I had my hook, though – we all did – we'd cut them down, nice and short, and mine was in my jeans at the back, where I could get it easy, and it was sharp all down the edge, because I have had to fight before, and cursed when I had nothing.
The little tea-house was dark, with shutters down, and I went straight in, not looking up, through to the table we'd used last time, right up by the kitchen, with a red lamp over it just bright enough to count out money. Marco was there before me, all alone – quite a big man, with a big, thick neck, and I slid in opposite him thinking, _Do it fast, do it fast_ – I was still walking in my mind, and I wanted to be walking out of there, even though it looked like no one was around, it all looked safe, and even the kitchen was quiet.
Marco, of course – he wanted to see the money first, so I counted every note, and I could see greed in those little eyes so I thought maybe I was safe really, and twenty thousand was enough for him: I counted it out, sitting on the edge of my seat, getting ready – and he pulled the Bible out of his bag, and laid it down on the table as the Chinese who owned the place put cups down in front of us.
I told him he needed to prove it was Gabriel Olondriz' book, because I was thinking how easy it would be to give me any old Bible, then come back asking for money all over again – but he opened the cover soon as I asked, and I could see where the man had signed it, and notes – best of all, I could also see lines of letters and numbers like the code he'd talked about. Also, the whole thing was so well worn I guessed that it had to be the real one.
So I left the money where it was, took up the book, and I moved fast.
Maybe Marco hadn't expected me to just cut and run like that, but I'd been thinking how to play it, and I remembered the kitchen being near, and that was where I'd go – I jumped up and ran straight for it. Even so, I wasn't fast enough, and he got me: he kind of threw himself over the table and grabbed me hard, shouting, and the cups all crashed to the floor, and the money went everywhere, all over the floor. He half let go, panicking about the money, I think, so I got an arm free – I twisted like a fish, and saw there was someone running towards us through the shop. I heard a whistle blow then, and people were shouting – the grip on my arm got tighter, but I bucked and tore myself away, fighting for my life, I guess, and Marco was shouting: 'I've got him! I've got him!'
My hook was in my hand then.
Yes, I dragged it from my pocket, and I turned and cut up at his face: I don't know what I cut but I felt it cut through something, and the man cried out and fell backwards. He let go, of course, and I think I must have got an eye – and I'll be honest, I hope so: I hope he's a one-eyed prison guard now, and telling his tale about how he tried to sell a little boy after a deal was made, and that boy turned round and took his eye out – I hope his whole cheating face is cut right through, my gift to a filthy traitor.
I didn't have time to look, though, because I was crashing out into that kitchen, straight into a policeman who was just running in: I went under him, and he tripped, and I slashed with my hook again but missed – and then I crashed out into a yard and over a fence, and I was running.
'Gardo! Gardo! Gardo!'
It was Rat, right on my heels: I heard two gunshots, but felt no bullets, but someone started to scream – I passed Rat the Bible and we separated, me crossing under a bridge through traffic, people watching but no one reaching for me, even when I jumped up on a taxi which was moving right at me, over the roof and rolled in the street – a moment later I was up and ducking into a fish market, and ditching my shirt – that lovely shirt – and I ran through where it was darkest, where there were boys cleaning fish over the drains, and no one was after me, but I still kept running right through and down to the canal. I swam fast to where the shacks come down to the water, and I hauled up and used my hook again to slash up my jeans and hack them short – my trainers too, I kicked them off and gave them to some kid who was watching me, and I walked along the bank, then in among the huts, praying to God that both my friends were safe, and shaking all over.
# 3
We were safe, but right away we knew we wouldn't be for long.
This is Raphael again, but writing it with Rat to get it just right – because the next part of this was my fault, I think. I just about saw Gardo run and Rat streak after him, and then a policeman was shouting at me, so I took off, right across the street, with the buses braking and blasting their horns. I think they must have followed me, and I'm not as quick – and even though I went the back ways, I think they saw the direction I took and made some guesses. Rat thinks maybe they photographed me and Gardo when we arrived at the tea-house.
Anyway, I think we came within an ace of being caught, and why they didn't just grab us first, I don't know. Maybe they wanted to be sure it was the Bible we wanted and needed to know why. Maybe they thought a prison guard could take on a little kid like Gardo and they'd have him for sure, cornered in a tea-house. I do not know.
Anyway, I think they must have had photographs because the next morning they were knocking on the door again, right where we lived. Rat reckons they put men out, showing our pictures and showing money, because someone gave us away...
# 4
Raphael.
We met up again early evening. We slunk in different ways, as planned, and climbed up to our little box of a house, way up the ladders to the top of the pile. We were so pleased to see each other, we just shook hands and hugged and laughed.
Rat went down to get food, as he couldn't read, and Gardo and I set to straight away, no messing. No messing.
We knew the clock was ticking, so we just drove on – you think we could have slept?
We lit a dozen candles, put them around the Bible and the paper. First we had to argue about what exactly a book-code was, and though he was the one who heard about it from the old man, I can say it was me who saw how it worked – no offence to Gardo, but I've got quicker eyes. He says we did it together, and that's true.
We sat and studied like two little schoolboys. The Bible covers were worn, the pages were dirty. Just inside the front was a column of numbers: 937, 940, 922... All high numbers like that, ten of them, down in a long column. Now, we'd never been educated in numbers, but to survive you have to add up and take away – none of us were stupid, so we had some ideas.
The pages they marked were all towards the end, and Gardo remembered the old man had been talking about the Gospel.
'St John,' he said. ' _It is finished_.'
That was where we started looking, and that's where a lot of fingers had been. All those pages were coloured in and used so well they were even thinner than the rest – we had to be careful they didn't come off in our hands. The bit about the crucifixion was on page 940 – the first number in the strip. So we concentrated on that page. All along the bottom, in someone's handwriting, was written:
_And at that time the sky grew dark and Jesus cried out, 'It is accomplished' – and the curtain of the temple was rent in two, top to bottom – the earth quaked and the graves were opened and the saints were raised..._
Gardo saw that each line of print had a tiny number to mark out the Bible verse, so now we tried out a hundred combinations, muddling backwards and forwards. We put the numbers in the strip against the numbers in the column. We tried counting down, and then across, but it wasn't easy because nobody knew what it was we were expecting – so he'd do one thing, I'd do another and contradict. We got to a point where we were going over the same ground again and again. All we knew was that the numbers we had – 940.4.18.13.14 – had to be set against the lines somehow, so as to turn them into letters – that was what the old man had said. But whatever we tried we ended up with gibberish.
Rat came back smelling of rum, with a nip for each of us. We ate, and he went to sleep for a while.
Gardo and me settled to trying more variations. We put out new candles, and we weren't fighting any more. He'd have a go, and hand over to me. While he tried again, I just sat and thought and thought, then he did the same.
Midnight came round, I think, and maybe that was the magic. It was the end of the month, and we were slipping into All Souls' Day – that's the Day of the Dead here. Maybe José Angelico and Gabriel Olondriz came and sat beside us – I swear it was crowded in the room. Maybe they put the answer right in his head – because Gardo hit the jackpot. Instead of going left to right, he went right to left. 4 lines down, 18 words to the left, he got a capital 'G'. 13 down, and 14 to the left, he got an 'o'. It was the first time we had a word.
He moved on 5 letters and got nowhere, so we decided that the slash might mean change the page, so we turned over. That didn't help us, so we turned the page back. 5 lines down, 3 letters in, we got 't'; then 6 down, 4 across, we got our next little 'o'. The slash meant 'turn back a page', and now we had two very meaningful words, and we just looked at them, hardly breathing:
_Go to_
We turned back a page whenever there was a slash, so we were going backwards through the book of John. It was falling out all over us, just counting carefully, straining our eyes because the words were so small. We made mistakes, but we were laughing, because the whole thing was opening up.
_Go to the map ref where we lay look for the brightest light my child_.
Rat woke up and we read it to him.
He shook our hands, then we hugged him, and he said: 'I know what a map ref is.' My, were his eyes big and shiny. 'I was in some class,' he said, 'and they're all doing maps. That's a map "reference", that's what it's talking about. _Where we lay_ is where we were – where we met, maybe? And he's thinking his little girl is reading this.'
'Open the map,' I said. I thought even then he was being a smart-arse, but we were learning to try everything anyone said, every way. 'Let's look at it again,' I said.
We'd stared at the map a hundred times, hunting it for arrows or crosses, wondering if they'd been marked and removed, straining our eyes over it. We stared and stared, and Rat said, 'A map ref is a reference to the numbers, OK? It's a line of numbers.'
'Numbers again?' I said. My head was aching, but we went back to the letter. There were no numbers apart from the code we'd just cracked, so we turned back to the map. Numbers all round the edges, but still no way in. Until I looked at the envelope and saw: _Prisoner 746229_.
I read it aloud.
'That wasn't his number,' said Gardo quietly.
'What wasn't? What are you saying?'
'When we arrived. We were in the waiting room, and the prison boss came in and asked Sister Olivia about the name. He said we had the number wrong, because at first I thought maybe we had the wrong guy completely.'
'You go up and down, that's all I remember,' said Rat – and that's what cracked it. We split the six numbers into two: 746 and 229. Sure enough, the map had a 74 and a 22, they were right there along the sides, and took us straight to a square in the middle. In it was a graveyard. In fact, the graveyard covered the square, and we never did find out what the 6 and 9 were.
'He put the fridge by a graveyard,' said Rat quietly. 'That's what the gardener said.'
' _Where we lay_ ,' I whispered. 'That means where we are... buried.'
There was a little silence, and then we all started to laugh again, quiet as we could. There was a little light coming through – we'd worked through the night, and had our answers. We held hands, we slapped our palms and Gardo kissed me right on the head. It had all just fallen all over us, and we were getting close. A graveyard in the centre of the city – the Naravo. We'd go and look for _the brightest light_ – a special grave, maybe? Or a part of the church? Once again, the trash boys were ahead of the trash police.
Or so we thought.
# 5
This time they came quietly.
This is Jun-Jun, because I remember exactly how it was. I am the best hearer, the best jumper, the best runner – they think I brag, but they know it's true!
Early morning they came, hoping to catch us asleep – plainclothes and uniforms, I believe, all pressing in around us. The boys had blown out the candles – we were just folding up the papers, and we heard a heavy step on the ladder below.
Why I stopped and noticed, I don't know. José and Gabriel again, like Raphael says – on the Day of the Dead, the dead look after you. Anyway, I said how quiet it was – we usually heard the old lady at the bottom of the house shouting and banging about because she had about ten children, who were up before dawn making mischief. So we all stopped still, and wondered where the morning sounds had gone.
Maybe she was the one who sold us? I don't know.
I could hear someone talking below, sounding worried. Then the feet coming up the ladder sounded too heavy, that's all I can say – they sounded heavier than any man who lived up in our part of the building, where you had to be light.
I went straight to the roof-hatch, opened it up.
Raphael was almost too scared to move – I had to smack him one. Gardo and he picked up what they could carry and we went so slow, so silent – because we didn't want to make a sound. If it was police, we wanted them to come right in and find an empty room. They might stick around, thinking we were close, and then bust up the next little room – the last thing we wanted was panic and for them to see us run. So even though my guts were aching and the voice inside was screaming, _Get yourself out of here!_ we made ourselves go slow.
I went first and guided Raph, who guided Gardo. I was waiting for a shout, or a gunshot even – I thought they had to have the place surrounded, they wouldn't be that dumb again – but there was nobody on the roof.
Then, just below, I heard someone call Gardo's name.
'Hey, Gardo! It's your cousin!'
Lies.
'Gardo? Hey! He's sick.'
Crazy lies, telling us only that we had to get moving.
We stayed low, poised there for a while, like three scared little cats. I beckoned, and we all crossed to the next roof, a TV aerial helping us swing down silently. There were wires stretching across, but we all knew not to touch them in case they were bad electrics – once you've had a zap off a power line you go careful. So we just went on our toes down into a dip in the roof-space where we definitely couldn't be seen.
Luck holding.
A man was sitting in his window, smoking a cigarette, just watching us. I saw some other people too – a woman flapping out some washing, and two children playing with a dog. Everyone stopped and stared at us, but no one said a word and the dog didn't bark.
Then down below we heard battering and hammering on doors, and we knew the police were moving. Right at once we heard feet running, we heard shouting – we could hear big dogs, and engines were revving. All of a sudden, over a ledge and level with us, there was a policeman coming up a ladder – and he was looking right at me.
He shouted something, and got a whistle in his mouth. Then I saw him go for his gun, but he was clinging to the ladder still, and we were gone before he could aim. Under us and all around us, though, the world was full of noise.
# 6
Raphael.
Running for your life two times in one day? We were so scared, both times, we thought our hearts would just blow apart. But the thing is, when we thought about it later, Rat had been chased so often, and grabbed at so often, that he must have had extra senses. When he was on the station, it was bad, but it could be bad at Behala too – someone thinks it's fun to grab the skinny kid with the crazy teeth and see what he's got. When Rat sees someone move, his feet get ready to jump.
The policeman with the gun was slow, but what was so dangerous was how many more there might be and how quick we had to be. Rat led, and got to the edge of our roof, and over a low wall. From that we hopped down onto a long warehouse roof, and we ran right along its guttering. We were clear for a moment, but then we saw a policeman in the grass below, bursting through a gate – and it's the same thing again: his gun's out and he's got a whistle to his lips. He had no chance to fire because we got straight round some chimneys and then up the slope – but he'd have a radio, and soon they'd be all around us, we all knew that. We had to think so quick – and let's just thank Rat again for being the one who'd got to know the area. He was the one who spent the time checking in with the street kids, so he was the one who saw the chance and went for it.
The next-door building was the very one where those children lived, where we'd all spent the one night. Rat saw at once we had to dive back in among them. How were the police going to take in a hundred kids? It was the smartest thing he ever did.
Now, the place they lived – the place we were opposite now – was a big old block of flats that had caught fire years ago – just a big, black, ugly cement thing, nobody knowing what to do with it. The gang lived there – a hundred or more, scavenging, begging, sweeping and doing things you don't want to know about. They'd get cleared out, and come back again, then a big clearout, and back they come – that's how it always was in these old places.
The roof we were on ran right up to it, and one jump would get us in the window. As we got to the edge, we could see some of the kids sorting out their breakfasts. A little one looked right up and waved.
It was a long jump to get to it, and I know Gardo and I just looked for a moment, too scared to try. But we did it, Rat first, and Gardo next, and me... I just threw myself, and they caught me somehow, dragged me up so I was bloody again. We ran then, through the kids that had come to see us, to help us, and they clustered around – they knew we were running because there's not many kids that haven't had to do the same thing – and they were wild for us. We all ran together. We found stairs down, and everyone was screaming and laughing, shouting to their friends, so suddenly we were a mighty crowd, pouring into the hallway.
It saved us, I swear.
When we reached the street, we just streamed out, wild as birds, screaming over the street in all directions. There were two police cars, another one roaring in. There were men with radios, guns out and arms wide to catch us, staring around wildly as this mass of little boys and girls rolled out over them. One grabbed a kid, and everyone flew away from him, howling out and laughing like it was a game, straight into the street, where a truck had to slam on its brakes and a bus swerved round up over the kerb, straight into the police car.
Then, just like birds, we were all gone, spreading out and ducking through the alleys and store-fronts, policemen running but hopeless. It was all three of us and about five or six other boys, but then they flew off on their own, and the three of us were safe, still running till we reached a road.
Then, an amazing thing.
Gardo did something so smart I think Rat kissed him, but he says he didn't! Cool as anything, he held up the money we had left to a slow-moving taxi cab. I think the driver was so stunned he just pulled over, and we piled in before he could smell us. A few minutes later we were off again, on the South Superhighway, and he had twice the fare in his hand and he was smiling too.
'Where you going?' he kept saying. 'Where you going?'
'Naravo Cemetery,' we said.
Where else would we go? The square on the map.
And on this particular day, you know – another funny thing – probably half the city was heading that way too – we were just running with the flow. The Day of the Dead, and the Naravo's the biggest graveyard in our city: everyone goes there, rich and poor alike. So we got down low in our seats, and soon our happy driver was up the ramp and driving fast, overtaking buses and trucks. He put his radio on, and we sang.
We wound down the windows and we sang louder as the sun came up higher, right in our eyes. OK, it wasn't over, not at all. But we were alive another day, and that was worth singing for!
# 7
My name is Frederico Gonz, and I make grave memorials.
One small detail from me, for Father Juilliard. You ask, sir, so I will tell you.
I met José Angelico the way I meet many of my customers. I have a workshop on the cemetery road, just past the coffin makers. I specialize in the small, simple stone. I am very aware that my clients have next to nothing, and renting the grave has often taken most of their money. So I modify and modify and get down to the very lowest cost. The dead, however, must have that stone: the reminder, the eternal reminder, that this man, this woman, this child – existed.
On some of the graves the name is marked in paint, or even pen, and everyone knows how sad that is. Make something out of stone, I say, and no one touches the grave. The poor are not buried, you see. There is not enough ground here any more, so in the Naravo they build upwards. The graves of the poor are concrete boxes, each just big enough for the coffin. They go up and up – in some parts twenty boxes high. A funeral here is to slide the coffin in and watch the sealing of the compartment. Part of my service is that I cement the stone that I've made into place, and thus seal the chamber.
José Angelico used me when his son died. I was sad to see him again with news that his daughter had died also. It meant he had no one in the world now.
He was a thin, lean, gentle man who always spoke quietly. I knew that he was a houseboy for a rich man, but that was all I knew. He found me early in the morning, and he looked as if he hadn't slept for a long, long time. He gave me just a morning to make the stone, which is unusual, but he said he had run out of money for the funeral home, and the coffin had to be moved that day. It would be a simple ceremony, he said, because there were no relatives.
I offered him all my sympathies, and he paid me two hundred as a deposit, and I set to work.
_Pia Dante Angelico: seeds to harvest, my child_ were the words he chose. _It is accomplished_.
I did not chisel it myself. My son is ten years old, and is a fine cutter now. He used to rough out and I would finish. Now, he finishes, and he's developing his own style of turning letters – small flourishes that add elegance to elegant words. He completed the stone in four hours, and we set it by for pick-up.
How was I to know it was lies? He looked to me so meek and so mild – there wasn't a lie in his face. He took the stone and paid me from a small leather bag. He had the coffin behind him, carried by two young men – street sweepers, they looked like. No priest. I went along and saw the coffin placed inside, and we said prayers for the child. I sealed it and fixed our little stone. All I could see was the worry and grief, like he was a man worn down to nothing. There wasn't a lie in his face.
When I read about him dying in a police station, I just thought, _Poor man_. I read the story to my son, and we said a prayer for him also.
# _STAR_ EXTRA:
**Police Closing in**
A spokesman for the city police said last night that important leads are being followed up 'professionally, vigorously and relentlessly', and that the undisclosed sum stolen from the vice-president's house would undoubtedly be recovered. 'You cannot keep this kind of money hidden. Experience tells us that somebody, somewhere, will blow the whistle soon. That is when we swoop.'
Requests for further details were firmly declined. 'We are at a sensitive stage. We are talking to people who have to stay anonymous. All we can say is that we are confident that a breakthrough is imminent.'
Vice-President Zapanta is no stranger to controversy and has been constantly dogged by accusations and scandal. Trained as a lawyer, he has been notoriously quick to challenge and in many cases prosecute critics of his policies and personal conduct – to date, successfully. A spokesman for the senator reported that he was in 'considerable distress but remains hopeful'.
Sources suggest the criminal was a member of the senator's domestic staff. The president herself, who visited Zapanta last Thursday, said, 'Our thoughts are with any colleague who experiences loss. Theft is theft: one feels violated, always.'
Vice-President Zapanta remains a key witness in the ongoing prosecution of his subsidiary company, Feed Us!, which collapsed with debts of two million dollars and was subsequently implicated in the hiking of rice import duties during the economic downturn last year.
The trial is now in its fourth year and the Star wishes to reaffirm that the vice-president denies all charges.
# _INQUIRER:_
**ZAPANTA MOURNS HIS LOSS!**
**Vice-President Senator 'We are the people'** Regis Zapanta is said to be 'extremely concerned' at the loss – that is, the theft – of an undisclosed sum of money from his property last week. Sources close to the great man say that you can hear a pin drop – a banknote fall – and even the occasional groan of despair. Sources even closer say our much-loved vice-president is 'enraged' – and we all know what the senator's rage has accomplished in the past.
Senator Zapanta achieved notoriety just three years ago when he ordered police to clear squatter camps to make way for his ground-breaking cinema/shopping complex. He was also made famous by a dramatic poster campaign aimed at the illiterate, featuring laughing orphans holding placards that spelled out his name – the children received no fee for their services.
The vice-president has always campaigned for wider education, whilst presiding over an education budget that has dwindled by 18% over two years.
He was not available for comment.
"WHAT THE HELL......?"
# _DAILY STAR:_
**Mohun's diary**
Check out the face of super-smiling Regis Zapanta, who's now wearing a frown – just as the wind appears to be changing! Could the rumours be true? Is our man, who's spent a lifetime swearing he's clean, as oily as a back-axle?
If he really has lost ten million dollars, someone's going to ask the question: 'What was ten million dollars doing in your house, sir?' We all need ready cash. We all keep a stash of change... But ten mill in dollars, just in case the ATMs are down?
Ten mill under the bed suggests someone's either not paying their taxes, or stealing other people's.
I didn't say that, sir – don't close my paper, don't shoot my family!
# _UNIVERSITY VOICE:_
**_ENOUGH_**
**is enough, say students**
**The very fact that Vice-President** Senator Regis Zapanta keeps millions of dollars of cash in his home suggests that he is part of a corrupt other world – and should not be re-elected. This country could still move forward, but it won't until we've said goodbye to bad, greedy old men.
It's time for someone young and new!
Charuvi Adarme, president of the students' union, made her feelings plain in an impassioned address yesterday to those on the diploma programme.
'Five years ago,' she said, 'Zapanta campaigned on the slogan, _The brightest smile, the sharpest mind_. I'd add to that, _The most questionable conscience and the blackest heart_. He's spent more than three decades lining his pockets, and his main achievement is that he's made the country's poor feel worthless and powerless.'
What does the country need right now?
THREE THINGS:
A revolution.
Then a revolution.
Then – when the dust has settled – a revolution.
# PART FIVE
# 1
Raphael, Gardo and Jun-Jun (Rat):
The Day of the Dead is about the biggest festival of the year out here – bigger even than Christmas and Easter together. It's when ten million candles get lit, and the ghosts come up and walk around arm in arm, and everyone goes to see their departed ones, who stand up out of the ground and say hello.
That was why the traffic soon got slow, and before too long we were in a long jam – at last the taxi dropped us on the road that led off to the cemetery, and we walked in the smell of flowers.
There were crowds pushing everywhere.
People walked with kids and babies in their arms, whole big families, and some of the men had tables on their heads and chairs in stacks, on trolleys; they had cases of beer, great big bottles of water, and the ice carriers were dragging great slabs of ice, shouting for a way through. Little stoves, bags of food, and people dressed up as best they could, as if for a carnival – little girls in new dresses and the boys in ties, even though it was a hot morning. This is the day when your family is together again. You set up house by the grave, and sit and chat and eat and drink right on to midnight. By the time it gets to evening, the whole cemetery is glittering with the candles – and that's when they say you need an extra chair, and an extra glass. That's when you can turn round, and dead Grandma's right beside you, old bones in whatever you buried her, smiling away with a hundred stories to tell. That's when the kid you lost is playing around at your feet again, and if you had some quarrel with a brother who died, you can talk it through and settle it. Father Juilliard told Rat all about the resurrection one time, and I guess it's this that he was talking about.
Rat says: I've never seen it, of course, but then I have no family here.
I do believe in ghosts, though, and on Sampalo island, where I'm from, people say they come out of the sea sometimes, if a boat goes down. They come into the village, sad as sad, and cry by your door all night. What do I know, though? I'd seen nothing like this.
Around us, the flower shacks got thicker and were overflowing with flowers till the scent lifted you off your feet. There were stores with sweet little Bible verses, plastic statues, plaques and postcards. The lottery sellers were everywhere, carrying wads of tickets and shouting. After all that, we came to the candle stalls – so many candles, thick and thin, tiny as your finger or too big to carry. Back from them there were food stalls, doing good business – and the three of us stopped and ate some fish, because we were hungry again and hadn't had breakfast.
Raphael: I cleaned the blood off my arms, and Gardo said it was time for a plan. Opening up the Bible, we sat eating and reading, and nobody bothered us, because who's going to get upset about even street kids, if they're reading the Bible on All Souls' Day? There was that breeze again, getting stronger still with all that flower smell, and we could feel the freak typhoon coming in on us again, ripping at the tents. It was going to be hard keeping the candles lit, so there were lots of people buying little jars for that reason.
I said, ' _Where we lay_ ,' and I scratched my head. 'I guess he's buried here. Does that make sense?'
'He won't be buried anywhere,' I said (this is Gardo). 'If the police killed him, he's going to be burned up by now and in the trash. Also, he must have wrote all that before he died.'
That was true and we all agreed. But we also thought, _What if his wife's buried here?_ If that was the case, then _Where we lay_ could mean the family grave. And that was what we decided to look for.
* * *
Rat now: I felt bad then, because that meant reading was needed. I couldn't read, and that meant I'd be no use. There was nothing for it, though, so we finished our fish and started, and I carried the papers and the book and followed on.
Like I said, it's the biggest graveyard in the city. Once through the gates, there were walkways spreading off to left and right, stretching for miles. We were soon lost in graves, trees and monuments. There were bushes and shrubs, and as we walked, great big angels would suddenly appear at you out of the leaves. Peaceful-looking Madonnas looking into the distance, and weepy little Jesuses on tiny little crosses, and then big-brother Jesuses stretched out, with eyes up to heaven. I had never been watched over by so many saints and I nearly got split up from the boys looking at them.
The tables were going up and picnics were opening. The parties were starting, and soon Raph and Gardo knew they'd never find one name in all these millions.
'We can ask,' said Raphael. 'There's an office with lists of names... is that a big risk?'
'Everything is,' said Gardo, looking around, still looking mean. 'Everything has been.'
That was when I said I would do it. I said, 'I can pretend Mrs Angelico did me a good turn and that I've come to say hi.'
So Gardo counted me back a bit of my money – he'd become the money-man after the deal with Marco. 'Get her some flowers,' he said. 'That'll make it real.'
That's what I did, and it took three hours or more. There was a big queue of people, and I kept getting shoved back. When I got a guard to see me, he said he needed twenty to check the record – which was a lie, but I gave it to him. Then he went off and took ages, answering all sorts of other questions from people, so I just sat with my flowers, hoping he wouldn't forget me altogether. It was late afternoon when I got my slip of paper, and Gardo thought I'd been off drinking.
'B twenty-four/eight,' I said to Raph. 'He says, "Top of the slope and look for a pink angel." '
'It's getting dark,' said Gardo. 'Can you see pink in the dark?'
Raphael led the way, strong again, and ready.
Raphael now.
It was getting busier and busier because the evening is the busiest part of the day. There were barbecues starting up now, and people selling snacks. We were amongst wealthy people in very fancy clothes, and we felt even greyer and dirtier, but there was nothing for it, and still nobody was worrying about us – no one seemed to see us, like _we_ were the ghosts.
After twenty minutes we got to the top of the slope.
I saw so many angels, and the light was way too bad to see a pink one, and I was ready to curse the guard who wasted our time – but then Gardo saw one made of marble, on a grave the size of a truck. In the candles it was pink as a salmon, and it was staring back over the city, arms up like it had just scored one hell of a goal. A great big family were sitting all around it, playing cards, and there were brandy bottles everywhere, and more people arriving, hugging each other.
We left them to it, and went in and out of the neighbouring graves, wondering what B24/8 might mean, and looking for the name 'Angelico', and finding nothing.
Soon it was completely dark, and we couldn't read the names any more. So we went back to the pink angel, and climbed up on a wall nearby, and wondered what to do.
And that is when we saw _the brightest light_.
# 2
Raphael, Gardo and Jun-Jun (Rat):
We'd been looking in the wrong place, and the fool of a guard who took our money must have thought we knew the cemetery and didn't bother to explain, or was just too lazy. The cemetery, you see, is divided by a wall – and that was the wall we were sitting on. The wall divides the rich quarter, where the dead get buried in earth, from the poor quarter, where the dead get stacked up in boxes.
We'd wasted the day walking among the rich when we should have been on the other side of the wall. The brightest light was the poor part of the cemetery, where thousands of candles were coming together as everyone streamed in after work. It was bright as day, bright as a furnace, and the candles were moving in great rivers as people made their way to their loved ones. It was like a little town down there, with narrow streets through all the tombs.
B24/8 would be the number of one of the concrete boxes.
Raphael: I remember Gardo looking at me and smiling, and then Rat gave me a hug because we'd cracked it again. We jumped down and came to a little broken doorway that let you into the other side. Right away, we saw a sign in the candlelight, high up on one of the grave-stacks. It said _G9_ , so we moved past it, trying to work out the system.
It really was like a town: people lived in this part of the cemetery – they had houses there. There were little shanties built round the back of the grave-boxes. There were shacks up on top too – little huts and bits of plastic, and to get to them you climbed ladders. We could see kids running on the tops with a kite, getting it up into the typhoon breeze. So many people always, and it struck me again what my auntie used to say: there is nowhere people will not live.
We passed so many graves.
Saddest were the open ones – the ones that were broken open – and everyone knows that story, and I found myself looking away. Each little concrete hole costs the family two thousand-five for five years. You cannot buy a box, you see – you can only rent one. After five years you pay again, or the box is taken back. And people move away, or people spend the money, and sometimes the payment just doesn't get made – so what happens? The sledgehammer is what happens. They break open the seal, and out comes the body. There's a part of the cemetery where old bones are thrown and left to rot amongst the trash. Somebody's child, or somebody's grandma – out on the rubbish like a dog. The empty holes scared me, because nothing is more sad than that, and I didn't want to look. They leave the bodies in there for a few weeks sometimes, hoping they'll be claimed, because I guess nobody likes throwing people away like that.
Gardo.
I was working it out, though.
I led them round the back, and talked to some kids perched up on the grave-stacks. They pointed, and we found the track that was D, then C, then B, so then we came along, counting – fifteen, twenty and twenty-two. Four graves up, and there she was, we found her: _Maria Angelico, wife of José Angelico_ , picked out on a little stone plaque. Raphael and me climbed up and leaned in to read, because the words under the name were small. _The brightest light_ , they said, and I went cold, because those words were the ones we'd been following, and what we'd seen, and it was all coming together – we were close to the end. Around the words were scorch marks, from the candles that had been lit. Raphael read the words out to Rat, calling out loud because there were people everywhere and a lot of drinking going on and a lot of laughter. I looked at the box underneath, and I called that out too:
' _Eladio "Joe" Angelico_ ,' I said. ' _My good, good son_.'
Raphael grabbed me and said, 'We're where we're supposed to be! This is his boy.'
I said, 'I know that.' That was clear. But I was also thinking... _What's there to find? We've found the poor man's family grave – is that really such a big deal now? This sad man, whose face we first saw when we found a wallet on the dumpsite... he loses his wife and his boy and we're poking around, hunting his money? He couldn't have hidden it here_.
'We're where we should be,' I said. 'But he can't have put it in a grave.'
'I agree, ' said Rat. 'How would he do it?'
'What's that one there?' said Raphael, looking up. 'Is that his as well?'
He was looking at the stone above the man's wife, and I had to climb higher up to see that one. It was clean and new, and the words were harder to read because the light was bad, so Rat handed me up a candle, and I figured them out slowly, Raphael helping.
' _Seeds_ ,' I said. 'Something about those seeds again... Then it says: _To har... vest. My. Child. It. Is_... Something long, I can't see.'
'Accomplished,' we said, together.
' _It is accomplished_ ,' I said. ' _It is accomplished. Love and... hope_. And there's a name – just a little name,' and I traced it with my finger.
* * *
Raphael.
The name on the stone was _Pia_. Then, _Dante_. _Pia Dante_. I looked down at Rat. 'Oh my,' I said, and I felt so sad. 'That's the little girl.'
I thought of the photo, of the little schoolgirl with her wondering eyes, and felt so bad. We'd all thought she was alive, or hoped she was.
Rat said, 'He lost everything, man...'
'He was sending her to school,' I said. 'That's what the paper said.'
'It was in the letter too,' said Gardo. 'The letter to Mr Olondriz. _If it comes to your hand, then you know I am taken. Ask after my daughter, please – use any influence you have, for I am afraid for Pia Dante now_.'
We were quiet a moment, and then I jumped down.
'What now?' I said. 'What are we expecting to find here? What do we do?'
Gardo said, 'I don't know.'
I said, 'A message, maybe? Look for another message...'
'Where?' said Rat. 'Where's he going to put it?'
We all looked around wildly, maybe thinking there'd be a letter, or some other clue – but it seemed pretty hopeless – it all seemed like a dead end.
'We've got this far,' said Gardo, getting angry like he does. 'There must be something!'
'Nothing,' said Rat. 'Where's there to look, and what are we looking for? I think he was taken and killed before he could do anything.'
'Maybe the police have been and got it?' I said. 'They tracked it other ways, maybe.'
Gardo sat down again. 'Why is this so crazy?' he said.
I sat next to him, and we thought and thought, but there was nothing to think. Then, right by us, a big family arrived, pressing into the graves with a load of candles and a cooking stove, so we moved off across the path and found a quieter place, higher up.
'Look,' I said. I couldn't let it go. 'If he had all that money... If he got away with it – if he really had a fridge full of money... Are we thinking he buried it here, with his wife and kids? Why would he do that?'
'To come back later and get it,' said Rat. 'No one's going to break open a paid-for grave, are they?'
'The police would,' said Gardo. 'If they had even one slight suspicion. That's why the code. If the police had got the letter we got – if they did what we did – went to the prison and saw Mr Gabriel... he would not have let on about the Bible and the book-code. So they would never have got this far.' He smiled, and said what we all knew: 'The man was smart.'
'OK,' said Rat. 'So José Angelico knew he could trust Gabriel Olondriz. Gabriel was like the... guardian of it. Without him it's never found. If it's in there, even.'
'You think it's in there?' I said.
'It's in one of them,' said Gardo. 'Maybe.'
'You want to break open three graves?' I said. I couldn't believe I was even thinking about it. I knew I couldn't do it.
Gardo stood up then. He walked up and down, and I could see him thinking so hard his eyes were bulging, getting madder and madder. 'It can't be!' he said. 'You don't do that, do you? You don't bust open your family grave! What about an empty one? Maybe there's a broken one nearby...'
We looked around, and there were several. You could see what looked like trash, or maybe bones. Who wanted to sort through that? One thing for sure was they weren't places you'd leave anything valuable. Gardo was beginning to really lose his cool, and I could see why – we'd come all this way, and had the police all over us – he'd been almost taken, fought his way out... and all for nothing? He looked at me and said, 'What do we do, Raphael?' and I didn't know. I just looked at him, and Rat was looking from him to me then back again.
It was just at that moment, as we were gazing around, that we heard a voice.
It was a small voice, and it was calling down to us, and was almost blown away by the wind. But we just caught the sound, and looked up to see a tiny little girl.
'What are you looking for?' she said.
# 3
Raphael, Gardo and Jun-Jun (Rat):
She was sitting up on the graves, higher than us, so she was looking down. She was hard to see, because like I said she was so small, and there weren't so many candles there. She had long black hair, and was sitting patiently, her hands in her lap. She was wearing school dress.
Rat said, 'What did you say?'
The little girl said, 'Who are you looking for?'
Raphael said: 'José Angelico.'
'I don't think he's coming,' said the child.
We didn't know what to say for a moment, and then Gardo said: 'Did he say he would? When?'
We were all staring up at her and she was just staring down, so still. The breeze blew her hair, but she was like a little statue.
'About a week ago,' she said quietly. 'I've been waiting.'
Gardo said, 'I don't think he's coming either – why don't you come down here?'
'What's your name?' said Rat softly. 'What are you looking for?'
'I'm not looking for anything,' she said. 'I just came here to wait for him.'
'But where do you live?'
'Here. I don't know now.'
'By yourself? What's your name, _chele_?'
'Pia Dante,' she said. 'My name is Pia Dante Angelico and I'm waiting for my father, José Angelico.'
Now, I (Raphael) speak only for myself and not for the other boys, but I went stone-cold all over and I nearly fell down. I heard Rat breathe in sharply too and take a pace back. Her hair was still blowing and she looked solid enough, and her voice was a child's voice... but my first thought was that we must be talking to a ghost, because we'd seen her grave with our own eyes.
The child was looking across at it – B25/8 – the grave with her own name on, in brand-new stone. And she was waiting for her dead father on the Day of the Dead. What kind of miracle was that?
# 4
Raphael, Gardo and Jun-Jun (Rat):
She was no ghost, of course, and when we got ourselves together, we helped her climb down. Rat went up and helped her, because she was small – and we decided to take her out of there fast. Things were getting so strange, and we were all having the same idea straight away, but we needed to get clear for a while. Little Pia was so weak she could hardly stand up, and we all realized none of us had eaten properly, and we thought, _We've come this far – the police aren't going to trace us here – can we just get a moment to think?_
Gardo counted out the money, and we were low – our stash was down to a few hundred only, but we all needed food – little Pia most of all. I tell you, she was skin and bone to touch, and dirty all over – she smelled bad. We went right out of the cemetery and found a shack and ate chicken and rice, thinking we might as well eat good – we so needed it. We were at the end of the trail, we had to be, and even at that point – before we talked – we knew what was happening, and we were getting excited, frightened, jittery. Cold and sweating – like a fever.
Rat and Pia were just about the same size, and he could see she was in a bad way more than me and Gardo. He's been starved like that and scared out of his wits, so he knew what to do. He made her eat really slow, mixing gravy into the rice and feeding her. He got her water and made her drink it, and then he found her some banana, which he chopped up small like she was a baby. In a way she _was_ a baby. She was scared, but she was so weak she didn't know what to do, and we still think Rat saved her life.
She told us she'd been in Naravo for a week, to meet her father. It was a place they often went together, because her little brother and her mother were there.
Some children had found her and taken her to one of the shanties – she'd been fed a bit and asked questions. She kept going back to her mother's grave and waiting, and of course she wasn't tall enough to read her own name on the grave above – or if she did, it didn't mean anything to her – she never said anything about it. Her father had sent her a message to meet him, and whoever looked after her had taken her there and left her. They must have read about his death, and knew they were well rid of her, what with no more rent coming in.
Pia Dante was alone.
* * *
Gardo: We talked to a boy at the eating house, and for fifty got her space out the back for the night, and Rat laid her down, and got an extra blanket because a typhoon wind is cold for a child. I saw him smoothing out her hair, wrapping her up, talking to her and promising we'd be back to look after her. Then he came over to me and Raphael – he was crying. I'm putting that in because I think it's important – it's the only time we ever saw Rat cry.
All of us knew now that this was the time to thrash it all out and do the final, final plan. We ordered tea, and I – Gardo – spent seventy on a bottle of brandy, and I made us all take three fingers, because what lay ahead was the hardest, and yet in a way it was also just free-fall now, the plan so clear we couldn't go outside it. Three fingers was enough, because we needed to be brave for the next bit – braver even than my friend and brother Raphael in the police station, because nobody goes among the graves on All Souls' Night after midnight, because that is when the dead are left to themselves again, so the ghosts are getting sad. We knew we had to, however – there was no question – because it was the only time we could do what we had to do. Can you blame us if we stoked up on drink?
'We need tools,' I said, and we worked out what we needed.
'We're going to need a way out too,' said Raphael, and we planned out our route.
I said, 'What does six million dollars look like?' I think the brandy was hitting me and making me smile. All of us then, we started to laugh – for the first time in what seemed a while. And do you know what, we knew it wasn't ours, even then – and couldn't be ours. We knew that a piece of it was all we wanted, and we knew we were so close, the air was buzzing around us, as if the ghosts were above us! That much money, if it really was there – six million. I promise you, the one thing we all knew was that it was not ours and we would not even try to take more than a little.
We split up to look for tools, saying we'd meet at the grave as soon as we could. We knew it without saying it: we had to go back and smash in the slab and get inside. I am sure we agreed that, without quite saying it. Raphael went off and found a sack and a cheap old broken knife. I went scavenging close up under the shanties where the graveyard turns to swamp and sea: I found a strong iron spike. It was tying up someone's boat, so I tied it to a wooden stake, and took the spike, quiet as the breeze. Rat found rope and a plastic sheet, which was everything we needed.
I'd said to Raphael, 'We do this job fast – once we start, we do not stop,' and we hugged each other.
I'm Raphael. I said to Gardo, 'It's going to make a noise. We do it fast, OK?' We finished the brandy and felt stronger and better.
* * *
Gardo again.
We climbed up to little Pia's grave-box. I think there were ghosts everywhere, just watching. Raphael held the spike and Rat passed up a stone.
Everyone had gone, and most of the candles had blown out, because the typhoon was getting closer and the wind was strong and cold, nagging at us – I didn't have a shirt and I could feel it, right in off the sea. I swear I could feel them all, those dead, around me still, watching me with wide-awake eyes. Dead men above and below, and dead kids and dead mothers – I could almost see them, watching and watching, and I so didn't want to look up.
The stone was good in my hand, just the right size. Raphael had the spike in the corner, and I leaned back and gave it the most almighty crack. The thing moved right off, and the noise was more of a thud – a real, deep, dead sound. I guess because the seal was so new, it hadn't got itself all fixed and hard, but the second blow punched it right in, and it fell on itself in three big pieces, one of them falling nearly on Rat's feet, so he jumped back. Then he was up with rope and candles, right up against me, and we were lighting them fast inside the grave-hole where the wind couldn't get.
The air was musty, but there was no bad smell. There was a coffin, white as white – for a child – and we all felt scared, I guess. It had a layer of dust, and the flowers on it were very dead – other than that, everything was fresh. No smell – and we all knew what dead things smell like, because people throw dead things out on the dumpsite. I found a dead kid once, and there's no mistaking that particular stink, once you've had it in your face.
We threw out the other bits of broken stone and eased her out.
Back to me, Raphael. Like Gardo says, the wind was getting up and it made us want to work faster than ever. Rat got the rope around the coffin. Then, as we slid her out, he squeezed right into the hole so he was safe and firm. That meant he could let it down to us, because six million dollars in a wooden box... I tell you, six million dollars in a box is heavy, if that's what was in the box – don't forget we didn't know that for sure. We only thought we knew, but it felt as heavy as that kind of money ought to be. We got her on the ground, and though we'd all said we'd move fast, we had to see what it was inside, right there and then.
The knife was our screwdriver. Eight screws held the lid, and I know, lifting a coffin lid... you think of all the evil things in the world – in a graveyard, in the middle of the night – but I think all three of us knew in our hearts now, so we just did those screws and lifted it, and like Gardo says, the ghosts were around us, watching.
Oh sweet Lord, the money was there.
The money was there. It was packed in so snug it was like the box was made for it.
You want to know what six million looks like? I will try to tell you.
To me, sitting next to it, it looked like food and drink, and changing my life – and getting a way out of the city for ever. It looked like change, it looked like the future. I don't know what it looked like. We stared a moment, and nobody spoke. We had the plan, and the plan was not finished yet, and none of us suddenly thought, _Let's keep it all_ – nobody even suggested we change the last part of our plan. We knew the money wasn't ours, because even though I never met that man, Gabriel Olondriz – the way Gardo had told us about him, I knew he was a good man, through and through. It was All Souls' Night, and he was there, I hope and believe, at the front of the ghost-crowd! Right there with us. I think he stayed with us too – I hope with José Angelico, arm in arm – with us all the way.
# 5
Jun – no longer Rat. My name is Jun-Jun.
And the boys have given me the last part of the story – I guess because the last part was my idea. They dispute that – Gardo says it was his, because he was the only one of us who met Mr Gabriel, but I was the one who knew how to do it – and it did get done at what was once my home, or just above it.
Also, Raphael – he had the whole first part of the story, and I think he knows we tell it together, better, because we are a team now. Who cares, in the end? Who cares who did what when the whole point was we did it together?
We'd talked it all out, asking the same questions: what do you do with six million dollars? How are you going to spend it? Or what would we do, the three of us? Line up in the bank the next morning and ask to put it in a safe? Bury it some place else?
The one thing we knew is that as soon as we had it, it would be taken away – you think we stood a chance of keeping even a million? So I said we should take it to Behala and put it in the trash for anyone who finds it.
Maybe it was the brandy, but what I remember is the boys just laughing at me, and laughing at each other.
We shook it all out of the coffin into the sack and the sheet. José Angelico's money: the money stolen by the senator-vice-president from hell, from all his own people. We roped up the sack and the sheet and got them on our backs. We took them over the wall, just in case the gates were guarded – every gate in this city is... We stopped off for Pia, of course, and she was so sleepy I had to carry her on my back, so Gardo took one sack, Raphael the other – and off we went into the wind, which was getting strong now, racing along the streets and making a noise, rolling trash ahead of it.
Who did we meet? Who else could we meet but a little gang of baby trash boys doing the night shift, scavenging about with a cart. Gardo showed them a note, and it was like a charm. Half a minute and our bags were in the cart, and Pia was on the crossbar, and we were pedalling through the streets, all of us clinging on and singing out. Who's going to stop a crowd of filthy trash kids fooling in the night? We passed a police car sitting by a junction, and we even waved. It was the early hours of the morning and the wind was behind us all the way, and we sailed past statues and all the quiet office blocks until we found the road that goes up to the dumpsite. We put Pia on the saddle, and the rest of us got off and pushed, running as fast as we could, so she was laughing too.
No police cars, nothing – but we still took no chances, saying goodbye to the cycle boys finally, and creeping in sideways up the canal.
My first thing was the school – the Mission School. So I took a great handful of notes, put them down my shirt, and I did just what Gardo had told me we'd do. I skinned up the corner and was in through the bars. It seemed my good old friend Father Juilliard – you still hadn't fixed them, sir, I could still get through: maybe you were hoping I'd be back – I'm joking. I put the money on his desk and grabbed a pen. I put my name again, big and black – and next to that all I could think of was flowers, so that's why I drew you a bunch, fast as I could, bursting up and open. Then I had my next very brilliant idea which – who knows? – maybe saved our lives like all the other times. Gardo says all I do is brag and take credit – we all had good ideas all the time, but this one was genius, because how else would we have blended into the morning?
Why it hit me, I don't know – I guess all of us have to keep thinking ahead and looking out for danger, or maybe Gabriel and José were still with us even this far – maybe they'd been pushing that bike with us. Or maybe I just saw the cupboard, I don't know. The point was – this was Father Juilliard's office – there were cupboards full of odds and ends, and one of them was the crazy school uniform store.
Little shirts and shorts! They'd been donated to us years before by some charity volunteer who thought all the kids ought to look the same, like proper schoolkids – but it never caught on. To make us feel like a real school, I imagine, this kind person had given about a hundred white shirts, and a hundred blue shorts and a hundred little dresses. There were packets and packets, little slippers too. There were backpacks – the kind kids put their schoolbooks in, but there was scarcely a book in the place! What are the kids here going to carry apart from trash? The backpacks had the charity name, big and bold, all over them so you'll never forget who's being so nice.
So I grabbed a load of everything, and pushed it out of the bars. Then I followed them down where they fell, and we didn't even need to speak – we knew where we were going.
First we opened up four of the backpacks and stuffed them with dollars. We stuffed them full and zipped them up.
Then we turned back to what was left, which was most of it, and we took off every paper band – the bands that keep hundreds bundled into ten thousands. They were blowing around already, so we got them in the sheet and the sack and bundled them up again. I tell you, the dumpsite was alive now, because of the wind. Dust and grit was blowing about, and little bits of trash were whirling. The plastic roofs were flapping too, and a bit of metal sheet was banging. There was a very little bit of light in the sky, way over by the dock cranes, but no one was about just yet – or nobody saw us. We probably had ten or fifteen minutes before dawn, before the ghosts had to say goodbye and slip away. So we hauled everything to my old home, to where the big broken belt – belt number fourteen – just points up at the sky doing nothing.
No, I did not go down to see my friends the rats! Pia stayed on the ground, looking up at us, with the clothes and the bags. Then I went up first with the rope end, and pulled on it. Gardo and Raphael came next, taking the weight, and I went up and up and up. The wind was just getting stronger, and my shirt was flapping – I felt like I was up on a ship because the whole belt-frame was moving. We got the first bundle up right to the top, right to the top, and I could see way over Behala, way over the city, way out to sea! Then Raphael came up next to me, crying out he was so happy – just shouting into the wind – and we held each other and howled. We took handfuls of the money then, and threw them up into the sky. The notes spilled out and whirled, and it was a storm of money. Typhoon Terese, I later heard, racing in from south China – and the next day the rains would burst. Right now, the wind got under all the cash we could throw, and pushed it up and out, and spun it right across the land.
Soon my arm was aching.
Raphael stopped shouting and just clung there, exhausted. We did the next bundle more slowly, and as it got lighter, Gardo came up too, right up to the top of the belt, and he had strong arms, and he helped us throw the rest. When Gardo came, the wind rose up even more, and we were clinging to that crane! It was a hurricane, and a hurricane of money. We must have thrown five and a half million dollars out over the dumpsite, and that wild wind took it all over the whole of our big, beautiful, terrible town.
At the bottom of it all, what did we find? We found another letter, slipped in with the cash. It was from José Angelico, so Gardo stuffed it down his shirt. We dropped the sheet. We slowly climbed down, and we were dizzy.
Pia was waiting for us by the rucksacks. She'd unwrapped the clothes, and put the plastic packets into a pile, and was sitting on them. We changed. We washed our faces by the school tap. Then we made our way out of Behala.
I wanted to watch. I wanted to hang back and see what happened when the first trash boy of the morning hooked up – not a stupp, but a hundred-dollar bill. Gardo was firm, though – and I'd come to see that you didn't cross Gardo, not to his face.
Raphael had goodbyes to say, and I could see him lingering. Then again, so did Gardo. In the end I think they knew it was easier to go without goodbyes – there was no choice – and I saw Gardo put his arm round Raph and lead him on.
He said we had a train to catch, so we went off and caught it.
# 6
Raphael, Gardo, Jun, Pia.
We are writing together for the last chapter.
Thank you, Father Juilliard and Sister Olivia. Thank you, Grace, and thank you, Mr Gonz, for helping us to tell our story. We are at the end, nearly where we started – just catching the train...
We caught it on the curve it makes south of Behala, where it slows down nice and safe. Yes, we were just three schoolboys and a little schoolgirl, in through the windows and onto the seats. There weren't many people on it at first, but at Central loads of kids got on, most of them dressed like us, and we bought our tickets with the last of our pesos.
Like those kids, we had our school bags. They carried books; we carried dollars. Soon they were getting down for their schools, and we just carried on.
It was a long way to Sampalo, but we always knew we'd get there. The train took us through the night, and put us, just before dawn, at the ferry port. We crossed over the sea for nine hours, to a little place called Fort Barton. Then we caught a bus to the eastern shore. We got a cycle rickshaw from there to the jetty, and another little boat took us way out, to where the water changes colour – to the deep turquoise you can see right through. It is paradise.
We stepped out at last onto a beach, and we started walking.
Yes. You walk far enough and the earth does turn to soft sand, and now we are in a place more beautiful than creation.
That was some time ago. We have since bought boats, and learned how to fish, and we can tell you the truth, for the lying is finished. We will fish for ever and live happy lives. That is our plan, and nothing will stop us.
THE END
# Appendix
A letter from José Angelico:
_To whom it may concern:_
_I am writing this knowing that if it is in another man's hands, then I am dead or soon to die. I took this money hoping that I would be the one to return it to where it belongs, and I had my schemes for doing that. But I write as a dead man, I think: for they will not take me and let me live_.
_My daughter is Pia Dante Angelico, and she has nobody in the world now. Perhaps I can appeal to you to make her safe and help her? She is as innocent as they are all innocent; I know I am betraying her. Pia, if ever you get to see this, know that my mission was simple, and what I did, I didfor you and children like you. From the day I came to know Mr Gabriel Olondriz – and I was a very young boy when I met him – a fire burned. He set me ablaze, as he started so many fires. He taught me many things, but he taught me most of all that Senator Zapanta's crime – the crime he uncovered and was jailed for – was monumental. Senator Zapanta stopped a nation in its tracks. He stopped our country making progress. Worse than that even, he gave other countries an excuse to stop helping us. For the millions he took, how many millions did he prevent even being offered? Worse, worse even than that – he reassured other politicians, officers, clerks, teachers, shopkeepers, neighbours that to steal is to rise, and to rise with your foot on the face of the poor is natural law. Even the poor believe that, and it is one of the reasons we stay poor_.
_Pia, I got tired waiting. There is a saying from St Matthew, 'Knock, and the door shall be opened' – and maybe that is true of God, but it is not true of man. The locks and chains that I have seen. The seals on the doors, my child. In our life, the doors remain shut. That is why I set my life to serving Senator Zapanta, in the hope that one day he would leave his door ajar, and let me through it_.
_I waited many years before he did, so let me tell you what happened, just so there is no mystery.Just so you know how simple it can be, to rob those who rob us_.
_Senator Zapanta has a traditional, frightened mind. His smiles are false: he is worried all the time. He has lost money in bad deals, and he despises banks. His own father lost a lot of money when a bank collapsed: Senator Zapanta trusts only cash. That is why in the basement of his home he built a vault, and that is why the dirty money from his crimes is kept under the ground_.
_He moves money from the vault to a smaller safe upstairs. He only moves small sums, keeping the main chamber locked. It requires a key and a combination. How do I know this? Because he came to trust me with both. To live without trust is difficult, and tiring. What he came to trust in me, Pia, was what he thought was my sweet, obedient stupidity. I have spent the years being only willing and obedient. I have followed orders, and smiled. I have spent a lifetime nodding, serving, providing, assisting – and no task has ever been too great, just as no task has ever been left undone. For those reasons, I rose and got closer. I became essential to Senator Zapanta, because I was one of the only men in whom he placed trust_.
_He took me down to the vault eight years ago. The door is metal, and so heavy it runs on wheels. Inside the room are locked boxes, but the cash waskept on a shelf, in bricks. Those bricks came and went. He told me he liked to have six million there, because six million filled the shelves. When the bricks of cash ran down, he would move money from his banks, and a briefcase would arrive. He started by always taking me down with him. Then – one day, three years ago – he gave me the key, and the combination, and sent me down alone. He would change the combination after every trip, of course – so there was never any danger of me visiting the vault without permission. I came to see that he only used five sets of numbers. He had five sons, so he used the birthdays of his boys. He thought I was too stupid to memorize numbers, and the key – he knew – could not be copied if it never left the house. He did not imagine that in my room I kept notes, and memorized them, and worked out the variations of numbers. Pia, I burned my notes in the kitchen stove lest anyone check. I learned from Gabriel Olondriz, and I burned them as soon as I made them_.
_He was right about the key, of course, but – once again – he did not think his houseboy would draw it and take the drawing to a locksmith on the other side of the city. He did not think the houseboy would return, and try the copy the next time he got a chance, and note how it failed to match_ , _drawing revisions carefully and crumpling the paper to look like trash, to smuggle it out again. He never thought that, just like my god father in jail, with years to think and plan – I, José Angelico, thought in years rather than days or hours. Sixteen times I tried the key-copies before we got it right. Then it was a question of waiting for the right combination of circumstances. When Senator Zapanta announced a three-month trip to Europe, it seemed the time. The house staff was scaled down. Repairs and re-decoration of several rooms was announced – this would mean so many visitors. I started to worry about the fridge in the servants' kitchen, and I broke the thermostat twice, and mended it again. When someone suggested we call in the repair man, I told my friends that I'd run out of patience and would buy a new one myself, out of my own wages. The housekeeper promised she would try to make it a house purchase, but I told her that in this hot country we needed a reliable fridge, and I would not wait_.
_The housekeeper trusted me. The guards trusted me. The thing I worried about most was that once I'd filled the fridge with money, we'd be stopped at the gate and searched – we are routinely searched, of course. But I was José Angelico, with the right papers, and there were delivery vehicles going inand out all morning, and I'd wrapped the thing in plastic and roped it ready for loading. We sailed through_.
_Getting the money from the vault to the fridge? It took two trips. I chose a Thursday, which is when I pull all the household trash together for the dump truck. Nobody is surprised to see the houseboy dragging two, three or four awkward bags of trash around – especially when the builders are at work, making so much mess. When Senator Zapanta discovers the simplicity with which six million dollars disappears, I hope that he will fall to his knees and howl. Remember, Pia – and remember, Senator – whatever is said about me, I was no thief. I simply took back the money that was ours, and now I am about to put it in this coffin_.
_I have, of course, created the alternative route: if you have travelled this route, it is only with the help of Mr Olondriz – so I hope you are a friend. My final letter to him will lie in box 101, for 101 is the thing you cannot resist. With it lie instructions that only he will understand. The key to the box will stay safe with me_.
_Now I am so tired_.
_I am about to place the coffin in a grave that will be marked with your name, my child. I mean to find a way of returning it to the people from whom it was stolen. But if someone is reading this_ , _it means I am almost certainly dead and the money is in their hands, and I can only say, 'Beware, because this money belongs to the poor. That is what you cannot resist.'_
_It seems fitting that the Day of the Dead is approaching. We will meet again, Pia Dante, but in the brightest light_.
_It is accomplished_.
# A Note from the Author: What is a book-code?
I first came across the device in a novel by John le Carré. It was explained as a very simple code that relied on two or more people having exactly the same copy of a book. For example, if I know that you have the Penguin 1975 edition of _Under the Volcano_ , I can get my own copy out and communicate thus:
234•15•1•3•3•7•4•16 •4/8• 2•6 •15•5•3•16 • 2•3•4•19•16•
The most important number is the first: it identifies the page. Now you're at that page, you count fifteen lines down. At line fifteen, you go just one letter in, which gives you a capital 'B'. Now go to line three, character three. It gives you an 'e'. On you plod and you end up with _Best_. You now hit an oblique stroke, which means you go onto the next page. Eight lines down and two characters in give you 'w', and soon you have 'wishes'.
So oblique strokes signify the turning of the page and the creation of a new word. Counting characters left to right must include spaces and punctuation marks. To avoid confusion, indented lines can be avoided – but there are endless variations, and you can personalize the rules to your own satisfaction, making things as complex as you wish. The joy of a book-code is that you can make it entirely your own.
The code can be cracked if you know the book the messengers are using, but it's impossible if you don't. The code used by José Angelico is revealed if you have the 1984 New King James Thomas Nelson edition of the Bible. Gabriel Olondriz had a copy, and those wishing to send him secret messages had copies too. They had personalized the code, working right to left, and turning pages backwards rather than forwards. I presume the messages exchanged were never of great importance, and it was done simply for the joy of encryption. But it was how José concealed the most important part of his trail, and he invoked his God at the same time.
# Acknowledgements
I am eternally grateful to Jane Turnbull and Joe, without whom I would not be in print. I am grateful to my own family and to a number of close friends, most especially Jane Fisher for her support, and Michael Hemsley, who gave me the idea that sparked the plot.
I wrote this book whilst teaching the children of British School Manila – a truly fine school that offers what every child is entitled to, but so few receive – and I thank them, as well as my colleagues, for their kindness.
I would also like to thank Linda, Hannah, Bella and David at David Fickling Books, as well as Clare and the whole Random House team. Ken, Sally and Jenne have also been – and continue to be – dynamic.
Behala dumpsite is based loosely on a place I visited whilst living in Manila. There really is a school there, and there really are children who will crawl through trash forever. If you come to the Philippines, do what Olivia did. See everything, and fall in love.
The characters and the plot are, of course, invented.
# About the author
Andy Mulligan was brought up in South London. He worked as a theater director for ten years, before travels in Asia prompted him to retrain as a teacher. He has taught English and drama in Britain, India, Brazil, and the Philippines. He now divides his time between London and Manila.
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Last Remaining Male Rhino
Music Teacher Accidentally Starts A Cult
Gold Coins Hidden In Piano
Undated handout photo issued by The Trustees of the British Museum of an upright piano in which a hoard of century-old gold coins was found, as a treasure inquest is being held in Shropshire to determine what should happen to it. PRESS ASSOCIATION Photo. Issue date: Thursday April 20, 2017. See PA story INQUEST Piano. Photo credit should read: Peter Reavill/The Trustees of the British Museum/PA Wire NOTE TO EDITORS: This handout photo may only be used in for editorial reporting purposes for the contemporaneous illustration of events, things or the people in the image or facts mentioned in the caption. Reuse of the picture may require further permission from the copyright holder.
The coins are 91.7% gold and would have been worth more than the cost of a house at the time they were covered up in the instrument.
Examiners have been left scratching their heads regarding why a fortune trove of gold coins was covered up in an old piano.
The gathering of 913 coins, announced as fortune by a coroner on Thursday, was discovered covered up underneath the instrument's console at a school in Shropshire as it was being retuned.
It is accounted for the store could be worth a huge number of pounds, however despite everything it must be formally esteemed.
Specialists from the British Museum say the coins extend in date from 1847 to 1915 and incorporate 633 full sovereigns and 280 half-sovereigns.
They were discovered conveniently stacked in a few hand-sewed packs and would have been worth around £773 at the time they were concealed, well over the normal house cost of £619.
Most of the coins date from the rule of Queen Victoria and were observed to be 91.7% immaculate gold.
At an examination into the disclosure, coroner John Ellery decided that the gold coins were fortune however stated: "We just don't know how they came to be hidden."
A universal media offer and additionally neighborhood inquire about neglected to reveal any insight into who put the 6kg store into the piano.
The instrument already had a place with Graham and Meg Hemmings, from Saffron Walden in Essex, however they gave it to Bishop's Castle Community College in Shropshire subsequent to moving adjacent in 2015.
The couple had possessed it for a long time with no learning of its mystery.
The accumulate was found by tuning expert Martin Backhouse, 61, who at first thought the "gobsmacking" disclosure was "moth repellent" before acknowledging it was too substantial.
Subsequent to slitting the sewing with his penknife, he understood there was "somewhat a considerable measure of gold in this".
Both Mr Backhouse and the school could be in line for a bonus from the accumulate's deal.
Mr and Mrs Hemmings said they didn't lament giving the piano to the school.
Mrs Hemmings stated: "The misery is, it's not a total story. They've searched and scanned for the general population and they tragically haven't approached.
"It's a deficient story – yet it's as yet an energizing story."
Amid the hearing, Peter Reavill, from the British Museum, said one of the parcels contained an old Shredded Wheat publicizing card, which means the accumulate was likely "repackaged" at some point amid the Great Depression time.
I Photographed Australia For Over 3 Months And Was Amazed By Its Diversity
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La 49.ª edición del Tour del Porvenir (nombre oficial en francés: Tour de l'Avenir) fue una carrera de ciclismo en ruta por etapas que se celebró entre el 26 de agosto y el 1 de septiembre de 2012 en Francia con inicio en la ciudad de Dole y final en Le Grand-Bornand sobre un recorrido total de 756,6 kilómetros.
La carrera formó parte del UCI Europe Tour 2011-2012, dentro de la categoría UCI 2.Ncup (Copa de las Naciones UCI sub-23 limitada a corredores menores de 23 años.)
La carrera fue ganada por el ciclista Warren Barguil de la selección nacional sub-23 de Francia. El podio lo completaron el ciclista Juan Ernesto Chamorro de la selección nacional sub-23 de Colombia y el ciclista Mattia Cattaneo de la selección nacional sub-23 de Italia.
Equipos participantes
Recorrido
El Tour del Porvenir dispuso de un prólogo y 6 etapas para un recorrido total de 756,6 kilómetros con inicio en la ciudad de Dole y final en Le Grand-Bornand, comprendiendo 2 contrarreloj individual, 2 etapas de montaña, 1 etapa de media montaña y 2 etapas llanas.
Clasificaciones finales
Las clasificaciones finalizaron de la siguiente forma:
Clasificación general
Clasificación por puntos
Clasificación de la montaña
Clasificación por equipos
Evolución de las clasificaciones
Referencias
Enlaces externos
Página oficial
UCI Europe Tour 2011-2012
2012
Ciclismo en Francia en 2012
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 39
|
Q: SwiftUI ForEach understanding variable usage The following code does work for me...
VStack {
ForEach(0..<self.rows, id: \.self) { row in
HStack {
ForEach(0..<self.columns, id: \.self) { column in
//let data = self.item(row: row, column: column)
Group {
if self.item(row: row, column: column) != nil {
self.content(self.item(row: row, column: column)!).frame(width: geometry.size.width/CGFloat(self.columns))
} else {
Spacer()
}
}
}
}
}
}
However, when I uncomment data variable and replaced item() calls with data usage, and even add return Group { } it stops working and cannot infer return type?
A: in Xcode 12 beta simply add type to param.
My sample code:
(I prefer to divide SwiftUi stuff.. too messy otherwise..)
See near color
struct Issue: Identifiable{
var id = UUID()
var name = ""
var fakeMsg = ""
var operatorInCharge = ""
var solved = false
}
struct CurrentIssuesView: View {
let roomIssues = [
Issue(name: "ROOM 1", fakeMsg: "2020-09-05 proiettore", operatorInCharge: "m.a", solved: true),
Issue(name: "ROOM 1", fakeMsg: "2020-09-04 wifi", operatorInCharge: "a.b"),
Issue(name: "ROOM 2", fakeMsg: "2020-09-04 Audio", operatorInCharge: "m.c", solved: true),
Issue(name: "ROOM 3", fakeMsg: "2020-09-04 KBD", operatorInCharge: "m.d")
]
var body: some View {
let vs = VStack{
Text("Current ISSUES")
List(roomIssues) { (issue: Issue) in
let color = issue.solved ? Color.green : Color.red
HStack{
Text(issue.name).font(.system(size: 20)).foregroundColor(color)
Text(issue.fakeMsg)
}
}
}
return vs
}
}
I got:
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 4,065
|
Jonkheer Imilius Josinus Hendrik Willem van Andringa de Kempenaar (Sint Annaparochie, 2 maart 1844 - Leeuwarden, 3 september 1895) was een telg uit het geslacht Van Andringa de Kempenaar. Hij was burgemeester van Ferwerderadeel van 1869 - 1878.
Burgemeester van Ferwerderadeel
Imilius Josinus
Nederlandse adel in de 19e eeuw
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 7,580
|
Q: execute sql query in zend framework 2 I need execute this SQL query in ZF2:
SELECT FA_VENTAS.EM_CODIGO,
FA_VENDED.VN_NOMBRE AS VENDEDOR ,
FA_CLIEN.CE_NOMBRE AS CLIENTE,
FA_TIPCLI.TC_DESCRI AS CANAL ,
MIN(FA_DETVEN.CL_NOMDEP) AS MARCA ,
IN_ITEM.IT_CODBAR AS CODBARRA ,
IN_ITEM.IT_NOMBRE AS PRODUCTO ,
TO_CHAR(FA_VENTAS.VE_FECHA,'MM')AS MESES ,
TO_CHAR(FA_VENTAS.VE_FECHA,'YYYY')AS ANIO ,
SUM(DV_SUBTOTAL-DV_VALIVA) AS VALOR ,
SUM(DV_CANPED) AS UNIDAD
FROM
DOUS.FA_VENTAS FA_VENTAS,
DOUS.FA_DETVEN FA_DETVEN,
DOUS.IN_ITEM IN_ITEM ,
DOUS.IN_CLASE IN_CLASE ,
DOUS.FA_VENDED FA_VENDED,
DOUS.FA_CLIEN FA_CLIEN,
DOUS.FA_TIPCLI FA_TIPCLI
WHERE
FA_TIPCLI.TC_CODIGO=FA_CLIEN.TC_CODIGO
AND FA_VENTAS.EM_CODIGO = FA_DETVEN.EM_CODIGO
AND FA_VENTAS.VE_CODIGO = FA_DETVEN.VE_CODIGO
AND FA_VENTAS.TP_CODIGO = FA_DETVEN.TP_CODIGO
AND FA_VENTAS.PE_CODIGO = FA_DETVEN.PE_CODIGO
AND FA_DETVEN.EM_CODIGO = IN_ITEM.EM_CODIGO
AND FA_DETVEN.IT_CODIGO = IN_ITEM.IT_CODIGO
AND IN_ITEM.EM_CODIGO = IN_CLASE.EM_CODIGO
AND IN_ITEM.CL_CODIGO = IN_CLASE.CL_CODIGO
AND FA_VENDED.VN_CODIGO=4
AND FA_VENTAS.CE_CODIGO=FA_CLIEN.CE_CODIGO
AND FA_VENTAS.EM_CODIGO = '4'
AND FA_VENTAS.TP_CODIGO = '2'
AND TRUNC(FA_VENTAS.VE_FECHA) between'01-jan-2009' and '31-jan-2009'
GROUP BY FA_VENTAS.EM_CODIGO,
FA_VENDED.VN_NOMBRE,
FA_CLIEN.CE_NOMBRE,
FA_DETVEN.CL_NOMDEP,
FA_VENTAS.VE_FECHA,
IN_ITEM.IT_CODBAR,
IN_ITEM.IT_NOMBRE,
FA_TIPCLI.TC_DESCRI
UNION ALL
SELECT FA_DEVOLU.EM_CODIGO,
FA_VENDED.VN_NOMBRE AS VENDEDOR ,
FA_CLIEN.CE_NOMBRE AS CLIENTE,
FA_TIPCLI.TC_DESCRI AS CANAL ,
MIN(FA_DETDEVOL.CL_NOMDEP)AS MARCA ,
IN_ITEM.IT_CODBAR AS CODBARRA ,
IN_ITEM.IT_NOMBRE AS PRODUCTO ,
TO_CHAR(FA_DEVOLU.DE_FECHA,'MM') AS MESES ,
TO_CHAR(FA_DEVOLU.DE_FECHA,'YYYY') AS ANIO ,
-SUM(FA_DETDEVOL.DD_SUBTOTAL- FA_DETDEVOL.DD_VALIVA) AS VALOR ,
-SUM(DD_CANTID) AS UNIDAD
FROM
DOUS.FA_DEVOLU,
DOUS.FA_DETDEVOL,
DOUS.IN_ITEM IN_ITEM ,
DOUS.IN_CLASE IN_CLASE ,
DOUS.FA_VENDED FA_VENDED,
DOUS.FA_CLIEN FA_CLIEN,
DOUS.FA_TIPCLI FA_TIPCLI
WHERE
FA_TIPCLI.TC_CODIGO=FA_CLIEN.TC_CODIGO
AND FA_DEVOLU.EM_CODIGO = FA_DETDEVOL.EM_CODIGO
AND FA_DEVOLU.DE_CODIGO = FA_DETDEVOL.DE_CODIGO
AND FA_DEVOLU.TP_CODIGO = FA_DETDEVOL.TP_CODIGO
AND FA_DETDEVOL.EM_CODIGO = IN_ITEM.EM_CODIGO
AND FA_DETDEVOL.IT_CODIGO = IN_ITEM.IT_CODIGO
AND IN_ITEM.EM_CODIGO = IN_CLASE.EM_CODIGO
AND IN_ITEM.CL_CODIGO = IN_CLASE.CL_CODIGO
AND FA_DETDEVOL.EM_CODIGO = 4
AND FA_DETDEVOL.TP_CODIGO = '2'
AND TRUNC(FA_DEVOLU.DE_FECHA) between '01-jan-2009' and '31-jan-2009'
AND FA_VENDED.VN_CODIGO=4
AND FA_DEVOLU.CE_CODIGO=FA_CLIEN.CE_CODIGO
GROUP BY FA_DEVOLU.EM_CODIGO,
FA_VENDED.VN_NOMBRE,
FA_CLIEN.CE_NOMBRE,
FA_DETDEVOL.CL_NOMDEP,
FA_DEVOLU.DE_FECHA,
IN_ITEM.IT_CODBAR,
IN_ITEM.IT_NOMBRE,
FA_TIPCLI.TC_DESCRI
but I don't understand what model, view and command use.
Please help me
A: With a query like this, you should use \Zend\Db\Adapter\Adapter
$sql = "SELECT SELECT FA_VENTAS.EM_CODIGO, ...";
$statement = $adapter->query($sql);
$result = $statement->execute();
hth
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 647
|
{"url":"http:\/\/physics.stackexchange.com\/tags\/harmonic-oscillator\/hot","text":"# Tag Info\n\nYour equation in the Liouville form is elementary for numerical integration, it is structurally just a linear advection equation with spatially varying coefficients. The transformed equation with the kernel F is not useful at all for numerical solution, don't bother with it. All we have here is a 2D advection equation (I use y instead of p): $\\partial_{t} ... 3 If there is no external force with explicit time dependence, then the harmonic oscillator contains no explicit time dependence. Then the system has time translation symmetry, i.e. the result can only depend on the difference$T =t_b-t_a$, not on$t_a$and$t_b$individually. 2 If an object is accelerating upwards at a rate of$a$m\/s$^2$, then the gravitational force felt by this object is effectively, $$g_{eff}=g+a$$ where$g\\sim9.8$m\/s$^2$is the canonical gravitational acceleration we all know and love. In your particular case, the common equation of motion for a pendulum, $$\\frac{d^2\\theta}{dt^2}=mg\\sin\\theta$$ replaced ... 2 The multi-dimensional analog of simple harmonic motion is an object subject only to a harmonic potential,$U = \\frac 1 2 k ||\\vec r - \\vec r_0||^2$, where$k$is a positive constant (oftentimes called the spring constant),$\\vec r$is the object's position, and$\\vec r_0$is the position of the center of the potential. By choosing the origin to be the center ... 1 In the first part of the linked document are not giving a formal derivation of the uncertainty principle. It is giving a particular example to show the general idea. The gaussian wavefunction is chosen because it is a particularly simple and happens to exactly satisfy the lower bound$\\sigma_x\\sigma_p = \\frac{1}{2}\\hbar$. For the harmonic oscillator being ... 1 Your reasoning is correct up to the point where you compare the accelerations of the mass and the spring. But the effect on the period is actually inverted. Intuitively, when the spring acceleration is higher (lower), this actually means that the spring is more (less) deformed and pulls back with a force correspondingly stronger (weaker) compared to case 1, ... 1 Well it depends on the context of your question. If you're being introduced to General Relativity, then you're just going to assume, in the spirit of the equivalence principle, that gravity and the acceleration cannot be told apart from the pendulum's standpoint, so the acceleration is obviously$a+g$. If you need to do it from first principles in a ... 1 It is true in both cases and an even more general statement can be made. For a potential of the form$V(r)=\\alpha r^n$, the expectation value of the kinetic an potential energy is related by $$2 \\langle T \\rangle = n \\langle V \\rangle.$$ For the case of the harmonic oscillator,$n=2$. See virial theorem for details. 1 The fact that you can eliminate the$\\sin$term tells you that its coefficient$[-\\omega^2 B_{2}-2\\beta\\omega B_{1}+\\omega_{0}^{2}B_{2}]$must be zero. This gives you another relation between$B_{1}$and$B_{2}$, and with two equations and two unknowns, you can solve cleanly for$B_{1}$and$B_{2}$. 1 You can think of the continuos formalism as being the limiting case of the discrete-momentum one: if the momentum is taken as a discrete variable (which amounts to constraining the particles to be in some finite volume$V) the fourier expansion of the (real, scalar) field is: $$\\tag{1} \\varphi(x) = \\sum_{\\textbf{k}} \\frac{1}{\\sqrt{2V \\omega_{\\textbf{k}}}} ... 1 Just look at the equation of motion. Suppose you hang a spring from the ceiling, and that it hangs a distance y_0 from the ceiling in equilibrium (we orient our axis so that positive y points downward). Then, the equation of motion is$$ m\\ddot{y}=-k(y-y_0)+mg, $$and so$$ \\tfrac{\\mathrm{d}^2}{\\mathrm{d}t^2}(y-y_0)+\\tfrac{k}{m}(y-y_0)=g. $$The square ... 1$$ \\sum _nf(n)\\int \\mathrm{d}p\\, |\\left< p|n\\right> |^2=\\sum _nf(n)\\int \\mathrm{d}p\\int \\mathrm{d}q\\, \\left< n|p\\right> \\left< p|n\\right> =2\\pi \\sum _nf(n)\\left< n|n\\right> =2\\pi \\cdot \\sum _nf(n), $$where I used the fact that$$ \\int \\mathrm{d}p\\, \\left| p\\right> \\left< p\\right| =2\\pi, $$which follows from$$ \\left< ... 1 We know that: \\begin{align} x(t) &= A \\cos(\\omega t - \\phi), && x(0)= A\\cos(-\\phi)=0.3,\\\\ \\dot x(t)&=-A\\omega\\sin(\\omega t - \\phi), && \\dot x(0)=-A\\omega\\sin(-\\phi)= 0.07,\\\\ \\ddot x(t)&=-A\\omega^2\\cos(\\omega t - \\phi), && \\ddot x(0)=-A\\omega^2\\cos(-\\phi)=-0.33. \\end{align} We know that\\phi=12.5\u00ba$or$\\phi=-12.5\u00ba$, lets ... 1 By definition of the momentum basis,$p$is diagonal in that basis as per $$\\langle k \\rvert p \\lvert k' \\rangle = \\delta(k - k')$$ since the momentum basis states are defined by$p \\lvert k \\rangle = k \\lvert k \\rangle$. 1 I don't see why you wouldn't get any imaginary terms in the matrix elements. Your suggestion of aproach is right and in this case the eigenstates$|n\\rangle$of the harmonic oscilator are represented by Hermite Functions in position representation, which happens to be Fourier transform's eigenfunctions as well. As the unitary map that changes form the ... 1 The first solution is not correct since it implies a strange connection$\\dot x (0)=-\\beta x(0)$. Check the general solution for its region of validity. 1$a^\\dagger a\\! \\mid \\! n \\rangle = n\\mid \\! n \\rangle$. For vacuum you can write$a^\\dagger a\\! \\mid \\! 0 \\rangle = 0\\mid \\! 0 \\rangle$, if you like. No need to write 0 solely. 1 Hints: OP's eq. (1) is the equation for a constant of motion$\\frac{df}{dt}=\\{f,H\\}_{PB}+\\frac{\\partial f}{\\partial t}=0$of a harmonic oscillator$H=\\frac{p^2}{2m}+\\frac{1}{2}m\\omega^2 x^2$. Let us assume for simplicity that$m\\omega=1$, and leave it to the reader to generalize to arbitrary$m$and$\\omega$. Complexify$z=x+ip\\in\\mathbb{C}\\$. Then the ...","date":"2014-11-27 19:35:09","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\": 1, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9982410073280334, \"perplexity\": 8374.499689835093}, \"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-2014-49\/segments\/1416931009084.22\/warc\/CC-MAIN-20141125155649-00141-ip-10-235-23-156.ec2.internal.warc.gz\"}"}
| null | null |
L'Aiguille du Grépon (3.482 ) è una montagna della catena delle Aiguilles de Chamonix, nel massiccio del Monte Bianco.
Descrizione
Si trova a ovest della Mer de Glace, a sud della Aiguille des Grands Charmoz.
La prima ascensione fu compiuta il 5 agosto 1881 da Albert Frederick Mummery con le guide Alexander Burgener e Benedikt Venetz, per la cresta nord.
La traversata Charmoz-Grépon è considerata una classica, anche facente parte del libro "Il massiccio del Monte Bianco - Le 100 più belle ascensioni, " di Gaston Rébuffat.
Note
Bibliografia
Altri progetti
Collegamenti esterni
Montagne del Rodano-Alpi
Montagne del Massiccio del Monte Bianco
Tremila delle Alpi Graie
|
{
"redpajama_set_name": "RedPajamaWikipedia"
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| 4,707
|
{"url":"http:\/\/websfog.blogspot.com\/2012\/09\/probability-5.html","text":"## Friday, September 7, 2012\n\n### Probability 5 - Conditional expectation the best guess\n\nFifth post in the series.\n\nConditional Expectation as best guess of the next result\n\nThink of some random Variable $X_n$ and its $\\sigma$-algebra $\\mathcal{F}_n$ (algebra of its level sets)\n\nlook at the figure above, each patch represents a \u201cminimal\u201d set in $\\mathcal{F}_n$. $X_n$ gives each of those sets constant value. Namely if $A$ is one of the patches then $\\forall \\omega \\in A \\in \\mathcal{F}_n$, $X_n(\\omega) = \\alpha_{A}$.\n\nNow what is $\\mathbb{E}[X_n|\\mathcal{F}_{n-1}]$?. Note that $\\mathcal{F}_{n-1}\\subseteq \\mathcal{F}_{n}$ so lets think of it as -\n\nLook how the new $\\sigma$-algebra is more coarse, some sets that are minimal here were finer divided in $\\mathcal{F}_{n}$. $X_n$ is not measurable on $\\mathcal{F}_{n-1}$, But $\\mathbb{E}[X_n|\\mathcal{F}_{n-1}]$ is, and $\\mathbb{E}[X_n|\\mathcal{F}_{n-1}]$ gives us the best guess we can make about the out come of $X_n$. For example If on step $n-1$, $X_n$ happened to fall on the sets that are minimal on both $\\sigma$-algebras then we know it cant change on step $n$ but if it hadn\u2019t then we will be able to narrow down possible outcomes of step $n$ but still there will be some uncertainty, our best guess will be the ecpected value of $X_n$ on the possible outcomes in $n$, which is exactly the conditional expectation. Step $n-1$ does not provide all the information but it give us the probabilities of our best guesses we will be able to do on step $n-1$.\n\nTechnorati Tags: ,,\n\nWindows Live Tags: best guess,Conditional Expectation,Probability\n\nWordPress Tags: best guess,Conditional Expectation,Probability\n\n#### 1 comment:\n\nDegang WU said...\n\nthanks for the great intuition!","date":"2018-05-26 01:55:11","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 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\": 0.6857045292854309, \"perplexity\": 581.4431556752678}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-22\/segments\/1526794867277.64\/warc\/CC-MAIN-20180526014543-20180526034543-00522.warc.gz\"}"}
| null | null |
This webcam is currently assigned to Akumal Bay Resort. It was originally added on 7 november 2018 and has been viewed 25 791 times since then. The current picture above was taken 9 perccel ezelőtt, thereby the webcam seems to be currently active. So far, it was added to their personal favorites on webcams.travel by 1 people.
|
{
"redpajama_set_name": "RedPajamaC4"
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| 3,933
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Waitresses at sea: gender, race and service labour on ocean liners, c.1930s¿1960s
Service labour on ships was feminised, but it was monopolised by men. Besides the limited role of the stewardess, women were not employed in general service positions until the 1930s when they began to be hired as waitresses in place of male dining-room stewards. This article considers the conditions of possibility for American and British lines recruiting white women in preference to men. This occurred at two significant junctures. Firstly, during the 1930s as race became more crucial to employment on American ships in transoceanic trades, and subsequently from the late 1950s as shipping companies responded to the rise of commercial aviation. By examining the changing face of service employment at sea and the labels used to designate male and female service labour as both parallel and foil to practices on land and in flight, this article casts new interpretive light on the relationship between gender, identity, work and status.
Women's History Review Journal
Steel, F. (2021). Waitresses at sea: gender, race and service labour on ocean liners, c.1930s¿1960s. Women's History Review, 30(2), 223-240. doi:10.1080/09612025.2020.1757866
Web Of Science Accession Number
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 8,682
|
Q: smartgwt browser history is there a way in smartgwt to go back in history?
E.g. I have an page with a button which does a Ajax page change of the current page to another. And on this new page there should be a button to return back to the previous page?
Can this be done with smartGWT? or do I have to make a new Ajax call to switch back to the previous page?
A: The functionality you want is provided by History class. Need to declare in web.xml and then use History.fireItem("SomeURL"), this will appear in app url as the string after # in URL is History ID ( something like http://google.com#SomeURL), you can use arbitrary IDs.
Use History.registerCallback() to register a function that opens requested History ID (eg. tab name/ID) on URL change (History's ValueChange function) and use History.addHistoryEntry() to update the page URL when other tab is selected.
If you implement this History class then you can use the browser's forward and back icon for the same purpose.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
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| 5,060
|
Lulu is excited to announce the first in a series of releases intended to improve your user experience on the Lulu.com website.
Following the July 24, 2012 release, everything about your Lulu account, including your email preferences, purchases, downloads, and shipping information will be managed from a sleek new My Account & Orders page. This change separates your user account information and purchasing history from the Lulu authoring tools.
What can you expect following this release?
The login / registration page has a new streamlined look.
When you click on the My Lulu tab, a new My Accounts & Orders button displays in the page header.
Click the My Accounts & Orders button to access your Order History, My Downloads page, and your saved Shipping & Billing information.
On the About Me page you can update your account information, username, and password.
On the Preferences page you can manage your email notification settings.
Check out the changes and see for yourself.
A GREAT start as far as "clarity" and ease of use go, as well as the cleaned up "look" … what I look forward to is the possibility of seeing reports on how many visits, clicks or some other record of actual visits to MY specific pages and books, AND it would be really nice to know how many of my FREE titles were viewed and/or downloaded. I realize we may never be able to know WHO, but the numbers would be great to know.
GREAT comments and feedback, Earl! We love the insight, especially from an author who is so familiar with our site already.
question: I have had my novels on Lulu and Amazon (via createaspace and Kindle) for 6 months, and durring that time my amazon account has sold over 200 books (Createspace =76 kindle =150 total sales) but my lulu account has 0 sales… why is it that the same titles and the same prices don't sell on lulu at all but they sell fast on amazon and also smashwords?
@Dr. Adam Ireland – It's a great question and one that we'd love to help you answer. To add to what Glenn said, there are many factors that could be at play here, including whether your book is in distribution, is set to public access, is enabled for Google Search and much more. Will you please fill out a case with our support team so that we can address the specifics of your book? Here is the link: http://ar.gy/.8Y. Thanks!
That is an interesting question Dr. Ireland. When promoting your books, do you direct your fans to Lulu.com to purchase your work, or to other sites? Also, do you have Google search activated for those projects in your Lulu account? If not you should consider activating this feature, as it will ensure your work published through Lulu.com is returned in Google search results.
17 days from the mainland?? Booked book signing event for Tuesday, Feb. 3 but no books (used up my inventory). See no tracking # on your last email (12/11/15). I ASSUME you shipped books by AIR ($65.24 shipping fee!). Very upset a bout delay. Cancel book signing? Part of my MARKETING that has been advertised. How can you help?
Jan 28 – my last order for 50 copies of my book was Jan. 11 (order #10170688 for $317.260 to Hawaii.) Not yet received, 17 days from the mainland?? Booked book signing event for Tuesday, Feb. 3. As of today, no books have arrived . See no tracking # on your last email (12/11/15). I ASSUME you shipped books by AIR ($65.24 shipping fee!). Very upset a bout delay. Cancel book signing? Part of my MARKETING that has been advertised. How can you help? Can this be saved?
|
{
"redpajama_set_name": "RedPajamaC4"
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| 6,247
|
<?php declare(strict_types=1);
namespace QuasarSource\Utils\RequestsHTTP\Binance\Traits\Params;
trait ParameterOrderID {
public function param_set_order_id(string $order_id): void {
$this->param_set('orderId', $order_id);
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
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| 3,859
|
declare namespace GridFSStream {
export interface Range {
startPos: number;
endPos: number;
}
export interface Options {
_id?: string;
filename?: string;
mode?: string;
range?: Range;
// any other options from the GridStore may be passed too, e.g.
chunkSize?: number;
content_type?: string;
root?: string;
metadata?: any;
}
export interface WriteStream extends NodeJS.WritableStream {
writable: boolean;
name: string;
id: string;
options: Options;
mode: string;
}
export interface ReadStream extends NodeJS.ReadableStream {
readable: boolean;
paused: boolean;
}
}
declare module "gridfs-stream" {
import mongo = require('mongodb');
// Merged declaration, g is both a callable function and a namespace
function g(db: any, mongo: any): g.Grid;
namespace g {
export class Grid {
files: mongo.Collection;
collection(name?: string): mongo.Collection;
curCol: string;
createWriteStream(options?: GridFSStream.Options): GridFSStream.WriteStream;
createReadStream(options?: GridFSStream.Options): GridFSStream.ReadStream;
createWriteStream(options?: string): GridFSStream.WriteStream;
createReadStream(options?: string): GridFSStream.ReadStream;
remove(options: GridFSStream.Options, callback: (err: Error) => void): void;
exist(options: GridFSStream.Options, callback: (err: Error, found: boolean) => void): void;
findOne(options: GridFSStream.Options, callback: (err: Error, record: any)=>void):void;
}
}
export = g;
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,892
|
from supriya.tools.ugentools.UGen import UGen
class LFClipNoise(UGen):
r'''A dynamic clipped noise generator.
::
>>> ugentools.LFClipNoise.ar()
LFClipNoise.ar()
'''
### CLASS VARIABLES ###
__documentation_section__ = 'Noise UGens'
__slots__ = ()
_ordered_input_names = (
'frequency',
)
_valid_calculation_rates = None
### INITIALIZER ###
def __init__(
self,
calculation_rate=None,
frequency=500,
):
UGen.__init__(
self,
calculation_rate=calculation_rate,
frequency=frequency,
)
### PUBLIC METHODS ###
@classmethod
def ar(
cls,
frequency=500,
):
r'''Constructs an audio-rate clipped noise generator.
::
>>> ugentools.LFClipNoise.ar(
... frequency=10,
... )
LFClipNoise.ar()
Returns unit generator graph.
'''
from supriya.tools import synthdeftools
calculation_rate = synthdeftools.CalculationRate.AUDIO
ugen = cls._new_expanded(
calculation_rate=calculation_rate,
frequency=frequency,
)
return ugen
@classmethod
def kr(
cls,
frequency=500,
):
r'''Constructs a control-rate clipped noise generator.
::
>>> ugentools.LFClipNoise.kr(
... frequency=10,
... )
LFClipNoise.kr()
Returns unit generator graph.
'''
from supriya.tools import synthdeftools
calculation_rate = synthdeftools.CalculationRate.CONTROL
ugen = cls._new_expanded(
calculation_rate=calculation_rate,
frequency=frequency,
)
return ugen
### PUBLIC PROPERTIES ###
@property
def frequency(self):
r'''Gets `frequency` input of LFClipNoise.
::
>>> frequency = 0.5
>>> lf_noise_0 = ugentools.LFClipNoise.ar(
... frequency=frequency,
... )
>>> lf_noise_0.frequency
0.5
Returns input.
'''
index = self._ordered_input_names.index('frequency')
return self._inputs[index]
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 7,957
|
package uk.org.nbn.nbnv.importer.validation
import uk.org.nbn.nbnv.importer.records.NbnRecord
class Nbnv197Validator extends DateFormatValidator {
def code = "NBNV-197"
def validate(record: NbnRecord) = {
val validFormats = List("dd/MM/yyyy", "dd-MM-yyyy", "yyyy/MM/dd", "yyyy-MM-dd", "dd MMM yyyy", "MMM yyyy", "yyyy")
validateDate(record, true, true, validFormats)
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,903
|
Q: Function to iterate over every column in a pandas DataFrame Hi, I created a function in Python that takes a dataframe as the first argument, and a column as the second argument.The goal is to find the total number of null values in that field. I'd like to loop over every column in the dataframe and apply the same function. Thanks!
def count_nulls(df, col_name):
col = df[col_name]
bool_col = pd.isna(col)
total_nulls = pd.Series.sum(bool_col)
total_rows = len(col)
pct_null = round((total_nulls / total_rows) * 100,2)
print("The","\'"+ str(col_name) + "\'", "field has", str(total_nulls), "nulls which account for",
str(pct_null) + "% of all values")
****Image****
enter image description here
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 5,060
|
Q: Difference between Hyperledger Projects There are around 5 projects under Hyperledger. I don't find any material which talks about distinctive features of every framework, how each framework is different from each other, when to use each? It would be of great help if someone provide that information
A: Hyperledger is a distributed ledger technology implementation of the Linux foundation with a some high-profile partners (IBM and Intel among others). The 5 projects under the Hyperledger banner are: fabric, sawtooth, indy, burrow, and Iroha. Here's a good article explaining the differences
In a nutshell fabric is the actual blockchain component that allows for 'plug-ins' of different types of consensus mechanisms. Consensus mechanisms are at the heart of blockchain and Sawtooth uses POET, proof of elapsed time, in an effort to speed up the process while making it less resource intensive (e.g., less electricity than BTCs proof of work (POW). Indy is an attempt to tackle the problem of Identity management, burrow is a smart contract implementation and Iroha folds in mobility components. To learn more consider this edx course from the Linux foundation
It will answer many of your questions.
A: As of 2019 there are more frameworks/tools under Hyperledger umbrella,
Update Aug 29th 2019: Hyperledger Composer has been deprecated
Hyperledger Composer has been deprecated and they suggested everyone to use Fabric instead.
Useful links:
https://www.hyperledger.org/projects
https://101blockchains.com/hyperledger-blockchain/
Below image is taken from 101blockchain.com
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,026
|
import { Method, doRequest } from 'lib/rest/RestRequests';
import FetchLoggedInUserTypes from './generated/FetchLoggedInUserTypes';
import { User } from 'models/User';
import { getEncodedURI } from 'lib/rest/URIHelper';
interface ResponseData {
user_id: string;
display: string;
loginType: string;
socialLogin?: string;
favourites?: Record<string, boolean>;
}
export const getAvatarUrl = (loginType: string, socialLogin?: string): string | undefined => {
if (socialLogin && loginType === 'GITHUB') {
return `https://github.com/${getEncodedURI(socialLogin)}.png`;
}
};
const createUser = (responseData: ResponseData): User => ({
userId: responseData.user_id,
display: responseData.display,
socialLogin: responseData.socialLogin,
avatarUrl: getAvatarUrl(responseData.loginType, responseData.socialLogin),
favourites: responseData.favourites,
});
export const fetchLoggedInUser = async (): Promise<User | void> => {
const url = `/rest/user/loggedin`;
return doRequest(Method.GET, url, 'rest.error.get', null, FetchLoggedInUserTypes, createUser);
};
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,199
|
I absolutely love these two by Russ B, but I didn't even realise I even had them until the other day. The bluebells were amazing, weren't they?
My wife pursuaded me a few years ago and I reluctantly dragged my heels along only to be hooked the first night.
c) I have never been so popular in a room full of women before!! I'm lovin' it!!
Man to man. Try it, it's cheaper than drinking and makes you twice as handsome LOL!!
Haha, Thanks Bob. I shall pass this excellent info on.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 2,273
|
Isaac Clason Delaplaine (October 27, 1817 – July 17, 1866) was a lawyer and politician who was a U.S. Representative from New York during the American Civil War.
Biography
Born in New York City, Delaplaine was the son of a successful merchant. He graduated from Columbia College (now Columbia University) in 1834. He received a gold medal for finishing first in his class, as well as silver medals for placing first in studies of: moral and political philosophy; Greek and Roman literature; and mathematics and astronomy. He received the bronze medal for second place in natural, experimental and mechanical philosophy.
Delaplaine received a master's degree from Columbia in 1837. He studied law, was admitted to the bar in 1840, and practiced in New York City.
He was elected as a Democrat to the Thirty-seventh Congress (March 4, 1861 – March 3, 1863). Serving during the American Civil War, Delaplaine joined most other Democrats in supporting Abraham Lincoln's war measures, but opposing the emancipation of slaves and the suspension of Habeas corpus.
He died in New York City on July 17, 1866. He was interred in Green-Wood Cemetery in Brooklyn, New York.
Family
Delaplaine was a son of John Ferris Delaplaine (1786-1854) and Julia Ann (Clason) Delaplaine (1794-1866). His brother John Ferris Delaplaine Jr. (1815-1885) served as secretary of the U.S. legation in Vienna from 1866 to 1883.
In 1838, Delaplaine married Matilda Post (1821-1907). They were the parents of two daughters, Julie (1840-1915) and Florence (1849-1926). Delaplaine's daughter Julie married attorney George Richard Schieffelin (1836-1910). His daughter Florence (1849-1926) was the second wife of Hamilton Fish II.
References
The Commencement of Columbia College. American Railroad Journal and Advocate of Internal Improvements. Volume 3. Pages 636–637. October 4–10, 1834.
1817 births
1866 deaths
Burials at Green-Wood Cemetery
Columbia College (New York) alumni
New York (state) lawyers
Democratic Party members of the United States House of Representatives from New York (state)
19th-century American politicians
19th-century American lawyers
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 4,480
|
New shared code with GOL
We will fly from Sao Paulo, Recife, Salvador de Bahia and Fortaleza, to 20 other cities in Brazil, thanks to an alliance with the Brazilian airline GOL. We are taking another step forward in our international development and, starting from January of next year, we will fly to more than 20 Brazilian cities from Sao […]
+ Europa
We will fly from Sao Paulo, Recife, Salvador de Bahia and Fortaleza, to 20 other cities in Brazil, thanks to an alliance with the Brazilian airline GOL.
We are taking another step forward in our international development and, starting from January of next year, we will fly to more than 20 Brazilian cities from Sao Paulo, Recife, Fortaleza and Salvador de Bahia, thanks to our shared code agreement with GOL Líneas Aéreas.
This alliance will allow Air Europa to deploy the code to 78 national flights and offer passengers travelling from Europe, via Madrid, a perfect connectivity and an extensive selection of flights to some of the most important Brazilian cities; expanding the existing shared code agreement.
The implementation of this shared code with GOL comes as a result of Air Europa's continued support and focus on Brazil and their commitment to grow internationally with broader domestic connectivity in the country.
The synergies from this agreement will result in both more European tourism into Brazil and important advantages for the passengers travelling on this shared code such as: single ticket, single check-in and better and easier connections with reduced in-transit waits.
Air Europa's commercial director, Mr. Imanol Pérez, expressed his satisfaction with this agreement, "this will allow us to offer all our passengers new and fascinating destinations in Brazil. We are very proud of our agreement with GOL. Moving forward together guaranties our growth in the Brazilian airways market.
In similar terms, expressed Mr. Randall Aguero, GOL's Alliances, Expansion and International Distribution Director: "We are very happy to close this shared code agreement with Air Europa. GOL is the market leader in Brazil with a wide and diverse network, offering our clients the best travelling experience and a wide range of high quality products and services. We invest in alliances that can provide increasing benefits for our clients. Frequent travellers will soon be able to collect and redeem miles with our Smiles and SUMA loyalty programmes".
With this agreement we are reaffirming our support and focus on Brazil, where we have operated for over 20 years. Currently, we have direct flights from Madrid to Sao Paulo, Salvador and Recife. By the end of December we will also be flying to Fortaleza. This destiny will close our presence in the touristic triangle of the north east of Brazil.
The alliance also includes an agreement between Air Europa's SUMA and GOL's Smiles, the loyalty programmes of each airline, allowing passengers obtain and redeem miles for their flights.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 9,381
|
<div class='row'>
<div class='text-center'>
<h1>
{{smodelId}}s
<button type="button" id="addData" class="btn btn-success" ng-click="addRow()">New</button>
</h1>
<div id="grid1" external-scopes="gridScope" ui-grid="{ data: gridInfo.rows, columnDefs:gridInfo.columnDefs}" class="grid">
</div>
</div>
</div>
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 7,733
|
TrekMovie has released an update on the production of the sequel to J.J. Abrams' Star Trek.
Much of the design for the film has been completed, with the production design team once again being headed by Scott Chambliss (Star Trek).
Location scouting has begun as well, with Abrams traveling to Hawaii to look for a location that might be considered for a jungle planet.
There are currently no comments on Star Trek Sequel Moves Ahead. Perhaps you would like to add one of your own?
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 9,299
|
Försäkringskassan (Forsikringskassen) er en svensk statslig myndighed, der har ansvaret for store dele af det offentlige svenske velfærdssystem. Myndigheden administrerer i alt omkring halvtreds forskellige typer ydelser indenfor socialforsikring.
Försäkringskassans opgave er et undersøge, beslutte og udbetale bidrag og erstatninger i forbindelse med socialforsikring. Socialforsikringen antog i 2009 cirka 481 milliarder svenske kronor, eller modsvarende 15 procent af det svenske bruttonationalprodukt (BNP). I 2010 var de totale udgifter for de forsikringer og bidrag som Försäkringskassan administrerede på cirka 211 milliarder svenske kronor, eller modsvarende 6 procent af Sveriges bruttonationalprodukt (BNP). Den store nedgang kommer sig af at forsikringer og bidrag, som udbetales til pensionister blev overført til det nyetablerede Pensionsmyndigheten. I 2010 fik godt og vel 3,2 millioner personer mindst én udbetaling fra Försäkringskassan, hvilket modsvarer omkring 54 procent af Sveriges befolkning i alderen 16–64 år.
Försäkringskassan er med sine omkring 12.500 ansatte en af Sveriges største statslige myndigheder. Den opstod den 1. januar 2005 ved at Riksförsäkringsverket og de almennyttige länsforsikringskasser blev slået sammen. Samtidig ophørte Försäkringskasseförbundet med at eksistere.
Hovedkontoret ligger på Klara Västra Kyrkogata 11 og Vasagatan 14 i Stockholm. Rundt om i Sverige findes cirka 60 lokale forsikringscentre (LFC) og 20 nationale centre (NFC). Kundekontakt sker på servicekontorer, gennem selvbetjening via Internet samt i telefonkundetjenesten. behandlings -og undersøgelsesarbejde sker i først og fremmest hos de forskellige forsikringscentre.
Kildehenvisninger
Eksterne henvisninger
Officiel hjemmeside
Svenske myndigheder
Forsikring
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 4,891
|
# **Contents**
Cover
Title Page
Introduction
Using the dictionary
**French –** **English**
Language plus
Animals
The body
Clothes
Colours
Family
Days and dates
The weather
Places
Food
Fruit and vegetables
Drinks
Furniture
Instruments
Jobs
Sports
At school
Numbers and time
French verbs
Illustrations
**English –** **French**
Copyright
About the Publisher
William Collins' dream of knowledge for all began with the publication of his first book in 1819. A self-educated mill worker, he not only enriched millions of lives, but also founded a flourishing publishing house. Today, staying true to this spirit, Collins books are packed with inspiration, innovation, and practical expertise. They place you at the centre of a world of possibility and give you exactly what you need to explore it.
Language is the key to this exploration, and at the heart of Collins Dictionaries is language as it is really used. New words, phrases, and meanings spring up every day, and all of them are captured and analysed by the Collins Word Web. Constantly updated, and with over 2.5 billion entries, this living language resource is unique to our dictionaries.
Words are tools for life. And a Collins Dictionary makes them work for you.
**Collins. Do more.**
# Introduction
The **Collins Primary Illustrated French Dictionary** is a bilingual dictionary aimed at primary school children who are starting to learn French.
Access to a dictionary which is pitched at an appropriate level is a vital part of the language-learning process. The content of this dictionary has been carefully selected to reflect current trends in primary education and help children with acquiring basic language-learning skills.
The key aims of the **Collins Primary Illustrated French Dictionary** are:
• to develop both language skills in French and language learning skills in general
• to cover the four key areas of language attainment: listening, speaking, reading and writing
• to reinforce key aspects of the language by the use of notes and feature boxes throughout the entries
• to extend cultural awareness by providing information about France, especially where traditions differ from those in Britain
The **Collins Primary Illustrated French Dictionary** supports language learning in a number of specific ways:
• it develops children's knowledge of how language works by encouraging them to understand, analyse and use simple aspects of grammar
• it develops children's individual learning skills by using a wide range of notes that explain things in a simple but interesting way
• it enables children to make comparisons between French and English by encouraging them to explore the similarities and differences between the two languages and cultures
• it introduces young learners to all the basic elements of a bilingual dictionary and provides detailed instructions on how to get the most out of using the dictionary
The **Collins Primary Illustrated French Dictionary** is presented in an easy-to-use format which is intended to appeal to children of primary school age. It provides lots of simple, relevant examples and tips on how to remember words, and how to avoid some of the pitfalls of translation. It also features key phrases, illustrations and information about life in France, making it an invaluable and exciting resource.
# Using the dictionary
**Step one:**
**Pick the right side**
Remember there are two halves to the dictionary. If you want to know what a French word means, look in the **French** - **English** half. It comes first.
If you want to translate an English word into French, look in the second half, which is **English** - **French**. It comes after the supplement in the middle of the dictionary.
**1** Which of these words would you look up in the **French** - **English** half?
** _demain brother horse bonbon_**
**2** Look at page 51 of the dictionary. Is this the French side or the English side? How can you tell?
**3** Look at page 411 of the dictionary. What is shown at the top of the page, above the row of dots?
**4** Is **fish** the first or the last word on page 411?
Remember that you do not read across the whole page in a dictionary – you have to read down the columns.
**5** Which word comes immediately after **fireworks** on page 411?
**Step two:**
**Find the right word**
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Words are in alphabetical order in the dictionary – like names in the phone book, and in a school register. The alphabet is shown down the edge of each page of the dictionary. You can sort words into alphabetical order by looking at the first letter of each word.
**6** Can you put these names in alphabetical order?
**Chantal, Luc, Sophie, Pierre, Jean-Marie, Hélène**
When two words start with the same letter, look at their second letters.
**7** In alphabetical order which comes first – **Hermione** or **Harry**?
This is the order of the days of the week on a calendar: **Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday**
**8** Which day comes first in a dictionary? Which comes last?
**9** **Thursday** comes before **Tuesday** in a dictionary. Why?
**10** Put the seven days of the week into alphabetical order. If the first letters are the same, and the second letters are the same, look at the third letters.
**11** **June, July, August** : which comes last in the dictionary?
**Step three:**
**Pick the right translation**
The translations are easy to spot in this dictionary because they are in red on the **French** - **English** side and blue on the **English** - **French** side.
Some French words can be masculine or feminine, or even plural. In the dictionary MASC, FEM, and PL are the abbreviations used for these. The dictionary also shows you the French word for 'the' (this can be **le** , **la** , **l'** or **les** ).
**doll** NOUN
la **poupée** _fem_
When you look up **doll** you can see that the word for doll in French is **poupée**.
You can tell that the French word for **doll** is feminine because it is given with **la** and the dictionary says that it is _fem_ (feminine).
So **the doll** is **la poupée** and **a doll** would be **une poupée**.
**penfriend** NOUN
le **correspondant** _masc_
la **correspondante** _fem_
**I'm Emma, your English penfriend.**
Je suis Emma, ta correspondante anglaise.
Here there are two translations, one masculine, one feminine. If your penfriend is a boy, you need the French word which is masculine ( _masc_ ) – **le correspondant**. If your penfriend is a girl, you need the French word which is feminine ( _fem_ ) – **la correspondante**.
**12** If you were talking about your penfriend, which would go in the gap, **correspondant** or **correspondante**?
**J'ai un** __________ **.
Il s'appelle Hugo.**
**animal** NOUN
l' **animal** _masc_ (pl les **animaux** )
Here there are two translations. The second one is plural (PL).
**13** If you want to say that you love animals, which translation would go in the gap?
**J'adore les** __________ **.**
Sometimes there is more than one translation, and each one has a number. If there is more than one translation, don't just pick the first one! Check to see which is the right one.
**ball** NOUN
**1** la **balle** _fem (for tennis, golf, cricket)_
**Hit the ball!**
Frappe la balle!
**2** le **ballon** _masc (for football, rugby)_
**Pass the ball!**
Passe le ballon!
**14** Which is the French word for a ball that you kick – **une balle** or **un ballon**? Look for the clue.
**Step four:**
**Parts of speech**
Sometimes, to pick the right translation, you need to know the _part of speech_ of a word, for example whether a word is a **noun** , an **adjective** , an **adverb** or a **verb**. Other parts of speech are **conjunction** , **exclamation** , **number** , **preposition** and **pronoun**.
**NOUNS**
**Nouns** are naming words for things or people. You often use the words 'a' or 'the' with a noun – eg a **girl** , a **boy** , the **school** , the **windows**.
Nouns can be singular, eg an **accident** , the **canteen** , my **dad** , **football** – or plural, eg **sweets** , the **children** , my **friends**.
**15** How many nouns are there in the sentence below? What are they?
** _The car has got a flat tyre and a big dent in the door._**
**ADJECTIVES**
An **adjective** is a describing word which tells you what things are like: **flat** shoes are shoes that don't have high heels. A **flat** tyre is a tyre with no air in it.
**16** How many adjectives are there in the sentence below? What are they?
** _She's got brown hair and blue eyes._**
Some words have a **noun** meaning and an **adjective** meaning. In the dictionary there is a box to tell you about this. The different meanings usually have different translations in French.
**sweet**
**sweet** _can be a noun or an adjective._
**A** NOUN
**1** le **bonbon** _masc (candy)_
**a bag of sweets**
un paquet de bonbons
**2** le **dessert** _masc (pudding)_
**Sweets: ice cream or chocolate mousse**
Desserts: glace ou mousse au chocolat
**B** ADJECTIVE
**1** **sucré** _masc_
**sucrée** _fem (sugary)_
**It's too sweet.**
C'est trop sucré.
**2** **gentil** _masc_
**gentille** _fem (kind)_
**She's a sweet person.**
Elle est gentille.
**3** **mignon** _masc_
**mignonne** _fem (cute)_
**Isn't she sweet?**
Comme elle est mignonne!
**17** You want to ask someone if they would like a sweet. Fill in the gap. How can you be sure this is the right translation?
**Tu veux un** __________ **?**
**ADVERBS**
An **adverb** is a word which describes a verb or an adjective:
She writes **neatly**. The film was **very** good.
**18** How many adverbs are there in the sentence below? What are they? What do they have in common?
** _The children sat quietly and played happily._**
Some words have an **adjective** meaning and an **adverb** meaning. The different meanings have different translations in French.
**hard**
**hard** _can be an adjective or an adverb._
**A** ADJECTIVE
**1** **difficile** _(difficult)_
**This question's too hard for me.**
Cette question est trop difficile pour moi.
**2** **dur** _masc_
**dure** _fem (not soft)_
**This cheese is very hard.**
Ce fromage est très dur.
**B** ADVERB
**dur**
**Colette works hard.**
Colette travaille dur.
**19** You want to say you work hard. Fill in the gap in the sentence below:
**Je travaille** __________ **.**
**VERBS**
**Verbs** are sometimes called 'doing words'. They often go with words like 'I' and 'you', and with names, eg I **play** football, What do you **want**?, Hugo **likes** mashed potato.
Verbs tell you about the present: eg I' **m listening** ; the past: I **scored** a goal; and the future: eg I' **m going to get** an ice cream.
**20** How many verbs are there in the sentence below? What are they?
** _School starts at 9.00 and finishes at 3.30._**
Some words have an **adjective** meaning and a **verb** meaning. The different meanings have different translations in French.
**clean**
**clean** _can be an adjective or a verb._
**A** ADJECTIVE
**propre**
**a clean shirt**
une chemise propre
**B** VERB
**nettoyer**
**Clean the board please!**
Nettoie le tableau s'il te plaît!
**21** If you want to ask for 'a clean glass', how do you know that **propre** is the translation, not **nettoyer**?
Some words have a **noun** meaning and a **verb** meaning.
**rain**
**rain** _can be a noun or a verb._
**A** NOUN
la **pluie** _fem_
**in the rain**
sous la pluie
**B** VERB
**pleuvoir**
**It's going to rain.**
Il va pleuvoir.
**It rains a lot here.**
Il pleut beaucoup par ici.
**It's raining.**
Il pleut.
**22** Is **la pluie** a noun or a verb?
**23** Why is **It rains a lot here.** in part **B**?
**Learn useful phrases**
In the dictionary you'll see phrases that are especially important in orange boxes. Try to learn these when you come across them, and you'll soon know lots of useful things to say in French.
**What time is it?**
Quelle heure est-il?
**It's lunch time.**
C'est l'heure du déjeuner.
**How many times?**
Combien de fois?
**Find out interesting things about life in France**
There are also boxes which tell you about French customs, and about differences between life in France and Britain.
**_Did you know...?_**
_In France, Easter eggs are said to be brought by the Easter bells or_ **cloches de Pâques** _which fly from Rome and drop them in people's gardens._
**Even more words**
At school you will learn to talk about subjects such as the time and the weather, your family, your pets, and your clothes. The most important words for talking about these subjects are shown in the dictionary itself, and even more words are given in **Language Plus** , the supplement in the middle part of the dictionary. Have a look!
**Answer key**
**1** demain and bonbon
**2** the French side; French words on it; French-English written at the side of the page.
**3** fire → fish
**4** It's the last word on page 411.
**5** first
**6** Chantal, Hélène, Jean-Marie, Luc, Pierre, Sophie
**7** Harry – because 'a' comes before 'e'
**8** Friday comes first and Wednesday comes last.
**9** because the second letter of Thursday is 'h', which comes before 'u', the second letter of Tuesday
**10** Friday, Monday, Thursday, Tuesday, Saturday, Sunday, Wednesday
**11** June
**12** correspondant
**13** animaux
**14** un ballon – the clue is in the example: un ballon de football
**15** 4 – car, tyre, dent, door
**16** 2 – brown, blue
**17** bonbon – a sweet is a noun, it means candy; the example helps too
**18** 2 – quietly, happily; they both end in -ly
**19** dur
**20** 2 – starts, finishes
**21** because clean has an adjective meaning in this sentence; the example helps too
**22** a noun
**23** because it's a verb
# **French – English**
# **A a**
**a** VERB _see_ **avoir**
**_Language tip_**
_Don't confuse_ **a** _with the preposition_ **à**.
**1** **has**
**Elle a beaucoup d'amis.**
She has lots of friends.
**_Language tip_**
_Sometimes_ **a** _is used to show that something has happened in the past._
**Il a joué au football.**
He played football.
**2** **is**
**Il a neuf ans.**
He is nine years old.
**il y a**
there is/there are
**_Language tip_**
**il y a** _has two translations. Look at the examples._
**Il y a un bon film à la télé.**
There's a good film on TV.
**Il y a beaucoup de monde.**
There are lots of people.
**_Language tip_**
**il y a** _can also mean_ **ago**.
**Elle est partie il y a dix minutes.**
She left ten minutes ago.
**Qu'est-ce qu'il y a?**
What's the matter?
**à** PREPOSITION
**_Language tip_**
_Don't confuse_ **à** _with the verb form_ **a**. _See also_ **au (= à + le)** _and_ **aux (= à + les)**.
**1** **at**
**Je suis à la maison.**
I am at home.
**Je finis à quatre heures.**
I finish at 4 o'clock.
**2** **in**
**Il est à Paris.**
He is in Paris.
**Elle habite au Portugal.**
She lives in Portugal.
**Mes grands-parents habitent à la campagne.**
My grandparents live in the country.
**au printemps**
in the spring
**au mois de juin**
in June
**3** **to**
**Je vais à Paris.**
I'm going to Paris.
**Elle va au Portugal.**
She's going to Portugal.
**Cet été je vais à la campagne.**
I'm going to the country this summer.
**Il l'a donné à son frère.**
He gave it to his brother.
**Je n'ai rien à faire.**
I've got nothing to do.
**Ce livre est à Paul.**
This book is Paul's.
**4** **by**
**Il est arrivé à bicyclette.**
He arrived by bicycle.
**à pied**
on foot
**Je vais à l'école à pied.**
I walk to school.
**à... d'ici**
... from here
**C'est à dix kilomètres d'ici.**
It's 10 kilometres from here.
**... à l'heure**
... an hour
**cent kilomètres à l'heure**
100 kilometres an hour
**À samedi!**
See you on Saturday!
**À tout à l'heure!**
See you later!
**À bientôt!**
See you soon!
**À demain!**
See you tomorrow!
**abandonner** VERB
**1** **to abandon**
**2** **to give up**
**Je veux abandonner la natation.**
I want to give up swimming.
l' **abeille** FEM NOUN
**bee**
**abominable** ADJECTIVE
**awful**
l' **abord** MASC NOUN
**d'abord**
first
**Je vais rentrer chez moi d'abord.**
I'll go home first.
l' **abricot** MASC NOUN
**apricot**
**absent** MASC ADJECTIVE
(FEM **absente** )
**absent**
**absolument** ADVERB
**absolutely**
l' **accent** MASC NOUN
**accent**
**un accent aigu**
an acute accent
**un accent grave**
a grave accent
**un accent circonflexe**
a circumflex
**_Language tip_**
_French vowels sometimes have an accent to change their sound. There are three kinds of accents: the acute ( **é** cole), the grave (m **è** re) and the circumflex (h **ô** tel). See also_ **aigu** , **grave** , **circonflexe**.
**accepter** VERB
**to accept**
l' **accident** MASC NOUN
**accident**
**accompagner** VERB
**to accompany**
**_Language tip_**
_There is the word_ **accompany** _in English, but it is quite a formal word and we will often use something different, such as_ **take**.
**Elle m'accompagne à l'école.**
She takes me to school.
l' **accord** MASC NOUN
**être d'accord**
to agree
**Tu es d'accord avec moi?**
Do you agree with me?
**D'accord!**
OK!
l' **accordéon** MASC NOUN
**accordion**
**Ray joue de l'accordéon.**
Ray plays the accordion.
l' **accueil** MASC NOUN
**reception**
**acheter** VERB
**to buy**
l' **acné** FEM NOUN
**acne**
l' **acteur** MASC NOUN
**actor**
**un acteur de cinéma**
a film actor
**actif** MASC ADJECTIVE
(FEM **active** )
**active**
l' **activité** FEM NOUN
**activity**
l' **actrice** FEM NOUN
**actress**
**une actrice de cinéma**
a film actress
les **actualités** FEM PL NOUN
**news**
**Je regarde les actualités tous les soirs.**
I watch the news every night.
l' **addition** FEM NOUN
**1** **sum**
**2** **bill**
**L'addition, s'il vous plaît!**
Can we have the bill, please?
**adhésif** MASC ADJECTIVE
(FEM **adhésive** )
**le ruban adhésif**
sticky tape
l' **adjectif** MASC NOUN
**adjective**
**'grand' est un adjectif.**
'grand' is an adjective.
**admettre** VERB
**1** **to admit**
**J'admets que j'ai eu tort.**
I admit I was wrong.
**2** **to allow**
**Les chiens ne sont pas admis dans le restaurant.**
Dogs are not allowed in the restaurant.
l' **adolescent** MASC NOUN
l' **adolescente** FEM NOUN
**teenager**
**adorable** ADJECTIVE
**lovely**
**adorer** VERB
**to love**
**Elle adore le chocolat.**
She loves chocolate.
**J'adore jouer au tennis.**
I love playing tennis.
l' **adresse** FEM NOUN
**address**
**_Language tip_**
_The French word has only one_ **d** , _and an extra_ **e**.
**mon adresse électronique**
my email address
l' **adulte** MASC/FEM NOUN
**adult**
**une chambre pour deux adultes et un enfant**
a room for two adults and a child
l' **adverbe** MASC NOUN
**adverb**
**'Beaucoup' est un adverbe.**
'Beaucoup' is an adverb.
l' **adversaire** MASC/FEM NOUN
**opponent**
l' **aérobic** MASC NOUN
**aerobics**
**Je fais de l'aérobic.**
I do aerobics.
l' **aéroport** MASC NOUN
**airport**
les **affaires** FEM PL NOUN
**1** **things**
**Va chercher tes affaires!**
Go and get your things!
**Rangez vos affaires!**
Put your things away!
**2** **business**
**un homme d'affaires**
a businessman
l' **affiche** FEM NOUN
**poster**
**affreux** MASC ADJECTIVE
(FEM **affreuse** )
**awful**
**africain** MASC ADJECTIVE
(FEM **africaine** )
**African**
l' **Africain** MASC NOUN
l' **Africaine** FEM NOUN
**African**
l' **Afrique** FEM NOUN
**Africa**
**agacer** VERB
**to get on somebody's nerves**
**Tu m'agaces!**
You're getting on my nerves!
l' **âge** MASC NOUN
**age**
**Écrivez votre nom et votre âge.**
Write down your name and age.
**Tu as quel âge?**
How old are you?
**Quel âge a-t-elle?**
How old is she?
**âgé** MASC ADJECTIVE
(FEM **âgée** )
**old**
l' **agence** FEM NOUN
**agency**
**une agence de voyages**
a travel agency
**une agence immobilière**
an estate agent's
l' **agenda** MASC NOUN
**diary**
**Elle note tous ses rendez-vous dans son agenda.**
She makes a note of all her appointments in her diary.
**_Language tip_**
_Be careful! The French word_ **agenda** _does not mean the same as the English word_ **agenda**.
l' **agent** MASC NOUN
**un agent de police**
a policeman
l' **agneau** MASC NOUN
(PL les **agneaux** )
**lamb**
**un gigot d'agneau**
a leg of lamb
l' **agrafeuse** FEM NOUN
**stapler**
**agréable** MASC ADJECTIVE
(FEM **agréable** )
**nice**
l' **agriculteur** MASC NOUN
**farmer**
**ai** VERB _see_ **avoir**
**J'ai deux chats.**
I have two cats.
**_Language tip_**
_Sometimes_ **ai** _is used to show that something has happened in the past._
**J'ai oublié mon livre.**
I've forgotten my book.
l' **aide** FEM NOUN
**help**
**aider** VERB
**to help**
**Tu peux m'aider?**
Can you help me?
**aïe** EXCLAMATION
**Ouch!**
**aigu** MASC ADJECTIVE
**un accent aigu**
an acute accent
l' **aiguille** FEM NOUN
**needle**
l' **ail** MASC NOUN
**garlic**
**Je n'aime pas l'ail.**
I don't like garlic.
l' **aile** FEM NOUN
**wing**
**une aile de poulet**
a chicken wing
**aimable** MASC ADJECTIVE
(FEM **aimable** )
**nice**
l' **aimant** MASC NOUN
**magnet**
**aimer** VERB
**1** **to love**
**Elle aime ses enfants.**
She loves her children.
**Je t'aime.**
I love you.
**2** **to like**
**Tu aimes le chocolat?**
Do you like chocolate?
**J'aime bien ce garçon.**
I like this boy.
**J'aime bien jouer au tennis.**
I like playing tennis.
**aîné** MASC ADJECTIVE (FEM **aînée** )
**C'est mon frère aîné.**
He's my big brother.
l' **aîné** MASC NOUN
l' **aînée** FEM NOUN
**oldest child**
**C'est l'aîné.**
He's the oldest child.
**C'est l'aînée.**
She's the oldest child.
l' **air** MASC NOUN
**air**
**Tu as l'air fatiguée.**
You look tired.
l' **aire de jeux** FEM NOUN
**playground**
**ajouter** VERB
**to add**
l' **alarme** FEM NOUN
**alarm**
l' **alcool** MASC NOUN
**alcohol**
**Je ne bois pas d'alcool.**
I don't drink alcohol.
l' **Algérie** FEM NOUN
**Algeria**
**algérien** MASC ADJECTIVE
(FEM **algérienne** )
**Algerian**
l' **Algérien** MASC NOUN
l' **Algérienne** FEM NOUN
**Algerian**
l' **alimentation** FEM NOUN
**groceries**
**le rayon alimentation**
the grocery department
l' **allée** FEM NOUN
**1** **path**
**les allées du parc**
the paths in the park
**2** **drive**
**5, allée Saint-Exupéry**
5 Saint-Exupéry Drive
l' **Allemagne** FEM NOUN
**Germany**
**allemand** MASC NOUN, MASC ADJECTIVE (FEM **allemande** )
**German**
l' **Allemand** MASC NOUN
l' **Allemande** FEM NOUN
**German**
**aller**
**aller** _can be a verb or a noun._
**A** VERB
**to go**
**Je vais à Londres.**
I'm going to London.
**Nous allons visiter un château.**
We're going to visit a castle.
**Allez! Dépêche-toi!**
Come on! Hurry up!
**Comment vas-tu? — Je vais bien.**
How are you? — I'm fine.
**Je vais mieux.**
I'm feeling better.
**Comment ça va? — Ça va bien.**
How are you? — I'm fine.
**B** MASC NOUN
**single**
**Je voudrais un aller pour Angers.**
I'd like a single to Angers.
**un aller simple**
a single
**un aller retour**
a return ticket
**allergique** ADJECTIVE
**allergique à**
allergic to
**Je suis allergique aux chats.**
I'm allergic to cats.
**allez** VERB _see_ **aller**
**Vous allez où?**
Where are you going?
**allô** EXCLAMATION
**hello!**
**Allô! Je voudrais parler à Monsieur Simon.**
Hello! I'd like to speak to Mr Simon.
**_Language tip_**
**allô** _is only used when talking to someone on the phone._
**allons** VERB _see_ **aller**
**Nous allons nous coucher.**
We're going to bed.
**allumer** VERB
**1** **to put on**
**Tu peux allumer la lumière?**
Can you put the light on?
**2** **to switch on**
**Allume l'ordinateur.**
Switch on the computer.
**3** **to light**
**Tu peux allumer cette bougie?**
Can you light this candle?
l' **allumette** FEM NOUN
**match**
**une boîte d'allumettes**
a box of matches
**alors** ADVERB
**1** **then**
**Alors, tu viens?**
Are you coming, then?
**2** **so**
**Alors tu habites ici?**
So you live here?
**Et alors?**
So what?
les **Alpes** FEM PL NOUN
**Alps**
**dans les Alpes**
in the Alps
l' **alphabet** MASC NOUN
**alphabet**
**alphabétique** ADJECTIVE
**alphabetical**
**par ordre alphabétique**
in alphabetical order
l' **amande** FEM NOUN
**almond**
**la pâte d'amandes**
marzipan
l' **ambulance** FEM NOUN
**ambulance**
**Appelez une ambulance!**
Call an ambulance!
l' **amende** FEM NOUN
**fine**
**une amende de trente euros**
a 30 euro fine
**amener** VERB
**to bring**
**Je peux amener un ami?**
Can I bring a friend?
**américain** MASC ADJECTIVE
(FEM **américaine** )
**American**
l' **Américain** MASC NOUN
l' **Américaine** FEM NOUN
**American**
l' **Amérique** FEM NOUN
**America**
l' **ami** MASC NOUN
l' **amie** FEM NOUN
**friend**
**J'ai beaucoup d'amis.**
I have lots of friends.
**mon meilleur ami**
my best friend
**ma meilleure amie**
my best friend
**un petit ami**
a boyfriend
**une petite amie**
a girlfriend
**amical** MASC ADJECTIVE
(FEM **amicale** )
**friendly**
**amicalement** ADVERB
**Amicalement, Pierre.**
Best wishes, Pierre.
l' **amitié** FEM NOUN
**friendship**
**Amitiés, Christelle.**
Best wishes, Christelle.
l' **amour** MASC NOUN
**love**
**une histoire d'amour**
a love story
**amoureux** MASC ADJECTIVE
(FEM **amoureuse** )
**in love**
**Il est amoureux de Naïma.**
He's in love with Naïma.
l' **ampoule** FEM NOUN
**1** **light bulb**
**Tu peux changer l'ampoule?**
Can you change the light bulb?
**2** **blister**
**J'ai une ampoule au pied.**
I've got a blister on my foot.
**amusant** MASC ADJECTIVE
(FEM **amusante** )
**amusing**
s' **amuser** VERB
**1** **to play**
**Les enfants s'amusent dehors.**
The children are playing outside.
**2** **to enjoy oneself**
**Amuse-toi bien!**
Enjoy yourself!
l' **an** MASC NOUN
**year**
**Elle a douze ans.**
She's twelve years old.
**le premier de l'an**
New Year's Day
**le nouvel an**
New Year
**J'ai dix ans.**
I'm ten years old.
l' **ananas** MASC NOUN
**pineapple**
l' **ancêtre** MASC/FEM NOUN
**ancestor**
l' **anchois** MASC NOUN
**anchovy**
**ancien** MASC ADJECTIVE
(FEM **ancienne** )
**1** **former**
**C'est une ancienne élève.**
She's a former pupil.
**2** **old**
**notre ancienne voiture**
our old car
**3** **antique**
**un fauteuil ancien**
an antique chair
l' **âne** MASC NOUN
**donkey**
l' **ange** MASC NOUN
**angel**
l' **angine** FEM NOUN
**throat infection**
**J'ai une angine.**
I've got a throat infection.
**anglais** MASC NOUN, MASC ADJECTIVE (FEM **anglaise** )
**English**
**Je suis anglais.**
I'm English.
l' **Anglais** MASC NOUN
**Englishman**
**les Anglais**
the English
l' **Anglaise** FEM NOUN
**Englishwoman**
l' **Angleterre** FEM NOUN
**England**
**J'habite en Angleterre.**
I live in England.
l' **animal** MASC NOUN
(PL les **animaux** )
**animal**
**un animal domestique**
a pet
**Tu as un animal domestique?**
Have you got a pet?
l' **animateur** MASC NOUN
l' **animatrice** FEM NOUN
**host**
**Il est animateur à la télé.**
He's a TV host.
**animé** MASC ADJECTIVE (FEM **animée** )
**lively**
**Cette ville est très animée.**
This is a very lively town.
**un dessin animé**
a cartoon
**J'adore les dessins animés.**
I love cartoons.
l' **année** FEM NOUN
**year**
**Cette année, j'apprends le français.**
I'm learning French this year.
**l'année dernière**
last year
**l'année prochaine**
next year
**Bonne année!**
Happy New Year!
l' **anniversaire** MASC NOUN
**1** **birthday**
**Aujourd'hui, c'est mon anniversaire.**
It's my birthday today.
**Quelle est la date de ton anniversaire?**
When is your birthday?
**Mon anniversaire, c'est le douze février.**
My birthday is on the twelfth of February.
**Joyeux anniversaire!**
Happy birthday!
**2** **anniversary**
**leur anniversaire de mariage**
their wedding anniversary
l' **annonce** FEM NOUN
**advert**
**J'ai vu une annonce dans le journal.**
I saw an advert in the newspaper.
**les petites annonces**
the small ads
**annuler** VERB
**to cancel**
l' **anorak** MASC NOUN
**anorak**
l' **antenne** FEM NOUN
**aerial**
les **Antilles** FEM PL NOUN
**West Indies**
l' **antiquité** FEM NOUN
**antique**
**un magasin d'antiquités**
an antique shop
**anxieux** MASC ADJECTIVE (FEM **anxieuse** )
**anxious**
**août** MASC NOUN
**August**
**en août**
in August
**le trois août**
the third of August
**apercevoir** VERB
**to see**
l' **apéritif** MASC NOUN
**En été, on prend l'apéritif dans le jardin.**
In the summer we have drinks in the garden.
**_Did you know...?_**
_An_ **apéritif** _is a drink that you have before dinner. You usually have a snack to go with it. Adults have something alcoholic and children have juice._
l' **appareil** MASC NOUN
**un appareil dentaire**
a brace
**Je dois porter un appareil dentaire.**
I have to wear a brace.
**un appareil photo**
a camera
**J'ai perdu mon appareil photo.**
I've lost my camera.
l' **appartement** MASC NOUN
**flat**
**appartenir** VERB
**Ça m'appartient.**
This belongs to me.
l' **appel** MASC NOUN
**1** **phone call**
**un appel d'Italie**
a phone call from Italy
**2** **register**
**faire l'appel**
to call the register
**Silence! Je fais l'appel.**
Quiet! I'm calling the register.
**appeler** VERB
**to call**
**Elle appelle le médecin.**
She's calling the doctor.
**s'appeler**
**to be called**
**Elle s'appelle Muriel.**
Her name's Muriel.
**Comment ça s'appelle?**
What is it called?
**Comment tu t'appelles?**
What's your name?
**Je m'appelle Alice.**
My name's Alice.
l' **appendicite** FEM NOUN
**appendicitis**
l' **appétit** MASC NOUN
**Bon appétit!**
Enjoy your meal!
**apporter** VERB
**to bring**
**Je vais apporter un gâteau.**
I'm going to bring a cake.
**apprendre** VERB
**to learn**
**J'apprends le français.**
I'm learning French.
**J'apprends à faire la cuisine.**
I'm learning to cook.
**appris** VERB _see_ **apprendre**
**Qu'est-ce que tu as appris aujourd'hui?**
What have you learned today?
s' **approcher** VERB
**to come closer**
**Approchez-vous.**
Come closer.
**appuyer** VERB
**to press**
**Il faut appuyer sur ce bouton.**
You have to press this button.
**après** PREPOSITION, ADVERB
**1** **after**
**après le déjeuner**
after lunch
**2** **afterwards**
**aussitôt après**
immediately afterwards
**après-demain** ADVERB
**the day after tomorrow**
l' **après-midi** MASC/FEM NOUN
**afternoon**
**L'après-midi, je vais à la piscine.**
In the afternoon, I go to the swimming pool.
**cet après-midi**
this afternoon
**arabe**
**arabe** _can be an adjective or a noun._
**A** ADJECTIVE
**Arab**
**les pays arabes**
the Arab countries
**B** MASC NOUN
**Arabic**
**Il parle arabe.**
He speaks Arabic.
l' **araignée** FEM NOUN
**spider**
**Il y a une araignée dans la baignoire!**
There's a spider in the bath!
l' **arbitre** MASC NOUN
**referee**
l' **arbre** MASC NOUN
**tree**
**un arbre généalogique**
a family tree
l' **arc** MASC NOUN
**bow**
**un arc et des flèches**
a bow and arrows
l' **arc-en-ciel** MASC NOUN
**rainbow**
l' **argent** MASC NOUN
**1** **money**
**Je n'ai pas d'argent.**
I haven't got any money.
**l'argent de poche**
pocket money
**2** **silver**
**une médaille d'argent**
a silver medal
l' **arme** FEM NOUN
**weapon**
l' **armée** FEM NOUN
**army**
l' **armoire** FEM NOUN
**wardrobe**
l' **arobase** FEM NOUN
**at symbol**
**mon adresse e-mail, c'est 'lola arobase europost point fr'**
my email address is 'lola@europost.fr'
**arranger** VERB
**1** **to arrange**
**Elle arrange des fleurs dans un vase.**
She's arranging flowers in a vase.
**2** **to suit**
**Ça m'arrange de partir plus tôt.**
It suits me to leave earlier.
l' **arrêt** MASC NOUN
**stop**
**un arrêt de bus**
a bus stop
**arrêter** VERB
**1** **to stop**
**Tu peux arrêter la cassette?**
Can you stop the tape?
**Arrête!**
Stop it!
**Arrête de copier!**
Stop copying!
**2** **to switch off**
**Il a arrêté le moteur.**
He switched the engine off.
**arrière**
**arrière** _can be a noun or an adjective._
**A** MASC NOUN
**back**
**l'arrière de la maison**
the back of the house
**B** MASC, FEM, PL ADJECTIVE
**back**
**le siège arrière**
the back seat
**les roues arrière**
the rear wheels
l' **arrière-grand-mère** FEM NOUN
**great-grandmother**
l' **arrière-grand-père** MASC NOUN
**great-grandfather**
l' **arrivée** FEM NOUN
**arrival**
**arriver** VERB
**1** **to arrive**
**J'arrive à l'école à huit heures.**
I arrive at school at 8 o'clock.
**2** **to come**
**J'arrive!**
I'm coming!
**3** **to happen**
**Qu'est-ce qui est arrivé à Christian?**
What happened to Christian?
l' **arrondissement** MASC NOUN
**district**
**_Did you know...?_**
_Paris, Lyons, and Marseilles are divided into numbered districts called_ **arrondissements**.
**arroser** VERB
**to water**
**Daphne arrose ses tomates.**
Daphne is watering her tomatoes.
l' **arrosoir** MASC NOUN
**watering can**
l' **artichaut** MASC NOUN
**artichoke**
l' **article** MASC NOUN
**article**
**un article de journal**
a newspaper article
l' **artiste** MASC/FEM NOUN
**artist**
**Paul est un véritable artiste.**
Paul is a real artist.
les **arts plastiques** MASC PL NOUN
**art**
**as**
**as** _can be part of the verb_ **avoir** _or a noun._
**A** VERB _see_ **avoir**
**Tu as de beaux cheveux.**
You've got nice hair.
**_Language tip_**
_Sometimes_ **as** _is used to show that something has happened in the past._
**Tu as aimé le film?**
Did you like the film?
**B** MASC NOUN
**ace**
**l'as de cœur**
the ace of hearts
l' **ascenseur** MASC NOUN
**lift**
**Il n'y a pas d'ascenseur dans mon immeuble.**
There's no lift in my building.
**asiatique** ADJECTIVE
**Asian**
**la cuisine asiatique**
Oriental cooking
l' **Asie** FEM NOUN
**Asia**
l' **asperge** FEM NOUN
**asparagus**
l' **aspirateur** MASC NOUN
**vacuum cleaner**
**passer l'aspirateur**
to vacuum
**Je déteste passer l'aspirateur!**
I hate vacuuming!
l' **aspirine** FEM NOUN
**aspirin**
**Prenez de l'aspirine.**
Take some aspirin.
l' **assassin** MASC NOUN
**murderer**
**assassiner** VERB
**to murder**
s' **asseoir** VERB
**to sit down**
**Je peux m'asseoir ici?**
Can I sit here?
**Asseyez-vous, tout le monde!**
Sit down everybody!
**Assieds-toi, Nicole!**
Sit down Nicole!
**assez** ADVERB
**1** **enough**
**Nous n'avons pas assez de temps.**
We don't have enough time.
**Est-ce qu'il y a assez de pain?**
Is there enough bread?
**J'en ai assez!**
I've had enough!
**2** **quite**
**Il faisait assez beau.**
The weather was quite nice.
l' **assiette** FEM NOUN
**plate**
**une assiette creuse**
a soup plate
**une assiette à dessert**
a dessert plate
**assis** MASC ADJECTIVE (FEM **assise** )
**sitting**
**Il est assis par terre.**
He's sitting on the floor.
l' **assistant** MASC NOUN
l' **assistante** FEM NOUN
**assistant**
**Il est assistant d'anglais à Tourcoing.**
He is an English assistant in Tourcoing.
**Elle est assistante de français à Oxford.**
She's a French assistant in Oxford.
**une assistante sociale**
a social worker
l' **asthme** MASC NOUN
**asthma**
**une crise d'asthme**
an asthma attack
l' **atelier** MASC NOUN
**1** **workshop**
**un atelier de poterie**
a pottery workshop
**2** **studio**
**L'artiste est dans son atelier.**
The artist is in his studio.
l' **athlète** MASC/FEM NOUN
**athlete**
l' **athlétisme** MASC NOUN
**athletics**
**Je fais de l'athlétisme.**
I do athletics.
l' **Atlantique** MASC NOUN
**Atlantic**
l' **atlas** MASC NOUN
**atlas**
**attacher** VERB
**to tie up**
**Elle attache ses cheveux avec un élastique.**
She ties her hair up with an elastic band.
**attaquer** VERB
**to attack**
**attendre** VERB
**to wait**
**J'attends ma copine.**
I'm waiting for my friend.
**Attends-moi!**
Wait for me!
**_Language tip_**
_Be careful! The French word_ **attendre** _does not mean the same as the English word_ **to attend**.
l' **attente** FEM NOUN
**wait**
**deux heures d'attente**
two hours' wait
**la salle d'attente**
the waiting room
l' **attention** FEM NOUN
**Attention!**
Watch out!
**faire attention**
to be careful
**Il ne fait pas attention.**
He's not careful.
**atterrir** VERB
**to land**
l' **attraction** FEM NOUN
**un parc d'attractions**
an amusement park
**attraper** VERB
**to catch**
**au** PREPOSITION _see_ **à**
**_Language tip_**
**au** _is made up of_ **à** \+ **le**.
**Je vais au cinéma.**
I am going to the cinema.
**au printemps**
in the spring
l' **aube** FEM NOUN
**dawn**
**Il se lève à l'aube.**
He gets up at dawn.
l' **auberge de jeunesse** FEM NOUN
**youth hostel**
**aucun**
**aucun** _can be an adjective or a pronoun._
**A** MASC ADJECTIVE (FEM **aucune** )
**no**
**Il n'a aucun ami.**
He's got no friends.
**B** MASC PRONOUN (FEM **aucune** )
**none**
**Aucune d'elles n'aime le football.**
None of them like football.
**au-dessous** ADVERB
**downstairs**
**Ils habitent au-dessous.**
They live downstairs.
**au-dessous de**
under
**au-dessous du pont**
under the bridge
**au-dessus** ADVERB
**upstairs**
**J'habite au-dessus.**
I live upstairs.
**au-dessus de**
above
**au-dessus de la table**
above the table
**aujourd'hui** ADVERB
**today**
**Aujourd'hui, c'est le onze juillet.**
Today is the eleventh of July.
**aura, aurai, auras, aurez, aurons, auront**
VERB _see_ **avoir**
**Demain, il y aura du soleil.**
It will be sunny tomorrow.
**J'aurai mon nouveau vélo mardi.**
I'm getting my new bike on Tuesday.
**Tu auras quel âge en juillet?**
How old will you be next July?
**Vous n'aurez pas le temps.**
You won't have time.
**Nous aurons une semaine de vacances.**
We'll have one week off.
**Ils n'auront pas le temps de venir nous voir.**
They won't have time to visit us.
**aussi** ADVERB
**1** **too**
**Dors bien. — Toi aussi.**
Sleep well. — You too.
**Moi aussi!**
Me too!
**2** **also**
**Je parle anglais et aussi français.**
I speak English and also French.
**aussi... que**
as... as
**Michael est aussi grand que moi.**
Michael is as tall as me.
**aussitôt** ADVERB
**aussitôt après son retour**
straight after his return
**aussitôt que**
as soon as
**aussitôt que possible**
as soon as possible
l' **Australie** FEM NOUN
**Australia**
**australien** MASC ADJECTIVE (FEM **australienne** )
**Australian**
**autant** ADVERB
**_Language tip_**
**autant de** _can either mean_ **so much** _or_ **so many.**
**Je ne veux pas autant de gâteau.**
I don't want so much cake.
**Je n'ai jamais vu autant de monde.**
I've never seen so many people.
**_Language tip_**
**autant... que** _can either mean_ **as much... as** _or_ **as many... as**.
**J'ai autant d'argent que toi.**
I've got as much money as you have.
**J'ai autant d'amis que lui.**
I've got as many friends as he has.
l' **auteur** MASC NOUN
**author**
l' **auto** FEM NOUN
**car**
l' **autobus** MASC NOUN
**bus**
**Je vais à l'école en autobus.**
I go to school by bus.
l' **autocar** MASC NOUN
**coach**
l' **autocollant** MASC NOUN
**sticker**
l' **auto-école** FEM NOUN
**driving school**
l' **automne** MASC NOUN
**autumn**
**en automne**
in autumn
**automobile**
**automobile** _can be a noun or an adjective._
**A** FEM NOUN
**car**
**une vieille automobile**
an old car
**B** ADJECTIVE
**une course automobile**
a motor race
l' **automobiliste** MASC/FEM NOUN
**motorist**
l' **autoradio** MASC NOUN
**car radio**
l' **autoroute** FEM NOUN
**motorway**
l' **auto-stop** MASC NOUN
**C'est dangereux de faire de l'auto-stop.**
Hitchhiking is dangerous.
**autour** ADVERB
**around**
**autour de la maison**
around the house
**autre** ADJECTIVE, PRONOUN
**other**
**Je viendrai un autre jour.**
I'll come some other day.
**J'ai d'autres projets.**
I've got other plans.
**autre chose**
something else
**Tu veux autre chose?**
Would you like something else?
**autre part**
somewhere else
**Je voudrais aller autre part.**
I'd like to go somewhere else.
**un autre**
another
**Tu veux un autre morceau de gâteau?**
Would you like another piece of cake?
**l'autre**
the other
**Non, pas celui-ci, l'autre.**
No, not that one, the other one.
**d'autres**
others
**Je t'en apporterai d'autres.**
I'll bring you some others.
**les autres**
the others
**Les autres sont arrivés plus tard.**
The others arrived later.
**ni l'un ni l'autre**
neither of them
**Je n'aime ni l'un ni l'autre.**
I like neither of them.
**autrefois** ADVERB
**in the old days**
**autrement** ADVERB
**1** **differently**
**Fais-le autrement.**
Do it differently.
**2** **otherwise**
**Je n'ai pas pu faire autrement.**
I couldn't do otherwise.
l' **Autriche** FEM NOUN
**Austria**
**autrichien** MASC ADJECTIVE (FEM **autrichienne** )
**Austrian**
l' **Autrichien** MASC NOUN
l' **Autrichienne** FEM NOUN
**Austrian**
l' **autruche** FEM NOUN
**ostrich**
**aux** PREPOSITION _see_ **à**
**_Language tip_**
**aux** _is made up of_ **à** \+ **les**.
**Il va aux États-Unis.**
He's going to the United States.
**avaler** VERB
**to swallow**
l' **avance** FEM NOUN
**être en avance**
to be early
**Je suis en avance.**
I am early.
**à l'avance**
beforehand
**Il faut réserver longtemps à l'avance.**
You need to book well beforehand.
**d'avance**
in advance
**Elle a payé d'avance.**
She paid in advance.
**avancer** VERB
**to go forward**
**Avance de trois cases.**
Go forward three squares.
**avant**
**avant** _can be a preposition, an adjective or a noun._
**A** PREPOSITION
**before**
**avant de partir**
before leaving
**B** MASC, FEM, PL ADJECTIVE
**front**
**la roue avant**
the front wheel
**le siège avant**
the front seat
**C** MASC NOUN
**front**
**l'avant de la voiture**
the front of the car
**à l'avant**
in front
**J'aime m'asseoir à l'avant.**
I like to sit in the front.
**en avant**
forward
**Fais un pas en avant.**
Take a step forward.
l' **avantage** MASC NOUN
**advantage**
**avant-dernier** MASC ADJECTIVE (FEM **avant-dernière** )
**last but one**
**l'avant-dernière page**
the last page but one
**Ils sont arrivés avant-derniers.**
They arrived last but one.
**avant-hier** ADVERB
**the day before yesterday**
**avec** PREPOSITION
**with**
**Je joue avec mes copains.**
I am playing with my friends.
**Et avec ça?**
Anything else?
l' **avenir** MASC NOUN
**future**
**à l'avenir**
in future
l' **aventure** FEM NOUN
**adventure**
l' **avenue** FEM NOUN
**avenue**
**J'habite au 3, avenue Pasteur.**
I live at 3 Pasteur Avenue.
l' **averse** FEM NOUN
**shower**
**Il y a des averses sur toute la France.**
There are showers all over France.
**aveugle** ADJECTIVE
**blind**
**avez** VERB _see_ **avoir**
**Vous avez des frères et sœurs?**
Have you got any brothers or sisters?
**_Language tip_**
_Sometimes_ **avez** _is used to show that something has happened in the past._
**Vous avez aimé le film?**
Did you like the film?
l' **avion** MASC NOUN
**plane**
**Tu préfères y aller en avion ou en train?**
Would you rather go by plane or by train?
**Il va en Italie en avion.**
He is flying to Italy.
**par avion**
by airmail
l' **avis** MASC NOUN
**opinion**
**à mon avis**
in my opinion
**J'ai changé d'avis.**
I've changed my mind.
l' **avocat** MASC NOUN
**1** **lawyer**
**Il est avocat.**
He's a lawyer.
**2** **avocado**
**Tu aimes les avocats?**
Do you like avocados?
l' **avocate** FEM NOUN
**lawyer**
**Elle est avocate.**
She's a lawyer.
l' **avoine** FEM NOUN
**oats**
**les flocons d'avoine**
porridge oats
**avoir** VERB
**1** **to have**
**Ils ont deux enfants.**
They have two children.
**Il a les yeux bleus.**
He's got blue eyes.
**_Language tip_**
**avoir** _is used to make the past tense of most verbs._
**Qu'est-ce que tu as fait hier?**
What did you do yesterday?
**2** **to be**
**Il a trois ans.**
He's three.
**J'ai faim.**
I'm hungry.
**3** **to get**
**J'ai des devoirs de maths deux fois par semaine.**
I get maths homework twice a week.
**Qu'est-ce que tu as eu pour Noël?**
What did you get for Christmas?
**il y a**
there is/there are
**_Language tip_**
**il y a** _has two translations. Look at the examples._
**Il y a quelqu'un à la porte.**
There's somebody at the door.
**Il y a des chocolats sur la table.**
There are some chocolates on the table.
**_Language tip_**
**il y a** _can also mean_ **ago**.
**Je l'ai rencontré il y a deux ans.**
I met him two years ago.
**Qu'est-ce qu'il y a?**
What's the matter?
**avons** VERB _see_ **avoir**
**Nous avons une grande maison.**
We have a big house.
**_Language tip_**
_Sometimes_ **avons** _is used to show that something has happened in the past._
**Nous avons regardé la télévision.**
We watched television.
**avouer** VERB
**to admit**
**avril** MASC NOUN
**April**
**en avril**
in April
**le deux avril**
the second of April
# **B b**
le **babillard** MASC NOUN _(Canada)_
**bulletin board**
le **baby-foot** MASC NOUN
**table football**
le **baby-sitting** MASC NOUN
**Ma sœur fait du baby-sitting le week-end.**
My sister babysits at the weekend.
le **bac** MASC NOUN = **baccalauréat**
le **baccalauréat** MASC NOUN
**A levels**
**Ma sœur passe son baccalauréat cette année.**
My sister is doing her A levels this year.
**_Did you know...?_**
_The_ **baccalauréat** _or_ **bac** _is an exam taken at the end of_ **lycée** , _when French students are 17 and 18 years old._
les **bagages** MASC PL NOUN
**luggage**
**Les bagages sont dans la voiture.**
The luggage is in the car.
**Je déteste faire les bagages!**
I hate packing!
la **bague** FEM NOUN
**ring**
**J'ai une belle bague.**
I have a beautiful ring.
la **baguette** FEM NOUN
**stick of French bread**
se **baigner** VERB
**to swim**
**J'aime me baigner.**
I like swimming.
la **baignoire** FEM NOUN
**bath**
**Il y a une araignée dans la baignoire!**
There's a spider in the bath!
le **bain** MASC NOUN
**bath**
**Je prends un bain.**
I'm having a bath.
le **baiser** MASC NOUN
**kiss**
**donner un baiser**
to give a kiss
**Donne-moi un baiser!**
Give me a kiss!
la **balade** FEM NOUN
**walk**
**Tu veux faire une balade?**
Do you want to go for a walk?
le **baladeur** MASC NOUN
**Walkman** ®
**un baladeur numérique**
an MP3 player
le **balai** MASC NOUN
**broom**
la **balançoire** FEM NOUN
**swing**
le **balcon** MASC NOUN
**balcony**
la **baleine** FEM NOUN
**whale**
la **balle** FEM NOUN
**ball**
**Le chien joue avec une balle.**
The dog is playing with a ball.
**une balle de ping-pong**
a ping-pong ball
**une balle de tennis**
a tennis ball
le **ballon** MASC NOUN
**1** **ball**
**un ballon de football**
a football
**2** **balloon**
**Je veux un ballon!**
I want a balloon!
la **banane** FEM NOUN
**banana**
le **banc** MASC NOUN
**bench**
la **bande dessinée** FEM NOUN
**comic strip**
**J'adore les bandes dessinées!**
I love comic strips!
**_Did you know...?_**
**Les bandes dessinées** _or_ **comic strips** _are very popular with people of all ages in France._
la **banlieue** FEM NOUN
**suburbs**
**J'habite en banlieue.**
I live in the suburbs.
la **banque** FEM NOUN
**bank**
le **banquier** MASC NOUN
la **banquière** FEM NOUN
**banker**
le **baptême** MASC NOUN
**christening**
le **bar** MASC NOUN
**bar**
**barbant** MASC ADJECTIVE (FEM **barbante** )
**boring**
**Il est vraiment barbant!**
He's so boring!
la **barbe** FEM NOUN
**beard**
**Il porte la barbe.**
He's got a beard.
**la barbe à papa**
candyfloss
le **barbecue** MASC NOUN
**barbecue**
la **barque** FEM NOUN
**rowing boat**
la **barrière** FEM NOUN
**fence**
le **bar-tabac** MASC NOUN
**_Did you know...?_**
_A_ **bar-tabac** _is a café which also sells cigarettes and stamps. It has a red diamond-shaped sign outside it._
le **bas** MASC NOUN
**bottom**
**le bas de la page**
the bottom of the page
**en bas**
downstairs
**La salle de bains est en bas.**
The bathroom is downstairs.
le **basilic** MASC NOUN
**basil**
le **basket** MASC NOUN
**basketball**
**Je joue au basket.**
I play basketball.
les **baskets** FEM PL NOUN
**trainers**
**une paire de baskets**
a pair of trainers
le **bassin** MASC NOUN
**pond**
le **bateau** MASC NOUN
(PL les **bateaux** )
**boat**
**Je vais en France en bateau.**
I'm going to France by boat.
le **bateau-mouche** MASC NOUN
**pleasure boat**
le **bâtiment** MASC NOUN
**building**
la **batterie** FEM NOUN
**drums**
**Je joue de la batterie.**
I play the drums.
**battre** VERB
**to beat**
**bavard** MASC ADJECTIVE (FEM **bavarde** )
**talkative**
**bavarder** VERB
**to chat**
le **bazar** MASC NOUN
**mess**
**Quel bazar!**
What a mess!
**Va ranger ton bazar!**
Go and tidy up your mess!
la **BD** FEM NOUN
**comic strip**
**Rose adore les BD.**
Rose loves comic strips.
**beau** MASC ADJECTIVE (MASC **bel** , FEM **belle** )
**_Language tip_**
**beau** _changes to_ **bel** _before a vowel sound._
**1** **lovely**
**un beau cadeau**
a lovely present
**une belle journée**
a lovely day
**2** **beautiful**
**une belle femme**
a beautiful woman
**3** **good-looking**
**un beau garçon**
a good-looking boy
**4** **handsome**
**un bel homme**
a handsome man
**Il fait beau aujourd'hui.**
It's a nice day today.
**beaucoup** ADVERB
**1** **a lot**
**Il mange beaucoup.**
He eats a lot.
**beaucoup de**
a lot of
**J'ai beaucoup de devoirs.**
I have a lot of homework.
**J'ai beaucoup de chance.**
I am very lucky.
**2** **much**
**Je n'ai pas beaucoup d'argent.**
I haven't got much money.
le **beau-fils** MASC NOUN
**1** **son-in-law**
**2** **stepson**
le **beau-frère** MASC NOUN
**brother-in-law**
le **beau-père** MASC NOUN
**1** **father-in-law**
**2** **stepfather**
le **bébé** MASC NOUN
**baby**
**beige** ADJECTIVE, MASC NOUN
**beige**
le **beignet** MASC NOUN
**fritter**
**des beignets aux pommes**
apple fritters
**bel** MASC ADJECTIVE _see_ **beau**
**un bel été**
a beautiful summer
**belge** ADJECTIVE
**Belgian**
le/la **Belge** MASC/FEM NOUN
**Belgian**
la **Belgique** FEM NOUN
**Belgium**
**belle** FEM ADJECTIVE _see_ **beau**
**une belle statue**
a beautiful statue
la **belle-fille** FEM NOUN
**1** **daughter-in-law**
**2** **stepdaughter**
la **belle-mère** FEM NOUN
**1** **mother-in-law**
**2** **stepmother**
la **belle-sœur** FEM NOUN
**sister-in-law**
le **berceau** MASC NOUN
(PL les **berceaux** )
**cradle**
le **berger** MASC NOUN
**shepherd**
le **besoin** MASC NOUN
**Je vais avoir besoin d'aide.**
I will need some help.
**J'ai besoin d'un stylo.**
I need a pen.
**bête** ADJECTIVE
**stupid**
les **bêtises** FEM PL NOUN
**faire des bêtises**
to misbehave
**Ma sœur fait toujours des bêtises.**
My sister is always misbehaving.
**dire des bêtises**
to talk nonsense
**Tu dis des bêtises!**
You're talking nonsense!
la **betterave** FEM NOUN
**beetroot**
le **beurre** MASC NOUN
**butter**
le **biberon** MASC NOUN
**bottle**
**Ma maman donne le biberon à ma sœur.**
My mum is giving my baby sister her bottle.
la **bibliothèque** FEM NOUN
**1** **library**
**2** **bookcase**
le **bic** ® MASC NOUN
**Biro** ® **J'ai deux bics dans ma trousse.**
I've got two Biros in my pencil case.
la **biche** FEM NOUN
**doe**
la **bicyclette** FEM NOUN
**bicycle**
**J'ai une nouvelle bicyclette.**
I've got a new bicycle.
**bien** ADJECTIVE, ADVERB
**1** **well**
**Daphné travaille bien.**
Daphné works well.
**2** **good**
**Ce livre est vraiment bien.**
This book is really good.
**J'aime bien les maths.**
I like maths.
**Comment ça va? — Ça va bien, merci.**
How are you? — Fine, thanks.
**bien sûr** ADVERB
**of course**
**Tu aimes les frites? — Oui, bien sûr!**
Do you like chips? — Yes, of course!
**bientôt** ADVERB
**soon**
**À bientôt!**
See you soon!
la **bienvenue** FEM NOUN
**welcome**
**Bienvenue à Paris!**
Welcome to Paris!
la **bière** FEM NOUN
**beer**
le **bijou** MASC NOUN
**jewel**
le **billard** MASC NOUN
**billiards**
le **bifteck** MASC NOUN
**steak**
la **bille** FEM NOUN
**marble**
**J'aime jouer aux billes.**
I like playing with marbles.
le **billet** MASC NOUN
**1** **ticket**
**un billet d'avion**
a plane ticket
**2** **banknote**
**un billet de 10€**
a €10 note
**bio** ADJECTIVE
**organic**
**Ma maman achète des produits bio.**
My mum buys organic produce.
la **biologie** FEM NOUN
**biology**
la **biscotte** FEM NOUN
**toasted bread**
le **biscuit** MASC NOUN
**biscuit**
la **bise** FEM NOUN
**kiss**
**Grosses bises de Bretagne.**
Love and kisses from Brittany.
**Viens me faire la bise.**
Come and give me a kiss.
**Je fais la bise à mes copines tous les matins.**
Every morning I give my friends a kiss.
**_Did you know...?_**
_Between girls and boys, and between girls, the normal French way of saying hello and goodbye is with kisses, usually one on each cheek. Boys shake hands with each other instead._
le **bisou** MASC NOUN
**kiss**
**Viens faire un bisou à maman!**
Come and give Mummy a little kiss!
**bizarre** ADJECTIVE
**strange**
la **blague** FEM NOUN
**joke**
**blanc**
**blanc** _can be an adjective or a noun._
**A** MASC ADJECTIVE (FEM **blanche** )
**white**
**un chemisier blanc**
a white blouse
**une chemise blanche**
a white shirt
**B** MASC NOUN
**white**
**Vous avez ce T-shirt en blanc?**
Do you have this T-shirt in white?
**blanche** FEM ADJECTIVE _see_ **blanc**
**de la peinture blanche**
white paint
le **blé** MASC NOUN
**wheat**
**blessé** MASC ADJECTIVE (FEM **blessée** )
**injured**
la **blessure** FEM NOUN
**injury**
**bleu**
**bleu** _can be an adjective or a noun._
**A** MASC ADJECTIVE (FEM **bleue** )
**blue**
**une veste bleue**
a blue jacket
**Mon uniforme est bleu et blanc.**
My uniform is blue and white.
**B** MASC NOUN
**blue**
**La couleur préférée de ma sœur, c'est le bleu.**
Blue is my sister's favourite colour.
le **bleuet** MASC NOUN ( _Canada_ )
**blueberry**
**_Did you know...?_**
_The Saguenay-Lac-St-Jean region of Quebec is famous for its blueberries. The people who live there are also known as_ **les Bleuets**.
**blond** MASC ADJECTIVE (FEM **blonde** )
**blond**
**Andrew a les cheveux blonds.**
Andrew has blond hair.
le **blouson** MASC NOUN
**jacket**
**un blouson en cuir**
a leather jacket
le **bocal** MASC NOUN
(PL les **bocaux** )
**jar**
le **bœuf** MASC NOUN
**beef**
**un rôti de bœuf**
a joint of beef
**bof** EXCLAMATION
**Comment ça va? — Bof! Pas terrible.**
How is it going? — Oh... not too well actually.
**boire** VERB
**to drink**
**Je bois du jus d'orange au petit déjeuner.**
I drink orange juice with my breakfast.
le **bois** MASC NOUN
**wood**
**en bois**
wooden
**une table en bois**
a wooden table
la **boisson** FEM NOUN
**drink**
**une boisson chaude**
a hot drink
la **boîte** FEM NOUN
**box**
**une boîte d'allumettes**
a box of matches
**une boîte aux lettres**
a letter box
**une boîte de conserve**
a tin
**une boîte de nuit**
a night club
le **bol** MASC NOUN
**bowl**
**un bol de céréales**
a bowl of cereal
**bon** MASC ADJECTIVE (FEM **bonne** )
**1** **good**
**un bon restaurant**
a good restaurant
**Je suis bon en maths.**
I'm good at maths.
**Bonne journée!**
Have a nice day!
**Bonne nuit!**
Good night!
**Bon anniversaire!**
Happy birthday!
**Bon courage!**
Good luck!
**Bon voyage!**
Have a good trip!
**Bon week-end!**
Have a nice weekend!
**Bonne chance!**
Good luck!
**Bonne année!**
Happy New Year!
**2** **right**
**C'est la bonne réponse.**
That's the right answer.
**Ah bon?**
Really?
**Bon, d'accord.**
OK then.
le **bonbon** MASC NOUN
**sweet**
**Ma sœur aime les bonbons.**
My sister likes sweets.
le **bonhomme de neige** MASC NOUN
**snowman**
**bonjour** EXCLAMATION
**1** **hello!**
**Bonjour madame!**
Hello Miss!
**2** **Good morning!**
**Bonjour, tout le monde!**
Good morning everyone!
**3** **Good afternoon!**
**_Language tip_**
**bonjour** _is used in the morning and in the afternoon; in the evening_ **bonsoir** _is used instead._
**bonne** FEM ADJECTIVE _see_ **bon**
**Elle est bonne en français.**
She's good at French.
le **bonnet** MASC NOUN
**hat**
**un bonnet de laine**
a woolly hat
**bonsoir** EXCLAMATION
**good evening!**
le **bord** MASC NOUN
**j'habite au bord de la mer.**
I live at the seaside.
**Cet été, je vais au bord de la mer.**
This summer, I'm going to the seaside.
**bordeaux**
**bordeaux** _can be a noun or an adjective._
**A** MASC NOUN
**Bordeaux wine**
**B** MASC, FEM, PL ADJECTIVE
**maroon**
**une jupe bordeaux**
a maroon skirt
la **bosse** FEM NOUN
**bump**
le **bossu** MASC NOUN
la **bossue** FEM NOUN
**hunchback**
la **botte** FEM NOUN
**boot**
**une paire de bottes**
a pair of boots
**des bottes en caoutchouc**
wellington boots
la **bouche** FEM NOUN
**mouth**
le **boucher** MASC NOUN
la **bouchère** FEM NOUN
**butcher**
la **boucherie** FEM NOUN
**butcher's**
**Où est la boucherie?**
Where is the butcher's?
le **bouchon** MASC NOUN
**1** **top**
**un bouchon en plastique**
a plastic top
**2** **cork**
**un bouchon de champagne**
a champagne cork
**3** **hold-up**
**Il y a beaucoup de bouchons sur l'autoroute.**
There are a lot of hold-ups on the motorway.
la **boucle d'oreille** FEM NOUN
**earring**
**des boucles d'oreille en or**
gold earrings
**bouclé** MASC ADJECTIVE (FEM **bouclée** )
**curly**
**J'ai les cheveux bouclés.**
I've got curly hair.
**bouder** VERB
**to sulk**
le **boudin** MASC NOUN
**le boudin noir**
black pudding
**le boudin blanc**
white pudding
la **boue** FEM NOUN
**mud**
la **bouée** FEM NOUN
**buoy**
**une bouée de sauvetage**
a life buoy
**bouger** VERB
**to move**
la **bougie** FEM NOUN
**candle**
la **bouillabaisse** FEM NOUN
**fish soup**
**bouillant** MASC ADJECTIVE (FEM **bouillante** )
**boiling**
**de l'eau bouillante**
boiling water
**bouillir** VERB
**to boil**
la **bouilloire** FEM NOUN
**kettle**
la **bouillotte** FEM NOUN
**hot-water bottle**
le **boulanger** MASC NOUN
la **boulangère** FEM NOUN
**baker**
la **boulangerie** FEM NOUN
**baker's**
**Je vais à la boulangerie.**
I'm going to the baker's.
la **boule** FEM NOUN
**ball**
**une boule de neige**
a snowball
**jouer aux boules**
to play bowls
**Mon grand-père aime jouer aux boules.**
My grandad likes playing bowls.
**_Did you know...?_**
**boules** _is played on rough ground, not smooth grass. The balls are slightly smaller than tennis balls, and are made of metal._
le **boulevard** MASC NOUN
**boulevard**
la **boum** FEM NOUN
**party**
**Je vais à une boum ce week-end.**
I'm going to a party this weekend.
le **bouquet** MASC NOUN
**bunch of flowers**
**un bouquet de roses**
a bunch of roses
la **Bourgogne** FEM NOUN
**Burgundy**
la **boussole** FEM NOUN
**compass**
le **bout** MASC NOUN
**1** **end**
**Elle habite au bout de la rue.**
She lives at the end of the street.
**2** **tip**
**le bout du nez**
the tip of the nose
la **bouteille** FEM NOUN
**bottle**
**une bouteille de limonade**
a bottle of lemonade
la **boutique** FEM NOUN
**shop**
le **bouton** MASC NOUN
**1** **button**
**Appuie sur le bouton.**
Press the button.
**2** **spot**
**Elle a des boutons.**
She's got spots.
le **bowling** MASC NOUN
**1** **tenpin bowling**
**J'aime aller au bowling.**
I like going bowling.
**2** **bowling alley**
**Il y a un bowling près de chez moi.**
There's a bowling alley near my house.
le **bracelet** MASC NOUN
**bracelet**
la **branche** FEM NOUN
**branch**
**branché** MASC ADJECTIVE (FEM **branchée** )
**trendy**
le **bras** MASC NOUN
**arm**
**J'ai mal au bras.**
My arm hurts.
la **brasserie** FEM NOUN
**café-restaurant**
**bravo** EXCLAMATION
**well done!**
le **Brésil** MASC NOUN
**Brazil**
la **Bretagne** FEM NOUN
**Brittany**
les **bretelles** FEM PL NOUN
**braces**
**Il porte des bretelles.**
He's wearing braces.
**breton** MASC ADJECTIVE (FEM **bretonne** )
**Breton**
le **brevet des collèges** MASC NOUN
**Mon frère passe son brevet des collèges.**
My brother is taking his GCSEs.
**_Did you know...?_**
_The_ **brevet des collèges** _is an exam you take at the end of_ **collège** , _at the age of 15._
le **bricolage** MASC NOUN
**DIY**
**Elle aime le bricolage.**
She likes doing DIY.
**bricoler** VERB
**to do DIY**
**Pascal aime bricoler.**
Pascal loves doing DIY.
**brillant** MASC ADJECTIVE (FEM **brillante** )
**1** **brilliant**
**une idée brillante**
a brilliant idea
**2** **shiny**
**des cheveux brillants**
shiny hair
**briller** VERB
**to shine**
la **brioche** FEM NOUN
**brioche**
**Je mange une brioche au petit déjeuner.**
I have a brioche for breakfast.
**_Did you know...?_**
**brioche** _is a kind of sweet bread._
la **brique** FEM NOUN
**brick**
le **briquet** MASC NOUN
**cigarette lighter**
**britannique** ADJECTIVE
**British**
**Je suis britannique.**
I am British.
la **brochette** FEM NOUN
**skewer**
la **brochure** FEM NOUN
**brochure**
la **bronchite** FEM NOUN
**bronchitis**
le **bronze** MASC NOUN
**bronze**
**la médaille de bronze**
the bronze medal
**bronzer** VERB
**to get a tan**
la **brosse** FEM NOUN
**brush**
**une brosse à cheveux**
a hairbrush
**une brosse à dents**
a toothbrush
**brosser** VERB
**to brush**
**se brosser les dents**
to brush one's teeth
**Je me brosse les dents tous les soirs.**
I brush my teeth every night.
le **brouillard** MASC NOUN
**fog**
**Demain il y aura du brouillard.**
It will be foggy tomorrow.
**Il y a du brouillard.**
It's foggy.
la **brouette** FEM NOUN
**wheelbarrow**
le **bruit** MASC NOUN
**noise**
**Il y a trop de bruit!**
There's too much noise!
**faire du bruit**
to make a noise
**Cette voiture fait beaucoup de bruit.**
This car makes a lot of noise.
**sans bruit**
without a sound
**brûlant** MASC ADJECTIVE (FEM **brûlante** )
**1** **blazing**
**un soleil brûlant**
a blazing sun
**2** **boiling**
**La soupe est brûlante.**
The soup is boiling.
**brûler** VERB
**to burn**
**Ne te brûle pas!**
Don't burn yourself!
la **brûlure** FEM NOUN
**burn**
**des brûlures d'estomac**
heartburn
la **brume** FEM NOUN
**mist**
**brun** MASC ADJECTIVE (FEM **brune** )
**brown**
**J'ai les cheveux bruns.**
I've got brown hair.
**Bruxelles** NOUN
**Brussels**
**bruyant** MASC ADJECTIVE (FEM **bruyante** )
**noisy**
la **bruyère** FEM NOUN
**heather**
**bu** VERB _see_ **boire**
**J'ai bu du jus d'orange.**
I drank some orange juice.
la **bûche** FEM NOUN
**la bûche de Noël**
the Yule log
**Le vingt-cinq décembre, on mange de la bûche de Noël.**
On the twenty-fifth of December we eat Yule log.
**_Did you know...?_**
**la bûche de Noël** _is what is usually eaten in France as a Christmas pudding._
le **buffet** MASC NOUN
**1** **sideboard**
**un buffet en chêne**
an oak sideboard
**2** **buffet**
**un buffet de gare**
a station buffet
le **buisson** MASC NOUN
**bush**
la **bulle** FEM NOUN
**bubble**
le **bulletin** MASC NOUN
**report**
**un bulletin scolaire**
a school report
le **bureau** MASC NOUN
(PL les **bureaux** )
**1** **desk**
**Il y a un bureau dans ma chambre.**
There's a desk in my room.
**2** **office**
**Ma mère travaille dans un bureau.**
My mum works in an office.
**un bureau de change**
a bureau de change
**le bureau de poste**
the post office
**le bureau de tabac**
the tobacconist's
le **bus** MASC NOUN
**bus**
**en bus**
by bus
**Je vais à l'école en bus.**
I go to school by bus.
le **but** MASC NOUN
**goal**
**marquer un but**
to score a goal
**J'ai marqué un but.**
I scored a goal.
# **C c**
**c'** PRONOUN _see_ **ce**
**C'est lui!**
That's him!
**ça** PRONOUN
**1** **this**
**Je voudrais un peu de ça.**
I'd like a bit of this.
**2** **that**
**Ne fais pas ça.**
Don't do that.
**3** **it**
**Ça ne fait rien.**
It doesn't matter.
**Ça va? — Oui, ça va, merci.**
How are you? — I'm fine thanks.
**Ça alors!**
Well, well!
**C'est ça.**
That's right.
**Ça y est!**
That's it!
la **cabane** FEM NOUN
**hut**
**une cabane à sucre** ( _Canada_ )
a sugar shack
la **cabine** FEM NOUN
**cabin**
**une cabine d'essayage**
a fitting room
**une cabine téléphonique**
a phone box
le **cabinet** MASC NOUN
**surgery**
la **cacahuète** FEM NOUN
**peanut**
le **cacao** MASC NOUN
**cocoa**
**cache-cache** MASC NOUN
**hide-and-seek**
**Tu veux jouer à cache-
cache?**
Do you want to play hide-and-seek?
le **cache-nez** MASC NOUN
**long woollen scarf**
**_Language tip_**
**cacher** _means 'hide' and_ **nez** _means 'nose', so this scarf covers your nose._
**cacher** VERB
**to hide**
**se cacher**
**to hide**
**Elle s'est cachée sous la table.**
She's hiding under the table.
le **cachet** MASC NOUN
**tablet**
**un cachet d'aspirine**
an aspirin
la **cachette** FEM NOUN
**hiding place**
le **cadavre exquis**
MASC NOUN
**consequences**
**_Did you know...?_**
_This is a game where one player writes something on a piece of paper, folds it over and passes it on to the next player to continue the story._
le **Caddie** ® MASC NOUN
**supermarket trolley**
le **cadeau** MASC NOUN
(PL les **cadeaux** )
**present**
**un cadeau d'anniversaire**
a birthday present
**un cadeau de Noël**
a Christmas present
**Je vais faire un cadeau à ma mère.**
I'm going to give my mum a present.
le **cadenas** MASC NOUN
**padlock**
**cadet** MASC ADJECTIVE
(FEM **cadette** )
**1** **younger**
**2** **youngest**
le **cadet** MASC NOUN
la **cadette** FEM NOUN
**youngest**
**Luc est le cadet de la famille.**
Luc is the youngest in the family.
**Muriel est la cadette de la famille.**
Muriel is the youngest in the family.
le **cafard** MASC NOUN
**cockroach**
**J'ai le cafard.**
I'm feeling down.
le **café** MASC NOUN
**1** **coffee**
**un café au lait**
a white coffee
**un café crème**
a strong white coffee
**_Did you know...?_**
_If you have asked for_ **un café** , _it will not have milk in it. If you want a coffee with milk, you must ask for_ **un café au lait**.
**2** **café**
**Rendez-vous au café à trois heures.**
Let's meet at the café at three o'clock.
le **café-tabac** MASC NOUN
**_Did you know...?_**
_A_ **café-tabac** _is a café which also sells cigarettes and stamps; you can tell a_ **café-tabac** _by the red diamond-shaped sign outside it._
la **cafétéria** FEM NOUN
**cafeteria**
la **cage** FEM NOUN
**cage**
la **cagoule** FEM NOUN
**balaclava**
**_Language tip_**
**une cagoule** _is something you wear on your head. It's not an anorak as it is in English._
le **cahier** MASC NOUN
**jotter**
**mon cahier de français**
my French jotter
le **caillou** MASC NOUN
(PL les **cailloux** )
**pebble**
la **caisse** FEM NOUN
**1** **checkout**
**Payez à la caisse.**
Pay at the checkout.
**2** **box**
**une caisse à outils**
a tool box
le **caissier** MASC NOUN
la **caissière** FEM NOUN
**cashier**
la **calculatrice** FEM NOUN
**calculator**
**calculer** VERB
**to work out**
**Calculez combien ça va coûter.**
Work out how much it's going to cost.
la **calculette** FEM NOUN
**pocket calculator**
le **caleçon** MASC NOUN
**boxer shorts**
le **calendrier** MASC NOUN
**calendar**
le **câlin** MASC NOUN
**cuddle**
**calme**
**calme** _can be an adjective or a noun._
**A** ADJECTIVE
**1** **quiet**
**un endroit calme**
a quiet place
**2** **calm**
**La mer est calme.**
The sea is calm.
**B** MASC NOUN
**peace and quiet**
**J'ai besoin de calme pour travailler.**
I need peace and quiet to work.
se **calmer** VERB
**to calm down**
**Calme-toi!**
Calm down!
le/la **camarade** MASC/FEM NOUN
**friend**
**un camarade de classe**
a school friend
la **caméra** FEM NOUN
**camera**
**une caméra de télévision**
a television camera
le **caméscope** ® MASC NOUN
**camcorder**
le **camion** MASC NOUN
**lorry**
la **camionnette** FEM NOUN
**van**
le **camp** MASC NOUN
**camp**
la **campagne** FEM NOUN
**country**
**à la campagne**
in the country
**camper** VERB
**to camp**
le **camping** MASC NOUN
**camping**
**Je n'aime pas le camping.**
I don't like camping.
**Je vais faire du camping.**
I'm going camping.
**un terrain de camping**
a campsite
le **Canada** MASC NOUN
**Canada**
**canadien** MASC ADJECTIVE
(FEM **canadienne** )
**Canadian**
le **Canadien** MASC NOUN
la **Canadienne** FEM NOUN
**Canadian**
le **canapé** MASC NOUN
**sofa**
le **canard** MASC NOUN
**duck**
le **canari** MASC NOUN
**canary**
le **caniche** MASC NOUN
**poodle**
le **canif** MASC NOUN
**penknife**
la **canne** FEM NOUN
**walking stick**
**une canne à pêche**
a fishing rod
la **cannelle** FEM NOUN
**cinnamon**
le **canoë** MASC NOUN
**canoe**
**Je vais faire du canoë.**
I'm going canoeing.
la **cantine** FEM NOUN
**canteen**
**Je mange à la cantine.**
I eat in the canteen.
le **caoutchouc** MASC NOUN
**rubber**
**des bottes en caoutchouc**
Wellington boots
le **capitaine** MASC NOUN
**captain**
la **capitale** FEM NOUN
**capital**
**Paris est la capitale de la France.**
Paris is the capital of France.
la **capuche** FEM NOUN
**hood**
**car**
**A** MASC NOUN
**coach**
**On va en France en car.**
We're going to France by coach.
**_Language tip_**
_The French_ **car** _holds a lot more people than the English_ **car**.
**B** CONJUNCTION
**because**
**Écoutez, car c'est très important.**
Listen, because it's very important.
le **caractère** MASC NOUN
**personality**
**Il a le même caractère que son père.**
He's got the same personality as his father.
**Il a bon caractère.**
He's good-natured.
**Elle a mauvais caractère.**
She's bad-tempered.
la **carafe** FEM NOUN
**jug**
les **Caraïbes** FEM PL NOUN
**Caribbean Islands**
le **caramel** MASC NOUN
**toffee**
la **caravane** FEM NOUN
**caravan**
le **carême** MASC NOUN
**Lent**
la **caresse** FEM NOUN
**faire des caresses**
to stroke
**Elle fait des caresses au chat.**
She's stroking the cat.
**caresser** VERB
**to stroke**
la **carie** FEM NOUN
**J'ai une carie.**
I've got a hole in my tooth.
le **carnaval** MASC NOUN
**carnival**
**_Did you know...?_**
_French children usually celebrate_ **carnaval** _on Shrove Tuesday, when they often go to school in fancy dress. There is a procession in the streets, and at the end of the day, a man made of papier mâché, called_ **bonhomme carnaval** _is burnt on a bonfire._
le **carnet** MASC NOUN
**1** **notebook**
**2** **book**
**un carnet d'adresses**
an address book
**un carnet de timbres**
a book of stamps
**un carnet de tickets**
a book of tickets
**_Did you know...?_**
_It is cheaper to buy tickets for the Paris Metro in a book of ten._
**un carnet de notes**
a school report
la **carotte** FEM NOUN
**carrot**
**carré**
**carré** _can be an adjective or a noun._
**A** MASC ADJECTIVE (FEM **carrée** )
**square**
**un mètre carré**
a square metre
**B** MASC NOUN
**un carré de chocolat**
a square of chocolate
le **carreau** MASC NOUN
(PL les **carreaux** )
**1** **check**
**une chemise à carreaux**
a checked shirt
**2** **window**
**Maxime a cassé un carreau.**
Maxime has broken a window.
**3** **diamonds**
**l'as de carreau**
the ace of diamonds
le **carrefour** MASC NOUN
**junction**
**Tournez à gauche au carrefour.**
Turn left at the junction.
le **cartable** MASC NOUN
**satchel**
**_Did you know...?_**
**un cartable** _is a large, rigid kind of satchel school children carry on their backs._
la **carte** FEM NOUN
**1** **card**
**une carte d'anniversaire**
a birthday card
**une carte postale**
a postcard
**une carte de vœux**
a Christmas card
**_Did you know...?_**
_In France, people send greetings cards_ ( **les cartes de vœux** ) _in January rather than at Christmas, with best wishes for the New Year._
**une carte de crédit**
a credit card
**une carte d'identité**
an identity card
**une carte téléphonique**
a phonecard
**un jeu de cartes**
a pack of cards/a card game
**_Language tip_**
**un jeu de cartes** _has two translations. Look at the examples._
**J'ai acheté un nouveau jeu de cartes.**
I've bought a new pack of cards.
**Tu connais ce jeu de cartes?**
Do you know this card game?
**2** **map**
**une carte de France**
a map of France
**une carte routière**
a road map
**3** **menu**
**Je voudrais la carte, s'il vous plaît.**
I'd like the menu, please.
le **carton** MASC NOUN
**1** **cardboard**
**un morceau de carton**
a piece of cardboard
**2** **cardboard box**
**un carton à chaussures**
a shoe box
le **cas** MASC NOUN (PL les **cas** )
**case**
**en tout cas**
in any case
**au cas où**
just in case
**Prends de l'argent au cas où.**
Take some money just in case.
**en cas de**
in case of
**En cas d'incendie, appelez
ce numéro.**
In case of fire, call this number.
le **casier** MASC NOUN
**locker**
le **casque** MASC NOUN
**1** **helmet**
**2** **headphones**
**J'ai cassé mon casque.**
I've broken my headphones.
la **casquette** FEM NOUN
**cap**
le **casse-croûte** MASC NOUN
**snack**
**casse-pieds** MASC, FEM, PL ADJECTIVE
**Il est vraiment casse-pieds!**
He's a real pain in the neck!
**casser** VERB
**to break**
**J'ai cassé un verre.**
I've broken a glass.
**se casser**
**to break**
**Je me suis cassé la jambe au ski.**
I broke my leg when I was skiing.
la **casserole** FEM NOUN
**saucepan**
le **cassis** MASC NOUN
**blackcurrant**
le **castor** MASC NOUN
**beaver**
la **catastrophe** FEM NOUN
**disaster**
**C'est une catastrophe!**
It's a disaster!
le **catéchisme** MASC NOUN
**catechism**
la **cathédrale** FEM NOUN
**cathedral**
**catholique** ADJECTIVE, MASC/FEM NOUN
**Catholic**
le **cauchemar** MASC NOUN
**nightmare**
**J'ai fait un cauchemar.**
I had a nightmare.
la **cause** FEM NOUN
**à cause de**
because of
**Il n'y a pas de courrier à cause de la grève.**
There's no post because of the strike.
la **cave** FEM NOUN
**cellar**
**_Did you know...?_**
**une cave** _is dark and underground, like a cave in English, but it often contains bottles of wine._
le **CD** MASC NOUN (PL les **CD** )
**CD**
**ce**
**ce** _can be an adjective or a pronoun._
**A** MASC ADJECTIVE (MASC **cet** , FEM **cette** , PL **ces** )
**_Language tip_**
**ce** _changes to_ **cet** _before a vowel sound._
**1** **this**
**Tu peux prendre ce livre.**
You can take this book.
**cet hiver**
this winter
**cette année**
this year
**cette semaine**
this week
**2** **that**
**Je n'aime pas du tout ce film.**
I don't like that film at all.
**ce livre-là**
that book
**cette nuit**
tonight/last night
**_Language tip_**
**cette nuit** _has two translations. Look at the examples._
**Il va neiger cette nuit.**
It's going to snow tonight.
**Je n'ai pas beaucoup dormi cette nuit.**
I didn't sleep much last night.
**B** PRONOUN
**it**
**Ce n'est pas facile.**
It's not easy.
**_Language tip_**
**ce** _changes to_ **c'** _in_ **c'est**.
**c'est**
it is/he is/she is
**_Language tip_**
**c'est** _has three translations. Look at the examples._
**C'est trop cher.**
It's too expensive.
**C'est un véritable artiste.**
He's a real artist.
**C'est une actrice très célèbre.**
She's a very famous actress.
**C'est super!**
It's great!
**C'est moi!**
It's me!
**ce sont**
they are
**Ce sont des amis à mes parents.**
They're friends of my parents.
**ce qui**
what
**C'est ce qui compte.**
That's what matters.
**ce que**
what
**Je vais lui dire ce que je pense.**
I'm going to tell him what I think.
le **CE1** MASC NOUN
**Year 3**
le **CE2** MASC NOUN
**Year 4**
**ceci** PRONOUN
**this**
**Prends ceci, tu en auras besoin.**
Take this, you'll need it.
**céder** VERB
**to give in**
**Elle ne veut pas céder.**
She won't give in.
**céder à**
to give in to
**Je ne veux pas céder à ses caprices.**
I'm not going to give in to her demands.
la **cédille** FEM NOUN
**cedilla**
**c cédille**
c with a cedilla
**_Language tip_**
_The cedilla looks like the number 5 with the top missing. It's attached to the bottom of the letter C as in the word_ **garçon**. _It makes a **c** sound like an **s** rather than a_ **k**.
la **ceinture** FEM NOUN
**belt**
**une ceinture en cuir**
a leather belt
**une ceinture de sécurité**
a seatbelt
**cela** PRONOUN
**1** **it**
**Cela dépend.**
It depends.
**2** **that**
**Je n'aime pas cela.**
I don't like that.
**célèbre** ADJECTIVE
**famous**
**célébrer** VERB
**to celebrate**
le **céleri** MASC NOUN
**le céleri-rave**
celeriac
**le céleri en branche**
celery
**célibataire**
**célibataire** _can be an adjective or a noun._
**A** ADJECTIVE
**not married**
**Ma tante est célibataire.**
My aunt isn't married.
**B** MASC NOUN
**bachelor**
**un célibataire de quarante ans**
a 40 year-old bachelor
**C** FEM NOUN
**single woman**
**une célibataire de trente-cinq ans**
a 35 year-old single woman
**celle** PRONOUN _see_ **celui**
**celles** PRONOUN _see_ **ceux**
**celui** MASC PRONOUN (FEM **celle** )
**the one**
**Prends celui que tu préfères.**
Take the one you like best.
**Ne prends pas mon appareil photo; prends celui de ma sœur!**
Don't take my camera, take my sister's!
**Ce n'est pas ma platine laser, c'est celle de mon frère.**
This isn't my CD player, it's my brother's.
**celui-ci**
this one
**celle-ci**
this one
**celui-là**
that one
**celle-là**
that one
le **cendrier** MASC NOUN
**ashtray**
**cent** NUMBER
**a hundred**
**cent euros**
a hundred euros
**trois cents ans**
three hundred years
**cent deux kilomètres**
a hundred and two kilometres
**trois cent cinquante kilomètres**
three hundred and fifty kilometres
la **centaine** FEM NOUN
**about a hundred**
**Il y a une centaine de personnes dans la salle.**
There are about a hundred people in the hall.
**des centaines de**
hundreds of
**J'ai des centaines de timbres dans ma collection.**
I've got hundreds of stamps in my collection.
**centième** ADJECTIVE
**hundredth**
le **centilitre** MASC NOUN
**centilitre**
le **centime** MASC NOUN
**1** **cent**
**un centime d'euro**
a euro cent
**_Did you know...?_**
_There are 100_ **centimes** _in a euro._
**2** **centime**
**une pièce de cinquante centimes**
a 50-centime coin
le **centimètre** MASC NOUN
**centimetre**
le **centre** MASC NOUN
**centre**
**un centre commercial**
a shopping centre
le **centre-ville** MASC NOUN
**town centre**
le **cercle** MASC NOUN
**circle**
la **céréale** FEM NOUN
**cereal**
**un bol de céréales**
a bowl of cereal
la **cérémonie** FEM NOUN
**ceremony**
le **cerf** MASC NOUN
**stag**
le **cerf-volant** MASC NOUN
**kite**
la **cerise** FEM NOUN
**cherry**
le **cerisier** MASC NOUN
**cherry tree**
**certain** MASC ADJECTIVE (FEM **certaine** )
**1** **certain**
**Ce n'est pas certain.**
It's not certain.
**2** **some**
**Les chiens sont interdits sur certaines plages.**
Dogs are forbidden on some beaches.
**certainement** ADVERB
**1** **definitely**
**C'est certainement le meilleur film de l'année.**
It's definitely the best film of the year.
**2** **of course**
**Est-ce que je peux t'emprunter ton stylo? — Mais certainement!**
Can I borrow your pen? — Of course!
**certains** PRONOUN
**1** **some**
**certains de ses amis**
some of his friends
**2** **some people**
**Certains pensent que c'est difficile.**
Some people think it's difficult.
le **certificat** MASC NOUN
**certificate**
le **cerveau** MASC NOUN
(PL les **cerveaux** )
**brain**
le **CES** MASC NOUN
**secondary school**
**Elle est au CES.**
She's in secondary school.
**_Did you know...?_**
_In France, pupils go to a_ **CES** _between the ages of 11 and 15, and then to a_ **lycée** _until the age of 18._
**ces** PL ADJECTIVE
**1** **these**
**Tu peux prendre ces photos si tu veux.**
You can have these photos if you like.
**ces photos-ci**
these photos
**2** **those**
**Ces montagnes sont dangereuses en hiver.**
Those mountains are dangerous in winter.
**ces livres-là**
those books
**c'est** _see_ **ce**
**c'est-à-dire** ADVERB
**that is**
**Est-ce que tu peux venir lundi prochain, c'est-à-dire le quinze?**
Can you come next Monday, that's the fifteenth?
**cet** MASC ADJECTIVE _see_ **ce**
**cette** FEM ADJECTIVE _see_ **ce**
**ceux** MASC PL PRONOUN
(FEM PL **celles** )
**the ones**
**Prends ceux que tu préfères.**
Take the ones you like best.
**Ne prends pas mes skis; prends ceux de ma sœur!**
Don't take my skis, take my sister's!
**Ce ne sont pas mes baskets, ce sont celles de mon frère.**
They're not my trainers, they're my brother's.
**ceux-ci**
these ones
**celles-ci**
these ones
**ceux-là**
those ones
**celles-là**
those ones
**chacun** PRONOUN
**1** **each**
**Nous avons chacun donné deux euros.**
We each gave two euros.
**2** **everyone**
**Chacun fait ce qu'il veut.**
Everyone does what they like.
la **chaîne** FEM NOUN
**1** **chain**
**une chaîne en or**
a gold chain
**2** **channel**
**Le film passe sur quelle chaîne?**
Which channel is the film on?
**une chaîne hi-fi**
a hi-fi system
**une chaîne laser**
a CD player
**une chaîne stéréo**
a music centre
la **chair** FEM NOUN
**flesh**
**la chair de poule**
goose pimples
**J'ai la chair de poule!**
I've got goose pimples!
**_Language tip_**
_The French actually means 'I've got hen's flesh'!_
la **chaise**
FEM NOUN
**chair**
**une chaise longue**
a deckchair
la **chaleur** FEM NOUN
**heat**
**Quelle chaleur!**
Phew! It's hot!
la **chambre** FEM NOUN
**bedroom**
**C'est la chambre de Camille.**
This is Camille's bedroom.
**une chambre à coucher**
a bedroom
**une chambre d'amis**
a spare room
**une chambre à un lit**
a single room
**une chambre pour une personne**
a single room
**une chambre pour deux personnes**
a double room
**'Chambres d'hôte'**
'Bed and Breakfast'
le **chameau** MASC NOUN
(PL les **chameaux** )
**camel**
le **champ** MASC NOUN
**field**
le **champignon** MASC NOUN
**mushroom**
le **champion** MASC NOUN
la **championne** FEM NOUN
**champion**
le **championnat** MASC NOUN
**championship**
**le championnat du monde**
the world championship
la **chance** FEM NOUN
**1** **luck**
**Tu as de la chance!**
You're lucky!
**Je n'ai pas de chance.**
I'm unlucky.
**Bonne chance!**
Good luck!
**2** **chance**
**Il n'a aucune chance.**
He's got no chance.
le **changement** MASC NOUN
**change**
**Est-ce qu'il y a un changement? — Non, c'est direct.**
Do you have to change? — No, it's a through train.
**changer** VERB
**to change**
**Tu peux changer les draps?**
Can you change the sheets?
**Je vais me changer.**
I'm going to get changed.
**Tu vas te changer?**
Are you going to get changed?
la **chanson** FEM NOUN
**song**
le **chant** MASC NOUN
**singing**
**des cours de chant**
singing lessons
**un chant de Noël**
a Christmas carol
**chanter** VERB
**to sing**
le **chanteur** MASC NOUN
la **chanteuse** FEM NOUN
**singer**
la **Chantilly** FEM NOUN
**whipped cream**
le **chapeau** MASC NOUN
(PL les **chapeaux** )
**hat**
le **chapitre** MASC NOUN
**chapter**
**chaque** ADJECTIVE
**every**
**chaque année**
every year
la **charade** FEM NOUN
**riddle**
le **charbon** MASC NOUN
**coal**
la **charcuterie** FEM NOUN
**1** **delicatessen**
**2** **cold meats**
**Comme entrée, je voudrais de la charcuterie.**
As a starter, I would like a plate of cold meats.
le **chariot** MASC NOUN
**trolley**
**charmant** MASC ADJECTIVE (FEM **charmante** )
**charming**
la **chasse** FEM NOUN
**1** **hunting**
**un chien de chasse**
a hunting dog
**2** **shooting**
**la chasse au canard**
duck shooting
**chasser** VERB
**to hunt**
le **chasseur** MASC NOUN
**hunter**
le **chat** MASC NOUN
**cat**
**J'ai deux chats.**
I've got two cats.
la **châtaigne** FEM NOUN
**chestnut**
le **châtaignier** MASC NOUN
**chestnut tree**
**châtain** MASC, FEM, PL ADJECTIVE
**brown**
**J'ai les cheveux châtain.**
I've got brown hair.
le **château** MASC NOUN
(PL les **châteaux** )
**1** **castle**
**2** **palace**
**le château de Versailles**
the palace of Versailles
**un château de sable**
a sandcastle
le **chaton** MASC NOUN
**kitten**
**chatouiller** VERB
**to tickle**
la **chatte** FEM NOUN
**cat**
**_Language tip_**
**te** _added to the word_ **chat** _shows you that the cat is female._
**chaud** MASC ADJECTIVE (FEM **chaude** )
**1** **warm**
**des vêtements chauds**
warm clothes
**2** **hot**
**de l'eau chaude**
hot water
**Il fait chaud.**
It's hot.
**J'ai chaud!**
I'm hot!
le **chauffage** MASC NOUN
**heating**
**le chauffage central**
central heating
le **chauffeur** MASC NOUN
**driver**
**un chauffeur de taxi**
a taxi driver
**_Language tip_**
_In English, a chauffeur drives a car for another person, but_ **chauffeur** _in French means any kind of driver._
la **chaussette** FEM NOUN
**sock**
le **chausson** MASC NOUN
**slipper**
**un chausson aux pommes**
an apple turnover
la **chaussure** FEM NOUN
**shoe**
**les chaussures de ski**
ski boots
**chauve** ADJECTIVE
**bald**
la **chauve-souris** FEM NOUN
**bat**
**_Language tip_**
_The French actually means 'bald mouse'!_
le **chef** MASC NOUN
**1** **boss**
**C'est toi le chef!**
You're the boss!
**2** **chef**
**la spécialité du chef**
the chef's speciality
**un chef d'orchestre**
a conductor
le **chef-d'œuvre** MASC NOUN
**masterpiece**
le **chemin** MASC NOUN
**1** **path**
**2** **way**
**Montre-moi le chemin.**
Show me the way.
**en chemin**
on the way
**les chemins de fer**
the railways
la **cheminée** FEM NOUN
**1** **chimney**
**2** **fireplace**
la **chemise** FEM NOUN
**1** **shirt**
**une chemise à carreaux**
a checked shirt
**une chemise de nuit**
a nightdress
**2** **folder**
le **chemisier** MASC NOUN
**blouse**
le **chêne** MASC NOUN
**oak**
la **chenille** FEM NOUN
**caterpillar**
le **chèque** MASC NOUN
**cheque**
**les chèques de voyage**
traveller's cheques
**cher**
**cher** _can be an adjective or an adverb._
**A** MASC ADJECTIVE (FEM **chère** )
**1** **dear**
**Chère Mélusine...**
Dear Mélusine...
**2** **expensive**
**C'est trop cher.**
It's too expensive.
**B** ADVERB
**coûter cher**
to be expensive
**Cet ordinateur coûte cher.**
This computer is expensive.
**chercher** VERB
**1** **to look for**
**Je cherche mes clés.**
I'm looking for my keys.
**2** **to look up**
**Cherche 'apple' dans le dictionnaire.**
Look up 'apple' in the dictionary.
**aller chercher**
to go to get
**Je vais chercher du pain pour le déjeuner.**
I'm going to get some bread for lunch.
le **chercheur** MASC NOUN
la **chercheuse** FEM NOUN
**scientist**
**chère** FEM ADJECTIVE _see_ **cher**
**chéri** MASC NOUN, MASC ADJECTIVE (FEM **chérie** )
**darling**
le **cheval** MASC NOUN
(PL les **chevaux** )
**horse**
**un cheval de course**
a racehorse
**à cheval**
on horseback
**Je fais du cheval le samedi.**
I go riding on Saturdays.
le **chevalier** MASC NOUN
**knight**
les **chevaux** MASC PL NOUN
**horses**
les **cheveux** MASC PL NOUN
**hair**
**Elle a les cheveux courts.**
She's got short hair.
la **cheville** FEM NOUN
**ankle**
la **chèvre** FEM NOUN
**goat**
**le fromage de chèvre**
goat's cheese
le **chevreuil** MASC NOUN
**1** **roe deer**
**2** **venison**
**On va manger du chevreuil à Noël.**
We'll eat venison at Christmas.
**chez** PREPOSITION
**_Language tip_**
**chez** _means either_ **at** _or_ **to** _someone's house._
**On va chez moi?**
Shall we go to my house?
**Je vais chez Marc.**
I'm going to Marc's house.
**Je rentre chez moi à quatre heures.**
I go home at four.
**Nicole va chez elle.**
Nicole is going home.
**Jean-Claude reste chez lui.**
Jean-Claude is staying at home.
**Tu rentres chez toi?**
Are you going home?
**_Language tip_**
**chez le dentiste** _means either_ **at the dentist's** _or_ **to the dentist's**.
**J'ai rendez-vous chez le dentiste.**
I've got an appointment at the dentist's.
**Je vais chez le dentiste.**
I'm going to the dentist's.
**Je suis chez moi.**
I'm at home.
**Je vais chez moi.**
I'm going home.
**chic** MASC, FEM, PL ADJECTIVE
**smart**
**une tenue chic**
a smart outfit
le **chien** MASC NOUN
**dog**
la **chienne** FEM NOUN
**bitch**
**C'est un chien ou une chienne?**
Is it a dog or a bitch?
le **chiffon** MASC NOUN
**cloth**
le **chiffre** MASC NOUN
**figure**
**Écris ce nombre en chiffres.**
Write this number in figures.
la **chimie** FEM NOUN
**chemistry**
la **Chine** FEM NOUN
**China**
**chinois** MASC NOUN, MASC ADJECTIVE (FEM **chinoise** )
**Chinese**
le **Chinois** MASC NOUN
**Chinese man**
**les Chinois**
the Chinese
la **Chinoise** FEM NOUN
**Chinese woman**
le **chiot** MASC NOUN
**puppy**
les **chips** FEM PL NOUN
**crisps**
**un paquet de chips**
a packet of crisps
**_Language tip_**
_Be careful! The French word_ **chips** _does not mean the same as the English word_ **chips**.
le **chirurgien** MASC NOUN
**surgeon**
le **chocolat** MASC NOUN
**chocolate**
**un chocolat chaud**
a hot chocolate
le **chœur** MASC NOUN
**choir**
**choisir** VERB
**to choose**
le **choix** MASC NOUN
**1** **choice**
**Je n'ai pas le choix.**
I don't have a choice.
**2** **selection**
**Il n'y a pas beaucoup de choix dans ce magasin.**
There's not much of a selection in this shop.
le **chômage** MASC NOUN
**unemployment**
**au chômage**
unemployed
**Mon père est au chômage.**
My dad is unemployed.
le **chômeur** MASC NOUN
la **chômeuse** FEM NOUN
**Il est chômeur.**
He's unemployed.
**Elle est chômeuse.**
She's unemployed.
la **chorale** FEM NOUN
**choir**
la **chose** FEM NOUN
**thing**
**J'ai fait beaucoup de choses pendant les vacances.**
I did lots of things in the holidays.
le **chou** MASC NOUN
(PL les **choux** )
**cabbage**
**les choux de Bruxelles**
Brussels sprouts
le **chouchou** MASC NOUN
la **chouchoute** FEM NOUN
**teacher's pet**
la **choucroute** FEM NOUN
**sauerkraut with sausages and ham**
**_Did you know...?_**
**Sauerkraut** _is a kind of pickled cabbage._
**chouette**
**chouette** _can be an adjective or a noun._
**A** ADJECTIVE
**brilliant**
**Chouette alors!**
Brilliant
**B** FEM NOUN
**owl**
le **chou-fleur** MASC NOUN
**cauliflower**
**chrétien** MASC ADJECTIVE (FEM **chrétienne** )
**Christian**
le **chronomètre** MASC NOUN
**stopwatch**
le **chrysanthème** MASC NOUN
**chrysanthemum**
**_Did you know...?_**
_People in France put bunches of chrysanthemum flowers on graves, and wouldn't give them to someone as a present._
**chuchoter** VERB
**to whisper**
**chut** EXCLAMATION
**shh!**
**-ci** ADVERB
**ce livre-ci**
this book
**ces bottes-ci**
these boots
la **ciboulette** FEM NOUN
**chives**
la **cicatrice** FEM NOUN
**scar**
**ci-contre** ADVERB
**opposite**
**la page ci-contre**
the opposite page
**ci-dessous** ADVERB
**below**
**la photo ci-dessous**
the picture below
**ci-dessus** ADVERB
**above**
le **cidre** MASC NOUN
**cider**
le **ciel** MASC NOUN
**sky**
**un ciel nuageux**
a cloudy sky
le **cigare** MASC NOUN
**cigar**
la **cigarette** FEM NOUN
**cigarette**
le **cil** MASC NOUN
**eyelash**
le **cimetière** MASC NOUN
**cemetery**
le **cinéma** MASC NOUN
**cinema**
**cinq** NUMBER
**five**
**Il est cinq heures du matin.**
It's five in the morning.
**Il a cinq ans.**
He's five.
**le cinq février**
the fifth of February
la **cinquantaine** FEM NOUN
**about fifty**
**Il y a une cinquantaine de personnes dans la salle.**
There are about fifty people in the hall.
**Il a la cinquantaine.**
He's in his fifties.
**cinquante** NUMBER
**fifty**
**Il a cinquante ans.**
He's fifty.
**cinquante et un**
fifty-one
**cinquante-deux**
fifty-two
**cinquième**
**cinquième** _can be an adjective or a noun._
**A** ADJECTIVE
**fifth**
**au cinquième étage**
on the fifth floor
**B** FEM NOUN
**Year 8**
**Mon frère est en cinquième.**
My brother's in Year 8.
**_Did you know...?_**
_In French secondary schools and sixth form colleges, years are counted from the_ **sixième** _(youngest) to the_ **première** _and the_ **terminale** _(oldest)._
**circonflexe** ADJECTIVE
**un accent circonflexe**
a circumflex
la **circulation** FEM NOUN
**traffic**
**Il y a beaucoup de circulation.**
There is a lot of traffic.
le **cirque** MASC NOUN
**circus**
les **ciseaux** MASC PL NOUN
**une paire de ciseaux**
a pair of scissors
la **cité** FEM NOUN
**estate**
**J'habite dans une cité.**
I live on an estate.
**_Did you know...?_**
**une cité** _is an inner-city housing estate._
le **citron** MASC NOUN
**lemon**
**un citron vert**
a lime
**un citron pressé**
a fresh lemon juice
la **citrouille** FEM NOUN
**pumpkin**
**clair** MASC ADJECTIVE (FEM **claire** )
**light**
**vert clair**
light green
**C'est une pièce très claire.**
It's a very light room.
**clairement** ADVERB
**clearly**
la **claque** FEM NOUN
**slap**
**claquer** VERB
**to slam**
les **claquettes** FEM PL NOUN
**faire des claquettes**
to tap-dance
**Je fais des claquettes le samedi.**
I do tap on Saturdays.
la **clarinette** FEM NOUN
**clarinet**
**Élodie joue de la clarinette.**
Élodie plays the clarinet.
la **classe** FEM NOUN
**1** **class**
**C'est la meilleure élève de la classe.**
She's the best pupil in the class.
**un aller simple en première classe**
a first class single
**2** **classroom**
**classer** VERB
**to arrange**
le **classeur** MASC NOUN
**ring binder**
**classique** ADJECTIVE
**1** **classical**
**la musique classique**
classical music
**2** **classic**
le **clavier** MASC NOUN
**keyboard**
la **clé** FEM NOUN
**key**
la **clef** FEM NOUN
**key**
le **client** MASC NOUN
la **cliente** FEM NOUN
**customer**
le **climat** MASC NOUN
**climate**
le **clin d'œil** MASC NOUN
**wink**
la **clinique** FEM NOUN
**private hospital**
**cliquer** VERB
**to click**
**Clique sur une icône.**
Click on an icon.
la **cloche** FEM NOUN
**bell**
**les cloches de Pâques**
Easter bells
**_Did you know...?_**
_In France, Easter eggs are said to be brought by the Easter bells_ ( **cloches de Pâques** ) _that fly from Rome and drop them in people's gardens._
le **clocher** MASC NOUN
**1** **church tower**
**2** **steeple**
le **club** MASC NOUN
**club**
le **CM1** MASC NOUN
**Year 5**
le **CM2** MASC NOUN
**Year 6**
le **cobaye** MASC NOUN
**guinea pig**
le **coca** MASC NOUN
**Coke** ®
la **coccinelle** FEM NOUN
**ladybird**
**cocher** VERB
**to tick**
**Cochez la bonne réponse.**
Tick the right answer.
le **cochon** MASC NOUN
**pig**
**un cochon d'Inde**
a guinea pig
le **coco** MASC NOUN
**une noix de coco**
a coconut
**cocorico** EXCLAMATION
**1** **Cock-a-doodle-doo!**
**2** **Three cheers for France!**
**_Did you know...?_**
_The symbol of France is the cockerel and so_ **cocorico!** _is sometimes used as an expression of French national pride._
le **cœur** MASC NOUN
**heart**
**la dame de cœur**
the queen of hearts
**J'ai mal au cœur!**
I feel sick!
**Il faut l'apprendre par cœur.**
You must learn it by heart.
**Apprenez ce petit poème par cœur.**
Learn this little poem by heart.
le **coffre** MASC NOUN
**car boot**
**un coffre à jouets**
a toybox
le **coffret** MASC NOUN
**un coffret à bijoux**
a jewellery box
**coiffé** MASC ADJECTIVE (FEM **coiffée** )
**Tu es bien coiffée.**
Your hair looks nice.
se **coiffer** VERB
**Maman se coiffe.**
Mum is doing her hair.
le **coiffeur** MASC NOUN
la **coiffeuse** FEM NOUN
**hairdresser**
la **coiffure** FEM NOUN
**hairstyle**
**Cette coiffure te va bien.**
That hairstyle suits you.
**un salon de coiffure**
a hairdresser's
le **coin** MASC NOUN
**corner**
**au coin de la rue**
on the corner of the street
le **col** MASC NOUN
**collar**
la **colère** FEM NOUN
**anger**
**en colère**
angry
**Je suis en colère.**
I'm angry.
**Il va se mettre en colère.**
He's going to get angry.
le **colin-maillard** MASC NOUN
**blind man's buff**
le **colis** MASC NOUN
**parcel**
**collant**
**collant** _can be an adjective or a noun._
**A** MASC ADJECTIVE (FEM **collante** )
**sticky**
**B** MASC NOUN
**tights**
**un collant en laine**
woollen tights
la **colle** FEM NOUN
**glue**
la **collection** FEM NOUN
**collection**
**une collection d'autocollants**
a sticker collection
**collectionner** VERB
**to collect**
le **collège** MASC NOUN
**secondary school**
**_Did you know...?_**
_In France, pupils go to a_ **collège** _between the ages of 11 and 15, and then to a_ **lycée** _until the age of 18._
le **collégien** MASC NOUN
la **collégienne** FEM NOUN
**secondary school pupil**
le/la **collègue** MASC/FEM NOUN
**colleague**
**coller** VERB
**1** **to stick**
**Colle cette feuille dans ton cahier.**
Stick this piece of paper in your book.
**2** **to be sticky**
**Elle a les mains qui collent.**
Her hands are sticky.
le **collier** MASC NOUN
**1** **necklace**
**un collier de perles**
a pearl necklace
**2** **collar**
**Où est le collier du chien?**
Where's the dog's collar?
la **colline** FEM NOUN
**hill**
la **colonie de vacances** FEM NOUN
**summer camp**
**Je n'aime pas partir en colonie de vacances.**
I don't like going to summer camp.
**_Did you know...?_**
_French schoolchildren often go to a_ **colonie de vacances** _for a fortnight in the summer holidays._
la **colonne** FEM NOUN
**column**
**colorier** VERB
**to colour in**
**combien** ADVERB
**1** **how much**
**Vous en voulez combien? Un kilo?**
How much do you want? One kilo?
**Combien est-ce que ça coûte?**
How much does it cost?
**Ça fait combien?**
How much does it come to?
**C'est combien?**
How much is that?
**2** **how many**
**Tu en veux combien? Deux?**
How many do you want? Two?
**combien de**
how much/how many
**_Language tip_**
**combien de** _has two translations. Look at the examples._
**Tu reçois combien d'argent de poche?**
How much pocket money do you get?
**Tu as combien de frères et sœurs?**
How many brothers and sisters have you got?
**combien de temps**
how long
**Combien de temps est-ce que ça dure?**
How long does it last?
**On est le combien aujourd'hui?**
What's the date today?
la **combinaison** FEM NOUN
**une combinaison de plongée**
a wetsuit
**une combinaison de ski**
a ski suit
la **comédie** FEM NOUN
**comedy**
le **comédien** MASC NOUN
la **comédienne** FEM NOUN
**actor**
**_Language tip_**
Be careful! **comédien** does not mean the same as **comedian**.
**comique**
**comique** _can be an adjective or a noun._
**A** ADJECTIVE
**comical**
**B** MASC NOUN
**comedian**
**commander** VERB
**to order**
**J'ai commandé un steak frites.**
I ordered steak and chips.
**comme** CONJUNCTION, ADVERB
**1** **like**
**Il est comme son père.**
He's like his father.
**comme ça**
like this
**Ça se plie comme ça.**
You fold it like this.
**C'était un poisson grand comme ça.**
The fish was this big.
**2** **for**
**Qu'est-ce que tu veux comme dessert?**
What would you like for pudding?
**3** **as**
**Elle travaille comme serveuse.**
She works as a waitress.
**Fais comme tu veux.**
Do as you like.
**4** **how**
**Comme tu as grandi!**
How you've grown!
**Regarde comme c'est beau!**
Look, isn't it lovely!
**Comment ça va? — Comme ci comme ça.**
How are you? — Okay, I suppose.
**commencer** VERB
**to start**
**comment** ADVERB
**how**
**Comment dit-on 'apple' en français?**
How do you say 'apple' in French?
**Comment tu t'appelles?**
What's your name?
**Comment s'appelle-t-il?**
What's his name?
**Comment ça va?**
How are you?
**Comment?**
What did you say?
**Comment ça s'écrit?**
How do you spell it?
le **commerce** MASC NOUN
**business**
**Il fait des études de commerce.**
He's studying business.
**commercial** MASC ADJECTIVE
**un centre commercial**
a shopping centre
le **commissariat** MASC NOUN
**police station**
les **commissions** FEM PL NOUN
**shopping**
**J'ai quelques commissions à faire.**
I've got some shopping to do.
**commode** FEM NOUN
**chest of drawers**
**commun** MASC ADJECTIVE (FEM **commune** )
**en commun**
in common
**Ils n'ont rien en commun.**
They've got nothing in common.
**les transports en commun**
public transport
**compact** MASC ADJECTIVE (FEM **compacte** )
**compact**
**un disque compact**
a compact disc
la **compagnie** FEM NOUN
**company**
**une compagnie aérienne**
an airline
**comparer** VERB
**to compare**
le **compartiment** MASC NOUN
**compartment**
le **compas** MASC NOUN
**compasses**
**Je peux emprunter ton compas?**
Can I borrow your compasses?
la **compétition** FEM NOUN
**competition**
**une compétition de natation**
a swimming competition
**complet** MASC ADJECTIVE (FEM **complète** )
**full**
**L'hôtel est complet.**
The hotel is full.
**'complet'**
'no vacancies'
**le pain complet**
wholemeal bread
**complètement** ADVERB
**completely**
**compléter** VERB
**to complete**
**compliqué** MASC ADJECTIVE (FEM **compliquée** )
**complicated**
**composter** VERB
**to punch**
**Tu as composté ton billet?**
Have you punched your ticket?
**_Did you know...?_**
_In France, you have to punch your ticket before you get on the train. If you don't you might get a fine._
la **compote** FEM NOUN
**stewed fruit**
**la compote de pommes**
stewed apple
**comprendre** VERB
**to understand**
**Tu comprends?**
Do you understand?
**Je ne comprends pas!**
I don't understand!
le **comprimé** MASC NOUN
**tablet**
**compris**
**compris** _can be part of a verb or an adjective._
**A** VERB _see_ **comprendre**
**Je n'ai pas compris.**
I don't understand.
**B** MASC ADJECTIVE (FEM **comprise** )
**included**
**Le service n'est pas compris.**
Service is not included.
le/la **comptable** MASC/FEM NOUN
**accountant**
le **compte** MASC NOUN
**account**
**un compte bancaire**
a bank account
**Ma mère travaille à son compte.**
My mum is self-employed.
**compter** VERB
**to count**
se **concentrer** VERB
**to concentrate**
**Il faut te concentrer!**
You've got to concentrate!
le **concert** MASC NOUN
**concert**
le/la **concierge** MASC/FEM NOUN
**caretaker**
le **concombre** MASC NOUN
**cucumber**
le **concours** MASC NOUN
**competition**
**un concours de chant**
a singing competition
la **condition** FEM NOUN
**condition**
**Je vais le faire à une condition.**
I'll do it, on one condition.
le **conducteur** MASC NOUN
la **conductrice** FEM NOUN
**driver**
**conduire** VERB
**to drive**
**Ma grand-mère ne sait pas conduire.**
My grandma can't drive.
**Ma mère me conduit à l'école.**
My mum drives me to school.
**se conduire**
**to behave**
**Il se conduit mal en classe.**
He behaves badly in class.
les **confettis** MASC PL NOUN
**confetti**
la **confiance** FEM NOUN
**trust**
**Tu peux avoir confiance en moi.**
You can trust me.
**Je n'ai pas confiance en lui.**
I don't trust him.
la **confiserie** FEM NOUN
**sweet shop**
**confit** MASC ADJECTIVE (FEM **confite** )
**des fruits confits**
crystallized fruits
la **confiture** FEM NOUN
**jam**
**la confiture de fraises**
strawberry jam
**la confiture d'oranges**
marmalade
**confortable** ADJECTIVE
**comfortable**
**des chaussures confortables**
comfortable shoes
le **congé** MASC NOUN
**holiday**
**une semaine de congé**
a week's holiday
**en congé**
on holiday
le **congélateur** MASC NOUN
**freezer**
**congeler** VERB
**to freeze**
**connaître** VERB
**to know**
**Je ne la connais pas.**
I don't know her.
**se connecter** VERB
**to log on**
**Comment est-ce qu'on se connecte sur internet?**
How do you log on to the internet?
**connu** MASC ADJECTIVE (FEM **connue** )
**well-known**
**C'est un acteur connu.**
He's a well-known actor.
le **conseil** MASC NOUN
**advice**
**Est-ce que je peux te demander conseil?**
Can I ask you for some advice?
**un conseil**
a piece of advice
**conseiller** VERB
**1** **to advise**
**Qu'est-ce que tu me conseilles de faire?**
What do you advise me to do?
**2** **to recommend**
**Je te conseille ce livre.**
I recommend this book.
le **conseiller** MASC NOUN
la **conseillère** FEM NOUN
**adviser**
**le conseiller d'orientation**
the careers adviser
le **conservatoire** MASC NOUN
**school of music**
la **conserve** FEM NOUN
**tin**
**une boîte de conserve**
a tin
**en conserve**
tinned
**des petits pois en conserve**
tinned peas
la **consigne** FEM NOUN
**left-luggage office**
**une consigne automatique**
a left-luggage locker
la **console de jeu** FEM NOUN
**games console**
**constamment** ADVERB
**constantly**
**construire** VERB
**to build**
**contacter** VERB
**to get in touch with**
**Tu peux me contacter par courrier électronique.**
You can get in touch with me by email.
le **conte de fées** MASC NOUN
**fairy tale**
**content** MASC ADJECTIVE (FEM **contente** )
**happy**
**Je suis content pour toi.**
I'm happy for you.
**content de**
pleased with
**Elle est contente de mon travail.**
She is pleased with my work.
**continuer** VERB
**to carry on**
**Continuez sans moi!**
Carry on without me!
le **contraire** MASC NOUN
**opposite**
**Il fait le contraire de ce que je lui demande.**
He does the opposite of what I ask him to.
**au contraire**
on the contrary
**contre** PREPOSITION
**against**
**Ne mets pas ton vélo contre le mur.**
Don't put your bike against the wall.
**Je suis contre cette idée.**
I'm against this idea.
**par contre**
on the other hand
la **contrebasse** FEM NOUN
**double bass**
**Je joue de la contrebasse.**
I play the double bass.
le **contrôle** MASC NOUN
**1** **control**
**le contrôle des passeports**
passport control
**2** **check**
**un contrôle d'identité**
an identity check
**le contrôle des billets**
ticket inspection
**contrôler** VERB
**to check**
le **contrôleur** MASC NOUN
la **contrôleuse** FEM NOUN
**ticket inspector**
la **conversation** FEM NOUN
**conversation**
**cool** MASC, FEM, PL ADJECTIVE
**cool**
**J'adore le français. C'est vraiment cool.**
I love French. It's really cool.
le **copain** MASC NOUN
**1** **friend**
**C'est un bon copain.**
He's a good friend.
**2** **boyfriend**
**Elle a un nouveau copain.**
She's got a new boyfriend.
la **copie** FEM NOUN
**1** **copy**
**2** **paper**
**Rendez vos copies!**
Hand in your papers!
**copier** VERB
**to copy**
**copier-coller**
to copy and paste
la **copine** FEM NOUN
**1** **friend**
**C'est une bonne copine.**
She's a good friend.
**2** **girlfriend**
**Il a une nouvelle copine.**
He's got a new girlfriend.
le **coq** MASC NOUN
**cockerel**
**_Did you know...?_**
_The cockerel is the symbol of France._
la **coque** FEM NOUN
**un œuf à la coque**
a soft-boiled egg
le **coquelicot** MASC NOUN
**poppy**
le **coquillage** MASC NOUN
**shell**
la **coquille** FEM NOUN
**shell**
**une coquille Saint-Jacques**
a scallop
**coquin** MASC ADJECTIVE (FEM **coquine** )
**cheeky**
le **corbeau** MASC NOUN
(PL les **corbeaux** )
**crow**
la **corbeille** FEM NOUN
**basket**
**une corbeille à papier**
a wastepaper basket
la **corde** FEM NOUN
**rope**
la **cordonnerie** FEM NOUN
**shoe repair shop**
le **cordonnier** MASC NOUN
**cobbler**
la **cornemuse** FEM NOUN
**bagpipes**
**Je joue de la cornemuse.**
I play the bagpipes.
le **cornet** MASC NOUN
**un cornet de frites**
a bag of chips
**un cornet de glace**
an ice cream cone
le **cornichon** MASC NOUN
**gherkin**
la **Cornouailles** FEM NOUN
**Cornwall**
le **corps** MASC NOUN
**body**
**correct** MASC ADJECTIVE (FEM **correcte** )
**correct**
**Est-ce que cette phrase est correcte?**
Is this sentence correct?
la **correspondance** FEM NOUN
**connection**
**Il y a une correspondance pour Toulouse à dix heures.**
There's a connection for Toulouse at ten o'clock.
le **correspondant** MASC NOUN
la **correspondante** FEM NOUN
**penfriend**
**correspondre** VERB
**to correspond**
**corriger** VERB
**to mark**
**Vous pouvez corriger cet exercice?**
Could you mark this exercise?
**corse** ADJECTIVE
**Corsican**
le/la **Corse** MASC/FEM NOUN
**Corsican**
la **Corse** FEM NOUN
**Corsica**
le **costume** MASC NOUN
**1** **man's suit**
**Fabien ne porte pas souvent de costume.**
Fabien doesn't often wear a suit.
**2** **costume**
**Je prépare mon costume pour le carnaval.**
I'm making my costume for the carnival.
la **côte** FEM NOUN
**1** **coastline**
**La route longe la côte.**
The road follows the coastline.
**la Côte d'Azur**
the French Riviera
**2** **hill**
**La maison est en haut d'une côte.**
The house is at the top of a hill.
**3** **rib**
**Elle a une côte cassée.**
She has a broken rib.
**4** **chop**
**une côte de porc**
a pork chop
**une côte de bœuf**
a rib of beef
**côte à côte**
side by side
le **côté** MASC NOUN
**side**
**de l'autre côté**
on the other side
**La pharmacie est de l'autre côté de la rue.**
The chemist's is on the other side of the street.
**à côté de**
next to/next door to
**_Language tip_**
**à côté de** _has two translations. Look at the examples._
**La poste est à côté du supermarché.**
The post office is next to the supermarket.
**Il habite à côté de chez moi.**
He lives next door to me.
la **côtelette** FEM NOUN
**chop**
**une côtelette d'agneau**
a lamb chop
le **coton** MASC NOUN
**cotton**
**une chemise en coton**
a cotton shirt
**le coton hydrophile**
cotton wool
le **coton-tige** ® MASC NOUN
**cotton bud**
le **cou** MASC NOUN
**neck**
**couchant** MASC ADJECTIVE
**le soleil couchant**
the setting sun
la **couche** FEM NOUN
**nappy**
**couché** MASC ADJECTIVE (FEM **couchée** )
**1** **lying down**
**Le chien est couché sur le tapis.**
The dog is lying down on the rug.
**2** **in bed**
**Tu es déjà couché?**
Are you in bed already?
le **coucher** MASC NOUN
**un coucher de soleil**
a sunset
se **coucher** VERB
**1** **to go to bed**
**Il faut se coucher tôt ce soir.**
You must go to bed early tonight.
**Tu te couches à quelle heure?**
What time do you go to bed?
**Je me couche à neuf heures.**
I go to bed at nine.
**2** **to set**
**Le soleil se couche vers neuf heures.**
The sun sets at around 9 o'clock.
la **couchette** FEM NOUN
**berth**
le **coude** MASC NOUN
**elbow**
**coudre** VERB
**to sew**
**Tu sais coudre?**
Can you sew?
la **couette** FEM NOUN
**duvet**
**les couettes**
bunches
**Ma petite sœur a des couettes.**
My little sister has bunches.
**couler** VERB
**1** **to run**
**J'ai le nez qui coule.**
My nose is running.
**2** **to flow**
**La rivière coule lentement.**
The river flows slowly.
**3** **to leak**
**Mon stylo coule.**
My pen's leaking.
**4** **to sink**
**Un bateau a coulé pendant la tempête.**
A boat sank during the storm.
la **couleur** FEM NOUN
**colour**
**De quelle couleur est ton stylo?**
What colour is your pen?
**Elle a les yeux de quelle couleur?**
What colour eyes has she got?
**C'est de quelle couleur?**
What colour is it?
le **couloir** MASC NOUN
**corridor**
le **coup** MASC NOUN
**1** **knock**
**2** **blow**
**un coup sur la tête**
a blow to the head
**du premier coup**
first time
**Il a eu son permis du premier coup.**
He passed his driving test first time.
**_Language tip_**
_There are lots of_ **coup de** _combinations of words. Look through this list to find the one you need._
**un coup de pied**
a kick
**un coup de poing**
a punch
**un coup de feu**
a shot
**un coup de fil**
a ring
**Donne-moi un coup de fil
ce soir.**
Give me a ring this evening.
**Tu peux me donner un coup de main?**
Can you give me a hand?
**Tu vas prendre un coup de soleil!**
You'll get sunburnt!
**un coup de téléphone**
a phone call
**un coup de tonnerre**
a clap of thunder
**coupable**
**coupable** _can be an adjective or a noun._
**A** ADJECTIVE
**guilty**
**B** MASC/FEM NOUN
**culprit**
la **coupe** FEM NOUN
**cup**
**la coupe du monde**
the World Cup
**une coupe de cheveux**
a haircut
**une coupe de champagne**
a glass of champagne
**couper** VERB
**to cut**
**Attention! Tu vas te couper!**
Careful! You're going to cut yourself!
**Je vais me faire couper les cheveux.**
I'm going to get my hair cut.
le **couple** MASC NOUN
**couple**
le **couplet** MASC NOUN
**verse**
**le premier couplet**
the first verse
la **coupure** FEM NOUN
**cut**
**une coupure de courant**
a power cut
la **cour** FEM NOUN
**yard**
**la cour de l'école**
the playground
**courageux** MASC ADJECTIVE (FEM **courageuse** )
**brave**
**couramment** ADVERB
**fluently**
**Elle parle couramment japonais.**
She speaks Japanese fluently.
**courant**
**courant** _can be an adjective or a noun._
**A** MASC ADJECTIVE
(FEM **courante** )
**common**
**'Marie' est un prénom courant.**
'Marie' is a common name.
**B** MASC NOUN
**1** **current**
**Le courant est fort.**
The current is strong.
**un courant d'air**
a draught
**2** **power**
**une panne de courant**
a power cut
**Tu es au courant?**
Have you heard about it?
le **coureur** MASC NOUN
la **coureuse** FEM NOUN
**runner**
**un coureur à pied**
a runner
**un coureur cycliste**
a racing cyclist
**un coureur automobile**
a racing driver
**courir** VERB
**to run**
**Ne courez pas dans le couloir.**
Don't run in the corridor.
**J'ai couru jusqu'à l'école.**
I ran all the way to school.
la **couronne** FEM NOUN
**crown**
**courons, courez** VERB _see_ **courir**
**Courons jusqu'à la barrière!**
Let's run as far as the gate!
**Vous courez trop vite!**
You're running too fast!
le **courriel** MASC NOUN
**email**
le **courrier** MASC NOUN
**mail**
**Le facteur apporte le courrier à huit heures.**
The postman brings the mail at 8 o'clock.
**le courrier électronique**
email
le **cours** MASC NOUN
**1** **lesson**
**un cours d'espagnol**
a Spanish lesson
**2** **class**
**un cours du soir**
an evening class
**3** **rate**
**le cours du change**
the exchange rate
la **course** FEM NOUN
**1** **running**
**la course de fond**
long-distance running
**2** **race**
**une course hippique**
a horse race
**3** **shopping**
**J'ai juste une course à faire.**
I've just got a bit of shopping to do.
**faire les courses**
to shop
**Je n'aime pas faire les courses au supermarché.**
I don't like shopping in supermarkets.
**court**
**court** _can be an adjective or a noun._
**A** MASC ADJECTIVE (FEM **courte** )
**short**
**B** MASC NOUN
**un court de tennis**
a tennis court
**couru** VERB _see_ **courir**
**J'ai couru jusqu'à la maison.**
I ran all the way home.
le **couscous** MASC NOUN
**couscous**
**_Did you know...?_**
**couscous** _is a grain from North Africa which is often eaten with spicy food._
le **cousin** MASC NOUN
la **cousine** FEM NOUN
**cousin**
le **coussin** MASC NOUN
**cushion**
le **couteau** MASC NOUN
(PL les **couteaux** )
**knife**
**coûter** VERB
**to cost**
**Est-ce que ça coûte cher?**
Does it cost a lot?
**Combien ça coûte?**
How much is it?
la **couture** FEM NOUN
**sewing**
**Je n'aime pas la couture.**
I don't like sewing.
le **couvercle** MASC NOUN
**1** **lid**
**le couvercle de la casserole**
the lid of the pan
**2** **top**
**le couvercle du pot de confiture**
the top of the jam jar
**couvert**
**couvert** _can be an adjective, a noun or part of the verb_ **couvrir**.
**A** MASC ADJECTIVE
(FEM **couverte** )
**overcast**
**Le ciel est couvert.**
The sky is overcast.
**couvert de**
covered with
**un arbre couvert de fleurs**
a tree covered with blossom
**B** MASC NOUN
**les couverts**
cutlery
**Les couverts sont dans le tiroir de gauche.**
The cutlery is in the left-hand drawer.
**C** VERB _see_ **couvrir**
**Il est couvert de boutons.**
He's covered with spots.
la **couverture** FEM NOUN
**blanket**
le **couvre-lit** MASC NOUN
**bedspread**
**couvrir** VERB
**to cover**
**Le chien est revenu couvert de boue.**
The dog came back covered in mud.
**se couvrir**
**to wrap up/to cloud over**
**_Language tip_**
**se couvrir** _has two translations. Look at the examples._
**Couvre-toi bien: il fait froid dehors.**
Wrap up well: it's cold outside.
**Le ciel se couvre.**
The sky's clouding over.
le **CP** MASC NOUN
**Year 2**
le **crabe** MASC NOUN
**crab**
**cracher** VERB
**to spit**
la **craie** FEM NOUN
**chalk**
**craindre** VERB
**to fear**
**Tu n'as rien à craindre.**
You've got nothing to fear.
**craintif** MASC ADJECTIVE (FEM **craintive** )
**timid**
la **crampe** FEM NOUN
**cramp**
**J'ai une crampe au pied.**
I've got cramp in my foot.
le **crapaud** MASC NOUN
**toad**
la **cravate** FEM NOUN
**tie**
le **crayon** MASC NOUN
**pencil**
**un crayon de couleur**
a coloured pencil
**un crayon feutre**
a felt-tip pen
la **crèche** FEM NOUN
**1** **nursery**
**Ma petite sœur va à la crèche.**
My little sister goes to nursery.
**2** **nativity scene**
**créer** VERB
**to create**
la **crème** FEM NOUN
**cream**
**la crème anglaise**
custard
**la crème Chantilly**
whipped cream
**une crème caramel**
a crème caramel
**une crème au chocolat**
a chocolate dessert
le **crème** MASC NOUN
**white coffee**
**un grand crème**
a large white coffee
la **crêpe** FEM NOUN
**pancake**
la **crêperie** FEM NOUN
**pancake restaurant**
le **cresson** MASC NOUN
**watercress**
la **Crète** FEM NOUN
**Crete**
**creuser** VERB
**to dig**
**crevé** MASC ADJECTIVE (FEM **crevée** )
**1** **punctured**
**un pneu crevé**
a puncture
**2** **knackered**
**Je suis complètement crevé!**
I'm really knackered!
**crever** VERB
**1** **to burst**
**Il a crevé mon ballon!**
He's burst my balloon!
**2** **to have a puncture**
**On a crevé en route.**
We had a puncture on the way.
la **crevette** FEM NOUN
**prawn**
le **cri** MASC NOUN
**scream**
**crier** VERB
**to shout**
le **crime** MASC NOUN
**1** **crime**
**2** **murder**
le **criquet** MASC NOUN
**grasshopper**
la **crise** FEM NOUN
**attack**
**une crise d'asthme**
an asthma attack
**une crise de foie**
an upset stomach
**critiquer** VERB
**to criticize**
le **crocodile** MASC NOUN
**crocodile**
**croire** VERB
**to believe**
**Je ne te crois pas.**
I don't believe you.
**Tu l'as cru?**
Did you believe him?
**croire que**
to think that
**Tu crois que c'est vrai?**
Do you think that's true?
**Il croit en Dieu.**
He believes in God.
**crois** VERB _see_ **croire**
**Je crois que tu as raison.**
I think you're right.
le **croisement** MASC NOUN
**crossroads**
**Tournez à gauche au croisement.**
Turn left at the crossroads.
**croiser** VERB
**croiser les bras**
to fold one's arms
**croiser les jambes**
to cross one's legs
**se croiser**
**to pass each other**
**Nous nous croisons dans la rue tous les matins.**
We pass each other on the street every morning.
le **croissant** MASC NOUN
**croissant**
**croit** VERB _see_ **croire**
**Il croit encore au Père Noël!**
He still believes in Santa!
la **croix** FEM NOUN
**cross**
le **croque-madame** MASC NOUN
le **croque-monsieur** MASC NOUN
**_Did you know...?_**
A **croque-monsieur** _is a toasted ham and cheese sandwich. A_ **croque-madame** _has an added fried egg._
**croquer** VERB
**to munch**
la **croûte** FEM NOUN
**1** **crust**
**en croûte**
in pastry
**2** **rind**
**Mon chat aime la croûte du fromage.**
My cat likes cheese rind.
**3** **scab**
**J'ai une croûte sur le genou.**
I've got a scab on my knee.
le **croûton** MASC NOUN
**1** **end of a baguette**
**2** **crouton**
**Tu veux des croûtons dans ta soupe?**
Would you like some croutons in your soup?
**cru**
**cru** _can be an adjective or part of the verb_ **croire**.
**A** MASC ADJECTIVE (FEM **crue** )
**raw**
**la viande crue**
raw meat
**le jambon cru**
Parma ham
**B** VERB _see_ **croire**
**Je l'ai cru.**
I believed him.
la **cruche** FEM NOUN
**jug**
les **crudités** FEM PL NOUN
**assorted raw vegetables**
**cruel** MASC ADJECTIVE (FEM **cruelle** )
**cruel**
les **crustacés** MASC PL NOUN
**shellfish**
le **cube** MASC NOUN
**cube**
**cueillir** VERB
**to pick**
**J'ai cueilli des fleurs dans le jardin.**
I picked some flowers in the garden.
la **cuiller** FEM NOUN
la **cuillère**
**spoon**
**une cuiller à café**
a teaspoon
**une cuiller à soupe**
a tablespoon
la **cuillerée** FEM NOUN
**spoonful**
le **cuir** MASC NOUN
**leather**
**un sac en cuir**
a leather bag
**cuire** VERB
**to cook**
**faire cuire**
to cook
**'faire cuire pendant une heure'**
'cook for one hour'
**bien cuit**
well done
**trop cuit**
overdone
la **cuisine** FEM NOUN
**1** **kitchen**
**La cuisine est très grande.**
The kitchen is very big.
**2** **food**
**Tu aimes la cuisine française?**
Do you like French food?
**faire la cuisine**
to cook
**Je ne fais jamais la cuisine.**
I never cook.
**cuisiner** VERB
**to cook**
**J'aime beaucoup cuisiner.**
I love cooking.
le **cuisinier** MASC NOUN
**cook**
la **cuisinière** FEM NOUN
**1** **cook**
**C'est une bonne cuisinière.**
She's a good cook.
**2** **cooker**
**une cuisinière à gaz**
a gas cooker
la **cuisse** FEM NOUN
**thigh**
**une cuisse de poulet**
a chicken leg
la **cuisson** FEM NOUN
**cooking**
**'une heure de cuisson'**
'cooking time: one hour'
**cuit** VERB _see_ **cuire**
**Est-ce que c'est cuit?**
Is it cooked?
le **cuivre** MASC NOUN
**copper**
la **culotte** FEM NOUN
**knickers**
le **cultivateur** MASC NOUN
la **cultivatrice** FEM NOUN
**farmer**
**cultiver** VERB
**to grow**
**Il cultive des légumes.**
He grows vegetables.
le **curé** MASC NOUN
**parish priest**
**curieux** MASC ADJECTIVE (FEM **curieuse** )
**curious**
le **curseur** MASC NOUN
**cursor**
le **cybercafé** MASC NOUN
**internet café**
**cyclable** ADJECTIVE
**une piste cyclable**
a cycle track
le **cyclisme** MASC NOUN
**cycling**
le/la **cycliste** MASC/FEM NOUN
**cyclist**
le **cyclone** MASC NOUN
**hurricane**
le **cygne** MASC NOUN
**swan**
# **D d**
**d'**
**d'** _can be an article or a preposition._
**_Language tip_**
**de** _changes to_ **d'** _before a vowel sound. See also_ **du (=de+le)** _and_ **des (=de+les)**.
**A** ARTICLE
**any**
**Je n'ai pas d'argent.**
I haven't got any money.
**Je n'ai pas d'animal domestique à la maison.**
I haven't got a pet.
**B** PREPOSITION
**1** **of**
**une bouteille d'orangina**
a bottle of orangina
**la voiture d'Hélène**
Hélène's car
**un bébé d'un an**
a one-year-old baby
**2** **from**
**une lettre d'Olivier**
a letter from Olivier
le **daim** MASC NOUN
**suede**
**une veste en daim**
a suede jacket
la **dame** FEM NOUN
**1** **lady**
**une dame de service**
a dinner lady
**2** **queen**
**la dame de pique**
the queen of spades
**les dames**
draughts
**un jeu de dames**
a game of draughts
le **Danemark** MASC NOUN
**Denmark**
**dangereux** MASC ADJECTIVE (FEM **dangereuse** )
**dangerous**
**danois** MASC NOUN, MASC ADJECTIVE (FEM **danoise** )
**Danish**
le **Danois** MASC NOUN
la **Danoise** FEM NOUN
**Dane**
**dans** PREPOSITION
**in**
**Il est dans sa chambre.**
He's in his bedroom.
**dans deux mois**
in two months
la **danse** FEM NOUN
**dance**
**la danse classique**
ballet
**Je fais de la danse.**
I go to dancing classes.
**danser** VERB
**to dance**
le **danseur** MASC NOUN
la **danseuse** FEM NOUN
**dancer**
la **date** FEM NOUN
**date**
**Quelle est ta date de naissance?**
What's your date of birth?
**Quelle est la date de ton anniversaire?**
What date is your birthday?
**Quelle est la date aujourd'hui?**
What's the date today?
le **dauphin** MASC NOUN
**dolphin**
**de**
**de** _can be an article or a preposition._
**_Language tip_**
**de** _changes to_ **d'** _before a vowel sound. See also_ **du (=de+le)** _and_ **des (=de+les)**.
**A** ARTICLE
**_Language tip_**
_You can use_ **de** _to mean either_ **some** _or_ **any**.
**Je voudrais de l'eau.**
I'd like some water.
**du pain et de la confiture**
bread and jam
**Il n'a pas de frères et sœurs.**
He hasn't got any brothers or sisters.
**Il n'y a plus de biscuits.**
There aren't any more biscuits.
**B** PREPOSITION
**1** **of**
**un paquet de biscuits**
a packet of biscuits
**la voiture de Paul**
Paul's car
**la voiture de mes parents**
my parents' car
**un billet de dix euros**
a ten-euro note
**2** **from**
**de Londres à Paris**
from London to Paris
**Il vient de Londres.**
He comes from London.
**une lettre de Victor**
a letter from Victor
**3** **in**
**à une heure de l'après-midi**
at one o'clock in the afternoon
le **dé** MASC NOUN
**dice**
**Lance le dé.**
Throw the dice.
**débarrasser** VERB
**to clear**
**Tu peux débarrasser la table, s'il te plaît?**
Can you clear the table please?
**debout** ADVERB
**Debout!**
Get up!
le **début** MASC NOUN
**beginning**
**au début**
at the beginning
**début mai**
in early May
le **débutant** MASC NOUN
la **débutante** FEM NOUN
**beginner**
le **décalage horaire** MASC NOUN
**time difference**
**Il y a une heure de décalage horaire entre la France et la Grande-Bretagne.**
There's an hour's time difference between France and Britain.
**décalquer** VERB
**to trace**
**Décalquez la carte de France.**
Trace the map of France.
**décapotable** ADJECTIVE
**une voiture décapotable**
a convertible
**décembre** MASC NOUN
**December**
**en décembre**
in December
**le dix décembre**
the tenth of December
**décevoir** VERB
**to disappoint**
**déchirer** VERB
**to tear**
**Le poster est tout déchiré.**
The poster is all torn.
**décider** VERB
**to decide**
**J'ai décidé d'y aller.**
I've decided to go.
le **décollage** MASC NOUN
**takeoff**
**décoller** VERB
**to take off**
**L'avion a décollé avec dix minutes de retard.**
The plane took off ten minutes late.
se **décontracter** VERB
**to relax**
**Il fait du yoga pour se décontracter.**
He goes to yoga to relax.
le **décorateur** MASC NOUN
la **décoratrice** FEM NOUN
**interior decorator**
les **décorations** FEM PL NOUN
**decorations**
**les décorations de Noël**
the Christmas decorations
**décorer** VERB
**to decorate**
**découper** VERB
**to cut out**
se **décourager** VERB
**Ne te décourage pas!**
Don't give up!
la **découverte** FEM NOUN
**discovery**
**découvrir** VERB
**to discover**
**Christophe Colomb a découvert l'Amérique en 1492.**
Christopher Colombus discovered America in 1492.
**décrire** VERB
**to describe**
**Décris quelqu'un de célèbre.**
Describe somebody famous.
**déçu** MASC ADJECTIVE
(FEM **déçue** )
**disappointed**
**dedans** ADVERB
**inside**
**C'est une jolie boîte: qu'est-ce qu'il y a dedans?**
That's a nice box: what's in it?
**défendre** VERB
**1** **to defend**
**Il ne sait pas se défendre.**
He doesn't know how to defend himself.
**2** **to forbid**
**Je te défends de lui dire.**
I forbid you to tell her.
**défendu** MASC ADJECTIVE (FEM **défendue** )
**forbidden**
**C'est défendu.**
It's not allowed.
la **défense** FEM NOUN
**tusk**
**une défense d'éléphant**
an elephant's tusk
**'défense de fumer'**
'no smoking'
le **défilé** MASC NOUN
**parade**
**un défilé de mode**
a fashion show
**dégoûtant** MASC ADJECTIVE (FEM **dégoûtante** )
**disgusting**
le **degré** MASC NOUN
**degree**
**Il fait trente degrés à l'ombre.**
It's thirty degrees in the shade.
le **déguisement** MASC NOUN
**dressing-up costume**
**un déguisement de sorcière**
a witch's costume
se **déguiser** VERB
**to dress up**
**J'aime me déguiser.**
I like dressing up.
la **dégustation** FEM NOUN
**tasting**
**dehors** ADVERB
**outside**
**Je t'attends dehors.**
I'll wait for you outside.
**déjà** ADVERB
**1** **already**
**J'ai déjà fini.**
I've already finished.
**2** **before**
**Tu es déjà venu en France?**
Have you been to France before?
**déjeuner**
**déjeuner** _can be a noun or a verb._
**A** MASC NOUN
**lunch**
**Pour le déjeuner, je mange souvent un sandwich.**
I often have a sandwich for lunch.
**B** VERB
**to have lunch**
**Je déjeune à midi et demi.**
I have lunch at half past twelve.
le **délégué** MASC NOUN
la **déléguée** FEM NOUN
**representative**
**les délégués de classe**
the class representatives
**_Did you know...?_**
_In French schools, each class elects two_ **délégués de classe** , _one boy and one girl._
**délicieux** MASC ADJECTIVE (FEM **délicieuse** )
**delicious**
le **deltaplane** MASC NOUN
**hang-glider**
**J'aimerais faire du deltaplane.**
I'd like to go hang-gliding.
**demain** ADVERB
**tomorrow**
**À demain!**
See you tomorrow!
**demander** VERB
**to ask for**
**J'ai demandé la permission.**
I've asked for permission.
**Je vais demander à mes parents si je peux sortir.**
I'll ask my parents if I can go out.
**_Language tip_**
_Be careful!_
**demander** _does not mean the same as_ **to demand**.
**se demander**
**to wonder**
**Je me demande quelle heure il est.**
I wonder what time it is.
le **déménagement** MASC NOUN
**move**
**un camion de déménagement**
a removal van
**déménager** VERB
**to move house**
**Nous déménageons dans un mois.**
We're moving house in a month's time.
le **déménageur** MASC NOUN
**removal man**
**demi** MASC ADJECTIVE (FEM **demie** )
**half**
**Il a trois ans et demi.**
He's three and a half.
**Il est trois heures et demie.**
It's half past three.
**Il est midi et demi.**
It's half past twelve.
la **demi-baguette** FEM NOUN
**half a baguette**
le **demi-cercle** MASC NOUN
**semicircle**
**en demi-cercle**
in a semicircle
la **demi-douzaine** FEM NOUN
**half a dozen**
**une demi-douzaine d'œufs**
half a dozen eggs
la **demi-finale** FEM NOUN
**semifinal**
le **demi-frère** MASC NOUN
**half-brother**
**mon demi-frère**
my half brother
la **demi-heure** FEM NOUN
**half an hour**
**dans une demi-heure**
in half an hour
**toutes les demi-heures**
every half an hour
le **demi-litre** MASC NOUN
**half a litre**
**un demi-litre de lait**
half a litre of milk
la **demi-livre** FEM NOUN
**half a pound**
**une demi-livre de tomates**
half a pound of tomatoes
**_Did you know...?_**
_A_ **demi-livre** _is 250g._
le/la **demi-pensionnaire** MASC/FEM NOUN
**_Did you know...?_**
_In French secondary schools, pupils are described as_ **externe** _if they go home for lunch,_ **demi-pensionnaire** _if they have a school lunch, or_ **interne** _if they stay at the school as a boarder._
**demi-sel** MASC, FEM, PL ADJECTIVE
**du beurre demi-sel**
slightly salted butter
la **demi-sœur** FEM NOUN
**half-sister**
**ma demi-soeur**
my half-sister
le **demi-tour** MASC NOUN
**faire demi-tour**
to turn back
**Il est temps de faire demi-tour.**
It's time we turned back.
**démodé** MASC ADJECTIVE (FEM **démodée** )
**old-fashioned**
la **demoiselle** FEM NOUN
**young lady**
**une demoiselle d'honneur**
a bridesmaid
**démolir** VERB
**to demolish**
la **dent** FEM NOUN
**tooth**
**une dent de lait**
a milk tooth
**une dent de sagesse**
a wisdom tooth
la **dentelle** FEM NOUN
**lace**
le **dentifrice** MASC NOUN
**toothpaste**
le/la **dentiste** MASC/FEM NOUN
**dentist**
le **dépanneur** MASC NOUN ( _Canada_ )
**convenience store**
la **dépanneuse** FEM NOUN
**breakdown lorry**
le **départ** MASC NOUN
**departure**
**Le départ est à onze heures quinze.**
The departure is at 11.15.
**Je vais lui téléphoner la veille de son départ.**
I'll phone him the day before he leaves.
le **département** MASC NOUN
**1** **administrative region**
**le département du Vaucluse**
the Vaucluse département
**_Did you know...?_**
_France is divided into 96_ **départements** , _which are similar to counties in the UK._
**2** **department**
**le département d'anglais à l'université**
the English department at the university
se **dépêcher** VERB
**to hurry**
**Dépêche-toi!**
Hurry up!
**dépendre** VERB
**Ça dépend du temps.**
It depends on the weather.
**dépenser** VERB
**to spend**
**J'ai dépensé tout mon argent.**
I've spent all my money.
le **dépliant** MASC NOUN
**leaflet**
**déposer** VERB
**to drop**
**Tu peux me déposer à la piscine?**
Can you drop me at the swimming pool?
**depuis** PREPOSITION
**1** **since**
**J'habite à Paris depuis 2005.**
I've been living in Paris since 2005.
**depuis que**
since
**Il a plu tous les jours depuis qu'il est arrivé.**
It's rained every day since he arrived.
**2** **for**
**Il habite Paris depuis cinq ans.**
He's been living in Paris for five years.
**3** **Tu le connais depuis combien de temps?**
How long have you known him?
**Tu le connais depuis quand?**
How long have you known him?
**Depuis quand?**
How long?
**depuis 2006**
since 2006
**Depuis combien de temps?**
How long?
**depuis cinq ans**
for five years
**déranger** VERB
**1** **to bother**
**Excusez-moi de vous déranger.**
I'm sorry to bother you.
**2** **to mess up**
**Ne dérange pas mes livres, s'il te plaît.**
Don't mess up my books, please.
**dernier** MASC ADJECTIVE (FEM **dernière** )
**1** **last**
**Il est arrivé dernier.**
He arrived last.
**la dernière fois**
the last time
**en dernier**
last
**Ajoutez le lait en dernier.**
Put the milk in last.
**2** **latest**
**le dernier film de Spielberg**
Spielberg's latest film
**derrière**
**derrière** _can be a preposition, an adverb or a noun._
**A** PREPOSITION, ADVERB
**behind**
**derrière moi**
behind me
**derrière la télévision**
behind the television
**Devant ou derrière?**
In front or behind?
**B** MASC NOUN
**1** **back**
**la porte de derrière**
the back door
**2** **backside**
**un coup de pied dans le derrière**
a kick up the backside
**des** ARTICLE
**_Language tip_**
**des** _is made up of **de + les**._
**1** **some**
**Tu veux des chips?**
Would you like some crisps?
**_Language tip_**
**des** _is sometimes not translated in English._
**J'ai des cousins en France.**
I have cousins in France.
**pendant des mois**
for months
**2** **any**
**Tu as des frères?**
Have you got any brothers?
**3** **of the**
**la fin des vacances**
the end of the holidays
**la voiture des Durand**
the Durands' car
**4** **from**
**Il arrive des États-Unis.**
He's arriving from the United States.
**dès** PREPOSITION
**from**
**dès le mois de novembre**
from November
**dès le début**
right from the start
**dès que**
as soon as
**Appelle-moi dès que tu arrives.**
Phone me as soon as you get there.
**Je t'appelle dès mon retour.**
I'll phone you as soon as I get back.
**désagréable** ADJECTIVE
**unpleasant**
le **désastre** MASC NOUN
**disaster**
**descendre** VERB
**1** **to go down**
**Je suis tombé en descendant l'escalier.**
I fell as I was going down the stairs.
**2** **to come down**
**Attends en bas; je descends!**
Wait downstairs; I'm coming down!
**3** **to get down**
**Vous pouvez descendre ma valise, s'il vous plaît?**
Can you get my suitcase down, please?
**4** **to get off**
**Nous descendons à la prochaine station.**
We're getting off at the next station.
la **descente** FEM NOUN
**slope**
**une descente abrupte**
a steep slope
**_Language tip_**
**descente** _is related to the verb_ **descendre** _which means 'to go down', so_ **une descente** _is a slope that goes downhill._
la **description** FEM NOUN
**description**
**désert**
**désert** _can be an adjective or a noun._
**A** MASC ADJECTIVE (FEM **déserte** )
**deserted**
**Le dimanche, le centre commercial est désert.**
On Sundays the shopping centre is deserted.
**une île déserte**
a desert island
**B** MASC NOUN
**desert**
**le désert du Sahara**
the Sahara desert
**déshabiller** VERB
**to undress**
**se déshabiller**
**to get undressed**
**Déshabille-toi, mets ton pyjama et vas te coucher.**
Get undressed, put on your pyjamas and go to bed.
**désirer** VERB
**to want**
**Vous désirez? — Je voudrais un coca.**
What would you like? — I'd like a coke.
**désolé** MASC ADJECTIVE (FEM **désolée** )
**sorry**
**Je suis vraiment désolé.**
I'm very sorry.
**Désolé!**
Sorry!
**désordonné** MASC ADJECTIVE (FEM **désordonnée** )
**untidy**
le **désordre** MASC NOUN
**untidiness**
**Quel désordre!**
What a mess!
**en désordre**
in a mess
**Sa chambre est toujours en désordre.**
His bedroom is always in a mess.
le **dessert** MASC NOUN
**pudding**
**Qu'est-ce que vous désirez comme dessert?**
What would you like for pudding?
le **dessin** MASC NOUN
**drawing**
**C'est un dessin de ma petite sœur.**
It's a drawing my little sister did.
**un dessin animé**
a cartoon
**un dessin humoristique**
a cartoon
**dessiner** VERB
**to draw**
**Dessinez votre animal préféré.**
Draw your favourite animal.
**dessous**
**dessous** _can be an adverb or a noun._
**A** ADVERB
**underneath**
**Le prix du vase est marqué dessous.**
The price of the vase is marked underneath.
**ci-dessous**
below
**Complétez les phrases ci-dessous.**
Complete the sentences below.
**B** MASC NOUN
**les voisins du dessous**
the downstairs neighbours
**dessus**
**dessus** _can be an adverb or a noun._
**A** ADVERB
**on top**
**un gâteau avec des bougies dessus**
a cake with candles on top
**au-dessus**
above
**au-dessus du lit**
above the bed
**ci-dessus**
above
**l'exemple ci-dessus**
the example above
**là-dessus**
on that
**Tu peux écrire là-dessus.**
You can write on that.
**par-dessus**
over
**Tu peux sauter par-dessus la barrière?**
Can you jump over the gate?
**B** MASC NOUN
**les voisins du dessus**
the upstairs neighbours
la **destination** FEM NOUN
**destination**
**les passagers à destination de Paris**
passengers travelling to Paris
le **détail** MASC NOUN
**detail**
**en détail**
in detail
le **détective** MASC NOUN
**detective**
**un détective privé**
a private detective
**détendre** VERB
**to relax**
**La lecture, ça me détend.**
I find reading relaxing.
**se détendre**
**to relax**
**J'écoute de la musique pour me détendre.**
I listen to music to relax.
**détester** VERB
**to hate**
**Je déteste les épinards.**
I hate spinach.
**deux** NUMBER
**two**
**Il est deux heures.**
It's two o'clock.
**Elle a deux ans.**
She's two.
**deux fois**
twice
**tous les deux**
both
**Allez-y toutes les deux.**
Go on, both of you.
**le deux février**
the second of February
**deuxième** ADJECTIVE
**second**
**au deuxième étage**
on the second floor
**devant**
**devant** _can be a preposition, an adverb or a noun._
**A** PREPOSITION
**in front of**
**Il y a un grand jardin devant la maison.**
There's a big garden in front of the house.
**passer devant**
to go past
**Nous passons tous les jours devant chez lui.**
We go past his house every day.
**B** ADVERB
**in front**
**Il marche toujours devant.**
He always walks in front.
**Allez-y, passez devant.**
Come on, you go in front.
**C** MASC NOUN
**front**
**le devant de la maison**
the front of the house
**les pattes de devant**
the front legs
**développer** VERB
**to develop**
**devenir** VERB
**to become**
**Ça devient de plus en plus difficile.**
It's becoming more and more difficult.
**devez** VERB _see_ **devoir**
**Vous devez attendre ici.**
You've got to wait here.
**deviner** VERB
**to guess**
**Devine à quel animal je pense.**
Guess which animal I'm thinking of.
la **devinette** FEM NOUN
**riddle**
**devoir** VERB
**1** **to have to**
**Je dois partir.**
I've got to go.
**2** **must**
**Tu dois être fatigué.**
You must be tired.
les **devoirs** MASC PL NOUN
**homework**
**Quand je rentre de l'école, je fais mes devoirs.**
When I get home from school I do my homework.
**devons** VERB _see_ **devoir**
**Nous devons partir tôt.**
We have to leave early.
**diabétique** ADJECTIVE
**diabetic**
le **diable** MASC NOUN
**devil**
le **diabolo** MASC NOUN
**fruit cordial and lemonade**
**un diabolo menthe**
a mint cordial and lemonade
le **dialogue** MASC NOUN
**dialogue**
le **diamant** MASC NOUN
**diamond**
la **diapositive** FEM NOUN
**slide**
la **diarrhée** FEM NOUN
**diarrhoea**
**J'ai la diarrhée.**
I've got diarrhoea.
la **dictée** FEM NOUN
**dictation**
**La maîtresse nous fait faire une dictée tous les samedis matins.**
The teacher gives us a dictation every Saturday morning.
**_Did you know...?_**
_French pupils do a lot of dictation exercises, to help them learn to spell. French is difficult to spell because there are a lot of letters that are not pronounced – such as the 's' on the end of plural words._
**dicter** VERB
**to dictate**
le **dictionnaire** MASC NOUN
**dictionary**
**Cherchez le mot 'piscine' dans le dictionnaire.**
Look up the word 'piscine' in the dictionary.
**diététique** ADJECTIVE
**un magasin diététique**
a health food shop
le **dieu** MASC NOUN (PL les **dieux** )
**god**
**Dieu**
God
la **différence** FEM NOUN
**difference**
**Quelle est la différence entre les écoles françaises et anglaises?**
What's the difference between French and British schools?
**différent** MASC ADJECTIVE (FEM **différente** )
**1** **different**
**Je n'aime pas le bleu. Je voudrais une couleur différente.**
I don't like blue. I'd like a different colour.
**2** **various**
**différents parfums de glace**
various flavours of ice cream
**difficile** ADJECTIVE
**difficult**
**Son accent est difficile à comprendre.**
His accent is difficult to understand.
le **dimanche** MASC NOUN
**1** **Sunday**
**Aujourd'hui, nous sommes dimanche.**
It's Sunday today.
**2** **on Sunday**
**Dimanche, nous allons déjeuner chez mes grands-parents.**
On Sunday we're having lunch at my grandparents'.
**Le dimanche, je fais la grasse matinée.**
I have a lie-in on Sundays.
**tous les dimanches**
every Sunday
**le dimanche**
on Sundays
**dimanche dernier**
last Sunday
**dimanche prochain**
next Sunday
**À dimanche!**
See you on Sunday!
le **diminutif** MASC NOUN
pet name
**Loulou est le diminutif de Louise.**
Loulou is Louise's pet name.
la **dinde** FEM NOUN
**turkey**
**la dinde de Noël**
the Christmas turkey
**_Language tip_**
**le dindon** _is a live turkey;_ **la dinde** _is the bird you eat._
le **dindon** MASC NOUN
**turkey**
**dîner**
**dîner** _can be a verb or a noun._
**A** VERB
**to have dinner**
**Le soir, nous dînons à sept heures.**
We have dinner at seven o'clock in the evening.
**B** MASC NOUN
**dinner**
**Le dîner est à quelle heure?**
What time is dinner?
le **diplôme** MASC NOUN
**qualification**
**Il n'a aucun diplôme.**
He hasn't got any qualifications.
**dire** VERB
**1** **to say**
**Comment est-ce qu'on dit 'dog' en français?**
How do you say 'dog' in French?
**2** **to tell**
**Je vais te dire un secret.**
I'm going to tell you a secret.
**Elle me dit toujours la vérité.**
She always tells me the truth.
**Ma mère me dit toujours de ranger ma chambre.**
My mother is always telling me to tidy up my room.
**Beaucoup de gens me disent que je ressemble à ma mère.**
Lots of people tell me I look like my mother.
**dire des bêtises**
to talk nonsense
le **directeur** MASC NOUN
la **directrice** FEM NOUN
**1** **headteacher**
**Elle est directrice.**
She's a headteacher.
**2** **manager**
**Il est directeur du personnel.**
He's a personnel manager.
**dis** VERB _see_ **dire**
**Dis-moi la vérité!**
Tell me the truth!
la **discothèque** FEM NOUN
**club**
**Florence aime aller danser dans les discothèques.**
Florence likes going clubbing.
**discuter** VERB
**to talk**
**Nous discutons toujours à la récréation.**
We always talk at break time.
**disent** VERB _see_ **dire**
**Qu'est-ce qu'ils disent?**
What are they saying?
**disons** VERB _see_ **dire**
**Nous disons des bêtises.**
We're talking nonsense.
**disparaître** VERB
**to disappear**
**Il peut faire disparaître le lapin.**
He can make the rabbit disappear.
la **disparition** FEM NOUN
**disappearance**
**une espèce en voie de disparition**
an endangered species
**dispensé** MASC ADJECTIVE (FEM **dispensée** )
**Elle est dispensée de gymnastique.**
She's excused from gym.
la **dispute** FEM NOUN
**argument**
**Depuis notre dispute, elle ne me parle plus.**
She hasn't been speaking to me since our argument.
se **disputer** VERB
**to argue**
**Je me dispute souvent avec ma sœur.**
I often argue with my sister.
**se faire disputer**
to get a telling-off
**Je vais me faire disputer par ma mère si je ne rentre pas tout de suite.**
I'll get a telling-off from my mother if I don't go home now.
le **disque** MASC NOUN
**record**
**un disque compact**
a compact disc
la **distance** FEM NOUN
**distance**
**Ton école est à quelle distance d'ici?**
How far is your school from here?
**distrait** MASC ADJECTIVE (FEM **distraite** )
**absent-minded**
**distribuer** VERB
**1** **to give out**
**Distribue les livres, s'il te plaît.**
Give out the books please.
**2** **to deal**
**Distribue les cartes, s'il te plaît.**
Deal the cards please.
le **distributeur** MASC NOUN
**un distributeur automatique**
a vending machine
**un distributeur de billets**
a cash dispenser
**dit** VERB _see_ **dire**
**Elle ne me dit jamais rien.**
She never tells me anything.
**Je te l'ai dit hier.**
I told you yesterday.
**dites** VERB _see_ **dire**
**Dites-moi ce que vous pensez.**
Tell me what you think.
**diviser** VERB
**to divide**
**Quatre divisé par deux égale deux.**
Four divided by two equals two.
**divorcé** MASC ADJECTIVE (FEM **divorcée** )
**divorced**
**Mes parents sont divorcés.**
My parents are divorced.
**divorcer** VERB
**to get divorced**
**Ils ont décidé de divorcer.**
They've decided to get divorced.
**dix** NUMBER
**ten**
**Elle a dix ans.**
She's ten.
**Il est dix heures.**
It's ten o'clock.
**le dix février**
the tenth of February
**dix-huit** NUMBER
**eighteen**
**Elle a dix-huit ans.**
She's eighteen.
**Il est dix-huit heures.**
It's six o'clock.
**le dix-huit mars**
the eighteenth of March
**_Did you know...?_**
_The 24-hour clock is used in France for travel times, appointments and other formal situations._
**dixième** ADJECTIVE
**tenth**
**au dixième étage**
on the tenth floor
**dix-neuf** NUMBER
**nineteen**
**Elle a dix-neuf ans.**
She's nineteen.
**Il est dix-neuf heures.**
It's seven o'clock.
**le dix-neuf avril**
the nineteenth of April
**dix-sept** NUMBER
**seventeen**
**Elle a dix-sept ans.**
She's seventeen.
**Il est dix-sept heures.**
It's five o'clock.
**le dix-sept avril**
the seventeenth of April
la **dizaine** FEM NOUN
**about ten**
**une dizaine de jours**
about ten days
le **docteur** MASC NOUN
**doctor**
**Je vais chez le docteur.**
I'm going to the doctor's.
le **documentaire** MASC NOUN
**documentary**
le/la **documentaliste** MASC/FEM NOUN
**librarian**
le **doigt** MASC NOUN
**finger**
**les doigts de pied**
the toes
**dois, doit, doivent** VERB _see_ **devoir**
**Je dois mettre la table.**
I have to lay the table.
**Il doit être tard.**
It must be late.
**Ils doivent rentrer à huit heures.**
They have to be home at eight o'clock.
**domestique**
**domestique** _can be an adjective or a noun._
**A** ADJECTIVE
**les animaux domestiques**
pets
**B** MASC/FEM NOUN
**servant**
le **domicile** MASC NOUN
**à domicile**
at home
**Il travaille à domicile.**
He works at home.
les **dominos** MASC PL NOUN
**dominoes**
**Je joue aux dominos avec ma sœur.**
I play dominoes with my sister.
le **dommage** MASC NOUN
**C'est dommage.**
It's a shame.
**Quel dommage!**
What a shame!
**donc** CONJUNCTION
**so**
**Il fait beau, donc nous pouvons faire un pique-nique.**
The weather's nice, so we can have a picnic.
**donner** VERB
**to give**
**Elle me donne toujours des bonbons.**
She always gives me sweets.
**Ça me donne faim.**
That makes me feel hungry.
**dont** PRONOUN
**1** **of which**
**deux livres, dont l'un est en anglais**
two books, one of which is in English
**le prix dont il est si fier**
the prize he's so proud of
**2** **of whom**
**dix blessés, dont deux grièvement**
ten people injured, two of them seriously
**la fille dont je t'ai parlé**
the girl I told you about
**doré** MASC ADJECTIVE (FEM **dorée** )
**golden**
**dormir** VERB
**1** **to sleep**
**Tu as bien dormi?**
Did you sleep well?
**2** **to be asleep**
**Ne faites pas de bruit, il dort.**
Don't make a noise, he's asleep.
le **dortoir** MASC NOUN
**dormitory**
le **dos** MASC NOUN
**back**
**dos à dos**
back to back
**J'ai mal au dos.**
I've got backache.
**dans mon dos**
behind my back
**Elle me critique dans mon dos.**
She criticizes me behind my back.
**le dos crawlé**
the backstroke
le **dossier** MASC NOUN
**1** **file**
**une pile de dossiers**
a stack of files
**2** **report**
**un bon dossier scolaire**
a good school report
**3** **back**
**le dossier de la chaise**
the back of the chair
la **douane** FEM NOUN
**customs**
**un contrôle de douane**
a customs inspection
le **douanier** MASC NOUN
**customs officer**
le **double** MASC NOUN
**le double**
twice as much
**Il gagne le double.**
He earns twice as much.
**le double du prix normal**
twice the normal price
**en double**
in duplicate
**Garde cette photo, je l'ai en double.**
Keep this photo, I've got a copy of it.
**doublé** MASC ADJECTIVE (FEM **doublée** )
**dubbed**
**un film doublé**
a dubbed film
**douce** FEM ADJECTIVE _see_ **doux**
**une peau douce**
soft skin
**doucement** ADVERB
**1** **gently**
**Il a frappé doucement à la porte.**
He knocked gently at the door.
**2** **slowly**
**Je ne comprends pas, parle plus doucement.**
I don't understand, speak more slowly.
la **douche** FEM NOUN
**shower**
**Je prends une douche tous les matins.**
I have a shower every morning.
se **doucher** VERB
**to have a shower**
**Je me douche le matin.**
I have a shower in the morning.
**doué** MASC ADJECTIVE (FEM **douée** )
**talented**
**Il est doué en maths.**
He's good at maths.
la **douleur** FEM NOUN
**pain**
le **doute** MASC NOUN
**doubt**
**sans doute**
probably
se **douter** VERB
**se douter de**
to suspect
**Elle ne se doute de rien.**
She doesn't suspect anything.
**Je m'en doutais.**
I thought as much.
**Douvres** NOUN
**Dover**
**doux** MASC ADJECTIVE
(FEM **douce** )
**1** **soft**
**un tissu doux**
soft material
**2** **sweet**
**du cidre doux**
sweet cider
**3** **mild**
**Il fait doux aujourd'hui.**
It's mild today.
**4** **gentle**
**C'est quelqu'un de très doux.**
He's a very gentle person.
la **douzaine** FEM NOUN
**dozen**
**une douzaine d'œufs**
a dozen eggs
**une douzaine de personnes**
about twelve people
**douze** NUMBER
**twelve**
**Il a douze ans.**
He's twelve.
**le douze février**
the twelfth of February
**douzième** ADJECTIVE
**twelfth**
**au douzième étage**
on the twelfth floor
la **dragée** FEM NOUN
**sugared almond**
**_Did you know...?_**
_French people give_ **dragées** _to family and friends at weddings and christenings._
le **drap** MASC NOUN
**sheet**
le **drapeau** MASC NOUN
(PL les **drapeaux** )
**flag**
**dressé** MASC ADJECTIVE (FEM **dressée** )
**trained**
**un chien bien dressé**
a well-trained dog
la **droguerie** FEM NOUN
**hardware shop**
**droit**
**droit** _can be an adjective or a noun._
**A** MASC ADJECTIVE (FEM **droite** )
**1** **right**
**la jambe droite**
the right leg
**le côté droit**
the right-hand side
**2** **straight**
**une ligne droite**
a straight line
**Tiens-toi droite sur ta chaise!**
Sit up straight on your chair!
**Allez tout droit.**
Go straight on.
**tout droit**
straight on
**B** MASC NOUN
**law**
**un étudiant en droit**
a law student
**Tu as le droit de sortir?**
Are you allowed to go out?
**Je n'ai pas le droit d'aller en ville toute seule.**
I'm not allowed to go into town by myself.
la **droite** FEM NOUN
**right**
**sur votre droite**
on your right
**à droite**
right/on the right
**_Language tip_**
**à droite** _has two translations. Look at the examples._
**Tournez à droite.**
Turn right.
**Prenez la troisième rue à droite.**
Take the third street on the right.
**C'est à droite.**
It's on your right.
**la deuxième rue à droite**
the second street on the right
**droitier** MASC ADJECTIVE (FEM **droitière** )
**right-handed**
**Elle est droitière.**
She's right-handed.
**drôle** ADJECTIVE
**funny**
**Ça n'est pas drôle.**
It's not funny.
**un drôle de temps**
funny weather
le **dromadaire** MASC NOUN
**camel**
**du** ARTICLE
**_Language tip_**
**du** _is made up of_ **de** _+ **le**._
**1** **some**
**Tu veux du fromage?**
Would you like some cheese?
**2** **any**
**Tu as du chocolat?**
Have you got any chocolate?
**3** **of the**
**la porte du garage**
the door of the garage
**la femme du directeur**
the headmaster's wife
**4** **from**
**Il rentre du Canada.**
He's back from Canada.
**à sept heures du soir**
at seven o'clock in the evening
le **duc** MASC NOUN
**duke**
la **duchesse** FEM NOUN
**duchess**
**dur**
**dur** _can be an adjective or an adverb._
**A** MASC ADJECTIVE (FEM **dure** )
**hard**
**Il est dur avec moi.**
He's hard on me.
**B** ADVERB
**hard**
**Elle travaille dur à l'école.**
She works hard at school.
**durant** PREPOSITION
**1** **during**
**durant la nuit**
during the night
**2** **for**
**durant des années**
for years
**durer** VERB
**to last**
**La leçon dure une heure.**
The lesson lasts an hour.
**dyslexique** ADJECTIVE
**dyslexic**
# **E e**
l' **eau** FEM NOUN
**water**
**Je voudrais de l'eau.**
I'd like some water.
**Qu'est-ce que tu veux boire? — De l'eau.**
What would you like to drink? – Water.
**l'eau minérale**
mineral water
**l'eau plate**
still water
**l'eau gazeuse**
fizzy water
l' **écart** MASC NOUN
**Je sais faire le grand écart.**
I can do the splits.
l' **échalote** FEM NOUN
**shallot**
l' **échange** MASC NOUN
**exchange**
**en échange de**
in exchange for
**échanger** VERB
**to swap**
**Je t'échange cet autocollant contre celui-là.**
I'll swap you this sticker for that one.
s' **échapper** VERB
**to escape**
l' **écharpe** FEM NOUN
**scarf**
s' **échauffer** VERB
**to warm up**
**Nous allons faire quelques exercices pour nous échauffer.**
We're going to do some exercises to warm up.
les **échecs** MASC PL NOUN
**chess**
**Je joue aux échecs.**
I play chess.
l' **échelle** FEM NOUN
**ladder**
l' **éclair** MASC NOUN
**flash of lightning**
**un éclair au chocolat**
a chocolate éclair
l' **école** FEM NOUN
**school**
**aller à l'école**
to go to school
**Je vais à l'école avec ma sœur.**
I go to school with my sister.
**une école privée**
a private school
**une école publique**
a state school
**une école maternelle**
a nursery school
**une école primaire**
a primary school
**_Did you know...?_**
_French children go to_ **l'école maternelle** _when they are three, and stay there until they are six. They then go to_ **l'école primaire** _and stay there until they are 11._
l' **écolier** MASC NOUN
**schoolboy**
l' **écolière** FEM NOUN
**schoolgirl**
les **économies** FEM PL NOUN
**savings**
**Je dois faire des économies.**
I must save up.
**économiser** VERB
**to save up**
**J'économise pour m'acheter une nouvelle raquette de tennis.**
I'm saving up to buy a new tennis racquet.
**écossais** MASC ADJECTIVE (FEM **écossaise** )
**1** **Scottish**
**Elle est écossaise.**
She's Scottish.
**2** **tartan**
**une jupe écossaise**
a tartan skirt
l' **Écossais** MASC NOUN
l' **Écossaise** FEM NOUN
**Scot**
**les Écossais**
the Scots
l' **Écosse** FEM NOUN
**Scotland**
**écouter** VERB
**to listen to**
**J'aime écouter de la musique.**
I like listening to music.
**Écoute-moi, Bruno!**
Listen Bruno!
**Écoutez tout le monde!**
Listen everybody!
**écraser** VERB
**1** **to crush**
**Écrasez une gousse d'ail.**
Crush a clove of garlic.
**2** **to run over**
**Attention, tu vas te faire écraser!**
Be careful or you'll get run over!
**écrire** VERB
**to write**
**Nous nous écrivons régulièrement.**
We write to each other regularly.
**Ça s'écrit comment?**
How do you spell that?
l' **écriture** FEM NOUN
**handwriting**
**J'aime bien ton écriture.**
I like your handwriting.
l' **écrivain** MASC NOUN
**writer**
**écru** MASC ADJECTIVE (FEM **écrue** )
**off-white**
l' **écureuil** MASC NOUN
**squirrel**
**Édimbourg** NOUN
**Edinburgh**
**éducatif** MASC ADJECTIVE (FEM **éducative** )
**educational**
**un jeu éducatif**
an educational game
l' **éducation** FEM NOUN
**education**
**l'éducation physique**
physical education
**effacer** VERB
**to rub out**
**Efface la dernière lettre.**
Rub out the last letter.
l' **effort** MASC NOUN
**effort**
**Il faut faire un effort.**
You've got to make an effort.
**effrayant** MASC ADJECTIVE (FEM **effrayante** )
**frightening**
**égal** MASC ADJECTIVE (FEM **égale** )
**equal**
**une quantité égale de farine et de sucre**
equal quantities of flour and sugar
**Ça m'est égal.**
I don't mind./I don't care.
**_Language tip_**
**ça m'est égal** _has two translations. Look at the examples._
**Tu préfères du riz ou des pâtes? — Ça m'est égal.**
Would you rather have rice or pasta? — I don't mind.
**Fais ce que tu veux, ça m'est égal.**
Do what you like, I don't care.
**égaler** VERB
**to equal**
**Deux plus trois égalent cinq.**
Two plus three equals five.
l' **église** FEM NOUN
**church**
**Nous allons à l'église tous les dimanches.** We go to church every Sunday.
**égoïste** ADJECTIVE
**selfish**
l' **Égypte** FEM NOUN
**Egypt**
**égyptien** MASC ADJECTIVE (FEM **égyptienne** )
**Egyptian**
l' **Égyptien** MASC NOUN
l' **Égyptienne** FEM NOUN
**Egyptian**
l' **élastique** MASC NOUN
**rubber band**
l' **électricien** MASC NOUN
**electrician**
**élégant** MASC ADJECTIVE (FEM **élégante** )
**smart**
**une robe élégante**
a smart dress
l' **éléphant** MASC NOUN
**elephant**
**élevé** MASC ADJECTIVE (FEM **élevée** )
**Elle est bien élevée.**
She has good manners.
**Il est très mal élevé.**
He has very bad manners.
l' **élève** MASC/FEM NOUN
**pupil**
**Il y a un nouvel élève dans ma classe.**
There's a new boy in my class.
**éliminer** VERB
**to eliminate**
**Tu es éliminé!**
You're out!
**elle** PRONOUN
**1** **she**
**Elle est institutrice.**
She is a primary school teacher.
**Elle, elle est toujours en retard!**
Oh, SHE's always late!
**2** **her**
**C'est ma copine; je joue toujours avec elle.**
She's my friend; I always play with her.
**Lui ou elle?**
Him or her?
**Elle l'a choisi elle-même.**
She chose it herself.
**elle-même**
herself
**3** **it**
**Prends cette chaise: elle est plus confortable.**
Take this chair: it's more comfortable.
**elles** PRONOUN
**1** **they**
**Où sont Anne et Rachel? — Elles sont dans le jardin.**
Where are Anne and Rachel? — They're in the garden.
**2** **them**
**Julie et Aurélie ont emmené le chien avec elles.**
Julie and Aurélie have taken the dog with them.
**elles-mêmes**
themselves
l' **Élysée** MASC NOUN
**Élysée Palace**
**_Did you know...?_**
_The_ **Élysée** _is the home of the French president._
l' **e-mail** MASC NOUN
**email**
**Je vais envoyer un e-mail à ma copine.**
I'm going to email my friend.
**embarrassant** MASC ADJECTIVE (FEM **embarrassante** )
**embarrassing**
**embêtant** MASC ADJECTIVE (FEM **embêtante** )
**annoying**
**embêter** VERB
**to pester**
**Il n'arrête pas de m'embêter.**
He's always pestering me.
**s'embêter**
**to be bored**
**Qu'est-ce qu'on s'embête ici!**
It's so boring here!
l' **embouteillage** MASC NOUN
**traffic jam**
**embrasser** VERB
**to kiss**
**Il l'a embrassée.**
He kissed her.
**s'embrasser**
**to kiss each other**
**Ils se sont embrassés.**
They kissed each other.
l' **émission** FEM NOUN
**programme**
**une émission de télévision**
a TV programme
**emménager** VERB
**to move in**
**Nous venons d'emménager dans une nouvelle maison.**
We've just moved into a new house.
**emmener** VERB
**to take**
**Ma grand-mère m'emmène à l'école le matin.**
My granny takes me to school in the morning.
**empêcher** VERB
**to stop**
**Tu m'empêches de travailler!**
You're stopping me doing my work.
l' **emploi** MASC NOUN
**1** **use**
**le mode d'emploi**
instructions for use
**un emploi du temps**
a timetable
**2** **job**
**Il recherche un emploi.**
He's looking for a job.
l' **employé** MASC NOUN
l' **employée** FEM NOUN
**employee**
**un employé de bureau**
an office worker
**une employée de banque**
a bank clerk
**employer** VERB
**to employ**
**empoisonner** VERB
**to poison**
**emporter** VERB
**to take**
**des plats à emporter**
take-away meals
l' **empreinte** FEM NOUN
**footprint**
**une empreinte digitale**
a fingerprint
**emprunter** VERB
**to borrow**
**Je peux emprunter ta gomme?**
Can I borrow your rubber?
**en**
**en** _can be a preposition or a pronoun._
**A** PREPOSITION
**1** **in**
**Il habite en France.**
He lives in France.
**2** **to**
**Je vais en France cet été.**
I'm going to France this summer.
**3** **by**
**en vélo**
by bike
**C'est plus rapide en voiture.**
It's quicker by car.
**4** **made of**
**C'est en verre.**
It's made of glass.
**un bracelet en or**
a gold bracelet
**5** **while**
**Il s'est coupé le doigt en ouvrant une boîte de conserve.**
He cut his finger while opening a tin.
**B** PRONOUN
**of it**
**Il a un beau jardin et il en est très fier.**
He's got a beautiful garden and is very proud of it.
**Si tu as un problème, tu peux m'en parler.**
If you've got a problem, you can talk to me about it.
**Tu peux me rendre ce livre? J'en ai besoin.**
Can you give me back that book? I need it.
**_Language tip_**
_When_ **en** _is used with_ **avoir** _and_ **il y a** , _it is not translated in English. Please see below for an example._
**Tu as un dictionnaire? — Oui, j'en ai un.**
Have you got a dictionary? — Yes, I've got one.
**Il y a combien d'élèves dans ta classe? — Il y en a trente.**
How many pupils are there in your class? — There are 30.
**J'en ai assez.**
I've had enough.
**enceinte** FEM ADJECTIVE
**pregnant**
**Ma tante est enceinte de six mois.**
My aunt is six months pregnant.
**enchanté** MASC ADJECTIVE (FEM **enchantée** )
**delighted**
**Ma mère est enchantée de sa nouvelle voiture.**
My mother's delighted with her new car.
**Enchanté!**
Pleased to meet you!
**encore** ADVERB
**1** **still**
**Il est encore au travail.**
He's still at work.
**Il reste encore deux morceaux de gâteau.**
There are two bits of cake left.
**2** **even**
**C'est encore mieux.**
That's even better.
**3** **again**
**Nous allons encore en Espagne cet été.**
We're going to Spain again this summer.
**encore une fois**
once again
**pas encore**
not yet
**Je n'ai pas encore fini.**
I haven't finished yet.
l' **encre** FEM NOUN
**ink**
l' **encyclopédie** FEM NOUN
**encyclopaedia**
l' **endive** FEM NOUN
**chicory**
**_Did you know...?_**
**endive** _is a leafy vegetable which is eaten raw in a salad, boiled, or baked with ham and cheese._
s' **endormir** VERB
**to go to sleep**
**Je m'endors vers neuf heures du soir.**
I go to sleep at about nine o'clock.
l' **endroit** MASC NOUN
**place**
**C'est un endroit très tranquille.**
It's a very quiet place.
**à l'endroit**
the right way out/the right way up
**_Language tip_**
**à l'endroit** _has two translations. Look at the examples._
**Remets ton pull à l'endroit.**
Turn your jumper the right way out.
**Tu ne tiens pas le livre à l'endroit.**
You're not holding the book the right way up.
l' **énergie** FEM NOUN
**energy**
**énerver** VERB
**to get on someone's nerves**
**Il m'énerve!**
He gets on my nerves!
**Ne t'énerve pas!**
Take it easy!
l' **enfant** MASC/FEM NOUN
**child**
**Ils ont trois enfants.**
They've got three children.
l' **enfer** MASC NOUN
**hell**
**enfin** ADVERB
**at last**
**Tu arrives enfin!**
Here you are at last!
**enflé** MASC ADJECTIVE (FEM **enflée** )
**swollen**
**J'ai la cheville enflée.**
I have a swollen ankle.
**enlever** VERB
**to take off**
**Enlève ton manteau!**
Take off your coat!
**enneigé** MASC ADJECTIVE (FEM **enneigée** )
**blocked with snow**
**Les routes sont encore enneigées.**
The roads are still blocked with snow.
l' **ennemi** MASC NOUN
l' **ennemie** FEM NOUN
**enemy**
**ennuyer** VERB
**J'espère que ça ne t'ennuie pas.**
I hope this isn't a problem for you.
**Ça t'ennuie?**
Do you mind?
**s'ennuyer**
**to be bored**
**Je m'ennuie quand Laura n'est pas là.**
I get bored when Laura isn't here.
**ennuyeux** MASC ADJECTIVE (FEM **ennuyeuse** )
**boring**
**énorme** ADJECTIVE
**huge**
**un énorme gâteau**
a huge cake
**énormément** ADVERB
**Il y a énormément de neige.**
There's a huge amount of snow.
**Il a énormément grossi.**
He's got terribly fat.
l' **enquête** FEM NOUN
**investigation**
**enquêter** VERB
**to investigate**
l' **enregistrement** MASC NOUN
**recording**
**un mauvais enregistrement**
a bad recording
**l'enregistrement des bagages**
baggage check-in
**enregistrer** VERB
**1** **to record**
**Ils viennent d'enregistrer un nouvel album.**
They've just recorded a new album.
**2** **to check in**
**Combien de valises voulez-vous enregistrer?**
How many bags do you want to check in?
**enrhumé** MASC ADJECTIVE (FEM **enrhumée** )
**Je suis enrhumé.**
I've got a cold.
l' **enseignant** MASC NOUN
l' **enseignante** FEM NOUN
**teacher**
**enseigner** VERB
**to teach**
**Mon père enseigne les maths dans un lycée.**
My father teaches maths in a secondary school.
**ensemble**
**ensemble** _can be an adverb or a noun._
**A** ADVERB
**together**
**tous ensemble**
all together
**B** MASC NOUN
**outfit**
**Elle porte un nouvel ensemble.**
She's wearing a new outfit.
**ensoleillé** MASC ADJECTIVE (FEM **ensoleillée** )
**sunny**
**une matinée ensoleillée**
a sunny morning
**ensuite** ADVERB
**then**
**Nous sommes allés au cinéma et ensuite au restaurant.**
We went to the cinema and then to a restaurant.
**entendre** VERB
**to hear**
**Je ne t'entends pas.**
I can't hear you.
**s'entendre**
**to get on**
**Il s'entend bien avec sa sœur.**
He gets on well with his sister.
**entendu** MASC ADJECTIVE
**bien entendu**
of course
l' **enterrement** MASC NOUN
**funeral**
**entier** MASC ADJECTIVE (FEM **entière** )
**whole**
**Il a mangé une quiche entière.**
He ate a whole quiche.
**Je n'ai pas lu le livre en entier.**
I haven't read the whole book.
**dans le monde entier**
in the whole wide world
**le lait entier**
full fat milk
**entièrement** ADVERB
**completely**
l' **entorse** FEM NOUN
**sprain**
**entourer** VERB
**to surround**
**Le jardin est entouré d'un mur de pierres.**
The garden is surrounded by a stone wall.
l' **entraînement** MASC NOUN
**training**
s' **entraîner** VERB
**to train**
**Il s'entraîne au foot tous les samedis matins.**
He does football training every Saturday morning.
l' **entraîneur** MASC NOUN
**trainer**
**l'entraîneur d'une équipe de rugby**
the trainer of a rugby team
**entre** PREPOSITION
**between**
**Il est assis entre son père et son oncle.**
He's sitting between his father and his uncle.
l' **entrecôte** FEM NOUN
**rib steak**
l' **entrée** FEM NOUN
**1** **starter**
**Que voulez-vous comme entrée?**
What would you like as a starter?
**2** **hall**
**Il y a un grand placard dans l'entrée.**
There's a big cupboard in the hall.
**3** **entrance**
**l'entrée du tunnel**
the tunnel entrance
l' **entreprise** FEM NOUN
**firm**
**entrer** VERB
**1** **to come in**
**Entrez!**
Come in!
**2** **to go in**
**Ils sont tous entrés dans la maison.**
They all went into the house.
l' **enveloppe** FEM NOUN
**envelope**
l' **envers** MASC NOUN
**à l'envers**
inside out
**Ton pull est à l'envers.**
Your jumper is inside out.
l' **envie** FEM NOUN
**J'ai envie de pleurer.**
I feel like crying.
**J'ai envie de dormir.**
I want to go to sleep.
**J'ai envie de faire pipi.**
I need a wee.
**envier** VERB
**to envy**
**Je t'envie.**
I envy you.
**environ** ADVERB
**about**
**C'est à soixante kilomètres environ.**
It's about 60 kilometres.
l' **environnement** MASC NOUN
**environment**
les **environs** MASC PL NOUN
**area**
**les environs de Nantes**
the Nantes area
**Il y a beaucoup de choses intéressantes à voir dans les environs.**
There are a lot of interesting things to see in the area.
**aux environs de**
around
**aux environs de dix-neuf heures**
around 7 p.m.
s' **envoler** VERB
**1** **to fly away**
**Le papillon s'est envolé.**
The butterfly flew away.
**2** **to blow away**
**Attention, tes dessins vont s'envoler!**
Be careful, your drawings are going to blow away!
**envoyer** VERB
**to send**
**Ma tante m'a envoyé une carte pour mon anniversaire.**
My aunt sent me a card for my birthday.
**Je vais t'envoyer un e-mail.**
I'm going to email you.
**épais** MASC ADJECTIVE (FEM **épaisse** )
**thick**
l' **épaule** FEM NOUN
**shoulder**
l' **épée** FEM NOUN
**sword**
**épeler** VERB
**to spell**
**Tu peux épeler ton nom s'il te plaît?**
Can you spell your name please?
**épicé** MASC ADJECTIVE (FEM **épicée** )
**spicy**
**Ce n'est pas assez épicé.**
It's not spicy enough.
l' **épicerie** FEM NOUN
**shop**
l' **épicier** MASC NOUN
l' **épicière** FEM NOUN
**grocer**
les **épinards** MASC PL NOUN
**spinach**
**Je n'aime pas les épinards.**
I don't like spinach.
**éplucher** VERB
**to peel**
l' **éponge** FEM NOUN
**sponge**
**épouvantable** ADJECTIVE
**awful**
l' **EPS** FEM NOUN
**PE**
**épuisé** MASC ADJECTIVE (FEM **épuisée** )
**exhausted**
l' **équilibre** MASC NOUN
**balance**
**J'ai failli perdre l'équilibre.**
I nearly lost my balance.
l' **équipe** FEM NOUN
**team**
l' **équipement** MASC NOUN
**equipment**
l' **équitation** FEM NOUN
**riding**
**Je fais de l'équitation.**
I go riding.
l' **erreur** FEM NOUN
**mistake**
**es** VERB _see_ **être**
**Tu es très gentille.**
You're very kind.
**_Language tip_**
_Sometimes_ **es** _is used to show that something has happened in the past._
**Tu es parti à quelle heure?**
What time did you leave?
l' **escalade** FEM NOUN
**climbing**
**Il fait de l'escalade.**
He goes climbing.
l' **escalier** MASC NOUN
**stairs**
l' **escargot** MASC NOUN
**snail**
l' **escrime** FEM NOUN
**fencing**
**Il fait de l'escrime.**
He does fencing.
les **espadrilles** FEM PL NOUN
**rope-soled sandals**
**_Did you know...?_**
_A lot of French people wear_ **espadrilles** _in the summer. They are cheap and colourful fabric sandals with soles made of rope._
l' **Espagne** FEM NOUN
**Spain**
**espagnol** MASC NOUN, MASC ADJECTIVE (FEM **espagnole** )
**Spanish**
l' **Espagnol** MASC NOUN
l' **Espagnole** FEM NOUN
**Spaniard**
l' **espèce** FEM NOUN
**sort**
**Elle porte une espèce de cape en velours.**
She's wearing a sort of velvet cloak.
**Espèce d'idiot!**
You idiot!
**espérer** VERB
**to hope**
**J'espère que tu passes de bonnes vacances.**
I hope you're having a nice holiday.
**J'espère bien!**
I hope so!
**J'espère que non.**
I hope not.
l' **esquimau** ® MASC NOUN (PL les **esquimaux** )
**choc ice on a stick**
l' **Esquimau** MASC NOUN
l' **Esquimaude** FEM NOUN
**Eskimo**
**les Esquimaux**
the Eskimos
**essayer** VERB
**1** **to try**
**Essaie de compter jusqu'à cent en français.**
Try to count up to 100 in French.
**2** **to try on**
**Je peux l'essayer?**
Can I try it on?
l' **essence** FEM NOUN
**petrol**
**essentiel**
**essentiel** _can be an adjective or a noun._
**A** MASC ADJECTIVE (FEM **essentielle** )
**essential**
**B** MASC NOUN
**Tu es là: c'est l'essentiel.**
You're here: that's the main thing.
**essuyer** VERB
**to wipe**
**Tu peux essuyer la table?**
Could you wipe the table?
**Il essuie la vaisselle.**
He's drying the dishes.
**Essuie-toi les mains avec cette serviette.**
Dry your hands on this towel.
**est**
**est** _can be part of the verb **être** , an adjective or a noun._
**A** VERB _see_ **être**
**Elle est merveilleuse.**
She's marvellous.
**_Language tip_**
_Sometimes_ **est** _is used to show that something has happened in the past._
**Hier soir, il est allé au cinéma.**
He went to the cinema last night.
**B** MASC, FEM, PL ADJECTIVE
**east**
**la côte est des États-Unis**
the east coast of the United States
**C** MASC NOUN
**east**
**Je vis dans l'est de la France.**
I live in the east of France.
**à l'est de Paris**
east of Paris
**est-ce que** ADVERB
**_Language tip_**
_One way of asking a question in French is to use_ **est-ce que**.
**Comment est-ce que tu t'appelles?**
What's your name?
**Est-ce que c'est cher?**
Is it expensive?
l' **estomac** MASC NOUN
**stomach**
**et** CONJUNCTION
**and**
l' **étage** MASC NOUN
**floor**
**au premier étage**
on the first floor
l' **étagère** FEM NOUN
**shelf**
**étaient** VERB _see_ **être**
**J'ai trouvé
mes baskets: elles étaient sous mon lit.**
I've found my trainers: they were under my bed.
**étais, était** VERB _see_ **être**
**J'étais dans le jardin.**
I was in the garden.
**C'était super!**
It was great!
l' **étang** MASC NOUN
**pond**
l' **état** MASC NOUN
**condition**
**en bon état**
in good condition
**en mauvais état**
in poor condition
les **États-Unis** MASC PL NOUN
**United States**
**été**
**été** _can be a noun or part of the verb **être**._
**A** MASC NOUN
**summer**
**cet été**
this summer
**en été**
in the summer
**B** VERB _see_ **être**
**Il a été puni.**
He has been punished.
**éteindre** VERB
**to switch off**
**Éteins la lumière s'il te plaît**
Switch off the light please.
**étendre** VERB
**étendre le linge**
to hang out the washing
**éternuer** VERB
**to sneeze**
**_Did you know...?_**
_When you sneeze in France people say_ **'À tes souhaits!'** , _which means_ **'May your wishes come true!'**.
**êtes** VERB _see_ **être**
**Vous êtes en retard.**
You're late.
**_Language tip_**
_Sometimes **êtes** is used to show that something has happened in the past._
**Vous êtes partis de bonne heure.**
You left early.
l' **étiquette** FEM NOUN
**label**
l' **étoile** FEM NOUN
**star**
**une étoile de mer**
a starfish
**une étoile filante**
a shooting star
**étonnant** MASC ADJECTIVE (FEM **étonnante** )
**amazing**
**une nouvelle étonnante**
amazing news
**étonner** VERB
**to surprise**
**Ça t'étonne?**
Does that surprise you?
**étourdi** MASC ADJECTIVE (FEM **étourdie** )
**scatterbrained**
**étrange** MASC, FEM ADJECTIVE
**strange**
**étranger** MASC ADJECTIVE (FEM **étrangère** )
**foreign**
**un pays étranger**
a foreign country
l' **étranger** MASC NOUN
l' **étrangère** FEM NOUN
**1** **foreigner**
**Il y a beaucoup d'étrangers ici.**
There are lots of foreigners here.
**à l'étranger**
abroad
**2** **stranger**
**Il ne faut pas parler aux étrangers.**
You mustn't speak to strangers.
**être**
**être** _can be a verb or a noun._
**A** VERB
**1** **to be**
**Je suis heureux.**
I'm happy.
**Mon père est instituteur.**
My father's a primary school teacher.
**Il est dix heures.**
It's 10 o'clock.
**2** **to have**
**_Language tip_**
**être** _is used to make the past tense of some verbs._
**Il n'est pas encore arrivé.**
He hasn't arrived yet.
**B** MASC NOUN
**being**
**un être humain**
a human being
les **étrennes** FEM PL NOUN
**_Did you know...?_**
**les étrennes** _are like a Christmas box, but one that is given after Christmas, to people like the postman and the dustmen. Children sometimes get money or a gift too._
les **études** FEM PL NOUN
**Mon frère va faire des études de droit.**
My brother is going to study law.
l' **étudiant** MASC NOUN
l' **étudiante** FEM NOUN
**student**
**étudier** VERB
**to study**
l' **étui** MASC NOUN
**case**
**un étui à lunettes**
a glasses case
**eu** VERB _see_ **avoir**
**J'ai eu une bonne note.**
I got a good mark.
**euh** EXCLAMATION
**er**
**Euh... je ne sais pas.**
Er... I don't know.
l' **euro** MASC NOUN
**euro**
**Ça coûte vingt-cinq euros.**
It costs 25 euros.
**50 €**
€50
l' **Europe** FEM NOUN
**Europe**
**européen** MASC ADJECTIVE (FEM **européenne** )
**European**
l' **européen** MASC NOUN
l' **européenne** FEM NOUN
**European**
**eux** PRONOUN
**them**
**Je pense souvent à eux.**
I often think of them.
**eux-mêmes**
themselves
**évident** MASC ADJECTIVE (FEM **évidente** )
**obvious**
**Elle est jalouse, c'est évident.**
It's obvious she's jealous.
l' **évier** MASC NOUN
**sink**
**exactement** ADVERB
**exactly**
**ex aequo** MASC, FEM, PL ADJECTIVE
**Huit points partout: vous êtes ex aequo.**
Eight points each: it's a tie.
**_Language tip_**
**ex aequo** _sounds like 'ex-echo'._
**exagérer** VERB
**to exaggerate**
**Il exagère toujours.**
He always exaggerates.
**Ça fait trois fois que tu arrives en retard: tu exagères!**
That's three times you've been late: it's not good enough!
l' **examen** MASC NOUN
**exam**
**un examen de français**
a French exam
**excellent** MASC ADJECTIVE (FEM **excellente** )
**excellent**
**excitant** MASC ADJECTIVE (FEM **excitante** )
**exciting**
l' **excuse** FEM NOUN
**excuse**
**un mot d'excuse**
a note
**C'est un mot d'excuse de mes parents.**
This is a note from my parents.
**excuser** VERB
**excusez-moi**
sorry/excuse me
**_Language tip_**
**excusez-moi** _is used to apologize and to attract someone's attention._
**Excusez-moi!**
Sorry!
**Excusez-moi, je suis en retard.**
Sorry I'm late.
**Excusez-moi!**
Excuse me!
**Excusez-moi, je cherche la poste.**
Excuse me, I'm looking for the post office.
**s'excuser**
**to apologize**
**Je m'excuse.**
I apologize.
l' **exemple** MASC NOUN
**example**
**par exemple**
for example
l' **exercice** MASC NOUN
**exercise**
**exister** VERB
**to exist**
**Ça n'existe pas.**
It doesn't exist.
**exotique** ADJECTIVE
**exotic**
**une plante exotique**
an exotic plant
**un yaourt aux fruits exotiques**
a tropical fruit yoghurt
l' **expéditeur** MASC NOUN
**sender**
l' **expérience** FEM NOUN
**1** **experience**
**2** **experiment**
**une expérience de chimie**
a chemistry experiment
l' **explication** FEM NOUN
**explanation**
**expliquer** VERB
**to explain**
**Je vais expliquer en anglais.**
I'm going to explain in English.
l' **exposition** FEM NOUN
**exhibition**
**exprès** ADVERB
**1** **on purpose**
**Je suis sûr qu'il l'a fait exprès.**
I'm sure he did it on purpose.
**2** **specially**
**J'ai fait ce gâteau exprès pour toi.**
I made this cake specially for you.
l' **extérieur** MASC NOUN
**outside**
**à l'extérieur**
outside
**Les toilettes sont à l'extérieur.**
The toilet is outside.
l' **externe** MASC/FEM NOUN
**_Did you know...?_**
_In French secondary schools, pupils are described as_ **externe** _if they go home for lunch,_ **demi-pensionnaire** _if they have a school lunch, or_ **interne** _if they stay at the school as boarders._
**extra** MASC, FEM, PL ADJECTIVE
**excellent**
**Ce fromage est extra!**
This cheese is excellent!
l' **extrait** MASC NOUN
**extract**
**extraordinaire** ADJECTIVE
**extraordinary**
**extrêmement** ADVERB
**extremely**
l' **Extrême-Orient** MASC NOUN
**the Far East**
# **F f**
**fabriquer** VERB
**to make**
**fabriqué en France**
made in France
la **face** FEM NOUN
**en face de**
opposite
**Le bus s'arrête en face de chez moi.**
The bus stops opposite my house.
**Pile ou face? — Face.**
Heads or tails? — Heads.
**fâché** MASC ADJECTIVE
(FEM **fâchée** )
**angry**
**Elle est fâchée contre moi.**
She's angry with me.
**Elle est fâchée avec sa sœur.**
She's fallen out with her sister.
se **fâcher** VERB
**to get angry**
**Je vais me fâcher.**
I'm going to get angry.
**Il s'est fâché avec son frère.**
He's fallen out with his brother.
**facile** ADJECTIVE
**easy**
**C'est facile à faire.**
It's easy to do.
**facilement** ADVERB
**easily**
la **façon** FEM NOUN
**way**
**Il a une drôle de façon de parler.**
He has a funny way of talking.
**de toute façon**
anyway
le **facteur** MASC NOUN
**postman**
**faible** ADJECTIVE
**weak**
**Je me sens encore faible.**
I still feel a bit weak.
**Il est faible en maths.**
He's not very good at maths.
la **faim** FEM NOUN
**hunger**
**Tu as faim?**
Are you hungry?
**J'ai faim.**
I'm hungry.
**faire** VERB
**1** **to make**
**Je vais faire un gâteau.**
I'm going to make a cake.
**Ils font trop de bruit.**
They're making too much noise.
**2** **to do**
**Qu'est-ce que tu fais?**
What are you doing?
**Il fait de l'italien.**
He's doing Italian.
**Elle fait la vaisselle.**
She's doing the dishes.
**3** **to play**
**Il fait du piano.**
He plays the piano.
**Je fais du basket.**
I play basketball.
**4** **to be**
**Il fait chaud.**
It's hot.
**Ça fait combien? — Ça fait dix euros.**
How much is that? — It's ten euros.
**5** **to go**
**Tu veux faire du vélo?**
Do you want to go cycling?
**Je fais du vélo.**
I go cycling.
**Ça fait trois ans qu'ils habitent à Paris.**
They've lived in Paris for three years.
**Ça ne fait rien.**
It doesn't matter.
**fais, faisaient, faisais, faisait** VERB _see_ **faire**
**_Language tip_**
_Look at the entry_ **faire** _to see all the meanings it can have._
**Ne fais pas ça!**
Don't do that!
**Ils faisaient beaucoup de bruit.**
They were making a lot of noise.
**Qu'est-ce que tu faisais?**
What were you doing?
**Il faisait très froid.**
It was very cold.
le **faisan** MASC NOUN
**pheasant**
**faisiez, faisions, faisons, fait** VERB _see_ **faire**
**_Language tip_**
_Look at the entry_ **faire** _to see all the meanings it can have._
**Vous faisiez du bruit.**
You were making a noise.
**Qu'est-ce que nous faisions hier?**
What were we doing yesterday?
**Nous faisons du vélo le week-end.**
We go cycling at the weekend.
**Il fait des bêtises.**
He does silly things.
**faites** VERB _see_ **faire**
**_Language tip_**
_Look at the entry **faire** to see all the meanings it can have._
**Qu'est-ce que vous faites?**
What are you doing?
la **falaise** FEM NOUN
**cliff**
**falloir** VERB _see_ **faut**
**Il va falloir se dépêcher.**
We'll have to hurry up.
**familier** MASC ADJECTIVE (FEM **familière** )
**familiar**
**les animaux familiers**
pets
la **famille** FEM NOUN
**1** **family**
**une famille nombreuse**
a big family
**2** **relatives**
**Il a de la famille à Paris.**
He's got relatives in Paris.
**fantastique** ADJECTIVE
**fantastic**
le **fantôme** MASC NOUN
**ghost**
la **farce** FEM NOUN
**practical joke**
**farci** MASC ADJECTIVE (FEM **farcie** )
**stuffed**
**des tomates farcies**
stuffed tomatoes
la **farine** FEM NOUN
**flour**
**fatigant** MASC ADJECTIVE (FEM **fatigante** )
**tiring**
**fatigué** MASC ADJECTIVE (FEM **fatiguée** )
**tired**
**Je suis fatigué.**
I'm tired.
**fausse** FEM ADJECTIVE _see_ **faux**
**Cette réponse est fausse.**
This answer's wrong.
**faut** VERB
**_Language tip_**
**faut** _is the present tense of_ **falloir**.
**Il faut faire attention.**
You've got to be careful.
la **faute** FEM NOUN
**1** **mistake**
**J'ai fait une faute.**
I've made a mistake.
**2** **fault**
**Ce n'est pas de ma faute.**
It's not my fault.
le **fauteuil** MASC NOUN
**armchair**
**un fauteuil roulant**
a wheelchair
**faux** MASC ADJECTIVE (FEM **fausse** )
**1** **untrue**
**C'est entièrement faux.**
It's totally untrue.
**2** **wrong**
**Ce mot est faux.**
The word is wrong.
**Vrai ou faux?**
True or false?
**favori** MASC ADJECTIVE (FEM **favorite** )
**favourite**
**Quel est ton sport favori?**
What's your favourite sport?
la **fée** FEM NOUN
**fairy**
**un conte de fées**
a fairy tale
les **félicitations** FEM PL NOUN
**congratulations**
**féliciter** VERB
**to congratulate**
**Je te félicite pour tes bons résultats.**
Congratulations on your good results!
la **femelle** FEM NOUN
**female**
**féminin** MASC ADJECTIVE (FEM **féminine** )
**feminine**
la **femme** FEM NOUN
**1** **woman**
**une jeune femme**
a young woman
**une femme de ménage**
a cleaning woman
**2** **wife**
**C'est la femme du directeur.**
She's the headmaster's wife.
**une femme au foyer**
a housewife
la **fenêtre** FEM NOUN
**window**
**Regardez par la fenêtre.**
Look out of the window.
le **fenouil** MASC NOUN
**fennel**
**_Did you know...?_**
**fenouil** _is white, looks a bit like celery but has a rounded shape. It tastes of aniseed._
le **fer** MASC NOUN
**iron**
**un fer à repasser**
an iron
**un fer à cheval**
a horseshoe
**fera, ferai, feras, ferez** VERB _see_ **faire**
**_Language tip_**
_Look at the entry_ **faire** _to see all the meanings it can have._
**Marc fera la vaisselle.**
Marc will do the washing up.
**Je te ferai un gâteau.**
I'll make you a cake.
**Qu'est-ce que tu feras l'année prochaine?**
What are you going to do next year?
**Vous ferez du cheval pendant les vacances?**
Will you go horse-riding during the holidays?
**férié** MASC ADJECTIVE
**un jour férié**
a public holiday
la **ferme** FEM NOUN
**farm**
**fermé** MASC ADJECTIVE (FEM **fermée** )
**closed**
**La pharmacie est fermée.**
The chemist's is closed.
**fermer** VERB
**1** **to close**
**Ferme la fenêtre s'il te plaît.**
Close the window please.
**2** **to turn off**
**Ferme le robinet.**
Turn the tap off.
**N'oublie pas de fermer la porte à clef!**
Don't forget to lock the door!
la **fermeture** FEM NOUN
**les heures de fermeture**
closing times
**une fermeture éclair** ®
a zip
le **fermier** MASC NOUN
**farmer**
la **fermière** FEM NOUN
**1** **woman farmer**
**2** **farmer's wife**
**féroce** ADJECTIVE
**fierce**
**un animal féroce**
a fierce animal
**ferons, feront** VERB _see_ **faire**
**_Language tip_**
_Look at the entry_ **faire** _to see all the meanings it can have._
**Nous le ferons si nous avons le temps.**
We'll do it if we have time.
**Ils feront des quiches pour la fête.**
They're going to make quiches for the party.
les **fesses** FEM PL NOUN
**bottom**
la **fête** FEM NOUN
**1** **party**
**Tu fais une fête pour ton anniversaire?**
Are you having a party for your birthday?
**faire la fête**
to party
**2** **name day**
**C'est ma fête aujourd'hui.**
It's my name day today.
**_Did you know...?_**
_Every day on a French calendar belongs to a saint. The fifteenth of March, for example, is St Louise's day, and people say 'Bonne fête Louise!' to anyone with that name. Girls called Louise might get presents too._
**une fête foraine**
a funfair
**les fêtes de fin d'année**
the festive season
**la Fête Nationale**
Bastille Day
**_Did you know...?_**
**Bastille Day** _is on the fourteenth of July. There are firework displays all over France to mark the storming of the Bastille (a prison), at the beginning of the French Revolution in 1789._
**fêter** VERB
**to celebrate**
**Aujourd'hui, ma mère fête ses quarante ans.**
My mum's celebrating her fortieth birthday today.
le **feu** MASC NOUN (PL les **feux** )
**1** **fire**
**Au feu!**
Fire!
**un feu d'artifice**
a firework display
**2** **traffic light**
**un feu rouge**
a red light
**le feu vert**
the green light
**Tournez à gauche aux feux.**
Turn left at the lights.
la **feuille** FEM NOUN
**1** **leaf**
**des feuilles mortes**
dead leaves
**2** **sheet**
**une feuille de papier**
a sheet of paper
le **feuilleton** MASC NOUN
**soap**
**Tu regardes les feuilletons à la télé?**
Do you watch soaps on telly?
le **feutre** MASC NOUN
**felt-tip pen**
**un stylo-feutre**
a felt-tip pen
la **fève** FEM NOUN
**broad bean**
**_Did you know...?_**
**la fève** _can also be a little figure which is baked in the cake traditionally eaten at Epiphany (the sixth of January). If you find_ **la fève** _in your slice of cake you are king (or queen) for the day._
**février** MASC NOUN
**February**
**en février**
in February
**au mois de février**
in February
**le six février**
the sixth of February
les **fiançailles** FEM PL NOUN
**engagement**
**une bague de fiançailles**
an engagement ring
**fiancé** MASC ADJECTIVE (FEM **fiancée** )
**être fiancé**
to be engaged
**Elle est fiancée.**
She's engaged.
se **fiancer** VERB
**to get engaged**
**Luc et Claire vont se fiancer.**
Luc and Claire are going to get engaged.
la **ficelle** FEM NOUN
**string**
la **fiche** FEM NOUN
**form**
**Remplissez cette fiche s'il vous plaît.**
Fill in this form please.
le **fichier** MASC NOUN
**file**
**fier** MASC ADJECTIVE (FEM **fière** )
**proud**
**Il est fier de toi.**
He's proud of you.
la **fièvre** FEM NOUN
**fever**
**J'ai de la fièvre.**
I've got a temperature.
la **figue** FEM NOUN
**fig**
la **figure** FEM NOUN
**face**
**Va te laver la figure!**
Go and wash your face!
le **fil** MASC NOUN
**thread**
**le fil de fer**
wire
**un coup de fil**
a phone call
la **file** FEM NOUN
**line**
**une file de gens**
a line of people
**en file indienne**
in single file
le **filet** MASC NOUN
**net**
la **fille** FEM NOUN
**1** **girl**
**une petite fille**
a little girl
**une grande fille**
a big girl
**une jeune fille**
a young girl
**2** **daughter**
**C'est leur fille aînée.**
She's their oldest daughter.
la **fillette** FEM NOUN
**little girl**
le **filleul** MASC NOUN
**godson**
la **filleule** FEM NOUN
**goddaughter**
le **film** MASC NOUN
**film**
**un film policier**
a thriller
**un film d'aventures**
an adventure film
**un film d'horreur**
a horror film
le **fils** MASC NOUN
(PL les **fils** )
**son**
**Ils ont deux fils et une fille.**
They have two sons and one daughter.
**fin**
**fin** _can be a noun or an adjective._
**A** FEM NOUN
**end**
**à la fin de la leçon**
at the end of the lesson
**'Fin'**
'The End'
**fin juin**
at the end of June
**la fin de semaine** ( _Canada_ )
the weekend
**B** MASC ADJECTIVE (FEM **fine** )
**slim**
**Elle est fine.**
She's slim.
la **finale** FEM NOUN
**final**
**Ils sont en finale.**
They're through to the final.
**les quarts de finale**
the quarter finals
**finalement** ADVERB
**1** **in the end**
**Finalement, ils ont perdu.**
They lost in the end.
**2** **after all**
**Finalement, tu avais raison.**
You were right after all.
**fini** MASC ADJECTIVE (FEM **finie** )
**finished**
**finir** VERB
**to finish**
**Le cours finit à onze heures.**
The lesson finishes at 11 o'clock.
**J'ai fini!**
I've finished!
**finlandais** MASC NOUN, MASC ADJECTIVE (FEM **finlandaise** )
**Finnish**
le **Finlandais** MASC NOUN
la **Finlandaise** FEM NOUN
**Finn**
la **Finlande** FEM NOUN
**Finland**
le **flacon** MASC NOUN
**bottle**
les **flageolets** MASC PL NOUN
**small haricot beans**
**flamand** MASC NOUN, MASC ADJECTIVE (FEM **flamande** )
**Flemish**
**_Did you know...?_**
_French is one of the languages spoken in Belgium. The other is Flemish; it is similar to Dutch._
le **Flamand** MASC NOUN
la **Flamande** FEM NOUN
**Fleming**
**_Did you know...?_**
_A_ **Flamand** _or a_ **Flamande** _is a Belgian person who speaks Flemish._
la **flamme** FEM NOUN
**flame**
**en flammes**
on fire
le **flan** MASC NOUN
**baked custard**
la **flaque** FEM NOUN
**puddle**
la **flèche** FEM NOUN
**arrow**
les **fléchettes** FEM PL NOUN
**darts**
**J'aime jouer aux fléchettes.**
I like playing darts.
la **fleur** FEM NOUN
**flower**
**un bouquet de fleurs**
a bunch of flowers
**Les arbres sont en fleurs.**
The trees are in blossom.
le/la **fleuriste** MASC/FEM NOUN
**florist**
le **fleuve** MASC NOUN
**river**
**_Did you know...?_**
_In France, only big rivers are called_ **fleuves** : _the Seine, the Loire, the Garonne, the Rhône, and the Rhine._
le **flipper** MASC NOUN
**pinball machine**
le **flocon** MASC NOUN
**flake**
**un flocon de neige**
a snow flake
**des flocons d'avoine**
oat flakes
**flotter** VERB
**to float**
la **flûte** FEM NOUN
**flute**
**Je joue de la flûte.**
I play the flute.
**une flûte à bec**
a recorder
le **foie** MASC NOUN
**liver**
**une crise de foie**
a stomach upset
le **foin** MASC NOUN
**hay**
**le rhume des foins**
hay fever
la **foire** FEM NOUN
**fair**
la **fois** FEM NOUN
**time**
**la première fois**
the first time
**à chaque fois**
each time
**deux fois deux font quatre**
two times two is four
**une fois**
once
**deux fois**
twice
**folklorique** ADJECTIVE
**folk**
**la musique folklorique**
folk music
**folle** FEM ADJECTIVE
**mad**
**Elle est folle!**
She's mad!
**foncé** MASC ADJECTIVE (FEM **foncée** )
**dark**
**une couleur très foncée**
a very dark colour
**des rideaux bleu foncé**
dark blue curtains
le/la **fonctionnaire** MASC/FEM NOUN
**civil servant**
le **fond** MASC NOUN
**1** **bottom**
**Mon porte-monnaie est au fond de mon sac.**
My purse is at the bottom of my bag.
**2** **end**
**Les toilettes sont au fond du couloir.**
The toilets are at the end of the corridor.
**fondre** VERB
**to melt**
**La neige fond.**
The snow is melting.
**fondu** MASC ADJECTIVE (FEM **fondue** )
**melted**
**Ma glace est toute fondue.**
My ice cream is all melted.
la **fondue** FEM NOUN
**fondue**
**_Did you know...?_**
_A_ **fondue** _is a Swiss dish. Guests around a table dip bits of dried bread into a pot of melted cheese. If you lose your bread in the cheese, you can be given a forfeit!_
**font** VERB _see_ **faire**
**Elles font leur devoirs ensemble.**
They do their homework together.
la **fontaine** FEM NOUN
**fountain**
le **foot** MASC NOUN
**football**
**Je fais du foot avec mes copains.**
I play football with my friends.
**_Did you know...?_**
**le foot** _is a slang way of saying_ **le football**. _A slang term for 'football' in English is 'footy'._
le **football** MASC NOUN
**football**
**Tu veux jouer au football?**
Do you want to play football?
le **footballeur** MASC NOUN
**footballer**
le **footing** MASC NOUN
**jogging**
**Tu veux faire du footing?**
Do you want to go jogging?
**forain**
**forain** _can be an adjective or a noun._
**A** MASC ADJECTIVE (FEM **foraine** )
**une fête foraine**
a funfair
**B** MASC NOUN
**fairground worker**
la **force** FEM NOUN
**strength**
**Je n'ai pas beaucoup de force dans les bras.**
I haven't got much strength in my arms.
la **forêt** FEM NOUN
**forest**
la **forme** FEM NOUN
**être en forme**
to be fit
**Ça va? Tu es en forme?**
How are you? Are you fit?
**Je ne suis pas en forme aujourd'hui.**
I'm not feeling too good today.
**formidable** ADJECTIVE
**great**
**Vous avez fini? Formidable!**
Have you finished? That's great!
le **formulaire** MASC NOUN
**form**
**Tu dois remplir le formulaire.**
You have to fill in the form.
**fort**
**fort** _can be an adjective or an adverb._
**A** MASC ADJECTIVE (FEM **forte** )
**1** **strong**
**Le café est trop fort.**
The coffee's too strong.
**2** **good**
**Il est très fort en maths.**
He's very good at maths.
**B** ADVERB
**1** **loud**
**Tu peux parler plus fort?**
Can you speak louder?
**2** **hard**
**Tu dois le frapper fort.**
You've got to hit it hard.
**fou** MASC ADJECTIVE (FEM **folle** )
**mad**
**Tu es fou?**
Are you mad?
la **foudre** FEM NOUN
**lightning**
le **foulard** MASC NOUN
**scarf**
la **foule** FEM NOUN
**crowd**
le **four** MASC NOUN
**oven**
**un four à micro-ondes**
a microwave oven
la **fourchette** FEM NOUN
**fork**
la **fourmi** FEM NOUN
**ant**
**J'ai des fourmis dans les jambes.**
I've got pins and needles in my legs.
**_Language tip_**
_The French actually means 'I've got ants in my legs'!_
les **fournitures** FEM PL NOUN
**les fournitures scolaires**
school stationery
la **fourrure** FEM NOUN
**fur**
**frais** MASC ADJECTIVE (FEM **fraîche** )
**1** **fresh**
**des œufs frais**
fresh eggs
**2** **chilly**
**Il fait un peu frais ce soir.**
It's a bit chilly this evening.
**3** **cool**
**des boissons fraîches**
cool drinks
la **fraise** FEM NOUN
**strawberry**
**les fraises des bois**
wild strawberries
la **framboise** FEM NOUN
**raspberry**
**franc**
**franc** _can be an adjective or a noun._
**A** MASC ADJECTIVE (FEM **franche** )
**frank**
**Pour être franc, je le trouve méchant.**
To be frank, I think he's horrible.
**B** MASC NOUN
**franc**
**_Did you know...?_**
_The euro replaced the franc as the unit of currency in France, Belgium and Luxembourg in 2002._
**français** MASC NOUN, MASC ADJECTIVE (FEM **française** )
**French**
**J'apprends le français.**
I'm learning French.
le **Français** MASC NOUN
**Frenchman**
**les Français**
the French
la **Française** FEM NOUN
**Frenchwoman**
la **France** FEM NOUN
**France**
**franche** FEM ADJECTIVE _see_ **franc**
**frank**
**francophone** ADJECTIVE
**French-speaking**
la **frange** FEM NOUN
**fringe**
**J'ai une frange.**
I've got a fringe.
**frapper** VERB
**Frappez dans vos mains.**
Clap your hands.
**On frappe à la porte.**
Somebody's knocking at the door.
le **frère** MASC NOUN
**brother**
**mon grand frère**
my big brother
**mon petit frère**
my little brother
le **frigidaire** ® MASC NOUN
**refrigerator**
le **frigo** MASC NOUN
**fridge**
**frisé** MASC ADJECTIVE (FEM **frisée** )
**curly**
**J'ai les cheveux frisés.**
I've got curly hair.
**frit** MASC ADJECTIVE (FEM **frite** )
**fried**
**du poisson frit**
fried fish
les **frites** FEM PL NOUN
**chips**
**J'adore le steak-frites.**
I love steak and chips.
**froid** MASC NOUN, MASC ADJECTIVE (FEM **froide** )
**cold**
**La soupe est froide!**
The soup is cold!
**J'ai froid.**
I'm cold.
**Il fait froid.**
It's cold.
le **fromage** MASC NOUN
**cheese**
**Tu veux du fromage ou un dessert?**
Would you like some cheese or a pudding?
**un sandwich au fromage**
a cheese sandwich
le **front** MASC NOUN
**forehead**
la **frontière** FEM NOUN
**border**
le **fruit** MASC NOUN
**fruit**
**J'aime les fruits.**
I like fruit.
**un fruit**
a piece of fruit
**les fruits de mer**
seafood
**fumé** MASC ADJECTIVE (FEM **fumée** )
**smoked**
**du saumon fumé**
smoked salmon
la **fumée** FEM NOUN
**smoke**
**fumer** VERB
**to smoke**
**Il fume la pipe.**
He smokes a pipe.
le **fumeur** MASC NOUN
**smoker**
**un compartiment fumeurs**
a smoking compartment
le **furet** MASC NOUN
**ferret**
**furieux** MASC ADJECTIVE (FEM **furieuse** )
**furious**
la **fusée** FEM NOUN
**rocket**
le **fusil** MASC NOUN
**gun**
le **futur** MASC NOUN
**future**
# **G g**
le **gage** MASC NOUN
**forfeit**
le **gagnant** MASC NOUN
la **gagnante** FEM NOUN
**winner**
**gagner** VERB
**to win**
**Qui a gagné?**
Who won?
**J'ai gagné!**
I've won!
la **galerie** FEM NOUN
**gallery**
**une galerie de peinture**
an art gallery
**une galerie marchande**
a shopping arcade
le **galet** MASC NOUN
**pebble**
la **galette** FEM NOUN
**1** **cake**
**2** **biscuit**
**des galettes pur beurre**
shortbread biscuits
**la galette des Rois**
**_Did you know...?_**
_A_ **galette des Rois** _is a cake eaten at Epiphany (the sixth of January) which contains a little figure. The person who finds it is the king (or queen) and gets a paper crown. They then choose someone to be their queen (or king)._
**Galles** FEM NOUN
**le pays de Galles**
Wales
**gallois** MASC NOUN, MASC ADJECTIVE (FEM **galloise** )
**Welsh**
le **Gallois** MASC NOUN
**Welshman**
**les Gallois**
the Welsh
la **Galloise** FEM NOUN
**Welshwoman**
le **gant** MASC NOUN
**glove**
**des gants en laine**
woollen gloves
**un gant de toilette**
a face cloth
le **garage** MASC NOUN
**garage**
le **garagiste** MASC NOUN
**garage owner**
le **garçon** MASC NOUN
**boy**
**Les garçons, levez-vous!**
Stand up, boys!
**garder** VERB
**1** **to keep**
**Tu peux garder ce crayon.**
You can keep this pencil.
**2** **to look after**
**Aujourd'hui, je garde ma nièce.**
I'm looking after my niece today.
la **garderie** FEM NOUN
**nursery**
le **gardien** MASC NOUN
la **gardienne** FEM NOUN
**caretaker**
**un gardien de musée**
a museum attendant
**un gardien de but**
a goalkeeper
la **gare** FEM NOUN
**station**
**Où est la gare?**
Where's the station?
**la gare routière**
the bus station
**garer** VERB
**to park**
**Où as-tu garé la voiture?**
Where have you parked the car?
**se garer**
**to park**
**Gare-toi devant la maison.**
Park in front of the house.
**garni** MASC ADJECTIVE (FEM **garnie** )
**un plat garni**
a main course
**_Did you know...?_**
_A_ **plat garni** _is a dish served with vegetables, salad, chips, or rice._
les **gars** MASC PL NOUN
**guys**
**Salut, les gars!**
Hi guys!
**gaspiller** VERB
**to waste**
le **gâteau** MASC NOUN
(PL les **gâteaux** )
**cake**
**un gâteau d'anniversaire**
a birthday cake
**un gâteau sec**
a biscuit
**gauche**
**gauche** _can be a noun or an adjective._
**A** FEM NOUN
**left**
**sur votre gauche**
on your left
**à gauche**
left/on the left
**_Language tip_**
**à gauche** _has two translations. Look at the examples._
**Tournez à gauche.**
Turn left.
**Prenez la troisième rue à gauche.**
Take the third street on the left.
**C'est à gauche.**
It's on your left.
**la deuxième rue à gauche**
the second street on the left
**B** ADJECTIVE
**left**
**Levez le bras gauche!**
Put up your left arm!
**gaucher** MASC ADJECTIVE (FEM **gauchère** )
**left-handed**
la **gaufre** FEM NOUN
**waffle**
la **gaufrette** FEM NOUN
**wafer**
le **Gaulois** MASC NOUN
la **Gauloise** FEM NOUN
**Gaul**
**J'aime les bandes dessinées d'Astérix le Gaulois.**
I like Asterix the Gaul comic strips.
le **gaz** MASC NOUN
**gas**
**gazeux** MASC ADJECTIVE (FEM **gazeuse** )
**une boisson gazeuse**
a fizzy drink
**de l'eau gazeuse**
sparkling water
**géant** MASC NOUN, MASC ADJECTIVE (FEM **géante** )
**giant**
la **gelée** FEM NOUN
**jelly**
**geler** VERB
**to freeze**
**Il gèle.**
It's freezing.
le **gendarme** MASC NOUN
**policeman**
la **gendarmerie** FEM NOUN
**police station**
**général** MASC ADJECTIVE (FEM **générale** )
**general**
**en général**
usually
**généralement** ADVERB
**generally**
**généreux** MASC ADJECTIVE (FEM **généreuse** )
**generous**
**génial** MASC ADJECTIVE (FEM **géniale** )
**great**
**C'est génial.**
That's great.
le **génie** MASC NOUN
**genius**
**C'est un vrai génie.**
She's a real genius.
le **genou** MASC NOUN
(PL les **genoux** )
**knee**
**Mettez-vous à genoux.**
Kneel down.
le **genre** MASC NOUN
**1** **kind**
**C'est un genre de gâteau à la crème.**
It's a kind of cream cake.
**2** **gender**
**De quel genre est 'chien'?**
What's the gender of 'chien'?
les **gens** MASC PL NOUN
**people**
**gentil** MASC ADJECTIVE (FEM **gentille** )
**1** **nice**
**Nos voisins sont très gentils.**
Our neighbours are very nice.
**2** **kind**
**C'est gentil.**
That's kind.
la **géographie** FEM NOUN
**geography**
la **géométrie** FEM NOUN
**geometry**
**germain** MASC ADJECTIVE (FEM **germaine** )
**Hugues est mon cousin germain.**
Hugues is my first cousin.
**Delphine est ma cousine germaine.**
Delphine is my first cousin.
le **gigot** MASC NOUN
**leg of lamb**
le **gilet** MASC NOUN
**1** **cardigan**
**2** **waistcoat**
la **girafe** FEM NOUN
**giraffe**
le **gîte** MASC NOUN
**holiday home**
**Nous avons loué un gîte pour cet été.**
We've rented a holiday home for this summer.
la **glace** FEM NOUN
**1** **ice cream**
**Je voudrais une glace à la fraise.**
I'd like a strawberry ice cream.
**2** **ice**
**Elle a glissé sur la glace.**
She slipped on the ice.
**3** **mirror**
**Il se regarde souvent dans la glace.**
He often looks at himself in the mirror.
**glacé** MASC ADJECTIVE (FEM **glacée** )
**1** **icy**
**un vent glacé**
an icy wind
**2** **iced**
**un thé glacé**
an iced tea
le **glaçon** MASC NOUN
**ice cube**
**glisser** VERB
**1** **to slip**
**Elle a glissé sur une peau de banane.**
She slipped on a banana skin.
**2** **to be slippery**
**Attention, ça glisse!**
Watch out, it's slippery!
le **goéland** MASC NOUN
**seagull**
le **golf** MASC NOUN
**1** **golf**
**Il joue au golf.**
He plays golf.
**2** **golf course**
**C'est un golf dix-huit trous.**
It's an 18-hole golf course.
la **gomme** FEM NOUN
**rubber**
**gommer** VERB
**to rub out**
la **gorge** FEM NOUN
**throat**
**J'ai mal à la gorge.**
I've got a sore throat.
le **gorille** MASC NOUN
**gorilla**
**gourmand** MASC ADJECTIVE (FEM **gourmande** )
**greedy**
le **goût** MASC NOUN
**taste**
**Ça a mauvais goût.**
It has a horrible taste.
**Ça a un goût sucré.**
It tastes sweet.
**Ça a bon goût.**
It tastes nice.
**goûter**
**goûter** _can be a noun or a verb._
**A** MASC NOUN
**afternoon snack**
**C'est l'heure du goûter.**
It's time for an afternoon snack.
**B** VERB
**1** **to taste**
**Tu veux goûter?**
Do you want to taste it?
**2** **to have an afternoon snack**
**Je goûte généralement vers quatre heures.**
I usually have a snack around four o'clock.
la **graine** FEM NOUN
**seed**
la **grammaire** FEM NOUN
**grammar**
le **gramme** MASC NOUN
**gramme**
**trois cents grammes de fromage**
three hundred grammes of cheese
**grand** MASC ADJECTIVE (FEM **grande** )
**1** **tall**
**Il est grand.**
He's tall.
**2** **big**
**C'est sa grande sœur.**
She's his big sister.
**les grandes vacances**
the summer holidays
**un grand magasin**
a department store
**grand-chose** NOUN
**pas grand-chose**
not much
la **Grande-Bretagne** FEM NOUN
**Britain**
**J'habite en Grande-Bretagne.**
I live in Britain.
**_Language tip_**
**Bretagne** _means 'Brittany'. Britain is bigger than Brittany, which is why its French name is_ **Grande-Bretagne**.
**grandir** VERB
**to grow**
**Il a beaucoup grandi.**
He's grown a lot.
la **grand-mère** FEM NOUN
**grandmother**
le **grand-père** MASC NOUN
**grandfather**
les **grands-parents** MASC PL NOUN
**grandparents**
**gras** MASC ADJECTIVE (FEM **grasse** )
**1** **fatty**
**Évitez les aliments gras.**
Avoid fatty foods.
**2** **greasy**
**J'ai les cheveux gras.**
I've got greasy hair.
**3** **oily**
**J'ai une peau grasse.**
I've got oily skin.
le **gratte-ciel** MASC NOUN
**skyscraper**
**gratter** VERB
**1** **to scratch**
**Ne gratte pas tes piqûres de moustiques!**
Don't scratch your mosquito bites!
**2** **to be itchy**
**Ce pull me gratte!**
This jumper's itchy.
**gratuit** MASC ADJECTIVE (FEM **gratuite** )
**free**
**entrée gratuite**
admission free
**grave** ADJECTIVE
**serious**
**C'est grave?**
Is it serious?
**Ce n'est pas grave.**
It doesn't matter.
**un accent grave**
a grave accent
**gravement** ADVERB
**seriously**
**Il est gravement blessé.**
He is seriously injured.
**grec** MASC NOUN, MASC ADJECTIVE (FEM **grecque** )
**Greek**
le **Grec** MASC NOUN
la **Grecque** FEM NOUN
**Greek**
la **Grèce** FEM NOUN
**Greece**
**grêler** VERB
**to hail**
**Il grêle.**
It's hailing.
la **grenadine** FEM NOUN
**grenadine**
**_Did you know...?_**
**grenadine** _is a popular drink with children in France. It is very pink!_
le **grenier** MASC NOUN
**attic**
la **grenouille** FEM NOUN
**frog**
la **grève** FEM NOUN
**strike**
**en grève**
on strike
**Les profs sont en grève.**
The teachers are on strike.
**griffer** VERB
**to scratch**
**Le chat m'a griffé.**
The cat scratched me.
la **grillade** FEM NOUN
**grilled food**
**une grillade d'agneau**
grilled lamb
le **grille-pain** MASC NOUN
**toaster**
**griller** VERB
**1** **to toast**
**du pain grillé**
toast
**2** **to grill**
**des saucisses grillées**
grilled sausages
la **grimace** FEM NOUN
**faire des grimaces**
to make faces
**Arrête de faire des grimaces.**
Stop making faces.
**grimper** VERB
**to climb**
**grincheux** MASC ADJECTIVE (FEM **grincheuse** )
**grumpy**
la **grippe** FEM NOUN
**flu**
**Carol a la grippe.**
Carol has got flu.
**gris** MASC ADJECTIVE (FEM **grise** )
**grey**
**grogner** VERB
**to growl**
**gronder** VERB
**se faire gronder**
to get a telling off
**Tu vas te faire gronder par ton père!**
You're going to get a telling off from your father!
**gros** MASC ADJECTIVE (FEM **grosse** )
**1** **big**
**une grosse pomme**
a big apple
**2** **fat**
**Il est un peu gros.**
He's quite fat.
la **groseille** FEM NOUN
**redcurrant**
la **grotte** FEM NOUN
**cave**
le **groupe** MASC NOUN
**group**
**Mettez-vous en groupes de quatre.**
Get into groups of four.
la **guêpe** FEM NOUN
**wasp**
**guérir** VERB
**to recover**
**Il est complètement guéri.**
He's fully recovered.
la **guerre** FEM NOUN
**war**
la **gueule** FEM NOUN
**mouth**
**Regarde, le chat a une souris dans sa gueule!**
Look, the cat has a mouse in its mouth!
le **guichet** MASC NOUN
**counter**
le **guide** MASC NOUN
**guide**
**guider** VERB
**to guide**
la **guirlande** FEM NOUN
**tinsel**
**Nous allons décorer le sapin de Noël avec des guirlandes.**
We're going to decorate the Christmas tree with tinsel.
**une guirlande en papier**
a paper chain
la **guitare** FEM NOUN
**guitar**
**Je joue de la guitare.**
I play the guitar.
la **gym** FEM NOUN
**PE**
le **gymnase** MASC NOUN
**gym**
**L'école a un nouveau gymnase.**
The school's got a new gym.
la **gymnastique** FEM NOUN
**gymnastics**
**Je fais de la gymnastique le mercredi.**
I do gymnastics on Wednesdays.
# **H h**
s' **habiller** VERB
**to get dressed**
**Je m'habille rapidement.**
I get dressed quickly.
l' **habitant** MASC NOUN
l' **habitante** FEM NOUN
**inhabitant**
**habiter** VERB
**to live**
**Il habite à Montpellier.**
He lives in Montpellier.
les **habits** MASC PL NOUN
**clothes**
l' **habitude** FEM NOUN
**habit**
**une mauvaise habitude**
a bad habit
**J'ai l'habitude.**
I'm used to it.
**d'habitude**
usually
**D'habitude, je vais à la piscine le mardi.**
I usually go to the pool on Tuesdays.
**comme d'habitude**
as usual
le **hachis** MASC NOUN
**le hachis Parmentier**
shepherd's pie
la **haie** FEM NOUN
**hedge**
**haïr** VERB
**to hate**
**Je la hais.**
I hate her.
les **halles** FEM PL NOUN
**covered market**
le **hamster** MASC NOUN
**hamster**
la **hanche** FEM NOUN
**hip**
le **handball** MASC NOUN
**handball**
**Le lundi, je joue au handball.**
I play handball on Mondays.
**_Did you know...?_**
**handball** _is a very popular game in French schools. It is played on a similar pitch to football but players throw the ball instead of kicking it._
**handicapé** MASC ADJECTIVE (FEM **handicapée** )
**disabled**
les **handicapés** MASC PL NOUN
**disabled people**
les **haricots** MASC PL NOUN
**beans**
**les haricots verts**
green beans
**les haricots blancs**
haricot beans
l' **harmonica** MASC NOUN
**mouth organ**
la **harpe** FEM NOUN
**harp**
le **hasard** MASC NOUN
**au hasard**
at random
**Choisis un numéro au hasard.**
Choose a number at random.
**par hasard**
by chance
**Je l'ai rencontrée par hasard au supermarché.**
I met her at the supermarket by chance.
**hausser** VERB
**hausser les épaules**
to shrug one's shoulders
**haut**
**haut** _can be an adjective or a noun._
**A** MASC ADJECTIVE (FEM **haute** )
**high**
**La fenêtre est trop haute.**
The window is too high.
**B** MASC NOUN
**en haut**
upstairs/at the top
**_Language tip_**
**en haut** _has two translations. Look at the examples._
**La salle de bain est en haut.**
The bathroom is upstairs.
**Le nid est tout en haut de l'arbre.**
The nest is right at the top of the tree.
**trois mètres de haut**
three metres high
la **hauteur** FEM NOUN
**height**
**hein?** EXCLAMATION
**eh?**
**Hein? Qu'est-ce que tu dis?**
Eh? What did you say?
l' **hélicoptère** MASC NOUN
**helicopter**
l' **herbe** FEM NOUN
**grass**
**les herbes de Provence**
mixed herbs
**les fines herbes**
mixed herbs
le **hérisson** MASC NOUN
**hedgehog**
l' **héroïne** FEM NOUN
**heroine**
**l'héroïne du roman**
the heroine of the novel
le **héros** MASC NOUN
**hero**
**C'est le héros du film.**
He's the hero of the film.
**hésiter** VERB
**to hesitate**
**J'hésite.**
I can't decide.
**J'hésite entre un hamster et un lapin.**
I don't know whether to choose a hamster or a rabbit.
l' **heure** FEM NOUN
**1** **hour**
**Le trajet dure six heures.**
The journey lasts six hours.
**2** **time**
**Vous avez l'heure?**
Have you got the time?
**À quelle heure?**
What time?
**À quelle heure arrivons-nous?**
What time do we arrive?
**Elle est toujours à l'heure.**
She's always on time.
**3** **o'clock**
**à deux heures du matin**
at two o'clock in the morning
**4** **period**
**une heure de français**
a period of French
**Quelle heure est-il?**
What time is it?
**Il est sept heures dix.**
It's ten past seven.
**à dix-neuf heures**
at seven o'clock
**_Did you know...?_**
_The 24-hour clock is used in France for travel times, appointments, and other formal situations._
**heureusement** ADVERB
**luckily**
**heureux** MASC ADJECTIVE (FEM **heureuse** )
**happy**
l' **hexagone** MASC NOUN
**hexagon**
**l'Hexagone**
France
**_Did you know...?_**
_A hexagon has six sides. France is often called_ **l'Hexagone** _because of its six-sided shape._
le **hibou** MASC NOUN
(PL les **hiboux** )
**owl**
**hier** ADVERB
**yesterday**
**avant-hier**
the day before yesterday
la **hi-fi** FEM NOUN
**une chaîne hi-fi**
a hifi
**hippique** ADJECTIVE
**un club hippique**
a riding centre
**un concours hippique**
a horse show
l' **hippopotame** MASC NOUN
**hippopotamus**
**_Language tip_**
**hippopotame** _is never shortened to 'hippo' in French as it is in English._
l' **hirondelle** FEM NOUN
**swallow**
l' **histoire** FEM NOUN
**1** **history**
**un cours d'histoire**
a history lesson
**2** **story**
l' **hiver** MASC NOUN
**winter**
**en hiver**
in winter
le **hockey** MASC NOUN
**hockey**
**Il joue au hockey.**
He plays hockey.
**le hockey sur glace**
ice hockey
**hollandais** MASC NOUN, MASC ADJECTIVE (FEM **hollandaise** )
**Dutch**
le **Hollandais** MASC NOUN
**Dutch man**
**les Hollandais**
the Dutch
la **Hollandaise** FEM NOUN
**Dutch woman**
la **Hollande** FEM NOUN
**Holland**
le **homard** MASC NOUN
**lobster**
l' **homme** MASC NOUN
**man**
**un homme d'affaires**
a businessman
la **Hongrie** FEM NOUN
**Hungary**
**honnête** ADJECTIVE
**honest**
la **honte** FEM NOUN
**avoir honte**
to be ashamed
**J'ai un peu honte.**
I'm a bit ashamed.
l' **hôpital** MASC NOUN
(PL les **hôpitaux** )
**hospital**
le **hoquet** MASC NOUN
**J'ai le hoquet.**
I've got hiccups.
l' **horaire** MASC NOUN
**timetable**
**les horaires de train**
the train timetable
l' **horloge** FEM NOUN
**clock**
l' **horreur** FEM NOUN
**J'ai horreur du chou.**
I hate cabbage.
**horrible** ADJECTIVE
**horrible**
le **hors-d'œuvre** MASC NOUN
**starter**
**Comme hors-d'œuvre, il y a des carottes râpées.**
As a starter there's carrot salad.
l' **hôtel** MASC NOUN
**hotel**
**Nous passons une semaine à l'hôtel.**
We are spending a week at a hotel.
**l'hôtel de ville**
the town hall
l' **hôtesse** FEM NOUN
**une hôtesse de l'air**
an air hostess
le **houx** MASC NOUN
**holly**
l' **huile** FEM NOUN
**oil**
**huit** NUMBER
**eight**
**Il est huit heures.**
It's eight o'clock.
**Il a huit ans.**
He's eight.
**dans huit jours**
in a week's time
**le huit février**
the eighth of February
la **huitaine** FEM NOUN
**une huitaine de jours**
about a week
**Nous rentrons dans une huitaine de jours.**
We'll be back in about a week.
**huitième** ADJECTIVE
**eighth**
**au huitième étage**
on the eighth floor
l' **huître** FEM NOUN
**oyster**
**humain** MASC NOUN, MASC ADJECTIVE (FEM **humaine** )
**un être humain**
a human being
l' **humeur** FEM NOUN
**mood**
**Il est de bonne humeur.**
He's in a good mood.
**Elle est de mauvaise humeur.**
She's in a bad mood.
**humide** ADJECTIVE
**damp**
l' **humour** MASC NOUN
**avoir le sens de l'humour**
to have a sense of humour
**Il n'a pas le sens de l'humour.**
He has no sense of humour.
**hurler** VERB
**1** **to howl**
**Le chien des voisins hurle tous les soirs.**
The neighbours' dog howls every evening.
**2** **to yell**
**Arrête de hurler comme ça!**
Stop yelling like that!
**hygiénique** MASC ADJECTIVE
**le papier hygiénique**
toilet paper
l' **hypermarché** MASC NOUN
**hypermarket**
# **I i**
**ici** ADVERB
**here**
**Viens ici.**
Come here.
l' **idée** FEM NOUN
**idea**
**C'est une bonne idée.**
It's a good idea.
**idéal** MASC ADJECTIVE (FEM **idéale** )
**ideal**
**Décrivez votre chambre idéale.**
Describe your ideal bedroom.
**identique** ADJECTIVE
**identical**
l' **identité** FEM NOUN
**identity**
**idiot** MASC ADJECTIVE (FEM **idiote** )
**stupid**
**C'est vraiment une plaisanterie idiote!**
It's really a stupid joke!
l' **idiot** MASC NOUN
l' **idiote** FEM NOUN
**idiot**
**il** PRONOUN
**1** **he**
**Il habite à Paris.**
He lives in Paris.
**2** **it**
**Il pleut.**
It's raining.
**Attention à ce chien: il mord.**
Watch that dog: it bites.
l' **île** FEM NOUN
**island**
**les îles Anglo-Normandes**
the Channel Islands
**l'île de Man**
the Isle of Man
**l'île de Wight**
the Isle of Wight
**ils** PRONOUN
**they**
**Ils sont à la piscine.**
They are at the swimming pool.
l' **image** FEM NOUN
**picture**
**Regardez les images.**
Look at the pictures.
**imaginaire** ADJECTIVE
**imaginary**
**C'est un personnage imaginaire.**
He's an imaginary character.
l' **imagination** FEM NOUN
**imagination**
**Elle a beaucoup d'imagination.**
She's got a vivid imagination.
**imaginer** VERB
**to imagine**
l' **imbécile** MASC/FEM NOUN
**idiot**
**C'est une imbécile.**
She's an idiot.
**Il fait l'imbécile dans la classe.**
He plays the fool in the class.
**imiter** VERB
**to imitate**
**immédiatement** ADVERB
**immediately**
**immense** ADJECTIVE
**huge**
**une maison immense**
a huge house
l' **immeuble** MASC NOUN
**block of flats**
**J'habite dans un immeuble.**
I live in a block of flats.
les **immigrés** MASC PL NOUN
**immigrants**
**immobilier** MASC ADJECTIVE (FEM **immobilière** )
**une agence immobilière**
an estate agent's
**impair** MASC ADJECTIVE
**un nombre impair**
an odd number
l' **impasse** FEM NOUN
**cul-de-sac**
**Ma maison est au bout d'une impasse.**
My house is at the end of a cul-de-sac.
**impeccable** ADJECTIVE
**1** **immaculate**
**Elle est toujours impeccable.**
She's always immaculate.
**2** **perfect**
**C'est impeccable!**
That's perfect!
l' **imper** MASC NOUN
**raincoat**
l' **imperméable** MASC NOUN
**raincoat**
**impoli** MASC ADJECTIVE (FEM **impolie** )
**rude**
l' **importance** FEM NOUN
**Ça n'a pas d'importance.**
It doesn't matter.
**important** MASC ADJECTIVE (FEM **importante** )
**1** **important**
**une lettre importante**
an important letter
**2** **large**
**un nombre important**
a large number
**importer** VERB
**Peu importe.**
It doesn't matter.
**impossible** ADJECTIVE
**impossible**
l' **impression** FEM NOUN
**impression**
**Ce n'est qu'une impression.**
It's only an impression.
**avoir l'impression que**
to have a feeling that
**J'ai l'impression qu'il va neiger.**
I have a feeling that it's going
to snow.
**impressionnant** MASC ADJECTIVE (FEM **impressionnante** )
**impressive**
**impressionné** MASC ADJECTIVE (FEM **impressionnée** )
**impressed**
**Je suis très impressionné.**
I'm very impressed.
l' **imprimante** FEM NOUN
**printer**
**imprimer** VERB
**to print**
l' **incendie** MASC NOUN
**fire**
**un incendie de forêt**
a forest fire
l' **incident** MASC NOUN
**incident**
l' **inconnu** MASC NOUN
l' **inconnue** FEM NOUN
**stranger**
**Ne parle pas à des inconnus.**
Don't speak to strangers.
l' **inconvénient** MASC NOUN
**disadvantage**
**incorrect** MASC ADJECTIVE (FEM **incorrecte** )
**incorrect**
**une réponse incorrecte**
an incorrect answer
**incroyable** ADJECTIVE
**incredible**
l' **Inde** FEM NOUN
**India**
**indépendant** MASC ADJECTIVE (FEM **indépendante** )
**independent**
l' **index** MASC NOUN
**index finger**
les **indications** FEM PL NOUN
**instructions**
**Suivez les indications.**
Follow the instructions.
l' **indice** MASC NOUN
**clue**
**Je te donne un indice?**
Shall I give you a clue?
**indien** MASC ADJECTIVE (FEM **indienne** )
**Indian**
l' **Indien** MASC NOUN
l' **Indienne** FEM NOUN
**Indian**
**les Indiens**
Indians
l' **industrie** FEM NOUN
**industry**
**infirme** ADJECTIVE
**disabled**
l' **infirmerie** FEM NOUN
**medical room**
**Elle est à l'infirmerie.**
She's in the medical room.
l' **infirmier** MASC NOUN
l' **infirmière** FEM NOUN
**nurse**
l' **informaticien** MASC NOUN
l' **informaticienne** FEM NOUN
**computer scientist**
les **informations** FEM PL NOUN
**1** **news**
**J'aime regarder les informations à la télé.**
I like watching the news on the TV.
**2** **information**
**Je voudrais quelques informations, s'il vous plaît.**
I'd like some information, please.
**une information**
a piece of information
l' **informatique** FEM NOUN
**1** **ICT**
**mon prof d'informatique**
my ICT teacher
**2** **computing**
**Il travaille dans l'informatique.**
He works in computing.
l' **infusion** FEM NOUN
**herbal tea**
l' **ingénieur** MASC NOUN
**engineer**
l' **inhalateur** MASC NOUN
**inhaler**
les **initiales** FEM PL NOUN
**initials**
**Quelles sont tes initiales?**
What are your initials?
l' **initiation** FEM NOUN
**introduction**
**un stage d'initiation au karaté**
an introductory course in karate
**injuste** ADJECTIVE
**unfair**
**C'est vraiment trop injuste.**
It is really quite unfair.
**innocent** MASC ADJECTIVE (FEM **innocente** )
**innocent**
l' **inondation** FEM NOUN
**flood**
**inquiet** MASC ADJECTIVE (FEM **inquiète** )
**worried**
s' **inquiéter** VERB
**to worry**
**Ne t'inquiète pas!**
Don't worry!
l' **insecte** MASC NOUN
**insect**
**insolent** MASC ADJECTIVE (FEM **insolente** )
**cheeky**
l' **inspecteur** MASC NOUN
l' **inspectrice** FEM NOUN
**inspector**
**Il y a une inspectrice à l'école.**
There's an inspector in the school.
l' **instant** MASC NOUN
**moment**
**Attendez un instant.**
Wait a moment.
l' **instituteur** MASC NOUN
l' **institutrice** FEM NOUN
**primary school teacher**
l' **instrument** MASC NOUN
**instrument**
**un instrument de musique**
a musical instrument
**insupportable** ADJECTIVE
**unbearable**
**intelligent** MASC ADJECTIVE (FEM **intelligente** )
**intelligent**
**Mon chien est très intelligent.**
My dog is very intelligent.
l' **interdiction** FEM NOUN
**'interdiction de fumer'**
'no smoking'
**'interdiction de stationner'**
'no parking'
**interdire** VERB
**to forbid**
**Ses parents lui ont interdit de sortir.**
His parents have forbidden him to go out.
**interdit** MASC ADJECTIVE (FEM **interdite** )
**forbidden**
**C'est interdit.**
It's forbidden.
**Il est interdit de courir dans les couloirs.**
Running in the corridors is forbidden.
**intéressant** MASC ADJECTIVE (FEM **intéressante** )
**interesting**
**intéresser** VERB
**to interest**
**L'histoire, ça m'intéresse.**
I'm interested in history.
**Je m'intéresse aux dinosaures.**
I'm interested in dinosaurs.
l' **intérêt** MASC NOUN
**Tu as intérêt à te dépêcher.**
You'd better hurry up.
**C'est un film sans intérêt.**
It's not a very interesting film.
l' **intérieur** MASC NOUN
**à l'intérieur**
inside
**Il fait plus frais à l'intérieur.**
It's cooler inside.
l' **internat** MASC NOUN
**boarding school**
**international** MASC ADJECTIVE (FEM **internationale** )
**international**
l' **interne** MASC/FEM NOUN
**boarder**
**_Did you know...?_**
_In French secondary schools, pupils can be described as_ **externe** _if they go home for lunch,_ **demi-pensionnaire** _if they have a school lunch, or_ **interne** _if they stay as boarders at the school._
l' **internet** MASC NOUN
**internet**
**sur internet**
on the internet
l' **interprète** MASC/FEM NOUN
**interpreter**
l' **interrogation** FEM NOUN
**test**
**une interrogation écrite**
a written test
**une interrogation orale**
an oral test
**interroger** VERB
**to ask questions**
**interrompre** VERB
**to interrupt**
**Ne m'interrompez pas.**
Don't interrupt me.
**intime** ADJECTIVE
**un journal intime**
a diary
**inutile** ADJECTIVE
**useless**
**inventer** VERB
**1** **to invent**
**J'ai inventé une machine.**
I have invented a machine.
**2** **to make up**
**Elle a inventé une excuse.**
She made up an excuse.
l' **inventeur** MASC NOUN
**inventor**
**inverse**
**inverse** _can be an adjective or a noun._
**A** ADJECTIVE
**dans le sens inverse des aiguilles d'une montre**
anti-clockwise
**B** MASC NOUN
**C'est l'inverse.**
It's the other way round.
l' **invité** MASC NOUN
l' **invitée** FEM NOUN
**guest**
**inviter** VERB
**to invite**
l' **iPod** ® MASC NOUN
**iPod** ®
**irai** VERB _see_ **aller**
**J'irai demain au supermarché.**
I'll go to the supermarket tomorrow.
l' **Irak** MASC NOUN
**Iraq**
l' **Iran** MASC NOUN
**Iran**
**irlandais** MASC ADJECTIVE (FEM **irlandaise** )
**Irish**
l' **Irlandais** MASC NOUN
**Irishman**
**les Irlandais**
the Irish
l' **Irlandaise** FEM NOUN
**Irishwoman**
l' **Irlande** FEM NOUN
**Ireland**
**la République d'Irlande**
the Irish Republic
**l'Irlande du Nord**
Northern Ireland
l' **ironie** FEM NOUN
**irony**
**ironique** ADJECTIVE
**ironical**
**irons** VERB _see_ **aller**
**Nous irons à la plage cet après-midi.**
We'll go to the beach this afternoon.
**irrégulier** MASC ADJECTIVE (FEM **irrégulière** )
**irregular**
**un verbe irrégulier**
an irregular verb
**irriter** VERB
**to irritate**
**Elle m'irrite.**
She's irritating me.
**islamique** ADJECTIVE
**Islamic**
l' **Islande** FEM NOUN
**Iceland**
**isolé** MASC ADJECTIVE (FEM **isolée** )
**isolated**
**une ferme isolée**
an isolated farm
**Israël** MASC NOUN
**Israel**
**israélien** MASC ADJECTIVE (FEM **israélienne** )
**Israeli**
l' **Israélien** MASC NOUN
l' **Israélienne** FEM NOUN
**Israeli**
l' **issue** FEM NOUN
**'issue de secours'**
'emergency exit'
**une voie sans issue**
a dead end
l' **Italie** FEM NOUN
**Italy**
**italien** MASC NOUN, MASC ADJECTIVE (FEM **italienne** )
**Italian**
l' **Italien** MASC NOUN
l' **Italienne** FEM NOUN
**Italian**
# **J j**
**j'** PRONOUN
**_Language tip_**
**je** _changes to_ **j'** _before a vowel sound._
**I**
**J'arrive!**
I'm coming!
**J'habite à Calais.**
I live in Calais.
la **jalousie** FEM NOUN
**jealousy**
**jaloux** MASC ADJECTIVE (FEM **jalouse** )
**jealous**
**jamais** ADVERB
**never**
**Tu vas souvent au cinéma? — Non, jamais.**
Do you go to the cinema often? — No, never.
**Elle ne fait jamais la vaisselle.**
She never does the washing-up.
la **jambe** FEM NOUN
**leg**
le **jambon** MASC NOUN
**ham**
**le jambon cru**
Parma ham
**janvier** MASC NOUN
**January**
**en janvier**
in January
**au mois de janvier**
in January
**le vingt-quatre janvier**
the twenty-fourth of January
le **Japon** MASC NOUN
**Japan**
**japonais** MASC NOUN, MASC ADJECTIVE (FEM **japonaise** )
**Japanese**
le **Japonais** MASC NOUN
**Japanese man**
**les Japonais**
the Japanese
la **Japonaise** FEM NOUN
**Japanese woman**
le **jardin** MASC NOUN
**garden**
**Nous avons un grand jardin derrière la maison.**
We have a big garden at the back of the house.
**un jardin d'enfants**
a kindergarten
le **jardinage** MASC NOUN
**gardening**
**Le passe-temps préféré de mon père, c'est le jardinage.**
My dad's favourite hobby is gardening.
le **jardinier** MASC NOUN
**gardener**
**jaune**
**jaune** _can be an adjective or a noun._
**A** ADJECTIVE
**yellow**
**une robe jaune**
a yellow dress
**B** MASC NOUN
**yellow**
**Ma couleur préférée, c'est le jaune.**
My favourite colour is yellow.
**un jaune d'œuf**
an egg yolk
le **jazz** MASC NOUN
**jazz**
**je** PRONOUN
**_Language tip_**
**je** _changes to_ **j'** _before a vowel sound._
**I**
**Je déteste les araignées.**
I hate spiders.
le **jean** MASC NOUN
**jeans**
**Elle porte un jean.**
She is wearing jeans.
**une veste en jean**
a denim jacket
la **jeannette** FEM NOUN
**Brownie**
**_Did you know...?_**
_The Brownies aren't as common in France as they are in Britain._
**jeter** VERB
**1** **to throw**
**Jette ton chewing-gum à la poubelle.**
Throw your chewing gum in the bin.
**2** **to throw away**
**J'ai jeté mes vieux jouets.**
I've thrown away my old toys.
le **jeton** MASC NOUN
**counter**
**Je vous donne six jetons chacun.**
I'm giving you six counters each.
le **jeu** MASC NOUN (PL les **jeux** )
**game**
**C'est un jeu qui s'appelle 'le Pendu'.**
It's a game called 'Hangman'.
**un jeu de mots**
a pun
**un jeu de société**
a board game
**un jeu électronique**
an electronic game
**un jeu vidéo**
a video game
**un jeu de cartes**
a pack of cards/a card game
**_Language tip_**
**un jeu de cartes** _has two translations. Look at the examples._
**J'ai acheté un nouveau jeu de cartes.**
I've bought a new pack of cards.
**Tu connais ce jeu de cartes?**
Do you know this card game?
le **jeudi** MASC NOUN
**1** **Thursday**
**Aujourd'hui, nous sommes jeudi.**
It's Thursday today.
**2** **on Thursday**
**Il va venir jeudi.**
He's coming on Thursday.
**Le musée est fermé le jeudi.**
The museum is closed on Thursdays.
**tous les jeudis**
every Thursday
**le jeudi**
on Thursdays
**jeudi dernier**
last Thursday
**jeudi prochain**
next Thursday
**À jeudi!**
See you on Thursday!
**jeune** ADJECTIVE
**young**
**un jeune homme**
a young man
**une jeune femme**
a young woman
**une jeune fille**
a girl
les **jeunes** MASC PL NOUN
**young people**
la **jeunesse** FEM NOUN
**youth**
le **jogging** MASC NOUN
**1** **jogging**
**Il fait du jogging.**
He goes jogging.
**2** **tracksuit**
**Clémentine porte un jogging rose.**
Clémentine's wearing a pink tracksuit.
**joli** MASC ADJECTIVE (FEM **jolie** )
**pretty**
la **jonquille** FEM NOUN
**daffodil**
la **joue** FEM NOUN
**cheek**
**Elle a les joues roses.**
She's got pink cheeks.
**jouer** VERB
**to play**
**Le soir, je joue avec ma petite sœur.**
I play with my little sister in the evening.
**jouer de**
to play
**Il joue de la guitare et du piano.**
He plays the guitar and the piano.
**jouer à**
to play
**Elle joue au tennis.**
She plays tennis.
**Ils jouent aux cartes.**
They are playing cards.
le **jouet** MASC NOUN
**toy**
**Range tes jouets!**
Tidy up your toys!
le **joueur** MASC NOUN
la **joueuse** FEM NOUN
**player**
le **jour** MASC NOUN
**day**
**On est quel jour aujourd'hui?**
What day is it today?
**Il fait jour.**
It's daylight.
**le jour de l'An**
New Year's Day
**un jour de congé**
a day off
**le jour de Noël**
Christmas Day
**un jour férié**
a public holiday
**dans huit jours**
in a week
**dans quinze jours**
in a fortnight
le **journal** MASC NOUN
(PL les **journaux** )
**1** **newspaper**
**Mon père aime lire le journal.**
My dad likes to read the newspaper.
**le journal télévisé**
the television news
**2** **diary**
**J'écris tous les jours dans mon journal.**
I write in my diary every day.
le/la **journaliste** MASC/FEM NOUN
**journalist**
la **journée** FEM NOUN
**day**
**Nous allons passer la journée au bord de la mer.**
We are going to spend the day at the seaside.
**toute la journée**
all day long
**joyeux** MASC ADJECTIVE (FEM **joyeuse** )
**happy**
**des enfants joyeux**
happy children
**Joyeux Noël!**
Merry Christmas!
**Joyeux anniversaire!**
Happy birthday!
**Joyeuses Pâques!**
Happy Easter!
le **judo** MASC NOUN
**judo**
**Le mercredi, je fais du judo.**
I do judo on Wednesdays.
**juif** MASC ADJECTIVE (FEM **juive** )
**Jewish**
**juillet** MASC NOUN
**July**
**en juillet**
in July
**le onze juillet**
the eleventh of July
**juin** MASC NOUN
**June**
**en juin**
in June
**au mois de juin**
in June
**le vingt-trois juin**
the twenty-third of June
**jumeau** MASC ADJECTIVE (FEM **jumelle** )
**twin**
**C'est mon frère jumeau.**
He's my twin brother.
**C'est ma sœur jumelle.**
She's my twin sister.
**Marcel et Léon sont jumeaux.**
Marcel and Léon are twins.
les **jumeaux** MASC PL NOUN
**twins**
**Les jumeaux s'appellent Jean et Marc.**
The twins are called Jean and Marc.
**jumeler** VERB
**to twin**
**Hastings est jumelée avec Béthune.**
Hastings is twinned with Béthune.
les **jumelles** FEM PL NOUN
**1** **twins**
**Les jumelles s'appellent Anna et Louise.**
The twins are called Anna and Louise.
**2** **binoculars**
la **jungle** FEM NOUN
**jungle**
la **jupe** FEM NOUN
**skirt**
**jurer** VERB
**to swear**
**Je jure que c'est vrai!**
I swear it's true!
le **jus** MASC NOUN
**juice**
**un jus de fruit**
a fruit juice
**du jus d'orange**
orange juice
**jusqu'à** PREPOSITION
**1** **as far as**
**Allez jusqu'à la mairie et tournez à droite.**
Go as far as the town hall, then turn right.
**2** **until**
**On est en vacances jusqu'à dimanche.**
We're on holiday until Sunday.
**juste** ADJECTIVE
**fair**
**Il est sévère, mais juste.**
He's strict but fair.
# **K k**
**kaki** ADJECTIVE
**khaki**
**des chaussures kaki**
khaki shoes
le **kangourou** MASC NOUN
**kangaroo**
le **karaté** MASC NOUN
**karate**
**Le lundi, je fais du karaté.**
I do karate on Mondays
la **kermesse** FEM NOUN
**fête**
**Au mois de juin, il y a une kermesse à mon école.**
There's a fête at our school in June.
le **kilo** MASC NOUN
**kilo**
**un kilo d'oranges**
a kilo of oranges
le **kilogramme** MASC NOUN
**kilogramme**
le **kilomètre** MASC NOUN
**kilometre**
**Mon école est à deux kilomètres de chez moi.**
My school is two kilometres from my house.
le/la **kinésithérapeute** MASC/FEM NOUN
**physiotherapist**
le **kiosque** MASC NOUN
**un kiosque à journaux**
a news stand
le **koala** MASC NOUN
**koala**
le **K-way** ® MASC NOUN
**cagoule**
# **L l**
**l'**
**l'** _can be an article or a pronoun._
**_Language tip_**
**le** _and_ **la** _both change to **l'** before a vowel sound._
**A** ARTICLE
**the**
**l'arbre**
the tree
**B** PRONOUN
**1** **him**
**C'est un homme intelligent: je l'admire beaucoup.**
He's an intelligent man: I admire him very much.
**2** **her**
**Ma maîtresse est gentille et je l'aime bien.**
My teacher is nice and I like her.
**3** **it**
**J'aime bien ce T-shirt. Je l'achète.**
I like this T-shirt. I'm going to buy it.
**la**
**la** _can be an article or a pronoun._
**A** ARTICLE
**the**
**la maison**
the house
**B** PRONOUN
**1** **her**
**C'est ma voisine: je la vois tous les jours.**
This is my neighbour: I see her every day.
**2** **it**
**Prends la gomme et mets-la dans la trousse.**
Take the rubber and put it in the pencil case.
**là** ADVERB
**1** **there**
**Ton livre est là, sur la table.**
Your book's there, on the table.
**2** **here**
**Elle n'est pas là.**
She isn't here.
**là-bas** ADVERB
**over there**
**Va t'asseoir là-bas.**
Go and sit over there.
le **laboratoire** MASC NOUN
**laboratory**
le **labyrinthe** MASC NOUN
**maze**
le **lac** MASC NOUN
**lake**
le **lacet** MASC NOUN
**lace**
**des chaussures à lacets**
lace-up shoes
**là-haut** ADVERB
**up there**
**Le ballon est là-haut sur le toit.**
The ball is up there on the roof.
**laid** MASC ADJECTIVE (FEM **laide** )
**ugly**
**Elle est très laide.**
She's very ugly.
la **laine** FEM NOUN
**wool**
**un pull en laine**
a woolly jumper
**laisser** VERB
**1** **to leave**
**Laisse ton cahier sur la table.**
Leave your jotter on the table.
**2** **to let**
**Laisse-le parler.**
Let him speak.
le **lait** MASC NOUN
**milk**
**Je voudrais du lait.**
I'd like some milk.
**un café au lait**
a white coffee
la **laitue** FEM NOUN
**lettuce**
la **lampe** FEM NOUN
**lamp**
**une lampe de poche**
a torch
**lancer** VERB
**to throw**
**Lance-moi le ballon!**
Throw me the ball!
le **landau** MASC NOUN
**pram**
la **langouste** FEM NOUN
**crayfish**
**_Did you know...?_**
_A_ **langouste** _is a popular kind of seafood in France and is similar to a lobster._
la **langue** FEM NOUN
**1** **tongue**
**Elle m'a tiré la langue!**
She stuck her tongue out at me!
**2** **language**
**une langue étrangère**
a foreign language
le **lapin** MASC NOUN
**rabbit**
le **lard** MASC NOUN
**streaky bacon**
les **lardons** MASC PL NOUN
**chunks of bacon**
**large** ADJECTIVE
**wide**
la **largeur** FEM NOUN
**width**
le **lavabo** MASC NOUN
**washbasin**
la **lavande** FEM NOUN
**lavender**
**laver** VERB
**to wash**
**Tu peux laver la voiture?**
Could you wash the car?
**se laver**
**to wash**
**Je me lave le matin.**
I get washed in the morning.
**se laver les mains**
to wash one's hands
**Lave-toi les mains.**
Wash your hands.
le **lave-vaisselle** MASC NOUN
**dishwasher**
**le**
**le** _can be an article or a pronoun._
**_Language tip_**
**le** _changes to_ **l'** _before a vowel sound._
**A** ARTICLE
**the**
**le livre**
the book
**Aujourd'hui nous sommes le douze mai.**
Today is the twelfth of May.
**B** PRONOUN
**1** **him**
**C'est mon voisin: je le vois tous les jours.**
He's my neighbour: I see him every day.
**2** **it**
**Où est mon stylo? Je ne le trouve pas.**
Where's my pen? I can't find it.
**lécher** VERB
**to lick**
la **leçon** FEM NOUN
**lesson**
**une leçon de piano**
a piano lesson
le **lecteur** MASC NOUN
**un lecteur de cassettes**
a cassette player
**un lecteur de CD**
a CD player
**un lecteur MP3**
an MP3 player
la **lecture** FEM NOUN
**reading**
**J'aime la lecture.**
I love reading.
**_Language tip_**
_Be careful! The French word_ **lecture** _does not mean the same as the English word_ **lecture**.
**léger** MASC ADJECTIVE (FEM **légère** )
**light**
**un déjeuner léger**
a light lunch
**légèrement** ADVERB
**slightly**
les **légumes** MASC PL NOUN
**vegetables**
**Je n'aime pas les légumes.**
I don't like vegetables.
le **lendemain** MASC NOUN
**next day**
**Il est parti le lendemain.**
He left the next day.
**lent** MASC ADJECTIVE (FEM **lente** )
**slow**
**lentement** ADVERB
**slowly**
**Parle plus lentement s'il te plaît.**
Please speak more slowly.
les **lentilles** FEM PL NOUN
**1** **contact lenses**
**Je porte des lentilles.**
I wear contact lenses.
**2** **lentils**
**un rôti de porc aux lentilles**
roast pork with lentils
le **léopard** MASC NOUN
**leopard**
**les**
**les** _can be an article or a pronoun._
**A** ARTICLE
**the**
**les arbres**
the trees
**B** PRONOUN
**them**
**J'ai deux chiens et je les promène tous les jours.**
I've got two dogs and I walk them every day.
la **lessive** FEM NOUN
**1** **washing powder**
**2** **washing**
**Maman n'aime pas faire la lessive.**
Mum doesn't like doing the washing.
la **lettre** FEM NOUN
**letter**
**J'écris une lettre à ma meilleure copine.**
I'm writing a letter to my best friend.
**leur**
**leur** _can be an adjective or a pronoun._
**A** ADJECTIVE
**their**
**leur ami**
their friend
**B** PRONOUN
**them**
**Donnez-leur le ballon.**
Give them the ball.
**leurs** PL ADJECTIVE
**their**
**leurs amis**
their friends
**lever** VERB
**to raise**
**Levez la jambe gauche.**
Raise your left leg.
**Levez la main!**
Put your hand up!
**se lever**
**to get up/to stand up**
**_Language tip_**
**se lever** _has two translations. Look at the examples._
**Il se lève souvent à six heures.**
He often gets up at six o'clock.
**Levez-vous!**
Stand up!
la **lèvre** FEM NOUN
**lip**
le **lézard** MASC NOUN
**lizard**
la **liberté** FEM NOUN
**freedom**
le/la **libraire** MASC/FEM NOUN
**bookseller**
la **librairie** FEM NOUN
**bookshop**
**J'aime acheter des livres à la librairie.**
I like to buy books in the bookshop.
**_Language tip_**
_Be careful!_
**librairie** _does not mean the same as_ **library**.
**libre** ADJECTIVE
**free**
**Tu es libre de faire ce que tu veux.**
You are free to do as you wish.
**Avez-vous une chambre de libre?**
Have you got a free room?
la **licence** FEM NOUN
**degree**
**une licence de droit**
a law degree
le **lièvre** MASC NOUN
**hare**
la **ligne** FEM NOUN
**line**
**Tracez deux lignes verticales.**
Draw two vertical lines.
**Mettez-vous en ligne.**
Line up.
le **lilas** MASC NOUN
**lilac**
la **limace** FEM NOUN
**slug**
la **limonade** FEM NOUN
**lemonade**
le **linge** MASC NOUN
**linen**
**le linge sale**
dirty linen
**Je vais étendre le linge.**
I'm going to hang out the washing.
le **lion** MASC NOUN
**lion**
la **lionne** FEM NOUN
**lioness**
**lire** VERB
**to read**
**Le soir, je lis dans mon lit.**
At night I read in bed.
**lis, lisent, lisez** VERB _see_ **lire**
**Je lis beaucoup.**
I read a lot.
**Qu'est-ce que tu lis?**
What are you reading?
**Ils lisent des BD.**
They read comics.
**Lisez la première phrase.**
Read the first sentence.
la **liste** FEM NOUN
**list**
**lit**
**lit** _can be a noun or part of the verb_ **lire**.
**A** MASC NOUN
**bed**
**aller au lit**
to go to bed
**Je vais au lit à sept heures.**
I go to bed at seven.
**faire son lit**
to make one's bed
**Je fais mon lit tous les matins.**
I make my bed every morning.
**un grand lit**
a double bed
**un lit de camp**
a campbed
**B** VERB _see_ **lire**
**Il lit des magazines.**
He reads magazines.
le **litre** MASC NOUN
**litre**
**un litre de lait**
a litre of milk
la **littérature** FEM NOUN
**literature**
le **livre** MASC NOUN
**book**
**un livre de poche**
a paperback
la **livre** FEM NOUN
**pound**
**Le guide coûte trois livres.**
The guide book costs £3.
**_Did you know...?_**
**une livre** _is also a weight – 500 grams, which is nearly the same as a British pound (450 grams)._
le **livret** MASC NOUN
**le livret scolaire**
the school report book
**logique** ADJECTIVE
**logical**
**loin** ADVERB
**far**
**La gare n'est pas très loin d'ici.**
The station is not very far from here.
**C'est un peu plus loin.**
It's a little further on.
**lointain** MASC ADJECTIVE (FEM **lointaine** )
**distant**
**un pays lointain**
a distant country
les **loisirs** MASC PL NOUN
**1** **free time**
**Qu'est-ce que tu fais d'habitude pendant tes loisirs?**
What do you usually do in your free time?
**2** **hobbies**
**Le ski et l'équitation sont des loisirs coûteux.**
Skiing and riding are expensive hobbies.
**Londres** NOUN
**London**
**J'habite à Londres.**
I live in London.
**Je vais à Londres.**
I'm going to London.
**long** MASC ADJECTIVE (FEM **longue** )
**long**
**une longue promenade**
a long walk
**Elle a les cheveux longs.**
She has long hair.
la **longueur** FEM NOUN
**length**
la **loterie** FEM NOUN
**lottery**
**la loterie nationale**
the National Lottery
le **lotissement** MASC NOUN
**housing estate**
le **loto** MASC NOUN
**1** **lottery**
**Mes parents jouent au loto toutes les semaines.**
My parents play the lottery every week.
**le loto sportif**
the pools
**2** **bingo**
**On va jouer au loto.**
We're going to play bingo.
la **louche** FEM NOUN
**ladle**
**louer** VERB
**1** **to let**
**Ils louent des chambres à des étudiants.**
They let rooms to students.
**'à louer'**
'to let'
**2** **to rent**
**L'été, nous louons un petit appartement au bord de la mer.**
In the summer we rent a little flat by the sea.
**3** **to hire**
**Est-ce que vous louez des vélos?**
Do you hire bikes?
le **loup** MASC NOUN
**wolf**
la **loupe** FEM NOUN
**magnifying glass**
**lourd** MASC ADJECTIVE (FEM **lourde** )
**heavy**
la **loutre** FEM NOUN
**otter**
la **luge** FEM NOUN
**sledge**
**J'aime bien faire de la luge.**
I like sledging.
**Quand il neige, je fais de la luge.**
I go sledging when it snows.
**lui** PRONOUN
**1** **him**
**Voilà ton père: demande-lui!**
Here's your dad – ask him!
**Je pense beaucoup à lui.**
I think about him a lot.
**Lui, il est toujours en retard!**
Oh, HE's always late!
**Il a construit son bateau lui-même.**
He built his boat himself.
**lui-même**
himself
**2** **to him**
**Michael m'énerve, alors je ne lui parle pas en ce moment.**
Michael's getting on my nerves so I'm not speaking to him at the moment.
**3** **her**
**Voilà ta mère: demande-lui!**
Here's your mum – ask her!
**4** **to her**
**C'est Julie au téléphone. Tu veux lui parler?**
Julie's on the phone. Do you want to speak to her?
**5** **it**
**Cette plante ne pousse pas vite; je vais lui donner plus d'eau.**
This plant isn't growing well; I'm going to give it more water.
la **lumière** FEM NOUN
**light**
**Sylvia, allume la lumière s'il te plaît.**
Sylvia, turn on the light please.
**lunatique** ADJECTIVE
**temperamental**
le **lundi** MASC NOUN
**1** **Monday**
**Aujourd'hui, nous sommes lundi.**
It's Monday today.
**2** **on Monday**
**Nous partons lundi.**
We're leaving on Monday.
**Le lundi, je vais à la piscine.**
I go swimming on Mondays.
**tous les lundis**
every Monday
**le lundi**
on Mondays
**lundi dernier**
last Monday
**lundi prochain**
next Monday
**À lundi!**
See you on Monday!
la **lune** FEM NOUN
**moon**
les **lunettes** FEM PL NOUN
**glasses**
**Je porte des lunettes.**
I wear glasses.
**des lunettes de soleil**
sunglasses
**des lunettes de plongée**
swimming goggles
la **lutte** FEM NOUN
**wrestling**
le **luxe** MASC NOUN
**luxury**
**de luxe**
luxury
**un hôtel de luxe**
a luxury hotel
**luxueux** MASC ADJECTIVE (FEM **luxueuse** )
**luxurious**
le **lycée** MASC NOUN
**secondary school**
**_Did you know...?_**
_In France, pupils go to a_ **collège** _between the ages of 11 and 15, and then to a_ **lycée** _until the age of 18._
**un lycée technique**
a technical college
le **lycéen** MASC NOUN
la **lycéenne** FEM NOUN
**secondary school pupil**
# **M m**
**M.** ABBREVIATION
**Mr**
**M. Bernard**
Mr Bernard
**m'** PRONOUN
**me**
**_Language tip_**
_The French word_ **me** _changes to_ **m'** _before a vowel sound._
**Dominique m'invite chez elle ce week-end.**
Dominique has invited me to her house this weekend.
**Il m'attend depuis une heure.**
He's been waiting for me for an hour.
**_Language tip_**
**m'** _is often not translated._
**Je m'habille à sept heures tous les matins.**
I get dressed at seven every morning.
**ma** FEM ADJECTIVE _see_ **mon**
**my**
**ma mère**
my mother
les **macaronis** MASC PL NOUN
**macaroni**
le **machin** MASC NOUN
**thingy**
**Passe-moi le machin pour râper les carottes.**
Pass me the thingy for grating carrots.
la **machine** FEM NOUN
**machine**
**une machine à sous**
a fruit machine
**une machine à laver**
a washing machine
le **maçon** MASC NOUN
**bricklayer**
**madame** FEM NOUN (PL **mesdames** )
**1** **Mrs**
**Madame Legall**
Mrs Legall
**2** **Madam**
**Madame,...**
Dear Madam,...
**_Language tip_**
**madame** _is a useful way of attracting a woman's attention._
**Madame! Vous avez oublié votre parapluie!**
Excuse me! You've forgotten your umbrella!
**mademoiselle** FEM NOUN (PL **mesdemoiselles** )
**Miss**
**Mademoiselle Martin**
Miss Martin
**_Language tip_**
**mademoiselle** _is a useful way of attracting a young or unmarried woman's attention._
**Mademoiselle! L'addition, s'il vous plaît!**
Excuse me, could I have the bill?
le **magasin** MASC NOUN
**shop**
**Les magasins ouvrent à huit heures.**
The shops open at eight o'clock.
**J'aime faire les magasins.**
I like going shopping.
**magasiner** VERB ( _Canada_ )
**to shop**
le **magazine** MASC NOUN
**magazine**
le **magicien** MASC NOUN
la **magicienne** FEM NOUN
**magician**
la **magie** FEM NOUN
**magic**
**un tour de magie**
a magic trick
**magique** ADJECTIVE
**magic**
**une baguette magique**
a magic wand
le **magnétophone** MASC NOUN
**tape recorder**
le **magnétoscope** MASC NOUN
**video recorder**
**magnifique** ADJECTIVE
**superb**
**mai** MASC NOUN
**May**
**en mai**
in May
**le trente mai**
the thirtieth of May
**le premier mai**
the first of May
**_Did you know...?_**
**le premier mai** _(May 1st) is a holiday in France. People give friends little bunches of lily of the valley_ ( **muguet** ) _for good luck._
**maigre** ADJECTIVE
**skinny**
le **mail** MASC NOUN
**email**
le **maillot de bain** MASC NOUN
**1** **swimsuit**
**J'adore le maillot de bain de Jacqueline.**
I love Jacqueline's swimsuit.
**2** **swimming trunks**
**Paul a un nouveau maillot de bain.**
Paul has new swimming trunks.
la **main** FEM NOUN
**hand**
**Donne-moi la main!**
Give me your hand!
**se serrer la main**
to shake hands
**Les garçons se serrent la main en arrivant à l'école le matin.**
The boys shake hands when they get to school in the morning.
**maintenant** ADVERB
**now**
le **maire** MASC NOUN
**mayor**
la **mairie** FEM NOUN
**town hall**
**mais** CONJUNCTION
**but**
**J'aime bien les maths mais c'est difficile.**
I like maths, but it's difficult.
le **maïs** MASC NOUN
**1** **sweetcorn**
**J'adore le maïs.**
I love sweetcorn.
**2** **maize**
la **maison** FEM NOUN
**house**
**Ils habitent dans une grande maison.**
They live in a big house.
**Viens à la maison si tu veux.**
Come to the house if you want.
**Je vais rester à la maison pendant les vacances.**
I'm going to stay at home in the holidays.
**rentrer à la maison**
to go home
**Rentrons à la maison.**
Let's go home.
le **maître** MASC NOUN
la **maîtresse** FEM NOUN
**1** **teacher**
**Cette année, j'ai un maître au lieu d'une maîtresse.**
This year I have a male teacher instead of a female one.
**Maîtresse!**
Miss!
**2** **master**
**Ce chien suit son maître partout.**
This dog follows his master everywhere.
**un maître nageur**
a lifeguard
**Majorque** FEM NOUN
**Majorca**
**majuscule**
**majuscule** _can be an adjective or a noun._
**A** ADJECTIVE
**capital**
**un M majuscule**
a capital M
**B** FEM NOUN
**capital letter**
**Les jours de la semaine ne prennent pas de majuscule en français.**
In French the days of the week don't start with a capital letter.
**mal**
**mal** _can be a noun, an adjective or an adverb._
**A** MASC NOUN (PL les **maux** )
**ache**
**J'ai mal aux dents.**
I've got toothache.
**J'ai mal au dos.**
My back hurts.
**Ça fait mal.**
It hurts.
**Où est-ce que tu as mal?**
Where does it hurt?
**J'ai mal à la tête.**
I've got a headache.
**B** MASC, FEM, PL ADJECTIVE
**pas mal**
not bad
**Ça va? — Oui, pas mal.**
How are you? — Not bad.
**C** ADVERB
**badly**
**C'est mal fait.**
It's badly done.
**malade** ADJECTIVE
**ill**
la **maladie** FEM NOUN
**illness**
**mâle** ADJECTIVE
**male**
**malheureusement** ADVERB
**unfortunately**
**malin** MASC ADJECTIVE (FEM **maligne** )
**cunning**
la **maman** FEM NOUN
**mum**
la **mamie** FEM NOUN
**granny**
la **manche** FEM NOUN
**sleeve**
**un T-shirt à manches longues**
a long-sleeved T-shirt
**la Manche**
the Channel
la **mandarine** FEM NOUN
**mandarin**
le **manège** MASC NOUN
**merry-go-round**
**manger** VERB
**to eat**
**Pour le petit déjeuner, je mange des céréales.**
I have cereal for breakfast.
la **mangue** FEM NOUN
**mango**
la **manifestation** FEM NOUN
**demonstration**
le **mannequin** MASC NOUN
**model**
**manquer** VERB
**to miss**
**Il manque des pages à ce livre.**
There are some pages missing from this book.
**Mes parents me manquent.**
I miss my parents.
**Ma sœur me manque.**
I miss my sister.
le **manteau** MASC NOUN
(PL les **manteaux** )
**coat**
**manuel** MASC ADJECTIVE (FEM **manuelle** )
**les travaux manuels**
arts and crafts
le **maquereau** MASC NOUN
(PL les **maquereaux** )
**mackerel**
la **maquette** FEM NOUN
**model**
le **maquillage** MASC NOUN
**make-up**
se **maquiller** VERB
**to put on one's make-up**
**J'adore me maquiller.**
I love to put on make-up.
le **marchand** MASC NOUN
la **marchande** FEM NOUN
**1** **shopkeeper**
**un marchand de journaux**
a newsagent
**un marchand de fruits et légumes**
a greengrocer
**2** **stallholder**
la **marche** FEM NOUN
**step**
**Fais attention à la marche!**
Mind the step!
le **marché** MASC NOUN
**market**
**marcher** VERB
**1** **to walk**
**Marchez deux par deux.**
Walk in twos.
**2** **to work**
**L'ascenseur ne marche pas.**
The lift isn't working.
**Ça marche?**
How are you getting on?
le **mardi** MASC NOUN
**1** **Tuesday**
**Aujourd'hui, nous sommes mardi.**
Today is Tuesday.
**Mardi gras**
Shrove Tuesday
**2** **on Tuesday**
**Ils reviennent mardi.**
They're coming back on Tuesday.
**Le mardi, je vais à la gym.**
I go to the gym on Tuesdays.
**tous les mardis**
every Tuesday
**le mardi**
on Tuesdays
**mardi dernier**
last Tuesday
**mardi prochain**
next Tuesday
**À mardi!**
See you on Tuesday!
la **marelle** FEM NOUN
**hopscotch**
la **margarine** FEM NOUN
**margarine**
la **marge** FEM NOUN
**margin**
**Laissez une marge à droite de la page.**
Leave a margin on the right-hand side of the page.
le **mari** MASC NOUN
**husband**
**son mari**
her husband
le **mariage** MASC NOUN
**wedding**
**Samedi, je vais à un mariage.**
I'm going to a wedding on Saturday.
**marié** MASC ADJECTIVE (FEM **mariée** )
**married**
**Ma sœur est mariée.**
My sister is married.
le **marié** MASC NOUN
**bridegroom**
**les mariés**
the bride and groom
la **mariée** FEM NOUN
**bride**
se **marier** VERB
**to get married**
**Mon frère se marie ce week-end.**
My brother is getting married this weekend.
**marin** MASC NOUN
**sailor**
**marine** MASC, FEM, PL ADJECTIVE
**bleu marine**
navy-blue
**des chaussettes bleu marine**
navy-blue socks
la **marionnette** FEM NOUN
**puppet**
la **marmelade** FEM NOUN
**la marmelade d'oranges**
marmalade
le **Maroc** MASC NOUN
**Morocco**
**marocain** MASC ADJECTIVE (FEM **marocaine** )
**Moroccan**
le **Marocain** MASC NOUN
la **Marocaine** FEM NOUN
**Moroccan**
la **marque** FEM NOUN
**1** **mark**
**des marques de doigts**
fingermarks
**2** **make**
**De quelle marque est ton jean?**
What make are your jeans?
**3** **brand**
**une marque de lessive**
a brand of washing powder
**À vos marques! prêts! partez!**
Ready, steady, go!
**marquer** VERB
**1** **to mark**
**Tu peux marquer où se trouve ton village sur la carte?**
Can you mark where your village is on the map?
**2** **to score**
**L'équipe irlandaise a marqué dix points.**
The Irish team scored ten points.
la **marraine** FEM NOUN
**godmother**
**marrant** MASC ADJECTIVE (FEM **marrante** )
**funny**
**marron**
**marron** _can be an adjective or a noun._
**A** MASC, FEM, PL ADJECTIVE
**brown**
**J'ai les yeux marron.**
I have brown eyes.
**B** MASC NOUN
**1** **chestnut**
**la crème de marrons**
chestnut purée
**2** **brown**
**Je n'aime pas le marron.**
I don't like the colour brown.
**Mars** NOUN
**Mars**
**la planète Mars**
Mars
**mars** MASC NOUN
**March**
**en mars**
in March
**le dix-huit mars**
the eighteenth of March
le **marteau** MASC NOUN
(PL les **marteaux** )
**hammer**
le **martien** MASC NOUN
la **martienne** FEM NOUN
**Martian**
**masculin** MASC ADJECTIVE (FEM **masculine** )
**masculine**
le **masque** MASC NOUN
**mask**
**masser** VERB
**to massage**
le **match** MASC NOUN
**match**
**un match de football**
a football match
**Match nul!**
It's a draw!
le **matelas** MASC NOUN
**mattress**
**un matelas pneumatique**
an air bed
**maternel** MASC ADJECTIVE (FEM **maternelle** )
**ma grand-mère maternelle**
my mother's mother
**l'école maternelle**
nursery school
la **maternelle** FEM NOUN
**nursery school**
**_Did you know...?_**
_The_ **maternelle** _is a state school for three to six year-olds._
les **mathématiques** FEM PL NOUN
**mathematics**
les **maths** FEM PL NOUN
**maths**
**J'adore les maths.**
I love maths.
le **matin** MASC NOUN
**morning**
**à trois heures du matin**
at three o'clock in the morning
**ce matin**
this morning
la **matinée** FEM NOUN
**toute la matinée**
all morning
**mauvais**
**mauvais** _can be an adjective or an adverb._
**A** MASC ADJECTIVE (FEM **mauvaise** )
**1** **bad**
**une mauvaise note**
a bad mark
**Je suis mauvais en maths.**
I'm bad at maths.
**Il fait mauvais.**
The weather's bad.
**2** **wrong**
**Vous avez fait le mauvais numéro.**
You've dialled the wrong number.
**B** ADVERB
**sentir mauvais**
to smell
**Ça sent mauvais ici!**
It smells in here!
la **mayonnaise** FEM NOUN
**mayonnaise**
**me** PRONOUN
**1** **me**
**Elle me téléphone tous les jours.**
She phones me every day.
**_Language tip_**
**me** _changes to_ **m'** _before a vowel sound._
**Tu peux m'aider?**
Can you help me?
**2** **to me**
**Il me parle en allemand.**
He talks to me in German.
**_Language tip_**
**me** _is often not translated._
**Je me lève à sept heures tous les matins.**
I get up at seven every morning.
le **mécanicien** MASC NOUN
**mechanic**
**méchant** MASC ADJECTIVE (FEM **méchante** )
**nasty**
**Elle est méchante avec moi.**
She's nasty to me.
la **médaille** FEM NOUN
**medal**
**la médaille de bronze**
the bronze medal
le **médecin** MASC NOUN
**doctor**
**aller chez le médecin**
to go to the doctor's
**Ce soir, je vais chez le médecin.**
I'm going to the doctor's this evening.
le **médicament** MASC NOUN
**medicine**
**Tu as pris tes médicaments?**
Have you taken your medicine?
la **Méditerranée** FEM NOUN
**Mediterranean**
**méditerranéen** MASC ADJECTIVE (FEM **méditerranéenne** )
**Mediterranean**
la **méduse** FEM NOUN
**jellyfish**
**meilleur** MASC ADJECTIVE (FEM **meilleure** )
**better**
**C'est meilleur avec du fromage râpé.**
It's better with grated cheese.
**Le livre est meilleur que le film.**
The book is better than the film.
le **meilleur** MASC NOUN
la **meilleure** FEM NOUN
**the best**
**C'est la meilleure en sport.**
She's the best at sport.
le **mélange** MASC NOUN
**mixture**
**mélanger** VERB
**to mix**
**Mélangez le tout.**
Mix everything together.
la **mélodie** FEM NOUN
**melody**
le **melon** MASC NOUN
**melon**
le **membre** MASC NOUN
**member**
la **mémé** FEM NOUN
**granny**
**même**
**même** _can be an adjective or an adverb._
**A** ADJECTIVE
**same**
**J'ai la même robe.**
I've got the same dress.
**en même temps**
at the same time
**Paul et moi, on arrive toujours en même temps à l'école.**
Paul and I always get to school at the same time.
**B** ADVERB
**even**
**Je sais faire l'équilibre, et je sais même faire la roue.**
I can do a handstand, and I can even do a cartwheel.
le/la **même** MASC/FEM NOUN
**same one**
**Tiens, c'est curieux j'ai le même!**
That's funny, I've got the same one!
la **mémoire** FEM NOUN
**memory**
**menacer** VERB
**to threaten**
le **ménage** MASC NOUN
**housework**
**faire le ménage**
to do the housework
**C'est mon père qui fait le ménage à la maison.**
My father is the one who does the housework.
**une femme de ménage**
a cleaning lady
le **mensonge** MASC NOUN
**lie**
**Il ne faut pas dire de mensonges.**
You shouldn't tell lies.
le **menteur** MASC NOUN
la **menteuse** FEM NOUN
**liar**
**C'est une menteuse.**
She's a liar.
la **menthe** FEM NOUN
**mint**
**des bonbons à la menthe**
mints
**mentir** VERB
**to lie**
**Tu mens!**
You're lying!
le **menton** MASC NOUN
**chin**
le **menu** MASC NOUN
**menu**
**le menu du jour**
today's menu
le **menuisier** MASC NOUN
**joiner**
la **mer** FEM NOUN
**sea**
**la mer du Nord**
the North Sea
**au bord de la mer**
at the seaside
**merci** EXCLAMATION
**thank you**
**merci beaucoup**
thank you very much
le **mercredi** MASC NOUN
**1** **Wednesday**
**Aujourd'hui, nous sommes le mercredi vingt-deux février.**
Today's Wednesday the twenty-second of February.
**2** **on Wednesday**
**Nous partons mercredi.**
We're leaving on Wednesday.
**Le musée est fermé le mercredi.**
The museum is shut on Wednesdays.
**tous les mercredis**
every Wednesday
**le mercredi**
on Wednesdays
**mercredi dernier**
last Wednesday
**mercredi prochain**
next Wednesday
**À mercredi!**
See you on Wednesday!
la **mère** FEM NOUN
**mother**
**Ma mère s'appelle Laura.**
My mother is called Laura.
la **merguez** FEM NOUN
**spicy sausage**
**mériter** VERB
**to deserve**
le **merlan** MASC NOUN
**whiting**
le **merle** MASC NOUN
**blackbird**
**merveilleux** MASC ADJECTIVE (FEM **merveilleuse** )
**marvellous**
**mes** PL ADJECTIVE _see_ **mon**
**my**
**mes parents**
my parents
**mesdames** FEM PL NOUN
**ladies**
**Bonjour, mesdames.**
Good morning, ladies.
**mesdemoiselles** FEM PL NOUN
**ladies**
**Bonjour, mesdemoiselles.**
Good morning, ladies.
le **message** MASC NOUN
**message**
**un message SMS**
a text message
la **messe** FEM NOUN
**mass**
**la messe de minuit**
midnight mass
**messieurs** MASC PL NOUN
**gentlemen**
**Bonjour, messieurs.**
Good morning, gentlemen.
**mesurer** VERB
**to measure**
**Mesurez la longueur et la largeur.**
Measure the length and the width.
**Il mesure un mètre quatre-vingts.**
He's six foot tall.
**_Did you know...?_**
_In France, people use metres and centimetres to say how tall someone is, not feet and inches._
**met** VERB _see_ **mettre**
**Il met la table.**
He is laying the table.
le **métal** MASC NOUN
(PL les **métaux** )
**metal**
la **météo** FEM NOUN
**weather forecast**
**Qu'est-ce que dit la météo pour cet après-midi?**
What's the weather forecast for this afternoon?
le **métier** MASC NOUN
**job**
**Quel métier est-ce que tu aimerais faire plus tard?**
What job would you like to do when you're older?
le **mètre** MASC NOUN
**metre**
**La piscine fait vingt-cinq mètres de long.**
The pool is 25 metres long.
**un mètre ruban**
a tape measure
le **métro** MASC NOUN
**underground**
**prendre le métro**
to take the underground
**Je prends toujours le métro pour aller en ville.**
I always take the underground into town.
**mets** VERB _see_ **mettre**
**Je ne mets jamais de jupe.**
I never wear a skirt.
**mettre** VERB
**1** **to put**
**Mets les jouets dans le placard s'il te plaît.**
Put the toys in the cupboard please.
**2** **to put on**
**Je mets mon manteau et j'arrive.**
I'll put on my coat and then I'll be ready.
**3** **to wear**
**Qu'est-ce que tu vas mettre pour la boum?**
What are you going to wear to the party?
**mettre la table**
to set the table
**Tu peux mettre la table?**
Could you set the table?
les **meubles** MASC PL NOUN
**furniture**
le **Mexique** MASC NOUN
**Mexico**
**miauler** VERB
**to mew**
**Mon chat miaule quand il a faim.**
My cat mews when he's hungry.
le **micro** MASC NOUN
**microphone**
le **micro-ondes** MASC NOUN
**microwave oven**
le **midi** MASC NOUN
**1** **midday**
**On déjeune à midi.**
We have lunch at midday.
**Il est midi et demi.**
It's half past twelve.
**Il est midi.**
It's midday.
**2** **lunchtime**
**Je rentre à la maison le midi.**
I go home at lunchtime.
**le Midi**
the South of France
le **miel** MASC NOUN
**honey**
le **mien** MASC PRONOUN
la **mienne** FEM PRONOUN
**mine**
**Ce vélo-là, c'est le mien.**
That bike's mine.
**Ces baskets-là, ce sont les miennes.**
Those trainers are mine.
**mieux**
**mieux** _can be an adverb, an adjective or a noun._
**A** ADVERB
**better**
**Elle va mieux.**
She's better.
**Je la connais mieux que son frère.**
I know her better than her brother.
**B** MASC, FEM, PL ADJECTIVE
**Il est mieux avec la moustache.**
He looks better with a moustache.
**C** MASC NOUN
**best**
**C'est la région que je connais le mieux.**
It's the region I know best.
**mignon** MASC ADJECTIVE (FEM **mignonne** )
**sweet**
**Qu'est-ce qu'il est mignon!**
Isn't he sweet!
le **milieu** MASC NOUN
(PL les **milieux** )
**middle**
**au milieu de**
in the middle of
**Mets le vase au milieu de la table.**
Put the vase in the middle of the table.
**mille** NUMBER
**a thousand**
**mille euros**
a thousand euros
**deux mille personnes**
two thousand people
le **millénaire** MASC NOUN
**millennium**
**le troisième millénaire**
the third millennium
le **milliard** MASC NOUN
**thousand million**
**milliardaire** MASC/FEM NOUN, ADJECTIVE
**multimillionaire**
le **millier** MASC NOUN
**thousand**
**des milliers de personnes**
thousands of people
le **million** MASC NOUN
**million**
**deux millions de personnes**
two million people
**millionnaire** MASC/FEM NOUN, ADJECTIVE
**millionaire**
**mimer** VERB
**to mimic**
**mince** ADJECTIVE
**slim**
**Il est grand et mince.**
He's tall and slim.
**Mince!**
Sugar!
**minéral** MASC ADJECTIVE (FEM **minérale** )
**mineral**
**l'eau minérale**
mineral water
**mineur** MASC ADJECTIVE (FEM **mineure** )
**under 18**
**Elle est mineure.**
She's under 18.
**les mineurs**
the under-18s
la **minijupe** FEM NOUN
**miniskirt**
le **minimessage** MASC NOUN
**text message**
le **minimum** MASC NOUN
**minimum**
**au minimum**
at the very least
le **ministre** MASC NOUN
**minister**
**le Premier ministre**
the Prime Minister
le **Minitel** ® MASC NOUN
**_Did you know...?_**
**Minitel** _is a mini-computer plugged into your phone. You can use it instead of a phone directory, and to book train tickets, etc._
la **minorité** FEM NOUN
**minority**
**Minorque** FEM NOUN
**Minorca**
**minuit** MASC NOUN
**midnight**
**L'avion arrive à minuit.**
The plane lands at midnight.
**Il est minuit et demi.**
It's half past twelve.
**Il est minuit.**
It's midnight.
**minuscule**
**minuscule** _can be an adjective or a noun._
**A** ADJECTIVE
**1** **tiny**
**un poisson minuscule**
a tiny fish
**2** **small**
**un m minuscule**
a small m
**B** FEM NOUN
**small letter**
**Ça s'écrit avec une minuscule, pas une majuscule.**
You spell it with a small letter, not a capital.
la **minute** FEM NOUN
**minute**
le **miracle** MASC NOUN
**miracle**
le **miroir** MASC NOUN
**mirror**
**mis** VERB _see_ **mettre**
**Tu as mis le lait au frigo?**
Have you put the milk in the fridge?
la **mi-temps** FEM NOUN
**half-time**
**La mi-temps dure quinze minutes.**
Half-time lasts fifteen minutes.
**à mi-temps**
part-time
**Elle travaille à mi-temps.**
She works part-time.
**Mlle** ABBREVIATION (PL **Mlles** )
**Miss**
**Mlle Renoir**
Miss Renoir
**Mme** ABBREVIATION (PL **Mmes** )
**Mrs**
**Mme Leroy**
Mrs Leroy
le **mobile** MASC NOUN
**mobile phone**
**Tu me donnes ton numéro de mobile?**
Can you give me your mobile number?
la **mobylette** ® FEM NOUN
**moped**
**moche** ADJECTIVE
**horrible**
**Cette couleur est vraiment moche.**
That colour's really horrible.
la **mode** FEM NOUN
**fashion**
**à la mode**
fashionable
**J'aime être à la mode.**
I like to be fashionable.
**Ce jean n'est pas vraiment à la mode.**
These jeans aren't really fashionable.
le **modèle** MASC NOUN
**model**
**C'est le nouveau modèle.**
It's the new model.
**Suivez le modèle.**
Follow the example.
**moderne** ADJECTIVE
**modern**
**moi** PRONOUN
**me**
**Coucou, c'est moi!**
Hello, it's me!
**à moi**
mine/my turn
**_Language tip_**
**à moi** _has two translations. Look at the examples._
**Ce livre n'est pas à moi.**
This book isn't mine.
**un ami à moi**
a friend of mine
**C'est à moi.**
It's my turn.
**moi-même** PRONOUN
**myself**
**Je l'ai fait moi-même.**
I did it myself.
**moins**
**moins** _can be an adverb, a preposition or a noun._
**A** ADVERB
**1** **less**
**Deux cents euros? — Non, beaucoup moins.**
Two hundred euros? — No, much less.
**Moins de bruit, s'il vous plaît.**
Less noise please.
**_Language tip_**
_When_ **moins de** _is followed by a number it means 'less than'._
**Ça coûte moins de deux cents euros.**
It costs less than two hundred euros.
**_Language tip_**
**de moins** _is used when talking about how many years younger someone is._
**Il a trois ans de moins que moi.**
He's three years younger than me.
**2** **fewer**
**Il y a moins de gens aujourd'hui.**
There are fewer people today.
**le moins**
the least
**_Language tip_**
**le moins** _changes to_ **la moins** _before a feminine adjective, and_ **les moins** _before a plural adjective._
**C'est le modèle le moins cher.**
It's the least expensive model.
**C'est la plage la moins polluée.**
It's the least polluted beach.
**La musique, c'est la matière que j'aime le moins.**
Music is my least favourite subject.
**B** PREPOSITION
**1** **minus**
**quatre moins trois**
four minus three
**Il fait moins cinq dehors.**
It's minus five outside.
**2** **to**
**Il est onze heures moins cinq.**
It's five to eleven.
**Il est onze heures moins le quart.**
It's quarter to eleven.
**C** MASC NOUN
**au moins**
at least
**Il reste au moins dix bonbons dans le paquet.**
There are at least ten sweets left in the packet.
le **mois** MASC NOUN
**month**
**au mois de juillet**
in July
la **moitié** FEM NOUN
**half**
**une moitié de pomme**
half an apple
**molle** FEM ADJECTIVE
**soft**
**La margarine est plus molle que le beurre.**
Margarine is softer than butter.
le **moment** MASC NOUN
**1** **moment**
**Attendez un moment.**
Wait a moment.
**en ce moment**
at the moment
**Nous avons beaucoup de travail en ce moment.**
We have a lot of work to do at the moment.
**2** **time**
**C'est le moment de partir.**
It's time to go.
**mon** MASC ADJECTIVE (FEM **ma** , PL **mes** )
**my**
**mon frère**
my brother
**mon ami**
my friend
**ma tante**
my aunt
**mes parents**
my parents
le **monde** MASC NOUN
**world**
**Je voudrais faire le tour du monde.**
I'd like to go round the world.
**Il y a du monde.**
There are a lot of people.
**beaucoup de monde**
a lot of people
**Il y a beaucoup de monde sur la plage.**
There are a lot of people on the beach.
**mondial** MASC ADJECTIVE (FEM **mondiale** )
**world**
**un nouveau record mondial**
a new world record
le **moniteur** MASC NOUN
**1** **instructor**
**un moniteur de voile**
a sailing instructor
**2** **monitor**
**le moniteur de mon ordinateur**
my computer monitor
la **monitrice** FEM NOUN
**instructor**
**une monitrice de ski**
a ski instructor
la **monnaie** FEM NOUN
**change**
**Voici la monnaie.**
Here's the change.
**une pièce de monnaie**
a coin
le **monsieur** MASC NOUN
**man**
**Il y a un monsieur qui veut te voir.**
There's a man wanting to see you.
**monsieur** MASC NOUN (PL **messieurs** )
**1** **Mr**
**Monsieur Dupont**
Mr Dupont
**2** **Sir**
**Monsieur,...**
Dear Sir,...
**_Language tip_**
**monsieur** _is a useful way of attracting a man's attention._
**Monsieur! Vous avez laissé tomber votre billet!**
Excuse me! You've dropped your ticket!
le **monstre** MASC NOUN
**monster**
la **montagne** FEM NOUN
**mountain**
**les montagnes russes**
the roller coaster
**montagneux** MASC ADJECTIVE (FEM **montagneuse** )
**mountainous**
**une région montagneuse**
a mountainous area
**monter** VERB
**to go up**
**Montez au deuxième étage.**
Go up to the second floor.
la **montre** FEM NOUN
**watch**
**montrer** VERB
**to show**
**Montre la carte.**
Show the card.
le **monument** MASC NOUN
**les monuments de Paris**
the sights of Paris
la **moquette** FEM NOUN
**fitted carpet**
le **morceau** MASC NOUN
(PL les **morceaux** )
**piece**
**un morceau de pain**
a piece of bread
**mordre** VERB
**to bite**
**Je me suis fait mordre par un chien.**
I was bitten by a dog.
**mort** MASC ADJECTIVE (FEM **morte** )
**dead**
la **mosquée** FEM NOUN
**mosque**
le **mot** MASC NOUN
**1** **word**
**C'est un mot de six lettres.**
It's a six-letter word.
**des mots croisés**
a crossword
**le mot de passe**
the password
**2** **note**
**J'écris un mot à Pierrot.**
I'm writing a note to Pierrot.
la **moto** FEM NOUN
**motorbike**
**mou** MASC ADJECTIVE (FEM **molle** )
**soft**
**Mon matelas est trop mou.**
My mattress is too soft.
la **mouche** FEM NOUN
**fly**
le **mouchoir** MASC NOUN
**handkerchief**
**un mouchoir en papier**
a tissue
la **mouette** FEM NOUN
**seagull**
**mouillé** MASC ADJECTIVE (FEM **mouillée** )
**wet**
le **moule** MASC NOUN
**tin**
**un moule à gâteaux**
a cake tin
les **moules** FEM PL NOUN
**mussels**
le **moulin** MASC NOUN
**mill**
**un moulin à vent**
a windmill
**mourir** VERB
**to die**
**Elle est morte.**
She's dead.
la **mousse** FEM NOUN
**une mousse au chocolat**
a chocolate mousse
la **moustache** FEM NOUN
**moustache**
**les moustaches**
whiskers
le **moustique** MASC NOUN
**mosquito**
la **moutarde** FEM NOUN
**mustard**
le **mouton** MASC NOUN
**1** **sheep**
**2** **mutton**
**un gigot de mouton**
a leg of mutton
**moyen** MASC ADJECTIVE (FEM **moyenne** )
**1** **average**
**Je suis plutôt moyen en maths.**
I'm just average at maths.
**2** **medium**
**Elle est de taille moyenne.**
She's of medium height.
**le moyen âge**
the Middle Ages
la **moyenne** FEM NOUN
**average**
**la moyenne d'âge**
the average age
**J'espère avoir la moyenne en maths.**
I hope to get a pass mark in maths.
le **Moyen-Orient** MASC NOUN
**Middle East**
le **muguet** MASC NOUN
**lily of the valley**
**_Did you know...?_**
_People give friends little bunches of lily of the valley on May 1st, which is a holiday in France_. **Le muguet** _is lucky – like white heather._
**municipal** MASC ADJECTIVE (FEM **municipale** )
**la bibliothèque municipale**
the public library
le **mur** MASC NOUN
**wall**
**mûr** MASC ADJECTIVE (FEM **mûre** )
**1** **ripe**
**Ces pêches ne sont pas mûres.**
These peaches aren't ripe.
**2** **mature**
**Elle est très mûre pour son âge.**
She's very mature for her age.
les **mûres** FEM PL NOUN
**blackberries**
**murmurer** VERB
**to whisper**
**Pense à un mot et murmure le mot à ton voisin.**
You think of a word and whisper the word to the person next to you.
**musclé** MASC ADJECTIVE (FEM **musclée** )
**muscular**
le **musée** MASC NOUN
**museum**
**J'adore faire les musées.**
I love going round museums.
le **musicien** MASC NOUN
la **musicienne** FEM NOUN
**musician**
la **musique** FEM NOUN
**music**
**J'aime écouter de la musique.**
I like listening to music.
**musulman** MASC NOUN, MASC ADJECTIVE (FEM **musulmane** )
**Muslim**
**myope** ADJECTIVE
**short-sighted**
le **mystère** MASC NOUN
**mystery**
**mystérieux** MASC ADJECTIVE (FEM **mystérieuse** )
**mysterious**
# **N n**
**n'** ADVERB
**_Language tip_**
**ne** _is changed to_ **n'** _before a vowel sound._
**Je n'ai pas d'argent.**
I haven't got any money.
**nager** VERB
**to swim**
**Tu sais nager?**
Can you swim?
le **nageur** MASC NOUN
la **nageuse** FEM NOUN
**swimmer**
**C'est une très bonne nageuse.**
She's a very good swimmer.
la **naissance** FEM NOUN
**birth**
**Quelle est ta date de naissance?**
What's your date of birth?
**naître** VERB
**to be born**
**Il est né en 1982.**
He was born in 1982.
**Elle est née le cinq octobre.**
She was born on the fifth of October.
la **natation** FEM NOUN
**swimming**
**Je fais de la natation tous les mercredis.**
I go swimming every Wednesday.
**national** MASC ADJECTIVE (FEM **nationale** )
**national**
**Aujourd'hui, c'est le quatorze juillet: c'est la fête nationale.**
Today is the fourteenth of July, the national holiday.
la **nationalité** FEM NOUN
**nationality**
**Tu es de quelle nationalité?**
What nationality are you?
**nature**
**nature** _can be a noun or an adjective._
**A** FEM NOUN
**nature**
**B** ADJECTIVE
**plain**
**un yaourt nature**
a plain yoghurt
**naturel** MASC ADJECTIVE (FEM **naturelle** )
**natural**
**naturellement** ADVERB
**of course**
**Naturellement, il est encore en retard.**
He's late again, of course.
**nautique** ADJECTIVE
**water**
**les sports nautiques**
water sports
**le ski nautique**
water-skiing
le **navet** MASC NOUN
**turnip**
**Je n'aime pas les navets.**
I don't like turnips.
la **navette** FEM NOUN
**shuttle**
**une navette spatiale**
a space shuttle
**ne** ADVERB
**_Language tip_**
**ne** _goes with_ **pas, personne, plus** _and_ **jamais** _in negatives._
**Je ne peux pas venir.**
I can't come.
**Ils ne vont jamais à la piscine.**
They never go to the swimming pool.
**Je ne connais personne ici.**
I don't know anyone here.
**Elle ne fait plus d'équitation.**
She doesn't go riding any more.
**_Language tip_**
**ne** _changes to_ **n'** _before a vowel sound._
**Je n'aime pas les maths.**
I don't like maths.
**né** VERB _see_ **naître**
**born**
**Elle est née en 1990.**
She was born in 1990.
**nécessaire** ADJECTIVE
**necessary**
**néerlandais** MASC ADJECTIVE (FEM **néerlandaise** )
**Dutch**
la **neige** FEM NOUN
**snow**
**une boule de neige**
a snowball
**un bonhomme de neige**
a snowman
**neiger** VERB
**to snow**
**Il neige.**
It's snowing.
**néo-zélandais** MASC ADJECTIVE (FEM **néo-zélandaise** )
**New Zealand**
**Elle est néo-zélandaise.**
She's from New Zealand.
le **Néo-Zélandais** MASC NOUN
la **Néo-Zélandaise** FEM NOUN
**New Zealander**
**nerveux** MASC ADJECTIVE (FEM **nerveuse** )
**nervous**
**n'est-ce pas** ADVERB
**_Language tip_**
**n'est-ce pas** _is used to check that something is true._
**Nous sommes le douze aujourd'hui, n'est-ce pas?**
It's the 12th today, isn't it?
**Elle a un chien, n'est-ce pas?**
She's got a dog, hasn't she?
le **Net** MASC NOUN
**the Net**
**nettoyer** VERB
**to clean**
**Nettoie la table, s'il te plaît.**
Clean the table please.
**neuf**
**neuf** _can be a number or an adjective._
**A** NUMBER
**nine**
**Il est neuf heures.**
It's nine o'clock.
**Claire a neuf ans.**
Claire's nine.
**le neuf février**
the ninth of February
**B** MASC ADJECTIVE (FEM **neuve** )
**new**
**des chaussures neuves**
new shoes
**neuvième** ADJECTIVE
**ninth**
**au neuvième étage**
on the ninth floor
le **neveu** MASC NOUN
(PL les **neveux** )
**nephew**
**mon neveu**
my nephew
le **nez** MASC NOUN
**nose**
**ni** CONJUNCTION
**ni... ni...**
neither... nor...
**Je n'aime ni Marie ni Luc.**
I like neither Marie nor Luc.
la **nièce** FEM NOUN
**niece**
**ma nièce**
my niece
le **Noël** MASC NOUN
**Christmas**
**Qu'est-ce que tu a eu pour Noël?**
What did you get for Christmas?
**le père Noël**
Father Christmas
**les cadeaux de Noël**
Christmas presents
**Joyeux Noël!**
Merry Christmas!
le **nœud** MASC NOUN
**knot**
**Fais un nœud à la corde.**
Tie a knot in the rope.
**un nœud papillon**
a bow tie
**_Language tip_**
_The French actually means 'butterfly knot'!_
**noir**
**noir** _can be an adjective or a noun._
**A** MASC ADJECTIVE (FEM **noire** )
**1** **black**
**une robe noire**
a black dress
**Elle est noire.**
She's black.
**2** **dark**
**Il fait noir dehors.**
It's dark outside.
**B** MASC NOUN
**1** **black**
**J'aime le noir.**
I like the colour black.
**2** **dark**
**J'ai peur du noir.**
I'm afraid of the dark.
le **Noir** MASC NOUN
**black man**
**les Noirs**
black people
la **Noire** FEM NOUN
**black woman**
la **noisette** FEM NOUN
**hazelnut**
la **noix** FEM NOUN (PL les **noix** )
**walnut**
**une noix de coco**
a coconut
**les noix de cajou**
cashew nuts
le **nom** MASC NOUN
**1** **name**
**Écrivez votre nom en haut de la feuille.**
Write your name at the top of the sheet.
**mon nom de famille**
my surname
**2** **noun**
**'la banane' est un nom féminin.**
'la banane' is a feminine noun.
le **nombre** MASC NOUN
**number**
**un nombre pair**
an even number
**un nombre impair**
an odd number
**nombreux** MASC ADJECTIVE (FEM **nombreuse** )
**Nous sommes trop nombreux.**
There are too many of us.
**Nous sommes peu nombreux.**
There aren't many of us.
**une famille nombreuse**
a large family
le **nombril** MASC NOUN
**navel**
**non** ADVERB
**no**
**Tu connais Jean-Pierre? — Non.**
Do you know Jean-Pierre? — No.
**Je n'aime pas les hamburgers. — Moi non plus.**
I don't like burgers. — Neither do I.
**nord**
**nord** _can be a noun or an adjective._
**A** MASC NOUN
**north**
**Ils vivent dans le nord de l'île.**
They live in the north of the island.
**au nord de Paris**
north of Paris
**l'Afrique du Nord**
North Africa
**B** MASC, FEM, PL ADJECTIVE
**le pôle Nord**
the North Pole
le **nord-est** MASC NOUN
**north-east**
**J'habite au nord-est de Paris.**
I live in north-east Paris.
le **nord-ouest** MASC NOUN
**north-west**
**J'habite au nord-ouest de Paris.**
I live in north-west Paris.
**normal** MASC ADJECTIVE (FEM **normale** )
**normal**
**une journée normale**
a normal day
**C'est normal.**
It's only natural.
**Ce n'est pas normal!**
That's not right!
**normalement** ADVERB
**normally**
**Normalement, il mange à midi.**
He normally eats at midday.
**normand** MASC ADJECTIVE (FEM **normande** )
**from Normandy**
**Ma grand-mère est normande.**
My grandmother is from Normandy.
la **Normandie** FEM NOUN
**Normandy**
la **Norvège** FEM NOUN
**Norway**
**norvégien** MASC NOUN, MASC ADJECTIVE (FEM **norvégienne** )
**Norwegian**
le **Norvégien** MASC NOUN
la **Norvégienne** FEM NOUN
**Norwegian**
**nos** PL ADJECTIVE _see_ **notre**
**our**
**Où sont nos affaires?**
Where are our things?
le **notaire** MASC NOUN
**solicitor**
la **note** FEM NOUN
**1** **mark**
**Vincent a de bonnes notes en maths.**
Vincent gets good marks in maths.
**2** **bill**
**La note, s'il vous plaît!**
The bill please!
**3** **note**
**Écoutez et prenez des notes.**
Listen and take notes.
**notre** ADJECTIVE (PL **nos** )
**our**
**Voici notre maison.**
This is our house.
le/la **nôtre** MASC/FEM PRONOUN
**ours**
**À qui est ce chien? — C'est le nôtre.**
Whose dog is it? — It's ours.
**Leur voiture est rouge, la nôtre est bleue.**
Their car is red, ours is blue.
**Ces places-là sont les nôtres.**
Those seats are ours.
les **nouilles** FEM PL NOUN
**noodles**
le **nounours** MASC NOUN
**teddy**
la **nourriture** FEM NOUN
**food**
**nous** PRONOUN
**1** **we**
**Nous avons deux chiens.**
We have two dogs.
**2** **us**
**Viens avec nous.**
Come with us.
**nous-mêmes**
ourselves
**nouveau** MASC ADJECTIVE (FEM **nouvelle** )
**new**
**Je voudrais un nouveau vélo.**
I'd like a new bike.
**Nous avons une nouvelle voiture.**
We've got a new car.
**_Language tip_**
**nouveau** _changes to_ **nouvel** _before a vowel sound._
**Il y a un nouvel élève dans ma classe.**
There's a new boy in my class.
**le nouvel an**
New Year
le **nouveau** MASC NOUN
la **nouvelle** FEM NOUN
**new person**
**Il y a plusieurs nouveaux dans la classe.**
There are several new people in the class.
**nouvel, nouvelle** ADJECTIVE _see_ **nouveau**
**new**
la **nouvelle** FEM NOUN
**1** **news**
**C'est une bonne nouvelle.**
That's good news.
**les nouvelles**
the news
**J'écoute les nouvelles à la radio.**
I listen to the news on the radio.
**2** **short story**
**un livre de nouvelles**
a book of short stories
la **Nouvelle-Zélande** FEM NOUN
**New Zealand**
**novembre** MASC NOUN
**November**
**en novembre**
in November
**le vingt-deux novembre**
the twenty-second of November
**nu** MASC ADJECTIVE (FEM **nue** )
**naked**
**tout nu**
stark naked
le **nuage** MASC NOUN
**cloud**
**un gros nuage noir**
a big black cloud
**Il y a des nuages.**
It's cloudy.
**nuageux** MASC ADJECTIVE (FEM **nuageuse** )
**cloudy**
**Il fait un temps nuageux.**
It's cloudy.
la **nuit** FEM NOUN
**night**
**La nuit est belle.**
It's a beautiful night.
**la nuit**
at night
**Tout est calme la nuit.**
Everything is quiet at night.
**cette nuit**
tonight
**Il va rentrer cette nuit.**
He'll be back tonight.
**Bonne nuit!**
Good night!
**Il fait nuit.**
It's dark.
**nul** MASC ADJECTIVE (FEM **nulle** )
**rubbish**
**Ce film est nul.**
This film's rubbish.
**Je suis nul en maths.**
I'm rubbish at maths.
**un match nul**
a draw
**Ils ont fait match nul.**
It was a draw.
**nulle part**
nowhere
**Je ne le vois nulle part.**
I can't see it anywhere.
**numérique** ADJECTIVE
**digital**
le **numéro** MASC NOUN
**number**
**J'habite au numéro trois.**
I live at number three.
**mon numéro de téléphone**
my phone number
# **O o**
l' **objet** MASC NOUN
**object**
**les objets dans la classe**
classroom objects
**obligé** MASC ADJECTIVE (FEM **obligée** )
**Je suis obligé de rester.**
I have to stay.
**observer** VERB
**to watch**
**J'aime bien observer les fourmis à la loupe.**
I like watching ants with my magnifying glass.
l' **occasion** FEM NOUN
**d'occasion**
second-hand
**une voiture d'occasion**
a second-hand car
**occupé** MASC ADJECTIVE (FEM **occupée** )
**1** **busy**
**Il est très occupé.**
He's very busy.
**2** **taken**
**Est-ce que cette place est occupée?**
Is this seat taken?
**3** **engaged**
**Les toilettes sont occupées.**
The toilet's engaged.
s' **occuper** VERB
**s'occuper de**
to be in charge of
**Elle s'occupe d'un club de sport.**
She's in charge of a sports club.
l' **océan** MASC NOUN
**ocean**
**octobre** MASC NOUN
**October**
**en octobre**
in October
**le quinze octobre**
the fifteenth of October
l' **odeur** FEM NOUN
**smell**
**Il y a une drôle d'odeur ici.**
There's a funny smell round here.
l' **œil** MASC NOUN (PL les **yeux** )
**eye**
**J'ai les yeux marron.**
I've got brown eyes.
**Est-ce que j'ai quelque chose dans l'œil?**
Have I got something in my eye?
l' **œuf** MASC NOUN
**egg**
**un œuf à la coque**
a soft-boiled egg
**un œuf dur**
a hard-boiled egg
**un œuf au plat**
a fried egg
**les œufs brouillés**
scrambled eggs
**un œuf de Pâques**
an Easter egg
**_Did you know...?_**
_In France, Easter eggs are said to be brought by the Easter bells_ ( **cloches de Pâques** ) _which fly from Rome and drop them in people's gardens._
**offert** VERB _see_ **offrir**
**Elle m'a offert un CD pour mon anniversaire.**
She gave me a CD for my birthday.
l' **office** MASC NOUN
**l' office du tourisme**
the tourist office
**offrir** VERB
**to give**
**Je vais offrir des fleurs à ma mère.**
I'm going to give my mum some flowers.
**Elle m'a offert un appareil photo.**
She gave me a camera.
l' **oie** FEM NOUN
**goose**
l' **oignon** MASC NOUN
**onion**
l' **oiseau** MASC NOUN
(PL les **oiseaux** )
**bird**
l' **olive** FEM NOUN
**olive**
**l'huile d'olive**
olive oil
**olympique** ADJECTIVE
**les Jeux olympiques**
the Olympic Games
l' **omelette** FEM NOUN
**omelette**
**on** PRONOUN
**1** **we**
**On va à la plage demain.**
We're going to the beach tomorrow.
**2** **someone**
**On m'a volé mon porte-monnaie.**
Someone has stolen my purse.
**3** **you**
**On peut visiter le parc en été.**
You can visit the park in the summer.
l' **oncle** MASC NOUN
**uncle**
**mon oncle**
my uncle
l' **ongle** MASC NOUN
**nail**
**ont** VERB _see_ **avoir**
**Ils ont beaucoup d'argent.**
They have got lots of money.
**_Language tip_**
_Sometimes_ **ont** _shows that something has happened in the past._
**Ils ont passé de bonnes vacances.**
They had a good holiday.
**onze** NUMBER
**eleven**
**Elle a onze ans.**
She's eleven.
**Il est onze heures.**
It's eleven o'clock.
**le onze février**
the eleventh of February
**onzième** ADJECTIVE
**eleventh**
**au onzième étage**
on the eleventh floor
**opérer** VERB
**se faire opérer**
to have an operation
**Je dois me faire opérer.**
I need to have an operation.
**Elle s'est fait opérer de l'appendicite.**
She's had her appendix out.
l' **opticien** MASC NOUN
l' **opticienne** FEM NOUN
**optician**
l' **or** MASC NOUN
**gold**
**en or**
gold
**un bracelet en or**
a gold bracelet
l' **orage** MASC NOUN
**thunderstorm**
**orageux** MASC ADJECTIVE (FEM **orageuse** )
**stormy**
**Le temps est orageux.**
It's stormy.
**orange**
**orange** _can be a noun or an adjective._
**A** FEM NOUN
**orange**
**J'adore les oranges.**
I love oranges.
**B** MASC NOUN
**orange**
**Vous avez ce T-shirt en orange?**
Do you have this T-shirt in orange?
**C** MASC, FEM, PL ADJECTIVE
**orange**
**des rideaux orange**
orange curtains
l' **orchestre** MASC NOUN
**1** **orchestra**
**un orchestre symphonique**
a symphony orchestra
**2** **band**
**un orchestre de jazz**
a jazz band
l' **ordinateur** MASC NOUN
**computer**
l' **ordre** MASC NOUN
**order**
**par ordre alphabétique**
in alphabetical order
**dans l'ordre**
in order
**Remettez les images dans l'ordre.**
Put the pictures in order.
l' **oreille** FEM NOUN
**ear**
**J'ai mal à l'oreille.**
I've got earache.
l' **oreiller** MASC NOUN
**pillow**
**organiser** VERB
**to organize**
**Nous organisons une tombola.**
We're organizing a raffle.
l' **orgue** MASC NOUN
**organ**
l' **orphelin** MASC NOUN
l' **orpheline** FEM NOUN
**orphan**
l' **orteil** MASC NOUN
**toe**
l' **orthographe** FEM NOUN
**spelling**
**Je suis bon en orthographe.**
I'm good at spelling.
l' **os** MASC NOUN
**bone**
**oser** VERB
**Je n'ose pas demander.**
I daren't ask.
**ou** CONJUNCTION
**or**
**Tu veux une limonade ou un coca?**
Would you like a lemonade or a coke?
**où**
**où** _can be an adverb or a pronoun._
**A** ADVERB
**where**
**Où est Nick?**
Where's Nick?
**Où vas-tu?**
Where are you going?
**Je sais où il est.**
I know where he is.
**B** PRONOUN
**that**
**Le jour où il est parti, tout le monde a pleuré.**
The day that he left, everyone cried.
**oublier** VERB
**1** **to forget**
**N'oublie pas de fermer la porte.**
Don't forget to shut the door.
**2** **to leave**
**J'ai oublié mon sac chez Sabine.**
I left my bag at Sabine's.
**ouest**
**ouest** _can be a noun or an adjective._
**A** MASC NOUN
**west**
**Elle vit dans l'ouest de l'Angleterre.**
She lives in the West of England.
**à l'ouest de Paris**
west of Paris
**l'Europe de l'Ouest**
Western Europe
**B** MASC, FEM, PL ADJECTIVE
**west**
**la côte ouest de l'Écosse**
the west coast of Scotland
**ouf** EXCLAMATION
**thank heavens for that!**
**Ouf! J'ai retrouvé mes lunettes!**
Thank heavens for that! I've found my glasses!
**oui** ADVERB
**yes**
**Tu aimes les fraises? — Oui.**
Do you like strawberries? — Yes.
l' **ours** MASC NOUN
**bear**
**un ours en peluche**
a teddy bear
les **outils** MASC PL NOUN
**tools**
**une boîte à outils**
a tool box
**ouvert** MASC ADJECTIVE (FEM **ouverte** )
**open**
**Le magasin est ouvert.**
The shop's open.
l' **ouverture** FEM NOUN
**les heures d'ouverture**
opening hours
l' **ouvrier** MASC NOUN
l' **ouvrière** FEM NOUN
**worker**
**ouvrir** VERB
**to open**
**Ouvre la porte s'il te plaît.**
Open the door please.
**Je peux ouvrir la fenêtre?**
Can I open the window?
l' **ovni** MASC NOUN
**UFO**
# **P p**
**Pacifique** ADJECTIVE, MASC NOUN
**Pacific**
**paf** EXCLAMATION
**wham!**
la **pagaille** FEM NOUN
**mess**
**Quelle pagaille!**
What a mess!
la **page** FEM NOUN
**page**
**Tournez la page.**
Turn the page.
la **paille** FEM NOUN
**straw**
le **pain** MASC NOUN
**bread**
**un morceau de pain**
a piece of bread
**le pain complet**
wholemeal bread
**le pain d'épice**
gingerbread
**le pain grillé**
toast
**pair** MASC ADJECTIVE (FEM **paire** )
**even**
**un nombre pair**
an even number
**une jeune fille au pair**
an au pair
la **paire** FEM NOUN
**pair**
**une paire de chaussures**
a pair of shoes
la **paix** FEM NOUN
**peace**
**J'espère qu'ils vont faire la paix.**
I hope they're going to make up.
le **palais** MASC NOUN
**palace**
**pâle** ADJECTIVE
**pale**
**bleu pâle**
pale blue
la **palme** FEM NOUN
**flipper**
**Tu as tes palmes?**
Have you got your flippers?
le **palmier** MASC NOUN
**palm tree**
le **pamplemousse** MASC NOUN
**grapefruit**
**pané** MASC ADJECTIVE (FEM **panée** )
**fried in breadcrumbs**
**du poisson pané**
fish fried in breadcrumbs
le **panier** MASC NOUN
**basket**
la **panique** FEM NOUN
**panic**
**Pas de panique!**
Don't panic!
la **panne** FEM NOUN
**en panne**
out of order
**L'ascenseur est en panne.**
The lift's not working.
**tomber en panne**
to break down
**une panne de courant**
a power cut
le **panneau** MASC NOUN
(PL les **panneaux** )
**sign**
le **pansement** MASC NOUN
**1** **dressing**
**2** **sticking plaster**
**J'ai mis un pansement sur ma coupure.**
I put a plaster on my cut.
le **pantalon** MASC NOUN
**trousers**
**Son pantalon est trop court.**
His trousers are too short.
la **panthère** FEM NOUN
**panther**
les **pantoufles** FEM PL NOUN
**slippers**
le **paon** MASC NOUN
**peacock**
le **papa** MASC NOUN
**dad**
la **papeterie** FEM NOUN
**stationer's**
**On peut acheter un cahier à la papeterie.**
You can buy an exercise book at the stationer's.
le **papi** MASC NOUN
**granddad**
le **papier** MASC NOUN
**paper**
**une feuille de papier**
a sheet of paper
**le papier cadeau**
wrapping paper
**le papier hygiénique**
toilet paper
**le papier peint**
wallpaper
le **papillon** MASC NOUN
**butterfly**
**Pâques** FEM PL NOUN
**Easter**
**les vacances de Pâques**
Easter holidays
**un œuf de Pâques**
an Easter egg
**_Did you know...?_**
_In France, Easter eggs are said to be brought by the Easter bells_ ( **cloches de Pâques** ) _which fly from Rome and drop them in people's gardens._
**Joyeuses Pâques!**
Happy Easter!
le **paquet** MASC NOUN
**1** **packet**
**2** **parcel**
**Il y a un paquet pour toi.**
There's a parcel for you.
**par** PREPOSITION
**1** **by**
**Il s'est fait disputer par sa mère.**
He was told off by his mum.
**Rangez-vous deux par deux.**
Get into twos.
**2** **with**
**Son nom commence par un H.**
His name begins with H.
**3** **out of**
**Regardez par la fenêtre.**
Look out of the window.
**4** **per**
**Le voyage coûte trois cents euros par personne.**
The trip costs three hundred euros per person.
**5** **via**
**Nous passons par Paris.**
We're going via Paris.
**6** **through**
**Il faut passer par la salle à manger pour aller dans la cuisine.**
You have to go through the dining room to get to the kitchen.
**par ici**
this way/near here
**_Language tip_**
**par ici** _has two translations. Look at the examples._
**Venez par ici.**
Come this way.
**Il y a une boulangerie par d'ici?**
Is there a baker's near here?
**paraître** VERB
**1** **to seem**
**Ça paraît incroyable.**
It seems incredible.
**2** **to look**
**Elle paraît plus jeune que son mari.**
She looks younger than her husband.
le **parapluie** MASC NOUN
**umbrella**
le **parasol** MASC NOUN
**umbrella**
le **parc** MASC NOUN
**park**
**un parc d'attractions**
an amusement park
**parce que** CONJUNCTION
**because**
**Paul pleure parce qu'il a mal à la jambe.**
Paul is crying because his leg is hurting.
**pardon** EXCLAMATION
**1** **sorry!**
**Pardon.**
I'm sorry.
**2** **excuse me!**
**Pardon, madame! Je cherche la poste.**
Excuse me, I'm looking for the post office.
**3** **pardon?**
**Pardon? Vous pouvez répéter?**
Pardon? Could you say that again?
**pardonner** VERB
**to forgive**
**Je te pardonne.**
I forgive you.
**pareil** MASC ADJECTIVE (FEM **pareille** )
**the same**
**Ces images ne sont pas pareilles.**
These pictures aren't the same.
les **parents** MASC PL NOUN
**parents**
**mes parents**
my parents
**paresseux** MASC ADJECTIVE (FEM **paresseuse** )
**lazy**
**parfait** MASC ADJECTIVE (FEM **parfaite** )
**perfect**
**parfaitement** ADVERB
**perfectly**
**Il parle parfaitement l'arabe.**
He speaks perfect Arabic.
**parfois** ADVERB
**sometimes**
le **parfum** MASC NOUN
**1** **perfume**
**2** **flavour**
**Paris** NOUN
**Paris**
**J'habite à Paris.**
I live in Paris.
**Je vais à Paris.**
I'm going to Paris.
**parisien** MASC ADJECTIVE (FEM **parisienne** )
**from Paris**
**Elle est parisienne.**
She's from Paris.
les **Parisiens** MASC PL NOUN
**people from Paris**
le **parking** MASC NOUN
**car park**
**_Language tip_**
_Be careful! The French word_ **parking** _does not mean the same as The English word_ **parking**.
**parler** VERB
**1** **to speak**
**Vous parlez français?**
Do you speak French?
**Je parle français.**
I speak French.
**2** **to talk**
**Arrêtez de parler!**
Stop talking!
**parmi** PREPOSITION
**among**
les **paroles** FEM PL NOUN
**lyrics**
**J'aime les paroles de cette chanson.**
I like the lyrics of this song.
le **parquet** MASC NOUN
**wooden floor**
le **parrain** MASC NOUN
**godfather**
**parrainer** VERB
**to sponsor**
**Tu veux me parrainer?**
Will you sponsor me?
**pars, part** VERB _see_ **partir**
**Je pars demain.**
I'm going tomorrow.
**Le train part à quelle heure?**
What time does the train leave?
la **part** FEM NOUN
**piece**
**une part de gâteau**
a piece of cake
**à part**
except
**Tout le monde va au pique-nique, à part Sandra.**
Everyone except Sandra is going to the picnic.
**partager** VERB
**1** **to share**
**Ils partagent un appartement.**
They share a flat.
**2** **to divide**
**Partage le gâteau en quatre.**
Divide the cake into four.
le/la **partenaire** MASC/FEM NOUN
**partner**
la **partie** FEM NOUN
**1** **game**
**une partie de cartes**
a game of cards
**2** **part**
**une partie de la classe**
part of the class
**Je fais partie d'une chorale.**
I belong to a choir.
**partir** VERB
**1** **to go**
**Je dois partir.**
I've got to go.
**Il part travailler à sept heures.**
He goes to work at seven o'clock.
**partir en vacances**
to go on holiday
**Nous partons en vacances lundi prochain.**
We're going on holiday next Monday.
**2** **to go away**
**Je pars demain et je rentre lundi.**
I'm going away tomorrow and coming back on Monday.
**_Language tip_**
**partir** _is related to the English word 'to depart'._
**à partir de maintenant**
from now on
**partout** ADVERB
**everywhere**
**pas**
**pas** _can be an adverb or a noun._
**A** ADVERB
**ne... pas**
not
**Il ne pleut pas.**
It's not raining.
**Ils n'ont pas de voiture.**
They haven't got a car.
**pas du tout**
not at all
**Je n'aime pas du tout ça.**
I don't like that at all.
**pas toi**
not you
**pas mal**
not bad
**Ça va? — Oui, pas mal.**
How are you? — Not bad.
**B** MASC NOUN
**step**
**Faites trois pas en avant.**
Take three steps forward.
**un pas en arrière**
a step backwards
le **passager** MASC NOUN
la **passagère** FEM NOUN
**passenger**
le **passé** MASC NOUN
**past**
le **passeport** MASC NOUN
**passport**
**passer** VERB
**1** **to go**
**Passez devant l'école et tournez à gauche.**
Go past the school and turn left.
**Nous passons par Paris pour aller à Tours.**
We go through Paris on our way to Tours.
**2** **to have**
**Je passe de bonnes vacances.**
I'm having a nice holiday.
**Vous avez passé de bonnes vacances?**
Did you have a nice holiday?
**3** **to spend**
**Ils passent toujours leurs vacances au Danemark.**
They always spend their holidays in Denmark.
**4** **to pass**
**Passe-moi le sel, s'il te plaît.**
Pass me the salt please.
**5** **to take**
**Gordon passe ses examens la semaine prochaine.**
Gordon is taking his exams next week.
**_Language tip_**
_Be careful!_ **passer un examen** _does not mean the same as_ **to pass an exam**.
**se passer**
**to take place/to go/
to happen**
**_Language tip_**
**se passer** _has several translations. Look at the examples._
**Cette histoire se passe à New York.**
This story takes place in New York.
**Tout se passe bien.**
Everything's going well.
**Qu'est-ce qu'il s'est passé?**
What happened?
**Qu'est-ce qu'il se passe?**
What's the matter?
le **passe-temps** MASC NOUN
**hobby**
**Quel est ton passe-temps préféré?**
What's your favourite hobby?
**passionnant** MASC ADJECTIVE (FEM **passionnante** )
**gripping**
la **pastèque** FEM NOUN
**watermelon**
la **pastille** FEM NOUN
**cough sweet**
la **pâte** FEM NOUN
**1** **pastry**
**2** **dough**
**3** **cake mixture**
**la pâte à crêpes**
pancake batter
**la pâte à modeler**
Plasticine®
**la pâte d'amandes**
marzipan
le **pâté** MASC NOUN
**pâté**
les **pâtes** FEM PL NOUN
**pasta**
**J'adore les pâtes.**
I love pasta.
le **patin** MASC NOUN
**le patin à glace**
ice skating
**Je fais du patin à glace tous les samedis.**
I go ice skating every Saturday.
**les patins à glace**
ice skates
**le patin à roulettes**
roller skating
**Je fais du patin à roulettes avec mes copains.**
I go roller skating with my friends.
**les patins à roulettes**
roller skates
le **patinage** MASC NOUN
**le patinage artistique**
figure skating
la **patinoire** FEM NOUN
**ice rink**
la **pâtisserie** FEM NOUN
**cake shop**
le **pâtissier** MASC NOUN
la **pâtissière** FEM NOUN
**aller chez le pâtissier**
to go to the cake shop
la **patte** FEM NOUN
**1** **paw**
**la patte du chat**
the cat's paw
**2** **leg**
**Cet oiseau a une patte cassée.**
This bird has a broken leg.
**pauvre** ADJECTIVE
**poor**
**Sa famille est pauvre.**
His family is poor.
**Pauvre Jean-Pierre!**
Poor Jean-Pierre!
**payant** MASC ADJECTIVE (FEM **payante** )
**C'est payant.**
You have to pay.
**payer** VERB
**to pay**
le **pays** MASC NOUN
**country**
le **paysage** MASC NOUN
**landscape**
les **Pays-Bas** MASC PL NOUN
**Netherlands**
le **pays de Galles** MASC NOUN
**Wales**
**J'habite au pays de Galles.**
I live in Wales.
**Cet été, je vais au pays de Galles.**
I'm going to Wales this summer.
la **pêche** FEM NOUN
**1** **peach**
**2** **fishing**
**aller à la pêche**
to go fishing
**Il va à la pêche tous les dimanches.**
He goes fishing every Sunday.
le **pêcheur** MASC NOUN
**fisherman**
le **peigne** MASC NOUN
**comb**
**peigner** VERB
**to comb**
**Elle peigne sa poupée.**
She's combing her doll's hair.
**se peigner**
**to comb one's hair**
**Je vais me peigner.**
I'm going to comb my hair.
**peindre** VERB
**to paint**
la **peine** FEM NOUN
**Ce n'est pas la peine.**
Don't bother.
**Ce n'est pas la peine de téléphoner.**
There's no point phoning.
le **peintre** MASC NOUN
**painter**
la **peinture** FEM NOUN
**paint**
la **pelle** FEM NOUN
**1** **shovel**
**2** **spade**
la **pellicule** FEM NOUN
**film**
**une pellicule couleur**
a colour film
la **pelouse** FEM NOUN
**lawn**
la **peluche** FEM NOUN
**soft toy**
**un ours en peluche**
a teddy bear
**pendant** PREPOSITION
**in**
**Pendant les vacances, je fais de l'équitation.**
I go riding in the holidays.
**pendant que**
while
**Ma petite sœur joue pendant que je fais mes devoirs.**
My little sister plays while I do my homework.
le **pendu** MASC NOUN
**hangman**
**On va jouer au pendu.**
We're going to play hangman.
la **pendule** FEM NOUN
**clock**
**penser** VERB
**to think**
**Je pense que Yann a raison.**
I think Yann is right.
**Je pense à mes vacances.**
I'm thinking about my holidays.
la **pension** FEM NOUN
**boarding school**
**Elle est en pension.**
She is at boarding school.
la **Pentecôte** FEM NOUN
**Whitsun**
**le dimanche de Pentecôte**
Whit Sunday
**le lundi de Pentecôte**
Whit Monday
**_Did you know...?_**
_Whit Sunday always occurs seven weeks after Easter, and the following Monday, Whit Monday, is a holiday in France._
le **perdant** MASC NOUN
la **perdante** FEM NOUN
**loser**
**Il est mauvais perdant.**
He's a bad loser.
**perdre** VERB
**to lose**
**Tu vas perdre!**
You're going to lose!
**perdu** VERB _see_ **perdre**
**J'ai perdu ma trousse.**
I've lost my pencil case.
le **père** MASC NOUN
**father**
**mon père**
my father
**le père Noël**
Father Christmas
le **perroquet**
MASC NOUN
**parrot**
la **perruche** FEM NOUN
**budgie**
le **persil** MASC NOUN
**parsley**
le **personnage** MASC NOUN
**character**
**le personnage principal du film**
the main character in the film
la **personnalité** FEM NOUN
**personality**
**personne**
**personne** _can be a noun or a pronoun._
**A** FEM NOUN
**person**
**la même personne**
the same person
**deux personnes**
two people
**une grande personne**
an adult
**une table pour quatre personnes**
a table for four
**B** PRONOUN
**1** **nobody**
**Qui est là? — Personne.**
Who's there? — Nobody.
**Personne ne la connaît.**
Nobody knows her.
**2** **anybody**
**Elle ne veut voir personne.**
She doesn't want to see anybody.
**peser** VERB
**to weigh**
**Elle pèse cent kilos.**
She weighs 100 kilos.
la **pétanque** FEM NOUN
**_Did you know...?_**
**pétanque** _is a kind of bowls game played on rough ground._
le **pétard** MASC NOUN
**banger**
**_Did you know...?_**
_There is a certain kind of_ **pétard** _firework that children in France throw at the pavement to make a bang._
**petit** MASC ADJECTIVE
(FEM **petite** )
**1** **small**
**Je suis petite.**
I'm small.
**2** **little**
**Phyllis a une jolie petite maison.**
Phyllis has got a nice little house.
**le petit déjeuner**
breakfast
**Je prends mon petit déjeuner à sept heures.**
I have my breakfast at seven o'clock.
**des petits pois**
garden peas
**un petit copain**
a boyfriend
**une petite copine**
a girlfriend
la **petite-fille** FEM NOUN
**granddaughter**
le **petit-fils** MASC NOUN
**grandson**
les **petits-enfants** MASC PL NOUN
**grandchildren**
**peu** ADVERB
**un peu**
a bit
**Elle est un peu timide.**
She's a bit shy.
**un peu de gâteau**
a bit of cake
**à peu près**
about
**Le voyage prend à peu près deux heures.**
The journey takes about two hours.
la **peur** FEM NOUN
**Tu as peur?**
Are you scared?
**J'ai peur!**
I'm scared!
**peut** VERB _see_ **pouvoir**
**Il ne peut pas venir.**
He can't come.
**peut-être** ADVERB
**perhaps**
**Tu viens? — Peut-être.**
Are you coming? — Perhaps.
**Je vais peut-être aller en Corse.**
I may go to Corsica.
**peuvent, peux** VERB _see_ **pouvoir**
**Ils ne peuvent pas venir.**
They can't come.
**Je ne peux pas le faire.**
I can't do it.
le **phare** MASC NOUN
**lighthouse**
la **pharmacie** FEM NOUN
**chemist's**
**_Did you know...?_**
_In France, chemists have a big green cross outside the shop._
le **pharmacien** MASC NOUN
la **pharmacienne** FEM NOUN
**pharmacist**
**aller chez le pharmacien**
to go to the chemist
le **phoque** MASC NOUN
**seal**
la **photo** FEM NOUN
**photo**
**Tu peux m'envoyer ta photo?**
Could you send me your photo?
**Je veux prendre une photo.**
I want to take a photo.
**Je vais te prendre en photo.**
I'm going to take a photo of you.
la **photocopie** FEM NOUN
**photocopy**
**photocopier** VERB
**to photocopy**
la **photocopieuse** FEM NOUN
**photocopier**
le/la **photographe** MASC/FEM NOUN
**photographer**
**On va chez le photographe.**
We're going to the photographer's.
le **photophone** MASC NOUN
**camera phone**
la **phrase** FEM NOUN
**sentence**
**Complétez la phrase.**
Complete the sentence.
**physique**
**physique** _can be an adjective or a noun._
**A** ADJECTIVE
**physical**
**l'éducation physique**
physical education
**B** FEM NOUN
**physics**
**Il est professeur de physique.**
He's a physics teacher.
le/la **pianiste** MASC/FEM NOUN
**pianist**
le **piano** MASC NOUN
**piano**
**Je joue du piano.**
I play the piano.
la **pièce** FEM NOUN
**1** **room**
**Il y a six pièces dans ma maison.**
There are six rooms in my house.
**2** **coin**
**une pièce de cinquante centimes**
a fifty centime coin
**une pièce de théâtre**
a play
**un maillot une-pièce**
a one-piece swimsuit
**un maillot deux-pièces**
a bikini
le **pied** MASC NOUN
**foot**
**J'ai mal aux pieds.**
My feet are hurting.
**à pied**
on foot
**Je vais à l'école à pied.**
I walk to school.
la **pierre** FEM NOUN
**stone**
le **piéton** MASC NOUN
la **piétonne** FEM NOUN
**pedestrian**
la **pieuvre** FEM NOUN
**octopus**
le **pigeon** MASC NOUN
**pigeon**
**pile**
**pile** _can be a noun or an adverb._
**A** FEM NOUN
**battery**
**Il faut changer les piles de ma lampe de poche.**
I need to change the batteries in my torch.
**B** ADVERB
**on the dot**
**à deux heures pile**
at two o'clock on the dot
**Pile ou face?**
Heads or tails?
le **pilote** MASC NOUN
**pilot**
**un pilote de ligne**
an airline pilot
**un pilote de course**
a racing driver
le **piment** MASC NOUN
**chilli**
le **pinceau** MASC NOUN (PL les **pinceaux** )
**paintbrush**
le **pingouin** MASC NOUN
**penguin**
le **ping-pong** MASC NOUN
**table tennis**
**Tu veux jouer au ping-pong?**
Do you want to play table tennis?
**piquant** MASC ADJECTIVE (FEM **piquante** )
**1** **prickly**
**un buisson piquant**
a prickly bush
**2** **spicy**
**une sauce très piquante**
a very spicy sauce
le **pique** MASC NOUN
**spades**
**l'as de pique**
the ace of spades
le **pique-nique** MASC NOUN
**picnic**
**pique-niquer** VERB
**to picnic**
**piquer** VERB
**1** **to bite**
**J'ai été piqué par un moustique.**
I have been bitten by a mosquito.
**2** **to burn**
**Cette sauce me pique la langue.**
This sauce is burning my tongue.
la **piqûre** FEM NOUN
**1** **injection**
**Je n'aime pas les piqûres.**
I don't like injections.
**2** **bite**
**une piqûre de moustique**
a mosquito bite
**3** **sting**
**une piqûre d'abeille**
a bee sting
le **pirate** MASC NOUN
**pirate**
**pire**
**pire** _can be an adjective or a noun._
**A** ADJECTIVE
**worse**
**C'est encore pire qu'avant.**
It's even worse than before.
**B** MASC/FEM NOUN
**the worst**
**Ce garçon est le pire de la bande.**
That boy is the worst in the group.
la **piscine** FEM NOUN
**swimming pool**
**Tu veux aller à la piscine?**
Do you want to go to the swimming pool?
**Je vais à la piscine le samedi.**
I go to the swimming pool on Saturdays.
la **pistache** FEM NOUN
**pistachio**
**une glace à la pistache**
a pistachio ice cream
**_Did you know...?_**
_Pistachio ice cream is green._
la **piste** FEM NOUN
**la piste de danse**
the dance floor
**une piste cyclable**
a cycle lane
**une piste de ski**
a ski slope
le **pistolet** MASC NOUN
**pistol**
le **placard** MASC NOUN
**cupboard**
la **place** FEM NOUN
**1** **place**
**Vincent a eu la troisième place.**
Vincent is in third place.
**2** **square**
**la place du village**
the village square
**3** **room**
**Ça prend de la place.**
It takes up a lot of room.
**4** **seat**
**Il reste une place.**
There's one seat left.
**sur place**
on the spot
**Courez sur place.**
Run on the spot.
**à la place**
instead
**Je n'ai pas de bonbons; tu veux une pomme à la place?**
I haven't got any sweets, do you want an apple instead?
le **plafond** MASC NOUN
**ceiling**
la **plage** FEM NOUN
**beach**
se **plaindre** VERB
**Arrête de te plaindre!**
Stop complaining!
**Elle se plaint tout le temps.**
She's always complaining.
**plaire** VERB
**Mon cadeau me plaît beaucoup.**
I like my present a lot.
**Elle lui plaît.**
He fancies her.
**Entrez, s'il vous plaît!**
Come in, please!
**plaisanter** VERB
**to joke**
**Je plaisante!**
I'm joking!
la **plaisanterie** FEM NOUN
**joke**
le **plaisir** MASC NOUN
**pleasure**
**Ça te fait plaisir?**
Are you happy?
**Cette photo va faire très plaisir à ma mère.**
My mum will love this photo.
**plaît** VERB _see_ **plaire**
**Ça te plaît?**
Do you like it?
**Ferme la porte, s'il te plaît.**
Close the door please.
**s'il te plaît**
please
**s'il vous plaît**
please
le **plan** MASC NOUN
**1** **map**
**un plan de la ville**
a street map
**2** **plan**
**Voici le plan de ma maison.**
This is a plan of my house.
la **planche** FEM NOUN
**board**
**une planche à repasser**
an ironing board
**une planche à roulettes**
a skateboard
**une planche à voile**
a windsurfer
le **plancher** MASC NOUN
**floor**
la **planète** FEM NOUN
**planet**
la **plante** FEM NOUN
**plant**
**planter** VERB
**to plant**
la **plaque** FEM NOUN
**une plaque de chocolat**
a slab of chocolate
**une plaque d'immatriculation**
a number plate
la **plaquette** FEM NOUN
**une plaquette de chocolat**
a bar of chocolate
**une plaquette de beurre**
a pack of butter
le **plastique** MASC NOUN
**plastic**
**un sac en plastique**
a carrier bag
**plat**
**plat** _can be a noun or an adjective._
**A** MASC NOUN
**1** **dish**
**un plat en verre**
a glass dish
**le plat du jour**
the dish of the day
**2** **course**
**le plat principal**
the main course
**le plat de résistance**
the main course
**B** MASC ADJECTIVE (FEM **plate** )
**flat**
**La Hollande est un pays plat.**
Holland is a flat country.
le **plateau** MASC NOUN
(PL les **plateaux** )
**tray**
**un plateau d'argent**
a silver tray
**le plateau de fromages**
the cheeseboard
la **platine** FEM NOUN
**une platine laser**
a CD player
le **plâtre** MASC NOUN
**plaster**
**J'ai le bras dans le plâtre.**
I've got my arm in plaster.
**plein** MASC ADJECTIVE (FEM **pleine** )
**full**
**Ton verre est encore plein.**
Your glass is still full.
**à plein temps**
full-time
**Elle travaille à plein temps.**
She works full-time.
**en plein jour**
in broad daylight
**en pleine nuit**
in the middle of the night
**en plein air**
in the open air
**plein de**
lots of
**un gâteau avec plein de crème**
a cake with lots of cream
**pleurer** VERB
**to cry**
**Pourquoi tu pleures?**
Why are you crying?
**pleut** VERB _see_ **pleuvoir**
**Il ne pleut plus.**
It's not raining any more.
**pleuvoir** VERB
**to rain**
**Il pleut.**
It's raining.
**plier** VERB
**to fold**
**Pliez la feuille en deux.**
Fold the paper in two.
le **plombier** MASC NOUN
**plumber**
la **plongée** FEM NOUN
**diving**
**plonger** VERB
**to dive**
**Tu sais plonger?**
Can you dive?
**plouf** EXCLAMATION
**splash!**
**plu** VERB _see_ **plaire, pleuvoir**
**La photo lui a plu.**
She loved the photo.
**Il a plu toute la journée.**
It rained all day.
la **pluie** FEM NOUN
**rain**
**sous la pluie**
in the rain
la **plume** FEM NOUN
**feather**
**un stylo à plume**
a fountain pen
**plupart** PRONOUN
**la plupart**
most of them
**Il y a quinze filles dans ma classe et la plupart sont sympas.**
There are fifteen girls in my class and most of them are nice.
**la plupart de**
most
**La plupart des gens ont peur des serpents.**
Most people are afraid of snakes.
**la plupart du temps**
most of the time
le **pluriel** MASC NOUN
**plural**
**au pluriel**
in the plural
**plus**
**plus** _can be an adverb or a conjunction._
**A** ADVERB
**more**
**C'est plus difficile.**
It's more difficult.
**Il fait plus chaud aujourd'hui.**
It's warmer today.
**ne... plus**
not... any more
**Je ne veux plus le voir.**
I don't want to see him any more.
**Je n'en ai plus.**
I haven't any left.
**Je n'ai plus d'argent.**
I've got no money left.
**plus... que**
more... than
**Elle est plus gaie que sa sœur.**
She's more cheerful than her sister.
**Elle est plus grande que moi.**
She's bigger than me.
**C'est le plus grand de la classe.**
He's the tallest in the class.
**plus de**
more/more than
**_Language tip_**
**plus de** _has two translations. Look at the examples._
**Il nous faut plus de pain.**
We need more bread.
**Le voyage dure plus de six heures.**
The journey takes more than six hours.
**en plus**
as well
**Il est bête, et en plus il est méchant.**
He's stupid and nasty as well.
**de plus en plus**
more and more
**Il y a de plus en plus de touristes par ici.**
There are more and more tourists round here.
**Il fait de plus en plus chaud.**
It's getting hotter and hotter.
**B** CONJUNCTION
**plus**
**Quatre plus deux égalent six.**
Four plus two is six.
**plusieurs** PRONOUN
**several**
**plusieurs personnes**
several people
**plutôt** ADVERB
**1** **quite**
**Elle est plutôt jolie.**
She's quite pretty.
**2** **rather**
**L'eau est plutôt froide.**
The water's rather cold.
**3** **instead**
**Demande-lui plutôt de rester.**
Ask her to stay instead.
**plutôt que**
instead of
**Invite Marie plutôt que Nathalie.**
Invite Marie instead of Nathalie.
la **poche** FEM NOUN
**pocket**
**l'argent de poche**
pocket money
**un livre de poche**
a paperback
la **poêle** FEM NOUN
**frying pan**
le **poème** MASC NOUN
**poem**
le **poids** MASC NOUN
**weight**
le **poids lourd** MASC NOUN
**lorry**
le **poignet** MASC NOUN
**wrist**
le **poil** MASC NOUN
**1** **hair**
**Il y a des poils de chat partout sur la moquette.**
There are cat hairs all over the carpet.
**2** **fur**
**Ton chien a un beau poil.**
Your dog's got lovely fur.
le **poing** MASC NOUN
**fist**
**un coup de poing**
a punch
le **point** MASC NOUN
**full stop**
**un point d'exclamation**
an exclamation mark
**un point d'interrogation**
a question mark
la **pointe** FEM NOUN
**sur la pointe des pieds**
on tiptoe
la **pointure** FEM NOUN
**size**
**Quelle est ta pointure?**
What size shoes do you take?
la **poire** FEM NOUN
**pear**
le **poireau** MASC NOUN
(PL les **poireaux** )
**leek**
les **pois** MASC PL NOUN
**les petits pois**
peas
**les pois chiches**
chickpeas
**à pois**
spotted
**une robe à pois**
a spotted dress
le **poison** MASC NOUN
**poison**
le **poisson** MASC NOUN
**fish**
**Je n'aime pas le poisson.**
I don't like fish.
**un poisson rouge**
a goldfish
**Poisson d'avril!**
April fool!
**_Did you know...?_**
_Pinning a paper fish to somebody's back is a traditional April fool's joke in France._
la **poissonnerie** FEM NOUN
**fish shop**
le **poissonnier** MASC NOUN
**fishmonger**
le **poivre** MASC NOUN
**pepper**
le **poivron** MASC NOUN
**pepper**
**un poivron rouge**
a red pepper
le **pôle** MASC NOUN
**pole**
**le pôle Nord**
the North Pole
**le pôle Sud**
the South Pole
**poli** MASC ADJECTIVE (FEM **polie** )
**polite**
la **police** FEM NOUN
**police**
**policier**
**policier** _can be a noun or an adjective._
**A** MASC NOUN
**policeman**
**B** MASC ADJECTIVE
(FEM **policière** )
**un roman policier**
a detective novel
**pollué** MASC ADJECTIVE (FEM **polluée** )
**polluted**
la **pollution** FEM NOUN
**pollution**
le **polo** MASC NOUN
**polo shirt**
la **Pologne** FEM NOUN
**Poland**
**polonais** MASC NOUN, MASC ADJECTIVE (FEM **polonaise** )
**Polish**
le **Polonais** MASC NOUN
la **Polonaise** FEM NOUN
**Pole**
la **Polynésie** FEM NOUN
**Polynesia**
la **pomme** FEM NOUN
**apple**
**les pommes de terre**
potatoes
**les pommes frites**
chips
**les pommes vapeur**
boiled potatoes
le **pompier** MASC NOUN
**fireman**
le **poney** MASC NOUN
**pony**
le **pont** MASC NOUN
**bridge**
**populaire** ADJECTIVE
**popular**
le **porc** MASC NOUN
**1** **pig**
**Ils élèvent des porcs.**
They breed pigs.
**2** **pork**
**du rôti de porc**
roast pork
le **port** MASC NOUN
**harbour**
le **portable** MASC NOUN
**1** **mobile phone**
**Je vais appeler Marie sur mon portable.**
I'll phone Marie on my mobile.
**2** **laptop**
**Je vais te montrer sur mon portable.**
I'll show you on my laptop.
le **portail** MASC NOUN
**gate**
la **porte** FEM NOUN
**door**
**Ferme la porte, s'il te plaît.**
Close the door, please.
le **porte-clés** MASC NOUN
**key ring**
le **portefeuille** MASC NOUN
**wallet**
le **portemanteau** MASC NOUN (PL les **portemanteaux** )
**1** **coat hanger**
**2** **coat rack**
le **porte-monnaie** MASC NOUN
**purse**
**porter** VERB
**1** **to carry**
**Tu peux me porter? — Non, tu es trop lourde!**
Can you carry me? — No, you're too heavy!
**2** **to wear**
**Elle porte une jolie robe bleue.**
She's wearing a lovely blue dress.
**portugais** MASC NOUN, MASC ADJECTIVE (FEM **portugaise** )
**Portuguese**
le **Portugais** MASC NOUN
la **Portugaise** FEM NOUN
**Portuguese**
le **Portugal** MASC NOUN
**Portugal**
**poser** VERB
**1** **to put down**
**Posez vos crayons.**
Put your pencils down.
**2** **to ask**
**Je peux te poser une question?**
Can I ask you a question?
**possible** ADJECTIVE
**possible**
**Ça n'est pas possible.**
It's not possible.
**le plus vite possible**
as quickly as possible
la **poste** FEM NOUN
**post office**
**poster**
**poster** _can be a noun or a verb._
**A** MASC NOUN
**poster**
**un poster de Madonna**
a poster of Madonna
**_Language tip_**
_When_ **poster** _is a noun, the ending sounds like 'air'._
**B** VERB
**to post**
**Je vais poster ce colis.**
I'm going to post this parcel.
le **pot** MASC NOUN
**pot**
**un pot de confiture**
a pot of jam
**un pot de yaourt**
a yogurt
le **potage** MASC NOUN
**soup**
le **potager** MASC NOUN
**vegetable garden**
le **pot-au-feu** MASC NOUN
**beef stew**
la **poterie** FEM NOUN
**pottery**
la **poubelle** FEM NOUN
**bin**
**Mets ton chewing-gum à la poubelle.**
Put your chewing gum in the bin.
le **pouce** MASC NOUN
**thumb**
la **poule** FEM NOUN
**hen**
le **poulet** MASC NOUN
**chicken**
**J'adore le poulet.**
I love chicken.
la **poupée** FEM NOUN
**doll**
**pour** PREPOSITION
**for**
**C'est un cadeau pour toi.**
It's a present for you.
**Qu'est-ce que tu veux pour ton petit déjeuner?**
What would you like for breakfast?
**Pour aller à la gare, s'il vous plaît?**
Which way is it to the station, please?
**pourquoi** ADVERB
**why**
**Pourquoi tu pleures?**
Why are you crying?
**Pourquoi pas?**
Why not?
**pourra, pourrai, pourras, pourrez, pourrons, pourront**
VERB _see_ **pouvoir**
**Quand est-ce qu'il pourra venir?**
When can he come?
**Je ne pourrai pas venir.**
I won't be able to come.
**Tu pourras me téléphoner ce soir?**
Can you ring me tonight?
**Vous pourrez arrêter à cinq heures.**
You can stop at five o'clock.
**Nous pourrons faire du vélo.**
We can go for bike rides.
**Ils ne pourront pas faire de natation.**
They won't be able to go swimming.
**pousser** VERB
**1** **to push**
**Arrêtez de pousser.**
Stop pushing.
**Pousse-toi, je ne vois rien.**
Move over, I can't see a thing.
**2** **to grow**
**Mes cheveux poussent vite.**
My hair grows quickly.
la **poussette** FEM NOUN
**pushchair**
le **poussin** MASC NOUN
**chick**
la **poutine** FEM NOUN ( _Canada_ )
**_Did you know...?_**
**poutine** _is a type of fast food popular in Quebec. It is French fries topped with cheese curds and gravy._
**pouvoir** VERB
**can**
**Je peux lui téléphoner si tu veux.**
I can phone her if you want.
**Il ne peut pas venir.**
He can't come.
**pratique** ADJECTIVE
**handy**
**Ce sac est très pratique.**
This bag's very handy.
**précieux** MASC ADJECTIVE (FEM **précieuse** )
**precious**
**préféré** MASC ADJECTIVE (FEM **préférée** )
**favourite**
**Quel est ton sport préféré?**
What's your favourite sport?
**préférer** VERB
**to prefer**
**Je préfère manger à la cantine.**
I prefer to eat in the canteen.
**Tu préfères le riz ou les pâtes?**
Would you prefer rice or pasta?
**préhistorique** ADJECTIVE
**prehistoric**
**premier**
**premier** _can be an adjective or a noun._
**A** MASC ADJECTIVE
(FEM **première** )
**first**
**au premier étage**
on the first floor
**C'est la première fois que je viens ici.**
This is the first time I've been here.
**le premier avril**
the first of April
**le premier mai**
the first of May
**B** MASC NOUN
**first**
**Tu veux être le premier?**
Do you want to be first?
la **première** FEM NOUN
**1** **first**
**Elle est arrivée la première.**
She came first.
**2** **year 12**
**Ma sœur est en première.**
My sister's in year 12.
**_Did you know...?_**
_In French secondary schools the years are counted from the_ **sixième** _(youngest) to the_ **première** _and the_ **terminale** _(oldest)._
**prendre** VERB
**1** **to take**
**Prends le plus gros!**
Take the biggest!
**2** **to get**
**Nous prenons le train de huit heures.**
We're getting the eight o'clock train.
**3** **to have**
**Je prends mon petit déjeuner à huit heures.**
I have breakfast at eight.
le **prénom** MASC NOUN
**first name**
**Quel est ton prénom?**
What's your first name?
**préparer** VERB
**to prepare**
**Elle prépare le dîner.**
She's preparing dinner.
**près** ADVERB
**près de**
near
**C'est près d'ici?**
Is it near here?
**tout près**
nearby
**J'habite tout près.**
I live nearby.
**présent**
**présent** _can be an adjective or a noun._
**A** MASC ADJECTIVE (FEM **présente** )
**present**
**Je vais faire l'appel; les garçons, répondez 'présent', et les filles, répondez 'présente'.**
I'm going to call the register. Boys, say 'présent', and girls, say 'présente'.
**B** MASC NOUN
**present**
**à présent**
now
**présenter** VERB
**to present**
**Il va présenter le spectacle.**
He's going to present the show.
**Marc, je te présente Anaïs.**
Marc, this is Anaïs.
**presque** ADVERB
**nearly**
**Il est presque six heures.**
It's nearly six o'clock.
**pressé** MASC ADJECTIVE (FEM **pressée** )
**in a hurry**
**Je ne peux pas rester, je suis pressé.**
I can't stay, I'm in a hurry.
**une orange pressée**
a glass of freshly squeezed orange juice
se **presser** VERB
**to hurry up**
**Allez, presse-toi, on va être en retard!**
Come on, hurry up, we're going to be late!
**prêt** MASC ADJECTIVE (FEM **prête** )
**ready**
**Vous êtes prêts?**
Are you ready?
**prêter** VERB
**to lend**
**Tu peux me prêter ta gomme?**
Could you lend me your rubber?
**prévenir** VERB
**Je te préviens, il est de mauvaise humeur.**
I'm warning you, he's in a bad mood.
la **prière** FEM NOUN
**prayer**
**primaire** ADJECTIVE
**l'école primaire**
primary school
le **prince** MASC NOUN
**prince**
la **princesse** FEM NOUN
**princess**
**principal**
**principal** _can be an adjective or a noun._
**A** MASC ADJECTIVE (FEM **principale** )
**main**
**le personnage principal**
the main character
**B** MASC NOUN
**1** **headmaster**
**_Did you know...?_**
**le principal** _is the headmaster of a_ **collège** – _a secondary school for pupils aged 11 to 15._
**2** **main thing**
**Personne n'a été blessé; c'est le principal.**
Nobody was injured; that's the main thing.
le **printemps** MASC NOUN
**spring**
**au printemps**
in spring
**pris** VERB _see_ **prendre**
**Il a pris le plus gros!**
He took the biggest!
la **prison** FEM NOUN
**prison**
**prisonnier** MASC ADJECTIVE (FEM **prisonnière** )
**captive**
le **prix** MASC NOUN
**1** **price**
**Je n'arrive pas à lire le prix de ce livre.**
I can't see the price of this book.
**2** **prize**
**Cécile a eu le prix de la meilleure actrice.**
Cécile got the prize for best actress.
le **problème** MASC NOUN
**problem**
**prochain** MASC ADJECTIVE (FEM **prochaine** )
**next**
**la prochaine fois**
next time
**À la semaine prochaine!**
See you next week!
le **produit** MASC NOUN
**product**
le/la **prof** MASC/FEM NOUN
**teacher**
**Elle est prof de maths.**
She's a maths teacher.
**_Did you know...?_**
**prof** _is a secondary school teacher._
le **professeur** MASC NOUN
**teacher**
**Christine est professeur d'histoire.**
Christine's a history teacher.
**un professeur des écoles**
a primary school teacher
la **profession** FEM NOUN
**profession**
**professionnel** MASC ADJECTIVE (FEM **professionnelle** )
**professional**
**profond** MASC ADJECTIVE (FEM **profonde** )
**deep**
le **programmeur** MASC NOUN
la **programmeuse** FEM NOUN
**programmer**
le **progrès** MASC NOUN
**progress**
**Tu fais des progrès!**
You're making progress!
**progresser** VERB
**to progress**
le **projet** MASC NOUN
**plan**
**des projets de vacances**
holiday plans
la **promenade** FEM NOUN
**1** **walk**
**Il y a de belles promenades par ici.**
There are some nice walks round here.
**Tu veux faire une promenade?**
Do you want to go for a walk?
**2** **ride**
**Il va faire une promenade à vélo.**
He's going to go for a bike ride.
**Je voudrais faire une promenade en voiture.**
I'd like to go for a drive.
**promener** VERB
**to take for a walk**
**Cordelia promène son chien tous les jours.**
Cordelia takes her dog for a walk every day.
**se promener**
**to go for a walk**
**Chantal veut se promener.**
Chantal wants to go for a walk.
la **promesse** FEM NOUN
**promise**
**Il m'a fait une promesse.**
He made me a promise.
**promettre** VERB
**to promise**
**Je te promets de venir.**
I promise I'll come.
**Je viendrai, c'est promis.**
I'll come, it's a promise.
**prononcer** VERB
**to pronounce**
**Le russe est difficile à prononcer.**
Russian is difficult to pronounce.
la **prononciation** FEM NOUN
**pronunciation**
**propre** ADJECTIVE
**clean**
**Ce verre n'est pas propre.**
This glass isn't clean.
le **prospectus** MASC NOUN
**leaflet**
**protéger** VERB
**to protect**
**protestant** MASC ADJECTIVE (FEM **protestante** )
**Protestant**
le **proverbe** MASC NOUN
**proverb**
la **province** FEM NOUN
**province**
**Ils habitent en province.**
They don't live in Paris.
le **proviseur** MASC NOUN
**headteacher**
**_Did you know...?_**
**le proviseur** _is the headmaster of a_ **lycée** – _a secondary school for pupils aged 15 to 18._
**prudent** MASC ADJECTIVE (FEM **prudente** )
**1** **careful**
**Soyez prudents!**
Be careful!
**2** **wise**
**Laisse ton passeport à la maison, c'est plus prudent.**
It would be wiser to leave your passport at home.
la **prune** FEM NOUN
**plum**
**_Did you know...?_**
_In English, a_ **prune** _is a dried plum, but a French_ **prune** _is a fresh plum._
le **pruneau** MASC NOUN
(PL les **pruneaux** )
**prune**
le/la **psychiatre** MASC/FEM NOUN
**psychiatrist**
le/la **psychologue** MASC/FEM NOUN
**psychologist**
**pu** VERB _see_ **pouvoir**
**Je n'ai pas pu venir.**
I couldn't come.
la **pub** FEM NOUN
**1** **advertising**
**Il y a trop de pub à la télé.**
There's too much advertising on TV.
**2** **advert**
**J'aime regarder les pubs à la télé.**
I like watching the adverts on the telly.
**_Language tip_**
**la pub** _is a slang word for_ **la publicité**.
**public** MASC ADJECTIVE (FEM **publique** )
**public**
**un jardin public**
a public park
**une école publique**
a state school
la **publicité** FEM NOUN
**1** **advertising**
**Muriel travaille dans la publicité.**
Muriel works in advertising.
**2** **advert**
**Il y a trop de publicités dans ce journal.**
There are too many adverts in this newspaper.
**publique** FEM ADJECTIVE _see_ **public**
**public**
**puer** VERB
**to stink**
**Ça pue le tabac ici!**
It stinks of tobacco in here!
**puis** ADVERB
**then**
**Faites dorer le poulet, puis ajoutez le vin blanc.**
Fry the chicken till golden, then add white wine.
**puisque** CONJUNCTION
**since**
**Puisque c'est si cher, nous irons manger ailleurs.**
Since it's so expensive, we'll eat somewhere else.
**puissant** MASC ADJECTIVE (FEM **puissante** )
**powerful**
le **puits** MASC NOUN
**well**
le **pull** MASC NOUN
**jumper**
le **pull-over** MASC NOUN
**jumper**
la **punaise** FEM NOUN
**drawing pin**
**punir** VERB
**être puni**
to be grounded
**Il est puni.**
He's grounded.
la **punition** FEM NOUN
**punishment**
la **purée** FEM NOUN
**mashed potatoes**
le **puzzle** MASC NOUN
**jigsaw puzzle**
le **pyjama** MASC NOUN
**pyjamas**
la **pyramide** FEM NOUN
**pyramid**
les **Pyrénées** FEM PL NOUN
**Pyrenees**
**dans les Pyrénées**
in the Pyrenees
# **Q q**
**quand** CONJUNCTION
**when**
**Quand est-ce que tu pars en vacances?**
When are you going on holiday?
la **quarantaine** FEM NOUN
**about forty**
**une quarantaine de personnes**
about forty people
**Elle a la quarantaine.**
She's in her forties.
**quarante** NUMBER
**forty**
**Elle a quarante ans.**
She's forty.
**quarante et un**
forty-one
**quarante-deux**
forty-two
le **quart** MASC NOUN
**quarter**
**un quart d'heure**
a quarter of an hour
**Il est deux heures et quart.**
It's a quarter past two.
**Il est dix heures moins le quart.**
It's a quarter to ten.
le **quartier** MASC NOUN
**area**
**un quartier tranquille**
a quiet area
**quatorze** NUMBER
**fourteen**
**Il a quatorze ans.**
He's fourteen.
**à quatorze heures**
at 2 p.m.
**_Did you know...?_**
_The 24-hour clock is used in France for travel times, appointments and other formal situations._
**le quatorze février**
the fourteenth of February
**quatre** NUMBER
**four**
**Il est quatre heures.**
It's four o'clock.
**Il a quatre ans.**
He's four.
**le quatre février**
the fourth of February
**quatre-vingts** NUMBER
**eighty**
**quatre-vingts euros**
eighty euros
**Elle a quatre-vingt-deux ans.**
She's eighty-two.
**quatre-vingt-dix**
ninety
**quatre-vingt-onze**
ninety-one
**quatre-vingt-quinze**
ninety-five
**quatre-vingt-dix-huit**
ninety-eight
**quatrième**
**quatrième** _can be an adjective or a noun._
**A** ADJECTIVE
**fourth**
**au quatrième étage**
on the fourth floor
**B** FEM NOUN
**year 9**
**Mon frère est en quatrième.**
My brother's in year 9.
**_Did you know...?_**
_In French secondary schools, years are counted from the_ **sixième** _(youngest) to the_ **première** _and the_ **terminale** _(oldest)._
**que**
**que** _can be a conjunction or a pronoun._
**A** CONJUNCTION
**that**
**J'espère que tu passes de bonnes vacances.**
I hope that you're having a nice holiday.
**plus... que**
more... than
**Il a plus d'argent que moi.**
He's got more money than me.
**Il est plus grand que moi.**
He's taller than me.
**aussi... que**
as... as
**Elle est aussi grande que moi.**
She's as tall as me.
**ne... que**
only
**Il ne boit que de l'eau.**
He only drinks water.
**B** PRONOUN
**what**
**Que fais-tu?**
What are you doing?
**Qu'est-ce que...?**
What...?
**Qu'est-ce que tu fais?**
What are you doing?
**Qu'est-ce que c'est?**
What's that?
**quel** MASC ADJECTIVE (FEM **quelle** )
**1** **who**
**Quel est ton chanteur préféré?**
Who's your favourite singer?
**2** **what**
**Quelle est ta couleur préférée?**
What's your favourite colour?
**3** **which**
**C'est quel jumeau celui-là?**
Which twin is that?
**Quelle heure est-il?**
What time is it?
**quelque** ADJECTIVE
**1** **some**
**Il a quelques amis à Paris.**
He has some friends in Paris.
**2** **a few**
**Il y a quelques tulipes dans le jardin.**
There are a few tulips in the garden.
**quelque chose**
something/anything
**_Language tip_**
**quelque chose** _has two translations. Look at the examples._
**J'ai quelque chose pour toi.**
I've got something for you.
**Je voudrais quelque chose de moins cher.**
I'd like something cheaper.
**Tu veux quelque chose d'autre?**
Would you like anything else?
**quelquefois** ADVERB
**sometimes**
**quelqu'un** PRONOUN
**1** **somebody**
**Il y a quelqu'un à la porte.**
There's somebody at the door.
**2** **anybody**
**Il y a quelqu'un?**
Is there anybody there?
**qu'est-ce que** _see_ **que**
**what**
**qu'est-ce qui** _see_ **qui**
**what**
la **question** FEM NOUN
**question**
le **questionnaire** MASC NOUN
**questionnaire**
la **queue** FEM NOUN
**tail**
**Il faut faire la queue.**
You have to queue.
**une queue de cheval**
a ponytail
**_Language tip_**
_Word for word this means 'horse's tail'._
**qui** PRONOUN
**1** **who**
**Qui a téléphoné?**
Who phoned?
**2** **that**
**J'aime bien les chaussures noires qui sont dans la vitrine.**
I like the black shoes that are in the window.
**Qu'est-ce qui...?**
What...?
**Qu'est-ce qui est sur la table?**
What's on the table?
**à qui**
whose
**À qui est ce sac?**
Whose bag is this?
la **quille** FEM NOUN
**un jeu de quilles**
skittles
la **quinzaine** FEM NOUN
**about fifteen**
**une quinzaine de personnes**
about fifteen people
**une quinzaine de jours**
a fortnight
**quinze** NUMBER
**fifteen**
**Elle a quinze ans.**
She's fifteen.
**quinze jours**
a fortnight
**à quinze heures**
at three p.m.
**_Did you know...?_**
_The 24-hour clock is used in France for travel times, appointments, and other formal situations_
**le quinze avril**
the fifteenth of April
**quitter** VERB
**to leave**
**Je quitte la maison à huit heures du matin.**
I leave the house at eight o'clock in the morning.
**quoi** PRONOUN
**what?**
**À quoi tu penses?**
What are you thinking about?
# **R r**
**raccompagner** VERB
**to take home**
**Tu peux me raccompagner?**
Can you take me home?
le **raccourci** MASC NOUN
**shortcut**
la **race** FEM NOUN
**1** **race**
**la race humaine**
the human race
**2** **breed**
**De quelle race est ton chat?**
What breed is your cat?
la **racine** FEM NOUN
**root**
le **racisme** MASC NOUN
**racism**
**raciste** ADJECTIVE
**racist**
**raconter** VERB
**to tell**
**Je vais te raconter une histoire.**
I'm going to tell you a story.
le **radiateur** MASC NOUN
**radiator**
**un radiateur électrique**
an electric heater
la **radio** FEM NOUN
**1** **radio**
**J'écoute la radio.**
I listen to the radio.
**une radio numérique**
a digital radio
**2** **X-ray**
**une radio des poumons**
an X-ray of the lungs
le **radio-réveil** MASC NOUN
**clock radio**
le **radis** MASC NOUN
**radish**
**_Did you know...?_**
_In France, people often eat radishes with bread and butter as a starter._
le **ragoût** MASC NOUN
**stew**
**raide** ADJECTIVE
**1** **straight**
**Laure a les cheveux raides.**
Laure has got straight hair.
**2** **steep**
**Cette côte est raide.**
This is a steep hill.
**3** **stiff**
**Son bras est encore raide.**
His arm's still stiff.
le **raisin** MASC NOUN
**grapes**
**le raisin noir**
black grapes
**le raisin blanc**
green grapes
**un grain de raisin**
a grape
**des raisins secs**
raisins
la **raison** FEM NOUN
**reason**
**Tu as raison.**
You're right.
**raisonnable** ADJECTIVE
**sensible**
**ramasser** VERB
**1** **to pick up**
**Ramasse le crayon, s'il te plaît.**
Pick up the pencil please.
**2** **to collect**
**Paul, ramasse les cahiers s'il te plaît.**
Paul, collect the books please.
**ramener** VERB
**1** **to bring back**
**Ramène-moi un souvenir!**
Bring me back a souvenir!
**2** **to take home**
**Tu me ramènes?**
Will you take me home?
la **randonnée** FEM NOUN
**une randonnée pédestre**
a ramble
**une randonnée à vélo**
a bike ride
le **rang** MASC NOUN
**row**
**au premier rang**
in the front row
**Mettez-vous en rang.**
Line up.
la **rangée** FEM NOUN
**row**
**une rangée de chaises**
a row of chairs
**ranger** VERB
**1** **to put away**
**Rangez vos affaires.**
Put your things away.
**2** **to tidy up**
**Va ranger ta chambre.**
Go and tidy up your room.
**Rangez-vous deux par deux.**
Get into twos.
**râper** VERB
**to grate**
**le fromage râpé**
grated cheese
**rapide** ADJECTIVE
**fast**
**rapidement** ADVERB
**quickly**
**rappeler** VERB
**1** **to call back**
**Je te rappelle dans cinq minutes.**
I'll call you back in five minutes.
**2** **to remind**
**Rappelle-moi de prendre mon maillot de bain.**
Remind me to take my swimming costume.
**Cette chanson me rappelle mes vacances.**
This song reminds me of my holiday.
**Tu te rappelles?**
Do you remember?
**Je ne me rappelle plus.**
I can't remember.
**rapporter** VERB
**to bring back**
**N'oublie pas de rapporter la clé.**
Don't forget to bring back the key.
la **raquette** FEM NOUN
**1** **racket**
**une raquette de tennis**
a tennis racket
**2** **bat**
**une raquette de ping-pong**
a table tennis bat
se **raser** VERB
**to shave**
**Il se rase tous les matins.**
He shaves every morning.
le **rasoir** MASC NOUN
**razor**
**rassembler** VERB
**to gather**
**Rassemblez vos affaires!**
Gather up your things!
**Rassemblez-vous!**
Gather round!
**Il faut se rassembler demain à huit heures devant l'école.**
We've got to meet at eight tomorrow in front of the school.
**rassurer** VERB
**to reassure**
**Je suis rassuré.**
I don't need to worry any more.
le **rat** MASC NOUN
**rat**
**raté** MASC ADJECTIVE (FEM **ratée** )
**Mes photos sont ratées.**
My photos are no good.
**Le gâteau est raté.**
The cake's a failure.
le **râteau** MASC NOUN
(PL les **râteaux** )
**rake**
**rater** VERB
**1** **to miss**
**Je ne veux pas rater mon train.**
I don't want to miss my train.
**2** **to fail**
**J'ai peur de rater mon examen de maths.**
I'm afraid I'm going to fail my maths exam.
**Elle rate toujours ses gâteaux.**
Her cakes are never any good.
**rayé** MASC ADJECTIVE (FEM **rayée** )
**striped**
**une chemise rayée**
a striped shirt
le **rayon** MASC NOUN
**1** **ray**
**un rayon de soleil**
a ray of sunshine
**2** **department**
**le rayon des jouets**
the toy department
la **rayure** FEM NOUN
**stripe**
**un T-shirt à rayures rouges et blanches**
a T-shirt with red and white stripes
le/la **réceptionniste** MASC/FEM NOUN
**receptionist**
la **recette** FEM NOUN
**recipe**
**recevoir** VERB
**to get**
**Je suis contente quand je reçois une lettre.**
I'm pleased when I get a letter.
**réchauffer** VERB
**to warm up**
**Un bon café va te réchauffer.**
A nice cup of coffee will warm you up.
**se réchauffer**
**to get warm**
**Je vais me réchauffer près du feu.**
I'll go and get warm by the fire.
le **récipient** MASC NOUN
**container**
la **récitation** FEM NOUN
**recitation**
**_Did you know...?_**
_A_ **récitation** _is a poem which pupils have to learn off by heart and recite in front of the whole class._
**réciter** VERB
**to recite**
**reçois, reçoit, reçoivent** VERB _see_ **recevoir**
**Tu reçois combien d'argent de poche?**
How much pocket money do you get?
**Il reçoit toujours des tas de lettres.**
He always gets loads of letters.
**Ils ne reçoivent jamais rien.**
They never get anything.
**recommencer** VERB
**to start again**
**Il recommence à pleuvoir.**
It's started raining again.
la **récompense** FEM NOUN
**reward**
**reconnaître** VERB
**to recognize**
**Elle ne va peut-être pas me reconnaître.**
She might not recognize me.
**Je ne l'ai pas reconnue.**
I didn't recognize her.
le **record** MASC NOUN
**record**
**J'essaie de battre le record.**
I'm trying to break the record.
la **récréation** FEM NOUN
**break**
**Les élèves sont en récréation.**
The pupils are having their break.
**la cour de récréation**
the playground
le **rectangle** MASC NOUN
**rectangle**
**reçu** VERB _see_ **recevoir**
**J'ai reçu un colis ce matin.**
I got a parcel this morning.
**être reçu à un examen**
to pass an exam
**reculer** VERB
**to step back**
**Reculez de trois cases.**
Go back three spaces.
**reculons** ADVERB
**à reculons**
backwards
**Marchez à reculons.**
Walk backwards.
la **rédaction** FEM NOUN
**essay**
**redoubler** VERB
**to repeat a year**
**_Did you know...?_**
_In French schools, pupils sometimes have to repeat a year if they've not done well._
**refaire** VERB
**1** **to do again**
**Je dois refaire mon dessin.**
I'll have to do my drawing again.
**2** **to start doing again**
**Je voudrais refaire de la gym.**
I'd like to start doing gymnastics again.
**réfléchir** VERB
**to think**
**Il est en train de réfléchir.**
He's thinking.
la **réflexion** FEM NOUN
**remark**
le **refrain** MASC NOUN
**chorus**
**refroidir** VERB
**to cool**
**Laissez le gâteau refroidir.**
Leave the cake to cool.
**regarder** VERB
**1** **to look at**
**Regardez l'image: qu'est-ce que c'est?**
Look at the picture: what is it?
**2** **to watch**
**Je regarde la télévision.**
I'm watching television.
le **régime** MASC NOUN
**diet**
**Il est au régime.**
He's on a diet.
la **région** FEM NOUN
**region**
la **règle** FEM NOUN
**ruler**
**regretter** VERB
**to be sorry**
**Je regrette, je ne peux pas venir.**
I'm sorry, I can't come.
**régulier** MASC ADJECTIVE (FEM **régulière** )
**regular**
**régulièrement** ADVERB
**regularly**
le **rein** MASC NOUN
**kidney**
la **reine** FEM NOUN
**queen**
le **relais** MASC NOUN
**relay race**
se **relaxer** VERB
**to relax**
la **religieuse** FEM NOUN
**1** **nun**
**Marie est religieuse.**
Marie is a nun.
**2** **choux cream bun**
**une religieuse au chocolat**
a choux bun with chocolate cream and chocolate icing
la **religion** FEM NOUN
**religion**
**relire** VERB
**to read again**
**remarquable** ADJECTIVE
**remarkable**
la **remarque** FEM NOUN
**remark**
**remarquer** VERB
**to notice**
**Regardez les deux dessins: que remarquez-vous?**
Look at the two pictures: what do you notice?
**remercier** VERB
**to thank**
**Je te remercie pour ton cadeau.**
Thank you for your present.
**remettre** VERB
**1** **to put back**
**Remettez les boîtes dans le placard, s'il vous plaît.**
Put the boxes back in the cupboard please.
**2** **to put back on**
**Remets ton pull, il fait froid.**
Put your sweater back on, it's cold.
**se remettre**
**to get better**
**J'espère que tu vas vite te remettre.**
I hope you will get better soon.
le **remonte-pente** MASC NOUN
**ski tow**
les **remparts** MASC PL NOUN
**city walls**
le **remplaçant** MASC NOUN
la **remplaçante** FEM NOUN
**supply teacher**
**remplacer** VERB
**to replace**
**remplacer par**
to replace with
**Le premier avril, j'ai remplacé le sel par du sucre.**
On April Fool's Day, I replaced the salt with sugar.
**Il remplace le prof de maths.**
He's covering for the maths teacher.
**remplir** VERB
**to fill in**
**Remplissez la grille.**
Fill in the grid.
**remuer** VERB
**to stir**
le **renard** MASC NOUN
**fox**
**rencontrer** VERB
**to meet**
**Je la rencontre souvent au marché.**
I often meet her at the market.
**Ils se sont rencontrés il y a deux ans.**
They met two years ago.
le **rendez-vous** MASC NOUN
**appointment**
**J'ai rendez-vous chez le coiffeur.**
I've got an appointment at the hairdresser's.
**rendre** VERB
**1** **to give back**
**Rends-moi ma gomme.**
Give me back my rubber.
**2** **to take back**
**Je vais rendre mes livres à la bibliothèque.**
I'm going to take my books back to the library.
**renifler** VERB
**to sniff**
le **renne** MASC NOUN
**reindeer**
le **renseignement** MASC NOUN
**piece of information**
**Il me manque un renseignement.**
There's one piece of information I still need.
**des renseignements**
information
**Je cherche des renseignements sur l'Écosse.**
I'm looking for information about Scotland.
la **rentrée** FEM NOUN
**la rentrée (des classes)**
the start of the new school year
**le jour de la rentrée**
the day the schools go back
**rentrer** VERB
**1** **to come in**
**Rentre, tu vas prendre froid.**
Come in, you'll catch cold.
**2** **to get home**
**Il rentre à sept heures du soir.**
He gets home at seven o'clock in the evening.
**réparer** VERB
**to repair**
le **repas** MASC NOUN
**meal**
**le repas de midi**
lunch
**le repas du soir**
dinner
le **repassage** MASC NOUN
**ironing**
**Ma mère déteste le repassage.**
My mum hates ironing.
**repasser** VERB
**to iron**
**répéter** VERB
**to repeat**
**Écoutez et répétez après moi.**
Listen and repeat after me.
la **répétition** FEM NOUN
**rehearsal**
le **répondeur** MASC NOUN
**answering machine**
**répondre** VERB
**to answer**
**Répondez par oui ou par non.**
Answer yes or no.
la **réponse** FEM NOUN
**answer**
**C'est la bonne réponse.**
That's the right answer.
se **reposer** VERB
**to have a rest**
**Le week-end, je me repose.**
I have a rest at the weekend.
le **représentant** MASC NOUN
la **représentante** FEM NOUN
**rep**
le **requin** MASC NOUN
**shark**
**réservé** MASC ADJECTIVE (FEM **réservée** )
**reserved**
**réserver** VERB
**to book**
la **résidence** FEM NOUN
**block of flats**
**une résidence secondaire**
a second home
**respirer** VERB
**to breathe**
**responsable** ADJECTIVE
**responsible**
**Elle est responsable de l'accident.**
She's responsible for the accident.
**ressembler** VERB
**ressembler à**
to look like
**Elle ressemble à sa sœur.**
She looks like her sister.
**On se ressemble.**
We look alike.
le **restaurant** MASC NOUN
**restaurant**
le **reste** MASC NOUN
**rest**
**Tu peux manger le reste des pâtes.**
You can eat the rest of the pasta.
**les restes**
the left-overs
**rester** VERB
**1** **to stay**
**Je reste à la maison ce week-end.**
I'm staying at home this weekend.
**2** **to be left**
**Il reste du pain.**
There's some bread left.
le **résultat** MASC NOUN
**result**
**les résultats des examens**
the exam results
le **retard** MASC NOUN
**Je suis en retard!**
I'm late!
**Tu ne dois pas être en retard.**
You mustn't be late.
la **retenue** FEM NOUN
**detention**
**Gerry est en retenue.**
Gerry's in detention.
**retirer** VERB
**to take off**
**Retire ton manteau.**
Take your coat off.
le **retour** MASC NOUN
**return**
**Il est de retour.**
He's back.
**retourner** VERB
**1** **to go back**
**Je dois retourner chez le dentiste la semaine prochaine.**
I have to go back to the dentist next week.
**2** **to turn over**
**Retourne la carte.**
Turn the card over.
**Retourne-toi.**
Turn round.
la **retraite** FEM NOUN
**être à la retraite**
to be retired
**Mon grand-père est à la retraite.**
My granddad's retired.
**prendre sa retraite**
to retire
**Il prend sa retraite l'année prochaine.**
He's retiring next year.
**retraité** MASC ADJECTIVE (FEM **retraitée** )
**retired**
**retrouver** VERB
**to find**
**Je n'arrive pas à retrouver mes gants.**
I can't find my gloves.
la **réunion** FEM NOUN
**meeting**
**réussi** MASC ADJECTIVE (FEM **réussie** )
**successful**
**une soirée très réussie**
a very successful party
**réussir** VERB
**réussir à un examen**
to pass an exam
le **rêve** MASC NOUN
**dream**
**la maison de mes rêves**
my dream house
le **réveil** MASC NOUN
**alarm clock**
**réveiller** VERB
**to wake up**
**Ma mère me réveille à sept heures.**
My mum wakes me up at seven o'clock.
**se réveiller**
**to wake up**
**Je me réveille à sept heures.**
I wake up at seven o'clock.
le **réveillon** MASC NOUN
**le réveillon du jour de l'An**
New Year's Eve celebrations
**le réveillon de Noël**
Christmas Eve celebrations
**_Did you know...?_**
_In France, people celebrate Christmas Eve and New Year's Eve with special meals in the evening. They eat delicacies such as oysters, smoked salmon, caviar, and quails cooked with white grapes. The special Christmas cake is_ **la bûche de Noël**.
**réveillonner** VERB
**1** **to celebrate New Year's Eve**
**2** **to celebrate Christmas Eve**
**revenez** VERB _see_ **revenir**
**Revenez vite!**
Come back soon!
**revenir** VERB
**to come back**
**Reviens vite!**
Come back soon!
**rêver** VERB
**to dream**
**reviens, revient** VERB _see_ **revenir**
**Tu reviens l'année prochaine?**
Are you coming back next year?
**Antoine revient souvent nous voir.**
Antoine often comes back to see us.
**réviser** VERB
**to revise**
**Je dois réviser mon anglais.**
I've got to revise my English.
**revoir** VERB
**to see again**
**J'aimerais bien la revoir.**
I'd really like to see her again.
**au revoir**
goodbye
la **révolution** FEM NOUN
**revolution**
**la Révolution française**
the French Revolution
le **revolver** MASC NOUN
**revolver**
le **rez-de-chaussée** MASC NOUN
**ground floor**
**au rez-de-chaussée**
on the ground floor
le **Rhin** MASC NOUN
**Rhine**
le **rhinocéros** MASC NOUN
**rhinoceros**
le **Rhône** MASC NOUN
**Rhone**
la **rhubarbe** FEM NOUN
**rhubarb**
le **rhum** MASC NOUN
**rum**
le **rhume** MASC NOUN
**cold**
**J'ai le rhume.**
I've got a cold.
**le rhume des foins**
hay fever
**riche** ADJECTIVE
**1** **well-off**
**Sa famille est très riche.**
His family's very well-off.
**2** **rich**
**riche en vitamines**
rich in vitamins
le **rideau** MASC NOUN
(PL les **rideaux** )
**curtain**
**Tire les rideaux.**
Draw the curtains.
**ridicule** ADJECTIVE
**ridiculous**
**Je trouve ça complètement ridicule.**
I think that's absolutely ridiculous.
**rien** PRONOUN
**1** **nothing**
**Qu'est-ce que tu veux boire? — Rien, merci.**
What would you like to drink? — Nothing, thanks.
**rien d'intéressant**
nothing interesting
**rien d'autre**
nothing else
**rien du tout**
nothing at all
**2** **anything**
**Il ne fait rien ce soir.**
He's not doing anything tonight.
**Elle ne mange rien.**
She's not eating anything.
**De rien!**
Not at all!
**Merci beaucoup! — De rien!**
Thank you very much! — Not at all!
**rigolo** MASC ADJECTIVE
(FEM **rigolote** )
**funny**
**rire** VERB
**to laugh**
**Il me fait toujours rire.**
He always makes me laugh.
le **risque** MASC NOUN
**risk**
la **rivière** FEM NOUN
**river**
le **riz** MASC NOUN
**rice**
**le riz au lait**
rice pudding
la **robe** FEM NOUN
**dress**
**une robe de mariée**
a wedding dress
**une robe de chambre**
a dressing gown
le **robinet** MASC NOUN
**tap**
**Ferme le robinet.**
turn off the tap.
le **robot** MASC NOUN
**robot**
le **rocher**
MASC NOUN
**rock**
le **rock** MASC NOUN
**rock**
**un chanteur de rock**
a rock singer
le **roi** MASC NOUN
**king**
**les Rois mages**
the Three Wise Men
**la fête des Rois**
Epiphany
**_Did you know...?_**
_The sixth of January is_ **la fête des Rois** , _when the Three Wise Men, or Three Kings, are said to have come to visit baby Jesus. This day is also called Twelfth Night, because it is the twelfth day after Christmas._
les **rollers** MASC PL NOUN
**Rollerblades** ®
**romain** MASC ADJECTIVE (FEM **romaine** )
**Roman**
**des ruines romaines**
Roman remains
le **roman** MASC NOUN
**novel**
**rond**
**rond** _can be an adjective or a noun._
**A** MASC ADJECTIVE (FEM **ronde** )
**round**
**La Terre est ronde.**
The earth is round.
**B** MASC NOUN
**circle**
**Dessinez un rond.**
Draw a circle.
**en rond**
in a circle
**Asseyez-vous en rond.**
Sit in a circle.
la **rondelle** FEM NOUN
**slice**
**une rondelle de citron**
a slice of lemon
le **rond-point** MASC NOUN
**roundabout**
**ronfler** VERB
**to snore**
le **rosbif** MASC NOUN
**roast beef**
**rose**
**rose** _can be an adjective or a noun._
**A** ADJECTIVE
**pink**
**des chaussettes roses**
pink socks
**B** FEM NOUN
**rose**
**une rose rouge**
a red rose
**C** MASC NOUN
**pink**
**Ma couleur préférée, c'est le rose.**
Pink is my favourite colour.
le **rosier** MASC NOUN
**rosebush**
**rôti**
**rôti** _can be a noun or an adjective._
**A** MASC NOUN
**roast meat**
**un rôti de bœuf**
a joint of beef
**B** MASC ADJECTIVE (FEM **rôtie** )
**roast**
**un poulet rôti**
a roast chicken
la **roue** FEM NOUN
**wheel**
**une roue de secours**
a spare wheel
**Je sais faire la roue.**
I can do cartwheels.
**rouge**
**rouge** _can be an adjective or a noun._
**A** ADJECTIVE
**red**
**des chaussettes rouges**
red socks
**B** MASC NOUN
**red**
**Ma couleur préférée, c'est le rouge.**
Red is my favourite colour.
**un rouge à lèvres**
a lipstick
**_Language tip_**
**rouge à lèvres** _means 'red for lips'._
la **rougeole** FEM NOUN
**measles**
**rougir** VERB
**to blush**
**Tu rougis!**
You're blushing!
la **rouille** FEM NOUN
**rust**
**rouillé** MASC ADJECTIVE
(FEM **rouillée** )
**rusty**
**roulant** MASC ADJECTIVE
(FEM **roulante** )
**une table roulante**
a trolley
**un fauteuil roulant**
a wheelchair
**rouler** VERB
**1** **to drive**
**Il roule trop vite.**
He drives too fast.
**2** **to roll up**
**Aide-moi à rouler le tapis.**
Help me to roll up the mat.
**Roulez la pâte.**
Roll out the pastry.
**roumain** MASC ADJECTIVE
(FEM **roumaine** )
**Romanian**
le **Roumain** MASC NOUN
la **Roumaine** FEM NOUN
**Romanian**
la **Roumanie** FEM NOUN
**Romania**
**rousse**
**rousse** _can be an adjective or a noun._
**A** FEM ADJECTIVE
**red**
**une poule rousse**
a red hen
**Elle est rousse.**
She's red-haired.
**B** FEM NOUN
**redhead**
la **route** FEM NOUN
**1** **road**
**une route nationale**
an A road
**au bord de la route**
at the roadside
**2** **way**
**Je ne connais pas la route.**
I don't know the way.
**en route**
on the way
**On s'arrête toujours en route.**
We always stop on the way.
**3** **journey**
**Bonne route!**
Have a good journey!
**Il y a trois heures de route.**
It's a three-hour journey.
le **routier** MASC NOUN
**lorry driver**
**roux**
**roux** _can be an adjective or a noun._
**A** MASC ADJECTIVE (FEM **rousse** )
**red**
**Harry a les cheveux roux.**
Harry has red hair.
**Il est roux.**
He's red-haired.
**B** MASC NOUN
**redhead**
**royal** MASC ADJECTIVE (FEM **royale** )
**royal**
**la famille royale**
the Royal Family
le **royaume** MASC NOUN
**kingdom**
**le Royaume-Uni**
the United Kingdom
le **ruban** MASC NOUN
**ribbon**
la **rubéole** FEM NOUN
**German measles**
la **rue** FEM NOUN
**street**
le **rugby** MASC NOUN
**rugby**
**Yann joue au rugby.**
Yann plays rugby.
la **ruine** FEM NOUN
**ruin**
**les ruines de la cathédrale**
the ruins of the cathedral
le **ruisseau** MASC NOUN
(PL les **ruisseaux** )
**stream**
**rusé** MASC ADJECTIVE (FEM **rusée** )
**cunning**
**russe** MASC NOUN, ADJECTIVE
**Russian**
le/la **Russe** MASC/FEM NOUN
**Russian**
la **Russie** FEM NOUN
**Russia**
le **rythme** MASC NOUN
**rhythm**
# **S s**
**s'** PRONOUN
**_Language tip_**
**s'** _is what_ **se** _changes to before a vowel sound._
**Ils s'aiment.**
They love each other.
**sa** FEM ADJECTIVE _see_ **son**
**1** **his**
**Benjamin est chez sa grand-mère.**
Benjamin is at his grandmother's.
**2** **her**
**Elle attend sa mère.**
She's waiting for her mother.
**3** **its**
**Remets la télécommande à sa place.**
Put the remote control back in its place.
le **sable** MASC NOUN
**sand**
le **sac** MASC NOUN
**bag**
**un sac à main**
a handbag
**un sac à dos**
a rucksack
**un sac de couchage**
a sleeping bag
**sage** ADJECTIVE
**well-behaved**
**Fatima est très sage.**
Fatima is very well-behaved.
**Sois sage.**
Be good.
**saignant** MASC ADJECTIVE
(FEM **saignante** )
**rare**
**Saignant ou à point?**
Rare or medium?
**saigner** VERB
**to bleed**
**Il saigne du nez.**
His nose is bleeding.
**saint** MASC ADJECTIVE (FEM **sainte** )
**holy**
**la Saint-Jean-Baptiste** ( _Canada_ )
Midsummer's Day
**_Did you know...?_**
**La Saint-Jean-Baptiste** _is a national holiday in Quebec. It is celebrated on the twenty-fourth of June._
**la Saint-Sylvestre**
New Year's Eve
**le vendredi saint**
Good Friday
le **saint** MASC NOUN
la **sainte** FEM NOUN
**saint**
**Aujourd'hui, c'est la sainte Louise.**
Today is Saint Louise's day.
**_Did you know...?_**
_Every day on a French calendar belongs to a saint. For example, on the fifteenth of March, St Louise's day, people say 'Bonne fête Louise!' to anyone with that name. Girls called Louise might get presents too._
**sais** VERB _see_ **savoir**
**Je ne sais pas.**
I don't know.
la **saison** FEM NOUN
**season**
**sait** VERB _see_ **savoir**
**Il sait que...**
He knows that...
**On ne sait jamais!**
You never know!
la **salade** FEM NOUN
**1** **lettuce**
**Les tortues aiment la salade.**
Tortoises like lettuce.
**2** **salad**
**une salade de fruits**
a fruit salad
le **saladier** MASC NOUN
**salad bowl**
**sale** ADJECTIVE
**dirty**
**salé** MASC ADJECTIVE (FEM **salée** )
**1** **salty**
**La soupe est trop salée.**
The soup's too salty.
**2** **salted**
**du beurre salé**
salted butter
**3** **savoury**
**des biscuits salés**
savoury biscuits
la **salle** FEM NOUN
**room**
**la salle à manger**
the dining room
**la salle de séjour**
the living room
**la salle de bains**
the bathroom
**la salle d'attente**
the waiting room
**une salle de classe**
a classroom
**la salle des professeurs**
the staffroom
le **salon** MASC NOUN
**lounge**
**un salon de thé**
a tearoom
**un salon de beauté**
a beauty salon
la **salopette** FEM NOUN
**dungarees**
**salut** EXCLAMATION
**Hi!**
le **samedi** MASC NOUN
**1** **Saturday**
**Aujourd'hui, nous sommes samedi.**
It's Saturday today.
**2** **on Saturday**
**Je suis allé au cinéma samedi.**
I went to the cinema on Saturday.
**Le magasin ferme à dix-huit heures le samedi.**
The shop closes at six p.m. on Saturdays.
**tous les samedis**
every Saturday
**le samedi**
on Saturdays
**samedi dernier**
last Saturday
**samedi prochain**
next Saturday
**À samedi!**
See you on Saturday!
les **sandales** FEM PL NOUN
**sandals**
le **sandwich** MASC NOUN
**sandwich**
**un sandwich au jambon**
a ham sandwich
le **sang** MASC NOUN
**blood**
le **sanglier** MASC NOUN
**wild boar**
**sans** PREPOSITION
**without**
**Elle est venue sans son frère.**
She came without her brother.
la **santé** FEM NOUN
**health**
**en bonne santé**
in good health
**Santé!**
Cheers!
le **sapin** MASC NOUN
**fir tree**
**un sapin de Noël**
a Christmas tree
la **sauce** FEM NOUN
**1** **sauce**
**la sauce tomate**
tomato sauce
**2** **gravy**
la **saucisse** FEM NOUN
**sausage**
le **saucisson** MASC NOUN
**salami**
**_Did you know...?_**
**le saucisson sec** _is a hard sausage that is eaten cold._
**sauf** PREPOSITION
**except**
**Tout le monde est venu sauf lui.**
Everyone came except him.
**sauf si**
unless
**Je n'irai pas sauf si tu viens.**
I won't go unless you come too.
le **saumon** MASC NOUN
**salmon**
le **saut** MASC NOUN
**jump**
**sauter** VERB
**to jump**
**sauter à la corde**
to skip
**sauvage** ADJECTIVE
**wild**
**les animaux sauvages**
wild animals
**sauver** VERB
**to save**
**Il m'a sauvé la vie.**
He saved my life.
le **savant** MASC NOUN
**scientist**
**savent, savez** VERB
_see_ **savoir**
**Ils ne savent pas ce qu'ils veulent.**
They don't know what they want.
**Est-ce que vous savez où elle habite?**
Do you know where she lives?
**savoir** VERB
**to know**
**Je ne sais pas où il est allé.**
I don't know where he's gone.
**Nous ne savons pas quoi faire.**
We don't know what to do.
**Tu savais que Canberra était la capitale de l'Australie?**
Did you know that Canberra is the capital of Australia?
**Tu sais nager?**
Can you swim?
le **savon** MASC NOUN
**soap**
la **savonnette** FEM NOUN
**bar of soap**
**savons** VERB _see_ **savoir**
**Nous savons où tu es caché.**
We know where you're hiding.
la **Scandinavie** FEM NOUN
**Scandinavia**
la **science** FEM NOUN
**science**
**Elle est forte en sciences.**
She is good at science.
**scolaire** ADJECTIVE
**school**
**l'année scolaire**
the school year
**les vacances scolaires**
the school holidays
**mon livret scolaire**
my school report
le **Scotch** ® MASC NOUN
**adhesive tape**
**se** PRONOUN
**_Language tip_**
**se** _changes to_ **s'** _before a vowel sound._
**1** **himself**
**Il se regarde dans la glace.**
He's looking at himself in the mirror.
**2** **herself**
**Elle se regarde dans la glace.**
She's looking at herself in the mirror.
**Elle s'admire dans sa nouvelle robe.**
She's admiring herself in her new dress.
**3** **itself**
**Le chat se regarde dans la glace.**
The cat's looking at itself in the mirror.
**4** **themselves**
**Ils se sont regardés dans la glace.**
They looked at themselves in the mirror.
**5** **each other**
**Ils se détestent.**
They hate each other.
**_Language tip_**
_Sometimes_ **se** _is not translated._
**Il s'appelle Paul.**
His name is Paul.
**Elle se brosse les dents trois fois par jour.**
She brushes her teeth three times a day.
le **seau** MASC NOUN (PL les **seaux** )
**bucket**
**sec** MASC ADJECTIVE
(FEM **sèche** )
**1** **dry**
**Mon jean n'est pas encore sec.**
My jeans aren't dry yet.
**2** **dried**
**des figues sèches**
dried figs
le **sèche-cheveux** MASC NOUN
**hair dryer**
le **sèche-linge** MASC NOUN
**tumble dryer**
**sécher** VERB
**to dry**
**second** MASC ADJECTIVE
(FEM **seconde** )
**second**
la **seconde** FEM NOUN
**1** **second**
**Attends une seconde!**
Wait a second!
**2** **year 11**
**Ma sœur est en seconde.**
My sister's in year 11.
**_Did you know...?_**
_In French secondary schools the years are counted from the_ **sixième** _(youngest) to the_ **première** _and the_ **terminale** _(oldest)._
le **secours** MASC NOUN
**help**
**Il est allé chercher du secours.**
He went to get help.
**une sortie de secours**
an emergency exit
**Au secours!**
Help!
le **secret**
**secret** _can be a noun or an adjective._
**A** MASC NOUN
**secret**
**J'ai un secret à te dire.**
I have a secret to tell you.
**B** MASC ADJECTIVE (FEM **secrète** )
**secret**
la **secrétaire** FEM NOUN
**secretary**
le **secrétariat** MASC NOUN
**secretary's office**
la **sécurité** FEM NOUN
**safety**
**une ceinture de sécurité**
a seatbelt
**seize** NUMBER
**sixteen**
**Elle a seize ans.**
She's sixteen.
**Il est seize heures.**
It's four p.m.
**_Did you know...?_**
_The 24-hour clock is used in France for travel times, appointments, and other formal situations._
**le seize novembre**
the sixteenth of November
**seizième** ADJECTIVE
**sixteenth**
le **sel** MASC NOUN
**salt**
le **self** MASC NOUN
**self-service restaurant**
**selon** PREPOSITION
**according to**
**Ils sont répartis selon leur âge.**
They're divided up according to age.
la **semaine** FEM NOUN
**week**
**en semaine**
on weekdays
le **semblant** MASC NOUN
**faire semblant**
to pretend
**Il fait semblant de dormir.**
He's pretending to be asleep.
**sembler** VERB
**to seem**
**Le temps semble s'améliorer.**
The weather seems to be improving.
la **semoule** FEM NOUN
**semolina**
le **sens** MASC NOUN
**1** **sense**
**Il a le sens de l'humour.**
He has a sense of humour.
**Je n'ai pas le sens de l'orientation.**
I've got no sense of direction.
**Ça n'a pas de sens.**
It doesn't make sense.
**2** **direction**
**Elle est partie dans le mauvais sens.**
She set off in the wrong direction.
**dans le sens des aiguilles d'une montre**
clockwise
**dans le sens contraire des aiguilles d'une montre**
anticlockwise
**sens dessus dessous**
upside down
**sensible** ADJECTIVE
**sensitive**
**Elle est très sensible.**
She's very sensitive.
**_Language tip_**
_Be careful! The French word_ **sensible** _does not mean the same as the English word_ **sensible**.
**sentir** VERB
**1** **to smell**
**Ça sent bon.**
That smells good.
**Ça sent mauvais.**
It smells horrible.
**2** **to smell of**
**Ça sent les frites ici.**
It smells of chips in here.
**3** **to feel**
**Ça t'a fait mal? — Non, je n'ai rien senti.**
Did it hurt? — No, I didn't feel a thing.
**Je ne me sens pas bien.**
I don't feel well.
**séparé** MASC ADJECTIVE
(FEM **séparée** )
**separated**
**séparer** VERB
**to separate**
**Séparez le blanc du jaune.**
Separate the yolk from the white.
**se séparer**
**to separate**
**Mes parents se sont séparés l'année dernière.**
My parents separated last year.
**sept** NUMBER
**seven**
**Je me lève à sept heures.**
I get up at seven o'clock.
**Elle a sept ans.**
She's seven.
**le sept février**
the seventh of February
**septembre** MASC NOUN
**September**
**en septembre**
in September
**le six septembre**
the sixth of September
**septième** ADJECTIVE
**seventh**
**au septième étage**
on the seventh floor
**sera, serai, seras, serez**
VERB _see_ **être**
**Il sera là demain.**
He'll be here tomorrow
**Je serai de retour à dix heures.**
I'll be back at 10 o'clock.
**Tu ne seras pas toute seule.**
You won't be alone.
**Vous serez chez vous demain?**
Will you be at home tomorrow?
la **série** FEM NOUN
**series**
**une série télévisée américaine**
an American TV series
**sérieux** MASC ADJECTIVE
(FEM **sérieuse** )
**1** **serious**
**Il plaisante? — Non, il est sérieux.**
Is he joking? — No, he's serious.
**2** **responsible**
**C'est un employé très sérieux.**
He's a very responsible employee.
**serons, seront** VERB
_see_ **être**
**Nous serons en vacances demain.**
We'll be on holiday tomorrow.
**Ils seront contents de te revoir.**
They'll be happy to see you again.
le **serpent** MASC NOUN
**snake**
se **serrer** VERB
**se serrer la main**
to shake hands
**Allez, serrez-vous la main!**
Come on, shake hands!
la **serrure** FEM NOUN
**lock**
**sers, sert** VERB _see_ **servir**
**Sers-toi.**
Help yourself.
**Ça ne sert à rien.**
That's no use.
le **serveur** MASC NOUN
**waiter**
la **serveuse** FEM NOUN
**waitress**
la **serviette** FEM NOUN
**1** **towel**
**une serviette de bain**
a bath towel
**2** **napkin**
**servir** VERB
**À quoi ça sert?**
What's it for?
**Ça ne sert à rien.**
It's no use.
**se servir de**
**to use**
**Tu te sers souvent de ton vélo?**
Do you use your bike a lot?
**Servez-vous.**
Help yourself.
**ses** PL ADJECTIVE _see_ **son**
**1** **his**
**Il est chez ses grands-parents.**
He's at his grandparents'.
**2** **her**
**Delphine joue avec ses copines.**
Delphine's playing with her friends.
**3** **its**
**la chatte et ses petits**
the cat and its kittens
**seul**
**seul** _can be an adjective or an adverb._
**A** MASC ADJECTIVE (FEM **seule** )
**1** **only**
**Il reste une seule nectarine.**
There's only one nectarine left.
**C'est la seule chose que je n'aime pas.**
It's the only thing I don't like.
**2** **alone**
**Elle vit seule.**
She lives alone.
**B** ADVERB
**tout seul**
by oneself
**Elle a fait ça toute seule?**
Did she do it by herself?
**seulement** ADVERB
**only**
**non seulement... mais**
not only... but
**Non seulement il pleut, mais en plus il fait froid.**
Not only is it raining, but it's cold as well.
**sévère** ADJECTIVE
**strict**
le **shampooing** MASC NOUN
**shampoo**
le **short** MASC NOUN
**shorts**
**Il est en short.**
He's wearing shorts.
**si**
**si** _can be a conjunction or an adverb._
**A** CONJUNCTION
**if**
**si tu veux**
if you like
**Je me demande si elle va venir.**
I wonder if she'll come.
**si seulement**
if only
**B** ADVERB
**1** **so**
**Elle est si gentille.**
She's so kind.
**2** **yes actually**
**Tu n'es pas allé à l'école habillé comme ça? — Si.**
You didn't go to school dressed like that? — Yes I did, actually.
la **Sicile** FEM NOUN
**Sicily**
le **siècle** MASC NOUN
**century**
le **siège** MASC NOUN
**seat**
le **sien** MASC PRONOUN
la **sienne** FEM PRONOUN
**_Language tip_**
**le sien** , **la sienne** , **les siens** , _and_ **les siennes** _can either mean_ **his** _or_ **hers**.
**C'est le vélo de Paul? — Oui, c'est le sien.**
Is this Paul's bike? — Yes, it's his.
**C'est le vélo d'Isabelle? — Oui, c'est le sien.**
Is this Isabelle's bike? — Yes, it's hers.
**C'est la montre de Paul? — Oui, c'est la sienne.**
Is this Paul's watch? — Yes, it's his.
**Ce sont les baskets de Christian? — Oui, ce sont les siennes.**
Are these Christian's trainers? — Yes, they're his.
la **sieste** FEM NOUN
**nap**
**faire la sieste**
to have a nap
**siffler** VERB
**to whistle**
le **sifflet** MASC NOUN
**whistle**
**signifier** VERB
**to mean**
**Que signifie ce mot?**
What does this word mean?
le **silence** MASC NOUN
**silence**
**Silence!**
Be quiet!
**silencieux** MASC ADJECTIVE
(FEM **silencieuse** )
**silent**
**simple** ADJECTIVE
**simple**
**simplement** ADVERB
**simply**
le **singe** MASC NOUN
**monkey**
le **singulier** MASC NOUN
**singular**
**au singulier**
in the singular
**sinon** CONJUNCTION
**otherwise**
**Dépêche-toi, sinon je pars sans toi.**
Hurry up, otherwise I'll leave without you.
la **sirène** FEM NOUN
**mermaid**
**la sirène d'alarme**
the fire alarm
le **sirop** MASC NOUN
**cordial**
**du sirop de framboise**
raspberry cordial
**_Did you know...?_**
_You dilute_ **le sirop** _with water, rather like squash. There are all kinds of flavours._
**le sirop contre la toux**
cough mixture
le **site** MASC NOUN
**un site Web**
a website
**six** NUMBER
**six**
**Il est rentré à six heures.**
He got back at six o'clock.
**Il a six ans.**
He's six.
**le six février**
the sixth of February
**sixième**
**sixième** _can be an adjective or a noun._
**A** ADJECTIVE
**sixth**
**au sixième étage**
on the sixth floor
**B** FEM NOUN
**year 7**
**Mon frère est en sixième.**
My brother's in year 7.
**_Did you know...?_**
_In French secondary schools the years are counted from the_ **sixième** _(youngest) to the_ **première** _and the_ **terminale** _(oldest)._
le **ski** MASC NOUN
**1** **ski**
**Mes skis sont trop petits.**
My skis are too small.
**2** **skiing**
**J'adore le ski.**
I love skiing.
**faire du ski**
to go skiing
**En hiver, je fais du ski.**
In winter I go skiing.
**le ski nautique**
water-skiing
**skier** VERB
**to ski**
le **skieur** MASC NOUN
la **skieuse** FEM NOUN
**skier**
le **slip** MASC NOUN
**pants**
**un slip de bain**
swimming trunks
le **SMS** MASC NOUN
**text message**
la **SNCF** FEM NOUN
**_Did you know...?_**
_You will see_ **SNCF** _on trains and stations in France. It's the name of the French railways, which are owned by the government._
la **société** FEM NOUN
**1** **society**
**2** **company**
la **sœur** FEM NOUN
**sister**
**ma grande sœur**
my big sister
**ma petite sœur**
my little sister
**soi** PRONOUN
**oneself**
**rester chez soi**
to stay at home
la **soie** FEM NOUN
**silk**
la **soif** FEM NOUN
**thirst**
**Tu as soif?**
Are you thirsty?
**J'ai soif.**
I'm thirsty.
**soi-même** PRONOUN
**oneself**
**Il vaut mieux le faire soi-même.**
It's better to do it oneself.
le **soin** MASC NOUN
**care**
**Prends bien soin de ce livre.**
Take good care of this book.
le **soir** MASC NOUN
**evening**
**ce soir**
this evening
**le soir**
in the evening
**demain soir**
tomorrow night
**hier soir**
last night
la **soirée** FEM NOUN
**evening**
**en tenue de soirée**
in evening dress
**sois** VERB _see_ **être**
**Sois sage!**
Be good!
**soit** CONJUNCTION
**soit..., soit...**
either... or...
**soit lundi, soit mardi**
either Monday or Tuesday
la **soixantaine** FEM NOUN
**about sixty**
**une soixantaine de personnes**
about sixty people
**Elle a la soixantaine.**
She's in her sixties.
**soixante** NUMBER
**sixty**
**Il a soixante ans.**
He's sixty.
**soixante et un**
sixty-one
**soixante-deux**
sixty-two
**soixante et onze**
seventy-one
**soixante-quinze**
seventy-five
**soixante-dix** NUMBER
**seventy**
**Il a soixante-dix ans.**
He's seventy.
**solaire** ADJECTIVE
**solar**
**le système solaire**
the solar system
**la crème solaire**
sun cream
le **soldat** MASC NOUN
**soldier**
le **solde** MASC NOUN
**en solde**
reduced
**Les baskets sont en solde.**
The trainers are reduced.
**les soldes**
the sales
le **soleil** MASC NOUN
**sun**
**au soleil**
in the sun
**Il y a du soleil.**
It's sunny.
**solide** ADJECTIVE
**strong**
**sombre** ADJECTIVE
**dark**
**Il fait un peu sombre ici.**
It's a little dark in here.
le **sommeil** MASC NOUN
**sleep**
**J'ai sommeil.**
I'm sleepy.
**sommes** VERB _see_ **être**
**Nous sommes en vacances.**
We're on holiday.
**_Language tip_**
_Sometimes_ **sommes** _shows that something has happened in the past._
**Nous sommes arrivés à une heure.**
We arrived at 1 o'clock.
**son**
**son** _can be an adjective or a noun._
**A** MASC ADJECTIVE
(FEM **sa** , PL **ses** )
**1** **his**
**Il est chez son grand-père.**
He's at his granddad's.
**2** **her**
**Elle joue avec son frère.**
She's playing with her brother.
**3** **its**
**Le chien est dans son panier.**
The dog's in its basket.
**B** MASC NOUN
**sound**
**Le son n'est pas très bon.**
The sound's not very good.
le **sondage** MASC NOUN
**survey**
**sonner** VERB
**to ring**
**Le téléphone sonne.**
The phone's ringing.
la **sonnerie** FEM NOUN
**1** **bell**
**2** **ringtone**
la **sonnette** FEM NOUN
**bell**
**la sonnette d'alarme**
the alarm bell
**sont** VERB _see_ **être**
**Ils sont en vacances.**
They're on holiday.
**_Language tip_**
_Sometimes_ **sont** _shows that something has happened in the past._
**Ils sont allés en France.**
They went to France.
la **sorcière** FEM NOUN
**witch**
le **sort** MASC NOUN
**spell**
**La sorcière lui a jeté un sort.**
The witch cast a spell on him.
**tirer au sort**
to draw lots
la **sorte** FEM NOUN
**sort**
**C'est une sorte de gâteau.**
It's a sort of cake.
la **sortie** FEM NOUN
**way out**
**Où est la sortie?**
Where's the way out?
**la sortie de secours**
the emergency exit
**Attends-moi à la sortie de l'école.**
Meet me after school.
**sortir** VERB
**1** **to go out**
**Il est sorti.**
He's gone out.
**2** **to come out**
**Il sort de l'hôpital aujourd'hui.**
He's coming out of hospital today.
**3** **to take out**
**Sortez vos affaires.**
Take out your things.
la **soucoupe** FEM NOUN
**saucer**
**une soucoupe volante**
a flying saucer
**soudain**
**soudain** _can be an adjective or an adverb._
**A** MASC ADJECTIVE
(FEM **soudaine** )
**sudden**
**une douleur soudaine**
a sudden pain
**B** ADVERB
**suddenly**
**Soudain, il s'est fâché.**
Suddenly, he got angry.
**souffler** VERB
**1** **to blow**
**Le vent souffle fort.**
The wind's blowing hard.
**2** **to blow out**
**Souffle les bougies!**
Blow out the candles!
le **souhait** MASC NOUN
**wish**
**faire un souhait**
to make a wish
**Atchoum! — À tes souhaits!**
Atchoo! — Bless you!
**_Did you know...?_**
_When you sneeze in France people say_ **'À tes souhaits!'** , _which means_ **'May your wishes come true!'**.
**souhaiter** VERB
**to wish**
**Nous te souhaitons un bon Noël.**
We wish you a happy Christmas.
le **soulier** MASC NOUN
**shoe**
**souligner** VERB
**to underline**
la **soupe** FEM NOUN
**soup**
le **sourcil** MASC NOUN
**eyebrow**
**sourd** MASC ADJECTIVE
(FEM **sourde** )
**deaf**
**souriant** MASC ADJECTIVE
(FEM **souriante** )
**cheerful**
**sourire**
**sourire** _can be a verb or a noun._
**A** VERB
**to smile**
**Elle ne sourit jamais.**
She never smiles.
**B** MASC NOUN
**smile**
**Elle a un joli sourire.**
She has a nice smile.
la **souris** FEM NOUN
**mouse**
**la petite souris**
the tooth fairy
**_Did you know...?_**
_French children believe that a little mouse (_ **la petite souris** _) comes at night to take their tooth from under the pillow and replace it with money._
**sous** PREPOSITION
**under**
**Le chat est sous la chaise.**
The cat's under the chair.
**sous la pluie**
in the rain
le **sous-marin** MASC NOUN
**submarine**
le **sous-sol** MASC NOUN
**basement**
les **sous-titres** MASC PL NOUN
**subtitles**
**sous-titré** MASC ADJECTIVE
(FEM **sous-titrée** )
**with subtitles**
**un film sous-titré**
a film with subtitles
la **soustraction** FEM NOUN
**subtraction**
**souvenir**
**souvenir** _can be a noun or a verb._
**A** MASC NOUN
**1** **memory**
**2** **souvenir**
**un souvenir de Paris**
a souvenir of Paris
**B** VERB
**se souvenir**
**to remember**
**Je ne me souviens pas de son adresse.**
I can't remember his address.
**Je me souviens qu'il neigeait ce jour-là.**
I remember it was snowing that day.
**souvent** ADVERB
**often**
**Tu vas souvent au cinéma?**
Do you go to the cinema often?
**soyez** VERB _see_ **être**
**Soyez sages!**
Be good!
la **SPA** FEM NOUN
**RSPCA**
**spécialement** ADVERB
**1** **specially**
**Il est venu spécialement pour te parler.**
He came specially to speak to you.
**2** **particularly**
**Ce n'est pas spécialement difficile.**
It's not particularly difficult.
le **spectacle** MASC NOUN
**show**
**un spectacle de Noël**
a Christmas show
**splendide** ADJECTIVE
**magnificent**
**Il fait un temps splendide.**
The weather is magnificent.
**sport**
**sport** _can be a noun or an adjective._
**A** MASC NOUN
**sport**
**Quel est ton sport préféré?**
What's your favourite sport?
**Qu'est-ce que tu fais comme sport?**
What sport do you do?
**Il fait beaucoup de sport.**
He does a lot of sport.
**aller aux sports d'hiver**
to go on a skiing holiday
**Je vais aux sports d'hiver en février.**
I'm going on a skiing holiday in February.
**B** ADJECTIVE
**casual**
**une veste sport**
a casual jacket
**des vêtements sport**
casual clothes
**sportif** MASC ADJECTIVE
(FEM **sportive** )
**1** **sporty**
**Elle est très sportive.**
She's very sporty.
**2** **sports**
**un club sportif**
a sports club
le **squelette** MASC NOUN
**skeleton**
le **stade** MASC NOUN
**stadium**
la **station** FEM NOUN
**une station de métro**
an underground station
**une station de ski**
a ski resort
le **steak** MASC NOUN
**steak**
**un steak frites**
steak and chips
**un steak haché**
a hamburger
**stressé** MASC ADJECTIVE
(FEM **stressée** )
**stressed out**
le **studio** MASC NOUN
**studio flat**
**stupide** ADJECTIVE
**stupid**
le **stylo** MASC NOUN
**pen**
**un stylo bille**
a ballpoint pen
**un stylo-feutre**
a felt-tip pen
**su** VERB _see_ **savoir**
**Si j'avais su...**
If I'd known...
le **succès** MASC NOUN
**success**
**Ce film a beaucoup de succès en ce moment.**
This film is very successful at the moment.
la **sucette** FEM NOUN
**lollipop**
le **sucre** MASC NOUN
**sugar**
**un sucre**
a sugar-lump
**Je prends deux sucres dans mon café.**
I take two lumps of sugar in my coffee.
**sucré** MASC ADJECTIVE (FEM **sucrée** )
**sweet**
**Ce gâteau est un peu trop sucré.**
This cake is a bit too sweet.
les **sucreries** FEM PL NOUN
**sweet things**
**sud**
**sud** _can be a noun or an adjective._
**A** MASC NOUN
**south**
**Ils vivent dans le sud de la France.**
They live in the South of France.
**au sud de Paris**
south of Paris
**l'Amérique du Sud**
South America
**B** ADJECTIVE
**south**
**le pôle sud**
the South Pole
le **sud-est** MASC NOUN
**south-east**
**au sud-est**
in the south-east
le **sud-ouest** MASC NOUN
**south-west**
**au sud-ouest**
in the south-west
la **Suède** FEM NOUN
**Sweden**
**suédois** MASC NOUN, MASC ADJECTIVE
(FEM **suédoise** )
**Swedish**
le **Suédois** MASC NOUN
la **Suédoise** FEM NOUN
**Swede**
**suffire** VERB
**to be enough**
**Tiens, voilà cinq euros. Ça te suffit?**
Here's five euros. Is that enough for you?
**Ça suffit!**
That's enough!
**suffisamment** ADVERB
**enough**
**suis** VERB _see_ **être**
**Je suis écossais.**
I'm Scottish.
**_Language tip_**
_Sometimes_ **suis** _shows that something has happened in the past._
**Je suis restée chez moi.**
I stayed at home.
**suisse** ADJECTIVE
**Swiss**
le **Suisse** MASC NOUN
**Swiss man**
la **Suisse** FEM NOUN
**1** **Swiss woman**
**2** **Switzerland**
la **suite** FEM NOUN
**rest**
**Je vous raconterai la suite de l'histoire demain.**
I'll tell you the rest of the story tomorrow.
**J'y vais tout de suite.**
I'll go straightaway.
**tout de suite**
straightaway
**suivre** VERB
**to follow**
**Suivez-moi, tout le monde!**
Follow me, everybody!
**Suis-moi, Alice!**
Follow me, Alice!
**Il me suit partout.**
He follows me everywhere.
**super** MASC, FEM, PL ADJECTIVE
**great**
**C'est super!**
It's great!
le **supermarché** MASC NOUN
**supermarket**
**superposé** MASC ADJECTIVE
**des lits superposés**
bunk beds
**supplémentaire** ADJECTIVE
**additional**
**supporter** VERB
**to stand**
**Je ne supporte pas le golf.**
I can't stand golf.
**Je ne peux pas la supporter.**
I can't stand her.
**_Language tip_**
_Be careful!_
**supporter** _does not mean_ **to support**.
**sur** PREPOSITION
**1** **on**
**Pose-le sur la table.**
Put it down on the table.
**une émission sur les ours polaires**
a programme on polar bears
**2** **in**
**une personne sur dix**
one person in ten
**3** **out of**
**J'ai eu quatorze sur vingt en maths.**
I got 14 out of 20 in maths.
**_Did you know...?_**
_In French schools, tests and homework are usually marked out of 20._
**sûr** MASC ADJECTIVE
(FEM **sûre** )
**sure**
**Tu es sûr?**
Are you sure?
**sûrement** ADVERB
**certainly**
**Sûrement pas!**
Certainly not!
le **surnom** MASC NOUN
**nickname**
**surpris** MASC ADJECTIVE
(FEM **surprise** )
**surprised**
**Il était surpris de me voir.**
He was surprised to see me.
la **surprise** FEM NOUN
**surprise**
**surtout** ADVERB
**especially**
**Il est assez timide, surtout avec les filles.**
He's rather shy, especially with girls.
**surveiller** VERB
**1** **to keep an eye on**
**Tu peux surveiller mes bagages?**
Can you keep an eye on my luggage?
**2** **to supervise**
**Nous sommes toujours surveillés pendant la récréation.**
We're always supervised during break.
le **survêtement** MASC NOUN
**tracksuit**
**SVP** ABBREVIATION
**please**
le **sweat** MASC NOUN
**sweatshirt**
**sympa** ADJECTIVE
**nice**
**Elle est très sympa.**
She's a really nice person.
**sympathique** ADJECTIVE
**nice**
**Ce sont des gens très sympathiques.**
They're very nice people.
**_Language tip_**
_Be careful!_
**sympathique** _does not mean the same as_ **sympathetic**.
le **syndicat** MASC NOUN
**le syndicat d'initiative**
the tourist information office
# **T t**
**t'** PRONOUN
**_Language tip_**
**te** _is changed to_ **t'** _before a vowel sound._
**Je ne t'entends pas.**
I can't hear you.
**Comment tu t'appelles?**
What's your name?
**ta** FEM ADJECTIVE _see_ **ton**
**your**
**Quel âge a ta sœur?**
How old is your sister?
le **tabac** MASC NOUN
**tobacco**
**_Did you know...?_**
**tabac** _is also the name for a shop that sells cigarettes and stamps._
la **table** FEM NOUN
**table**
**une table de nuit**
a bedside table
**Mets la table, s'il te plaît.**
Lay the table please.
**À table!**
Dinner's ready!
le **tableau** MASC NOUN
(PL les **tableaux** )
**1** **painting**
**2** **blackboard**
**C'est écrit au tableau.**
It's on the blackboard.
**3** **whiteboard**
la **tablette** FEM NOUN
**une tablette de chocolat**
a bar of chocolate
le **tablier** MASC NOUN
**apron**
le **tabouret** MASC NOUN
**stool**
la **tache** FEM NOUN
**mark**
**Tu as une tache sur ton T-shirt.**
You've got a mark on your T-shirt.
**des taches de rousseur**
freckles
la **taille** FEM NOUN
**1** **waist**
**Elle a la taille fine.**
She has a slim waist.
**2** **height**
**un homme de taille moyenne**
a man of average height
**3** **size**
**Avez-vous ma taille?**
Have you got my size?
le **taille-crayon** MASC NOUN
**pencil sharpener**
se **taire** VERB
**to stop talking**
**Taisez-vous!**
Stop talking!
le **tambour** MASC NOUN
**drum**
**Il joue du tambour.**
He is playing the drum.
la **Tamise** FEM NOUN
**Thames**
**tant** ADVERB
**so much**
**Je l'aime tant!**
I love him so much!
**tant de**
so much/so many
**_Language tip_**
**tant de** _has two translations. Look at the examples._
**tant de nourriture**
so much food
**tant de livres**
so many books
**Tant mieux!**
_So much the better!_
**Tant pis!**
_Never mind!_
la **tante** FEM NOUN
**aunt**
**ma tante**
my aunt
**taper** VERB
**to bang**
**Arrêtez de taper sur la table.**
Stop banging on the table.
**Maman, il m'a tapé!**
Mum, he hit me!
**taper des pieds**
to stamp one's feet
**Ma petite sœur tape des pieds quand elle est en colère.**
My little sister stamps her feet when she's angry.
**taper des mains**
to clap
**Elle chante et nous tapons des mains.**
She sings and we clap.
le **tapis** MASC NOUN
**rug**
la **tapisserie** FEM NOUN
**wallpaper**
**tard** ADVERB
**late**
**Il est tard.**
It's late.
**plus tard**
later on
la **tarte** FEM NOUN
**tart**
**une tarte aux pommes**
an apple tart
la **tartine** FEM NOUN
**slice of bread**
**une tartine de confiture**
a slice of bread and jam
la **tasse** FEM NOUN
**cup**
**une tasse de thé**
a cup of tea
le **taureau** MASC NOUN
(PL les **taureaux** )
**bull**
le **taxi** MASC NOUN
**taxi**
**tchèque** ADJECTIVE
**Czech**
**te** PRONOUN
**_Language tip_**
**te** _is often not translated into English._
**1** **you**
**Je te vois.**
I can see you.
**Il t'a vu?**
Did he see you?
**2** **to you**
**Est-ce qu'il te parle en français?**
Does he talk to you in French?
**Elle t'a parlé?**
Did she speak to you?
**3** **yourself**
**Tu vas te rendre malade.**
You'll make yourself sick.
**Ne t'en fais pas.**
Don't worry yourself.
**_Language tip_**
**te** _is often not translated into English._
**Je compte jusqu'à dix pendant que tu te caches.**
I'll count to ten while you hide.
la **techno** FEM NOUN
**techno music**
la **télé** FEM NOUN
**telly**
**à la télé**
on telly
la **télécommande**
FEM NOUN
**remote control**
le **téléphérique** MASC NOUN
**cable car**
le **téléphone** MASC NOUN
**telephone**
**Elle est au téléphone.**
She's on the phone.
**un téléphone portable**
a mobile phone
**un téléphone appareil photo**
a camera phone
**téléphoner** VERB
**to phone**
**Je vais téléphoner à Claire.**
I'll phone Claire.
**Je peux téléphoner?**
Can I make a phone call?
la **télévision** FEM NOUN
**television**
**à la télévision**
on television
**tellement** ADVERB
**1** **so**
**Andrew est tellement gentil.**
Andrew's so nice.
**2** **so much**
**Il a tellement mangé que...**
He ate so much that...
**3** **so many**
**Il y avait tellement de monde!**
There were so many people!
la **température** FEM NOUN
**temperature**
la **tempête** FEM NOUN
**storm**
le **temps** MASC NOUN
**1** **weather**
**Il fait mauvais temps.**
The weather's bad.
**Quel temps fait-il?**
What's the weather like?
**2** **time**
**Je n'ai pas le temps.**
I haven't got time.
**de temps en temps**
from time to time
**en même temps**
at the same time
**Elle travaille à plein temps.**
She works full time.
**Elle travaille à temps partiel.**
She works part-time.
**tenir** VERB
**to hold**
**Tu peux tenir la lampe, s'il te plaît?**
Can you hold the torch, please?
**Tiens, voilà un stylo.**
Here's a pen.
le **tennis** MASC NOUN
**1** **tennis**
**Elle joue au tennis.**
She plays tennis.
**2** **tennis court**
**Il est au tennis.**
He's at the tennis court.
les **tennis** FEM PL NOUN
**trainers**
la **tente** FEM NOUN
**tent**
**tenu** VERB _see_ **tenir**
**Il n'a pas tenu sa promesse.**
He didn't keep his promise.
la **tenue** FEM NOUN
**clothes**
**en tenue de soirée**
in evening dress
la **terminale** FEM NOUN
**year 13**
**Elle est en terminale.**
She's in year 13.
**_Did you know...?_**
_In French secondary schools the years are counted from the_ **sixième** , _(youngest), to the_ **première** _and the_ **terminale** , _(oldest)._
**terminer** VERB
**to finish**
**se terminer**
**to end**
**Les vacances se terminent demain.**
The holidays end tomorrow.
le **terrain** MASC NOUN
**un terrain de camping**
a campsite
**un terrain de football**
a football pitch
**un terrain de golf**
a golf course
**un terrain de jeu**
a playground
**un terrain de sport**
a sports ground
la **terrasse** FEM NOUN
**terrace**
**L'été, il y a beaucoup de gens assis aux terrasses de cafés.**
In the summer there are a lot of people sitting at pavement cafés.
la **terre** FEM NOUN
**earth**
**la Terre**
the Earth
**par terre**
on the floor
**Asseyez-vous par terre.**
Sit on the floor.
**terrible** ADJECTIVE
**terrible**
**Quelque chose de terrible est arrivé.**
Something terrible has happened.
**pas terrible**
nothing special
**Ce film n'est pas terrible.**
The film's nothing special.
**tes** PL ADJECTIVE _see_ **ton**
**your**
**J'aime bien tes baskets.**
I like your trainers.
le **têtard** MASC NOUN
**tadpole**
la **tête** FEM NOUN
**head**
**têtu** MASC ADJECTIVE (FEM **têtue** )
**stubborn**
le **Texto** ® MASC NOUN
**text message**
le **TGV** MASC NOUN
**high-speed train**
**_Did you know...?_**
_French railways are very modern_.
**TGVs** _go so fast that they are a good alternative to planes for long journeys._
le **thé** MASC NOUN
**tea**
**_Did you know...?_**
_French people usually drink tea wih lemon, rather than with milk._
le **théâtre** MASC NOUN
**theatre**
**J'aime aller au théâtre.**
I like going to the theatre.
**faire du théâtre**
to act
**Est-ce que tu as déjà fait du théâtre?**
Have you ever acted?
la **théière** FEM NOUN
**teapot**
le **thon** MASC NOUN
**tuna**
**un sandwich au thon mayonnaise**
a tuna mayonnaise sandwich
**tiède** ADJECTIVE
**warm**
le **tien** MASC PRONOUN
la **tienne** FEM PRONOUN
**yours**
**J'ai oublié mon stylo. Tu peux me prêter le tien?**
I've forgotten my pen. Can you lend me yours?
**Ce n'est pas ma raquette, c'est la tienne.**
It's not my racket, it's yours.
**Ce ne sont pas mes baskets, ce sont les tiennes.**
These aren't my trainers, they're yours.
**tiens** VERB _see_ **tenir**
**Tiens, prends un biscuit.**
Go on, have a biscuit.
le **tiers** MASC NOUN
**third**
**Un tiers de la classe a un chien.**
A third of the class own a dog.
**le tiers monde**
the Third World
le **tigre** MASC NOUN
**tiger**
le **timbre** MASC NOUN
**stamp**
**timide** ADJECTIVE
**shy**
le **tire-bouchon** MASC NOUN
**corkscrew**
la **tirelire** FEM NOUN
**money box**
**tirer** VERB
**1** **to pull**
**Il m'a tiré les cheveux.**
He pulled my hair.
**'Tirez'**
'Pull'
**2** **to draw**
**Tire les rideaux s'il te plaît.**
Draw the curtains please.
**tirer au sort**
to draw lots
**Nous avons tiré au sort et j'ai gagné.**
We drew lots and I won.
**tirer les rois**
to cut the galette des Rois
**_Did you know...?_**
_A_ **galette des Rois** _is a cake eaten at Epiphany (the sixth of January) which contains a little figure. The person who finds it is the king (or queen) and gets a paper crown. They then choose somebody to be their queen (or king)._
le **tiroir** MASC NOUN
**drawer**
la **tisane** FEM NOUN
**herbal tea**
le **tissu** MASC NOUN
**material**
**C'est un joli tissu.**
It's nice material.
le **titre** MASC NOUN
**title**
la **TNT** FEM NOUN
**digital television**
le **toast** MASC NOUN
**piece of toast**
**des toasts beurrés**
buttered toast
le **toboggan** MASC NOUN
**slide**
**toi** PRONOUN
**you**
**Ça va? — Oui, et toi?**
How are you? — Fine, and you?
**J'ai faim, pas toi?**
I'm hungry, aren't you?
**Assieds-toi.**
Sit down.
**à toi**
your turn/yours
**_Language tip_**
**à toi** _has two translations. Look at the examples._
**C'est à toi de jouer.**
It's your turn to play.
**Est-ce que ce stylo est à toi?**
Is this pen yours?
la **toile** FEM NOUN
**canvas**
**un sac de toile**
a canvas bag
**une toile d'araignée**
a cobweb
la **toilette** FEM NOUN
**faire sa toilette**
to have a wash
**Le matin, je me lève, je fais ma toilette et je m'habille.**
In the morning I get up, have a wash and get dressed.
les **toilettes** FEM PL NOUN
**toilet**
**Je peux aller aux toilettes, s'il vous plaît?**
May I go to the toilet please?
**toi-même** PRONOUN
**yourself**
**Tu as fait ça toi-même?**
Did you do it yourself?
le **toit** MASC NOUN
**roof**
la **tomate** FEM NOUN
**tomato**
**tomber** VERB
**to fall**
**Attention, tu vas tomber!**
Be careful, you'll fall!
**laisser tomber**
to drop/to give up/to let down
**_Language tip_**
**laisser tomber** _has three translations. Look at the examples._
**Elle a laissé tomber son stylo.**
She dropped her pen.
**Je vais laisser tomber le piano.**
I'm going to give up the piano.
**Il ne laisse jamais tomber ses amis.**
He never lets his friends down.
**ton** MASC ADJECTIVE
(FEM **ta** , PL **tes** )
**your**
**C'est ton stylo?**
Is this your pen?
**Ce sont tes feutres?**
Are these your felt-tips?
le **tonnerre** MASC NOUN
**thunder**
**tordre** VERB
**Je me suis tordu la cheville.**
I've twisted my ankle.
la **tortue** FEM NOUN
**tortoise**
**une tortue d'eau douce**
a terrapin
**une tortue de mer**
a turtle
**tôt** ADVERB
**early**
**Il se lève très tôt.**
He gets up very early.
**totalement** ADVERB
**totally**
**toucher** VERB
**to touch**
**Ne touche pas à mes livres!**
Don't touch my books!
**toujours** ADVERB
**1** **always**
**Il est toujours très gentil.**
He's always very nice.
**pour toujours**
forever
**2** **still**
**Quand nous sommes revenus, il était toujours là.**
When we got back he was still there.
la **tour** FEM NOUN
**1** **tower**
**la Tour Eiffel**
the Eiffel Tower
**2** **tower block**
**J'habite dans une tour de vingt étages.**
I live in a twenty-storey tower block.
le **tour** MASC NOUN
**turn**
**C'est ton tour de jouer.**
It's your turn to play.
**faire un tour**
to go for a walk
**Allons faire un tour dans le parc.**
Let's go for a walk in the park.
**faire un tour en voiture**
to go for a drive
**faire un tour à vélo**
to go for a bike ride
**Tu veux aller faire un tour à vélo?**
Do you want to go for a bike ride?
**faire le tour du monde**
to travel round the world
**tourner** VERB
**to turn**
**Tournez à droite au prochain feu.**
Turn right at the lights.
le **tournesol** MASC NOUN
**sunflower**
le **tournoi** MASC NOUN
**tournament**
**tous** MASC PL ADJECTIVE, MASC PL PRONOUN
**1** **all**
**tous les biscuits**
all the biscuits
**Nous y sommes tous allés.**
We all went.
**2** **every**
**tous les ans**
every year
la **Toussaint** FEM NOUN
**All Saints' Day**
**_Did you know...?_**
**la Toussaint** _is on the first of November, when people in France traditionally go to the cemetery to visit the graves of their relatives._
**les vacances de la Toussaint**
autumn half term
**tousser** VERB
**to cough**
**tout**
**tout** _can be an adjective, an adverb, a pronoun or a noun._
**A** MASC ADJECTIVE
(FEM **toute** )
**1** **all**
**tout le lait**
all the milk
**tous les livres**
all the books
**tout le temps**
all the time
**toute la journée**
all day
**toute la nuit**
all night
**tous les deux**
both
**Aurélie et moi avons toutes les deux un chien.**
Aurélie and I both have a dog.
**Je les ai invités tous les trois.**
I invited all three of them.
**2** **every**
**tous les jours**
every day
**tous les deux jours**
every two days
**tout le monde**
everybody
**tout ce qui**
everything that
**tout ce qui est en face de toi**
everything that's in front of you
**tout ce que**
everything
**Tu peux avoir tout ce que tu veux.**
You can have everything you want.
**B** ADVERB
**very**
**Il habite tout près.**
He lives very close.
**Elle est toute petite.**
She's very small.
**tout à l'heure**
just now/in a moment
**_Language tip_**
**tout à l'heure** _has two translations. Look at the examples._
**Je l'ai vu tout à l'heure.**
I saw him just now.
**Je finirai ça tout à l'heure.**
I'll finish it in a moment.
**À tout à l'heure!**
See you later!
**tout de suite**
straight away
**tout droit**
straight ahead
**tout d'abord**
first of all
**tout à coup**
suddenly
**tout à fait**
absolutely
**C** PRONOUN
**everything**
**Il a tout organisé.**
He organized everything.
**D** MASC NOUN
**pas du tout**
not at all
**toutes** FEM PL ADJECTIVE, FEM PL PRONOUN
**1** **all**
**toutes les photos**
all the photos
**Je les connais toutes.**
I know them all.
**2** **toutes les semaines**
every week
le **tracteur** MASC NOUN
**tractor**
**traduire** VERB
**to translate**
le **train** MASC NOUN
**train**
**un train électrique**
a train set
**Il est en train de manger.**
He's eating.
**Ils sont en train de dormir.**
They're sleeping.
le **traîneau** MASC NOUN
(PL les **traîneaux** )
**sledge**
le **trait** MASC NOUN
**line**
**traiter** VERB
**Il m'a traité d'imbécile.**
He called me an idiot.
le **tramway** MASC NOUN
**tram**
la **tranche** FEM NOUN
**slice**
**tranquille** ADJECTIVE
**quiet**
**Cette rue est très tranquille.**
This is a very quiet street.
**Tiens-toi tranquille!**
Behave yourself!
**Laisse-moi tranquille.**
Leave me alone.
le **travail** MASC NOUN
**1** **work**
**J'ai beaucoup de travail.**
I've got a lot of work.
**2** **job**
**Il a un travail intéressant.**
He's got an interesting job.
**_Language tip_**
_Be careful!_
**travail** _does not mean the same as_ **travel**.
**travailler** VERB
**to work**
**Elle travaille dans un bureau.**
She works in an office.
**_Language tip_**
_Be careful!_
**travailler** _does not mean the same as_ **travel**.
**travailleur** MASC ADJECTIVE
(FEM **travailleuse** )
**hard-working**
les **travaux** MASC PL NOUN
**roadworks**
**Il y a beaucoup de bruit à cause des travaux dans la rue.**
There's a lot of noise from the roadworks.
**les travaux manuels**
handicrafts
le **travers** MASC NOUN
**à travers**
through
**Passe à travers la haie.**
Go through the hedge.
la **traversée** FEM NOUN
**crossing**
**La traversée de la Manche dure une heure.**
The Channel crossing takes an hour.
**traverser** VERB
**1** **to cross**
**Traversez la rue.**
Cross the street.
**2** **to go through**
**Nous avons traversé la France pour aller en Espagne.**
We went through France on our way to Spain.
le **traversier** MASC NOUN ( _Canada_ )
**ferry**
le **trèfle** MASC NOUN
**1** **clover**
**un trèfle à quatre feuilles**
a four-leaved clover
**2** **clubs**
**le roi de trèfle**
the king of clubs
**treize** NUMBER
**thirteen**
**Il a treize ans.**
He's thirteen.
**à treize heures**
at one p.m.
**_Did you know...?_**
_The 24-hour clock is used in France for travel times, appointments, and other formal situations._
**le treize février**
the thirteenth of February
**treizième** ADJECTIVE
**thirteenth**
le **tremblement de terre** MASC NOUN
**earthquake**
**trembler** VERB
**to shake**
**trembler de froid**
to shiver
**trempé** MASC ADJECTIVE
(FEM **trempée** )
**soaking wet**
la **trentaine** FEM NOUN
**about thirty**
**une trentaine de personnes**
about thirty people
**Il a la trentaine.**
He's in his thirties.
**trente** NUMBER
**thirty**
**Elle a trente ans.**
She's thirty.
**trente et un**
thirty-one
**trente-deux**
thirty-two
**le trente janvier**
the thirtieth of January
**très** ADVERB
**very**
le **trésor** MASC NOUN
**treasure**
**tricher** VERB
**to cheat**
**Tu as triché!**
You cheated!
**tricolore** ADJECTIVE
**three-coloured**
**le drapeau tricolore**
the French tricolour
**_Did you know...?_**
**le drapeau tricolore** _is the French flag: its three colours are blue, white, and red._
**tricoter** VERB
**to knit**
le **trimestre** MASC NOUN
**term**
**triste** ADJECTIVE
**sad**
**trois** NUMBER
**three**
**trois fois**
three times
**à trois heures du matin**
at three in the morning
**Elle a trois ans.**
She's three years old.
**le trois septembre**
the third of September
**troisième**
**troisième** _can be an adjective or a noun._
**A** ADJECTIVE
**third**
**au troisième étage**
on the third floor
**B** FEM NOUN
**year 10**
**Mon frère est en troisième.**
My brother's in year 10.
**_Did you know...?_**
_In French secondary schools the years are counted from the_ **sixième** _(youngest) to the_ **première** _and the_ **terminale** _(oldest)._
les **trois-quarts** MASC PL NOUN
**three-quarters**
**les trois-quarts de la classe**
three-quarters of the class
le **trombone** MASC NOUN
**1** **trombone**
**Il joue du trombone.**
He plays the trombone.
**2** **paper clip**
la **trompe** FEM NOUN
**trunk**
**la trompe d'un éléphant**
an elephant's trunk
se **tromper** VERB
**to make a mistake**
**Je me suis trompé.**
I've made a mistake.
**se tromper de jour**
to get the wrong day
la **trompette** FEM NOUN
**trumpet**
**Il joue de la trompette.**
He plays the trumpet.
le **tronc** MASC NOUN
**trunk**
**un tronc d'arbre**
a tree trunk
**trop** ADVERB
**1** **too**
**Il conduit trop vite.**
He drives too fast.
**2** **too much**
**J'ai trop mangé.**
I've eaten too much.
**trop de**
too much/too many
**_Language tip_**
**trop de** _has two translations. Look at the examples._
**J'ai trop de devoirs à faire.**
I've got too much homework to do.
**Il y a trop de monde.**
There are too many people.
le **trottoir** MASC NOUN
**pavement**
le **trou** MASC NOUN
**hole**
la **trousse** FEM NOUN
**pencil case**
**une trousse de toilette**
a toilet bag
**trouver** VERB
**1** **to find**
**Je ne trouve pas mes lunettes.**
I can't find my glasses.
**2** **to think**
**Je trouve que c'est bête.**
I think it's stupid.
**se trouver**
**to be**
**Où se trouve la poste?**
Where is the post office?
**Marseille se trouve dans le sud de la France.**
Marseilles is in the South of France.
le **truc** MASC NOUN
**thing**
la **truite** FEM NOUN
**trout**
le **T-shirt** MASC NOUN
**T-shirt**
**tu** PRONOUN
**you**
**Tu as un animal?**
Have you got a pet?
le **tube** MASC NOUN
**1** **tube**
**un tube de dentifrice**
a tube of toothpaste
**2** **hit**
**Ça va être le tube de l'été.**
It's going to be this summer's hit.
**tuer** VERB
**to kill**
la **Tunisie** FEM NOUN
**Tunisia**
**tunisien** MASC ADJECTIVE
(FEM **tunisienne** )
**Tunisian**
le **Tunisien** MASC NOUN
la **Tunisienne** FEM NOUN
**Tunisian**
le **tunnel** MASC NOUN
**tunnel**
**le tunnel sous la Manche**
the Channel Tunnel
**turc** MASC NOUN, MASC ADJECTIVE
(FEM **turque** )
**Turkish**
le **Turc** MASC NOUN
la **Turque** FEM NOUN
**Turk**
la **Turquie** FEM NOUN
**Turkey**
**tutoyer** VERB
**tutoyer quelqu'un**
to call somebody 'tu'
**On ne doit pas tutoyer la maîtresse.**
We can't call the teacher 'tu'.
**_Did you know...?_**
_There are two words for 'you' in French,_ **tu** _and_ **vous**.
**Tu** _is the less formal one. You would call your teacher 'vous' but your friend 'tu'._
**typique** ADJECTIVE
**typical**
# **U u**
l' **UE** FEM NOUN
**EU**
**un**
**un** _can be an article or a number._
**A** ARTICLE
**_Language tip_**
**un** _is used in front of a masculine noun._
**1** **a**
**un garçon**
a boy
**2** **an**
**un œuf**
an egg
**B** NUMBER
**_Language tip_**
**un** _is used for masculine nouns._
**one**
**un citron et deux oranges**
one lemon and two oranges
**Combien de timbres? — Un.**
How many stamps? — One.
**un de mes meilleurs copains**
one of my best friends
**un par un**
one by one
**Sortez un par un.**
Go out one by one.
**Elle a un an.**
She's one year old.
**une**
**une** _can be an article or a number._
**A** ARTICLE
**_Language tip_**
**une** _is used in front of a feminine noun._
**1** **a**
**une fille**
a girl
**2** **an**
**une pomme**
an apple
**B** NUMBER
**_Language tip_**
**une** _is used for feminine nouns._
**one**
**une pomme et deux bananes**
one apple and two bananas
**Combien de cartes postales? — Une.**
How many postcards? — One.
**une de mes meilleures copines**
one of my best friends
**une par une**
one by one
**Elles sont entrées une par une.**
They went in one by one.
**Il est une heure.**
It's one o'clock.
l' **uniforme** MASC NOUN
**uniform**
**unique** ADJECTIVE
**unique**
**C'est une occasion unique.**
It's a unique opportunity.
**Il est fils unique.**
_He's an only child._
**Elle est fille unique.**
_She's an only child._
**uniquement** ADVERB
**only**
l' **université** FEM NOUN
**university**
l' **usine** FEM NOUN
**factory**
**Mon père travaille dans une usine.**
My dad works in a factory.
**utile** ADJECTIVE
**useful**
**utiliser** VERB
**to use**
# **V v**
**va** VERB _see_ **aller**
**Il va à l'école avec ses copains.**
He goes to school with his friends.
**Elle va partir demain.**
She'll leave tomorrow.
les **vacances** FEM PL NOUN
**holidays**
**Je vais passer les vacances chez ma grand-mère.**
I'm going to spend the holidays with my grandmother.
**aller en vacances**
to go on holiday
**Où est-ce que tu vas en vacances cet été?**
Where are you going on holiday this summer?
**Nous partons en vacances ce soir.**
We're setting off on holiday this evening.
**en vacances**
on holiday
**les vacances de Noël**
the Christmas holidays
**les vacances de Pâques**
the Easter holidays
**les grandes vacances**
the summer holidays
**Bonnes vacances!**
Have a good holiday!
la **vache** FEM NOUN
**cow**
la **vague** FEM NOUN
**wave**
le **vainqueur** MASC NOUN
**winner**
**vais** VERB _see_ **aller**
**Je vais écrire à mes cousins.**
I'm going to write to my cousins.
le **vaisseau** MASC NOUN
(PL les **vaisseaux** )
**un vaisseau spatial**
a spaceship
la **vaisselle** FEM NOUN
**washing-up**
**Je vais faire la vaisselle.**
I'll do the washing-up.
le **valet** MASC NOUN
**jack**
**le valet de carreau**
the jack of diamonds
la **valise** FEM NOUN
**suitcase**
**faire sa valise**
to pack
la **vallée** FEM NOUN
**valley**
**valoir** VERB
**to be worth**
**Ça vaut la peine.**
It's worth it.
la **vanille** FEM NOUN
**vanilla**
**vas** VERB _see_ **aller**
**Tu vas souvent au cinéma?**
Do you go to the cinema often?
**vaut** VERB _see_ **valoir**
**Ça vaut mieux.**
That would be better.
le **veau** MASC NOUN
(PL les **veaux** )
**1** **calf**
**la vache et son veau**
the cow and her calf
**2** **veal**
la **vedette** FEM NOUN
**star**
**une vedette de cinéma**
a film star
**végétarien** MASC ADJECTIVE
(FEM **végétarienne** )
**vegetarian**
la **veille** FEM NOUN
**the day before**
**la veille de son départ**
the day before he left
**la veille de Noël**
Christmas Eve
le **vélo** MASC NOUN
**bike**
**faire du vélo**
to go cycling
**un vélo tout-terrain**
a mountain bike
les **vendanges** FEM PL NOUN
**grape harvest**
le **vendeur** MASC NOUN
la **vendeuse** FEM NOUN
**shop assistant**
**vendre** VERB
**to sell**
**Il m'a vendu son vélo.**
He sold me his bike.
**'à vendre'**
'for sale'
le **vendredi** MASC NOUN
**1** **Friday**
**Aujourd'hui, nous sommes vendredi.**
It's Friday today.
**2** **on Friday**
**Il est venu vendredi.**
He came on Friday.
**Je joue au foot le vendredi.**
I play football on Fridays.
**tous les vendredis**
every Friday
**le vendredi**
on Fridays
**vendredi dernier**
last Friday
**vendredi prochain**
next Friday
**À vendredi!**
See you on Friday!
**le Vendredi saint**
Good Friday
**vénéneux** MASC ADJECTIVE
(FEM **vénéneuse** )
**poisonous**
**venimeux** MASC ADJECTIVE
(FEM **venimeuse** )
**poisonous**
**un serpent venimeux**
a poisonous snake
**venir** VERB
**to come**
**Il viendra demain.**
He'll come tomorrow.
**Viens t'asseoir.**
Come and sit down.
**venir de**
to have just
**Je viens de le voir.**
I've just seen him.
le **vent** MASC NOUN
**wind**
**Il y a du vent.**
It's windy.
le **ventre** MASC NOUN
**stomach**
**J'ai mal au ventre.**
I've got tummy ache.
**venu** VERB _see_ **venir**
**Il est venu nous voir.**
He came to see us.
le **ver** MASC NOUN
**worm**
**un ver de terre**
an earthworm
le **verbe** MASC NOUN
**verb**
le **verglas** MASC NOUN
**black ice**
**vérifier** VERB
**to check**
la **vérité** FEM NOUN
**truth**
le **vernis** MASC NOUN
**varnish**
**le vernis à ongles**
nail varnish
**verra, verrai, verras** VERB
_see_ **voir**
**on verra...**
we'll see...
**Je le verrai demain.**
I'll see him tomorrow.
**Tu verras, c'est facile.**
You'll see, it's easy.
le **verre** MASC NOUN
**glass**
**une table en verre**
a glass table
**un verre d'eau**
a glass of water
**vers** PREPOSITION
**1** **towards**
**Il allait vers la poste.**
He was going towards the post office.
**2** **at about**
**Je me couche vers huit heures.**
I go to bed at about eight o'clock.
**vert**
**vert** _can be an adjective or a noun._
**A** MASC ADJECTIVE
(FEM **verte** )
**green**
**J'ai les yeux verts.**
I've got green eyes.
**B** MASC NOUN
**green**
**J'aime le vert.**
I like the colour green.
la **veste** FEM NOUN
**jacket**
**une veste en jean**
a denim jacket
le **vestiaire** MASC NOUN
**1** **changing room**
**2** **cloakroom**
les **vêtements** MASC PL NOUN
**clothes**
le/la **vétérinaire** MASC/FEM NOUN
**vet**
**Elle est vétérinaire.**
She's a vet.
le **veuf** MASC NOUN
**widower**
**veulent, veut** VERB
_see_ **vouloir**
**Ils ne veulent pas jouer.**
They don't want to play.
**Qui veut jouer?**
Who wants to play?
la **veuve** FEM NOUN
**widow**
**veux** VERB
_see_ **vouloir**
**Tu veux aller au cinéma?**
Do you want to go to the cinema?
la **viande** FEM NOUN
**meat**
**la viande hachée**
mince
**vide** ADJECTIVE
**empty**
**vidéo** MASC, FEM, PL ADJECTIVE
**video**
**une cassette vidéo**
a video cassette
**un jeu vidéo**
a video game
le **vidéoclip** MASC NOUN
**music video**
le **vidéoclub** MASC NOUN
**video shop**
**vider** VERB
**to empty**
la **vie** FEM NOUN
**life**
**vieil** MASC ADJECTIVE
**_Language tip_**
When **vieux** _in the singular comes before a vowel sound, it changes to_ **vieil**.
**old**
**un vieil arbre**
an old tree
**un vieil homme**
an old man
**vieille**
**vieille** _can be an adjective or a noun._
**A** FEM ADJECTIVE
**old**
**une vieille dame**
an old lady
**Elle est plus vieille que moi.**
She's older than me.
**B** FEM NOUN
**old woman**
**une petite vieille**
a little old lady
**vieillir** VERB
**to age**
**viendrai, viens** VERB
_see_ **venir**
**Je viendrai dès que possible.**
I'll come as soon as possible.
**Viens ici!**
Come here!
**vieux**
**vieux** _can be an adjective or a noun._
**A** MASC, MASC PL ADJECTIVE
(FEM **vieille** )
**old**
**un vieux monsieur**
an old gentleman
**Il est plus vieux que moi.**
He's older than me.
**_Language tip_**
**vieux** _in the singular changes to_
**vieil** _before a vowel sound._
**un vieil homme**
an old man
**B** MASC NOUN
**old man**
**un petit vieux**
a little old man
**les vieux**
old people
**vif** MASC ADJECTIVE
(FEM **vive** )
**bright**
**rouge vif**
bright red
la **vigne** FEM NOUN
**vine**
**des champs de vigne**
vineyards
le **vigneron** MASC NOUN
**wine grower**
le **vignoble** MASC NOUN
**vineyard**
**vilain** MASC ADJECTIVE
(FEM **vilaine** )
**1** **naughty**
**C'est très vilain de dire des mensonges.**
It's very naughty to tell lies.
**2** **horrible**
**Il a de vilaines dents.**
He's got horrible teeth.
**une vilaine sorcière**
an evil witch
le **village** MASC NOUN
**village**
la **ville** FEM NOUN
**town**
**Je vais en ville.**
I'm going into town.
**une grande ville**
a city
le **vin** MASC NOUN
**wine**
**du vin blanc**
white wine
**du vin rouge**
red wine
le **vinaigre** MASC NOUN
**vinegar**
la **vinaigrette** FEM NOUN
**French dressing**
**vingt** NUMBER
**twenty**
**Elle a vingt ans.**
She's twenty.
**à vingt heures**
at 8 p.m.
**_Did you know...?_**
_The 24-hour clock is used in France for travel times, appointments, and other formal situations._
**vingt et un**
twenty-one
**vingt-deux**
twenty-two
**le vingt février**
the twentieth of February
la **vingtaine** FEM NOUN
**about twenty**
**une vingtaine de personnes**
about twenty people
**Il a une vingtaine d'années.**
He's about twenty.
**vingtième** ADJECTIVE
**twentieth**
**violet**
**violet** _can be an adjective or a noun._
**A** MASC ADJECTIVE
(FEM **violette** )
**purple**
**une robe violette**
a purple dress
**B** MASC NOUN
**purple**
**J'aime le violet.**
I like the colour purple.
le **violon** MASC NOUN
**violin**
**Je joue du violon.**
I play the violin.
le **violoncelle** MASC NOUN
**cello**
**Elle joue du violoncelle.**
She plays the cello
la **vipère** FEM NOUN
**viper**
la **virgule** FEM NOUN
**comma**
**vis** VERB _see_ **vivre**
**Je vis en Écosse.**
I live in Scotland.
le **visage** MASC NOUN
**face**
**Elle a le visage rond.**
She's got a round face.
la **visite** FEM NOUN
**rendre visite à quelqu'un**
to visit somebody
**Je vais rendre visite à mon grand-père.**
I'm going to visit my grandfather.
**une visite guidée**
a guided tour
**visiter** VERB
**to visit**
**Nous avons visité des châteaux.**
We visited some castles.
**vit** VERB _see_ **vivre**
**Il vit chez ses parents.**
He lives with his parents.
**vite** ADVERB
**1** **quick**
**Vite, ils arrivent!**
Quick, they're coming!
**Prenons la voiture, ça ira plus vite.**
Let's take the car, it'll be quicker.
**2** **fast**
**Il roule trop vite.**
He drives too fast.
**Il court plus vite que moi.**
He runs faster than me.
**3** **soon**
**Il va vite oublier.**
He'll soon forget.
la **vitesse** FEM NOUN
**1** **speed**
**en vitesse**
quickly
**2** **gear**
**J'ai un vélo à dix vitesses.**
I've got a bike with ten gears.
le **viticulteur** MASC NOUN
**wine grower**
le **vitrail** MASC NOUN
(PL les **vitraux** )
**stained-glass window**
la **vitre** FEM NOUN
**window**
la **vitrine** FEM NOUN
**shop window**
**vivant** MASC ADJECTIVE (FEM **vivante** )
**living**
**vive**
**vive** _can be an adjective or an exclamation._
**A** FEM ADJECTIVE
**bright**
**les couleurs vives**
bright colours
**B** EXCLAMATION
**Vive le roi!**
Long live the king!
**vivement** EXCLAMATION
**Vivement les vacances!**
Roll on the holidays!
**vivre** VERB
**to live**
**J'aimerais vivre à l'étranger.**
I'd like to live abroad.
le **vocabulaire** MASC NOUN
**vocabulary**
le **vœu** MASC NOUN
(PL les **vœux** )
**wish**
**faire un vœu**
to make a wish
**Meilleurs vœux de bonne année!**
Best wishes for the New Year!
**voici** PREPOSITION
**this is**
**Voici mon frère et voilà ma sœur.**
This is my brother and that's my sister.
**voilà** PREPOSITION
**1** **there is**
**Tiens! Voilà Paul.**
Look! There's Paul.
**Les voilà!**
There they are!
**Voilà!**
There you are!
**2** **that is**
**Voilà ma sœur.**
That's my sister.
la **voile** FEM NOUN
**sailing**
**faire de la voile**
to go sailing
**un bateau à voile**
a sailing boat
le **voilier** MASC NOUN
**sailing boat**
**voir** VERB
**to see**
**Venez me voir quand vous serez à Paris.**
Come and see me when you're in Paris.
**faire voir**
to show
**Il m'a fait voir sa collection de timbres.**
He showed me his stamp collection.
**vois** VERB _see_ **voir**
**Je n'y vois rien sans mes lunettes.**
I can't see anything without my glasses.
le **voisin** MASC NOUN
la **voisine** FEM NOUN
**neighbour**
la **voiture** FEM NOUN
**car**
**une voiture de sport**
a sports car
la **voix** FEM NOUN (PL les **voix** )
**voice**
le **vol** MASC NOUN
**flight**
**voler** VERB
**1** **to fly**
**2** **to steal**
**On a volé mon appareil photo.**
My camera's been stolen.
le **volet** MASC NOUN
**shutter**
**_Did you know...?_**
_Traditional French houses have wooden shutters._
le **voleur** MASC NOUN
la **voleuse** FEM NOUN
**thief**
**Au voleur !**
Stop thief!
le **volley** MASC NOUN
**volleyball**
**jouer au volley**
to play volleyball
le/la **volontaire** MASC/FEM NOUN
**volunteer**
**vomir** VERB
**to be sick**
**vont** VERB _see_ **aller**
**Ils vont à la piscine.**
They're going to the pool.
**vos** PL ADJECTIVE _see_ **votre**
**your**
**Rangez vos jouets, les enfants!**
Put your toys away, children.
**J'ai trouvé vos clés, M. Durand.**
I've found your keys, Mr Durand.
**voter** VERB
**to vote**
**votre** ADJECTIVE (PL **vos** )
**your**
**C'est votre manteau, Mme Leblanc?**
Is this your coat, Mrs Leblanc?
**Restez à votre place, les enfants!**
Stay in your seats children.
le/la **vôtre** MASC/FEM PRONOUN
**yours**
**À qui est cette écharpe? C'est la vôtre?**
Whose is this scarf? Is it yours?
**Ce ne sont pas mes clés, ce sont les vôtres.**
These aren't my keys, they're yours.
**voudrais** VERB _see_ **vouloir**
**Je voudrais deux litres de lait, s'il vous plaît.**
I'd like two litres of milk, please.
**vouloir** VERB
**to want**
**Elle veut un vélo pour Noël.**
She wants a bike for Christmas.
**Je ne veux pas de dessert.**
I don't want any pudding.
**On va au cinéma? — Si tu veux.**
Shall we go to the cinema? — If you like.
**voulu** VERB _see_ **vouloir**
**Elle n'a pas voulu venir.**
She didn't want to come.
**vous** PRONOUN
**1** **you**
**Vous voulez de l'eau, monsieur?**
Would you like some water, sir?
**Vous devez faire attention, les enfants.**
You must be careful, children.
**2** **to you**
**Je vous écrirai bientôt.**
I'll write to you soon.
**3** **yourself**
**Vous vous êtes fait mal?**
Have you hurt yourself?
**vous-même**
yourself
**Vous l'avez fait vous-même?**
Did you do it yourself?
**vouvoyer** VERB
**vouvoyer quelqu'un**
to call somebody 'vous'
**Est-ce que je dois vouvoyer ta sœur?**
Should I say 'vous' to your sister?
**_Did you know...?_**
_There are two words for 'you' in French_ , **tu** _and_ **vous**. **Vous** _is the formal one. You would call your teacher 'vous' but your friend 'tu'._
le **voyage** MASC NOUN
**journey**
**Avez-vous fait bon voyage?**
Did you have a good journey?
**Bon voyage!**
Have a good trip!
**voyager** VERB
**to travel**
**voyez** VERB _see_ **voir**
**Vous voyez l'arc-en-ciel là-bas?**
Can you see the rainbow over there?
**voyons** VERB _see_ **voir**
**Nous ne les voyons pas souvent.**
We don't see them very often.
**vrai** ADJECTIVE
**true**
**une histoire vraie**
a true story
**C'est vrai?**
Is that true?
**vraiment** ADVERB
**really**
le **VTT** MASC NOUN
**mountain bike**
**vu** VERB _see_ **voir**
**J'ai vu un film au cinéma.**
I saw a film at the cinema.
la **vue** FEM NOUN
**1** **eyesight**
**2** **view**
**Il y a une belle vue d'ici.**
There's a lovely view from here.
# **W w**
**wallon** MASC NOUN, MASC ADJECTIVE
(FEM **wallonne** )
**Walloon**
le **Wallon** MASC NOUN
la **Wallonne** FEM NOUN
**Walloon**
les **Wallons** MASC PL NOUN
**Walloons**
**_Did you know...?_**
_Walloons are Belgian people who speak French, one of the two languages spoken in Belgium. The other language is Flemish, which is spoken by_ **les Flamands**.
la **Wallonie** FEM NOUN
**French-speaking Belgium**
les **WC** MASC PL NOUN
**toilet**
**Où sont les WC?**
Where's the toilet?
**_Language tip_**
_The French word_ **WC** _is pronounced 'vay-say'._
le **Web** MASC NOUN
**World Wide Web**
la **webcam** FEM NOUN
**webcam**
le **week-end** MASC NOUN
**weekend**
**Ce week-end, nous allons à Paris.**
We're going to Paris this weekend.
**Qu'est-ce que tu as fait pendant le week-end?**
What did you do at the weekend?
**Bon week-end!**
Have a nice weekend!
le **western** MASC NOUN
**western**
# **X x**
le **xylophone** MASC NOUN
**xylophone**
**Elle joue du xylophone.**
She plays the xylophone.
# **Y y**
**y** PRONOUN
**1** **there**
**Nous y sommes allés l'été dernier.**
We went there last summer.
**Vas-y!**
Go on!
**2** **it**
**Arrête d'y penser!**
Stop thinking about it!
le **yaourt** MASC NOUN
**yoghurt**
**un yaourt nature**
a plain yoghurt
**un yaourt aux fruits**
a fruit yoghurt
les **yeux** MASC PL NOUN
**eyes**
**Elle a les yeux bleus.**
She's got blue eyes.
le **yoga** MASC NOUN
**yoga**
**Elle fait du yoga.**
She does yoga.
**youpi** EXCLAMATION
**Yippee!**
le **yoyo** MASC NOUN
**yo-yo**
# **Z z**
le **zèbre** MASC NOUN
**zebra**
le **zéro** MASC NOUN
**zero**
**Ils ont gagné trois à zéro.**
They won three-nil.
la **zone** FEM NOUN
**zone**
**une zone industrielle**
an industrial estate
le **zoo** MASC NOUN
**zoo**
**zut** EXCLAMATION
**Oh heck**
# **Language plus**
# **Language plus**
Animals
The body
Clothes
Colours
Family
Days and dates
The weather
Places
Food
Fruit and vegetables
Drinks
Furniture
Instruments
Jobs
Sports
At school
Numbers and time
French verbs
Illustrations
# **Animals – Les animaux**
**• Pets**
**budgie** NOUN la **perruche** _fem_
**canary** NOUN le **canari** _masc_
**cat** NOUN le **chat** _masc_ , la **chatte** _fem_
**dog** NOUN le **chien** _masc_ , la **chienne** _fem_
**ferret** NOUN le **furet** _masc_
**gerbil** NOUN la **gerbille** _fem_
**goldfish** NOUN le **poisson rouge** _masc_
**guinea pig** NOUN le **cochon d'Inde** _masc_
**hamster** NOUN le **hamster** _masc_
**kitten** NOUN le **chaton** _masc_
**mouse** NOUN la **souris** _fem_
**parrot** NOUN le **perroquet** _masc_
**poodle** NOUN le **caniche** _masc_
**puppy** NOUN le **chiot** _masc_
**rabbit** NOUN le **lapin** _masc_
**rat** NOUN le **rat** _masc_
**stick insect** NOUN le **phasme** _masc_
**tortoise** NOUN la **tortue** _fem_
**• Farm animals**
**bull** NOUN le **taureau** _masc_
**calf** NOUN le **veau** _masc_
**chick** NOUN le **poussin** _masc_
**chicken** NOUN la **poule** _fem_
**cock** NOUN le **coq** _masc_
**cow** NOUN la **vache** _fem_
**donkey** NOUN l' **âne** _masc_
**duck** NOUN le **canard** _masc_
**goat** NOUN la **chèvre** _fem_
**goose** NOUN l' **oie** _fem_
**hen** NOUN la **poule** _fem_
**horse** NOUN le **cheval** _masc_
**lamb** NOUN l' **agneau** _masc_
**mare** NOUN la **jument** _fem_
**pig** NOUN le **cochon** _masc_
**pony** NOUN le **poney** _masc_
**ram** NOUN le **bélier** _masc_
**sheep** NOUN le **mouton** _masc_
**sheepdog** NOUN le **chien de berger** _masc_
**turkey** NOUN le **dindon** _masc_
**• Other animals**
**ant** NOUN la **fourmi** _fem_
**bat** NOUN la **chauve-souris** _fem_
**bear** NOUN l' **ours** _masc_
**bee** NOUN l' **abeille** _fem_
**beetle** NOUN le **scarabée** _masc_
**bird** NOUN l' **oiseau** _masc_
**butterfly** NOUN le **papillon** _masc_
**camel** NOUN le **chameau** _masc_
**crab** NOUN le **crabe** _masc_
**crocodile** NOUN le **crocodile** _masc_
**cub** NOUN le **petit** _masc_
**dinosaur** NOUN le **dinosaure** _masc_
**dolphin** NOUN le **dauphin** _masc_
**dragon** NOUN le **dragon** _masc_
**duck** NOUN le **canard** _masc_
**elephant** NOUN l' **éléphant** _masc_
**fish** NOUN le **poisson** _masc_
**fly** NOUN la **mouche** _fem_
**fox** NOUN le **renard** _masc_
**frog** NOUN la **grenouille** _fem_
**giraffe** NOUN la **girafe** _fem_
**gorilla** NOUN le **gorille** _masc_
**hare** NOUN le **lièvre** _masc_
**hedgehog** NOUN le **hérisson** _masc_
**hippo** NOUN l' **hippopotame** _masc_
**insect** NOUN l' **insecte** _masc_
**jellyfish** NOUN la **méduse** _fem_
**kangaroo** NOUN le **kangourou** _masc_
**ladybird** NOUN la **coccinelle** _fem_
**leopard** NOUN le **léopard** _masc_
**lion** NOUN le **lion** _masc_
**lizard** NOUN le **lézard** _masc_
**mammoth** NOUN le **mammouth** _masc_
**midge** NOUN le **moucheron** _masc_
**mole** NOUN la **taupe** _fem_
**monkey** NOUN le **singe** _masc_
**mosquito** NOUN le **moustique** _masc_
**moth** NOUN le **papillon de nuit** _masc_
**octopus** NOUN la **pieuvre** _fem_
**ostrich** NOUN l' **autruche** _fem_
**owl** NOUN le **hibou** _masc_
**panther** NOUN la **panthère** _fem_
**peacock** NOUN le **paon** _masc_
**penguin** NOUN le **pingouin** _masc_
**pheasant** NOUN le **faisan** _masc_
**pigeon** NOUN le **pigeon** _masc_
**polar bear** NOUN l' **ours blanc** _masc_
**red deer** NOUN le **cerf** _masc_
**reindeer** NOUN le **renne** _masc_
**rhinoceros** NOUN le **rhinocéros** _masc_
**seagull** NOUN la **mouette** _fem_
**seal** NOUN le **phoque** _masc_
**shark** NOUN le **requin** _masc_
**slug** NOUN la **limace** _fem_
**snail** NOUN l' **escargot** _masc_
**snake** NOUN le **serpent** _masc_
**spider** NOUN l' **araignée** _fem_
**squirrel** NOUN l' **écureuil** _masc_
**swan** NOUN le **cygne** _masc_
**tadpole** NOUN le **têtard** _masc_
**tiger** NOUN le **tigre** _masc_
**toad** NOUN le **crapaud** _masc_
**trout** NOUN la **truite** _fem_
**turtle** NOUN la **tortue** _fem_
**wasp** NOUN la **guêpe** _fem_
**whale** NOUN la **baleine** _fem_
**wolf** NOUN le **loup** _masc_
**worm** NOUN le **ver** _masc_
**zebra** NOUN le **zèbre** _masc_
# **The body – Le corps**
**ankle** NOUN la **cheville** _fem_
**arm** NOUN le **bras** _masc_
**back** NOUN le **dos** _masc_
**beard** NOUN la **barbe** _fem_
**blood** NOUN le **sang** _masc_
**body** NOUN le **corps** _masc_
**bottom** NOUN le **derrière** _masc_
**brain** NOUN le **cerveau** _masc_
**cheek** NOUN la **joue** _fem_
**chest** NOUN la **poitrine** _fem_
**chin** NOUN le **menton** _masc_
**ear** NOUN l' **oreille** _fem_
**elbow** NOUN le **coude** _masc_
**eye** NOUN l' **œil** _masc_
**eyebrow** NOUN le **sourcil** _masc_
**eyelash** NOUN le **cil** _masc_
**eyelid** NOUN la **paupière** _fem_
**face** NOUN la **figure** _fem_
**finger** NOUN le **doigt** _masc_
**fist** NOUN le **poing** _masc_
**foot** NOUN le **pied** _masc_
**forehead** NOUN le **front** _masc_
**freckles** NOUN PL les **taches de rousseur** _fem_ _pl_
**fringe** NOUN la **frange** _fem_
**hair** NOUN les **cheveux** _masc_ _pl_
**hand** NOUN la **main** _fem_
**head** NOUN la **tête** _fem_
**heart** NOUN le **cœur** _masc_
**heel** NOUN le **talon** _masc_
**hip** NOUN la **hanche** _fem_
**jaw** NOUN la **mâchoire** _fem_
**knee** NOUN le **genou** _masc_
**leg** NOUN la **jambe** _fem_
**lip** NOUN la **lèvre** _fem_
**moustache** NOUN la **moustache** _fem_
**mouth** NOUN la **bouche** _fem_
**muscle** NOUN le **muscle** _masc_
**nail** NOUN l' **ongle** _masc_
**neck** NOUN le **cou** _masc_
**nose** NOUN le **nez** _masc_
**palm** NOUN la **paume** _fem_
**rib** NOUN la **côte** _fem_
**shin** NOUN le **tibia** _masc_
**shoulder** NOUN l' **épaule** _fem_
**skeleton** NOUN le **squelette** _masc_
**skin** NOUN la **peau** _fem_
**skull** NOUN le **crâne** _masc_
**stomach** NOUN l' **estomac** _masc_
**thigh** NOUN la **cuisse** _fem_
**throat** NOUN la **gorge** _fem_
**thumb** NOUN le **pouce** _masc_
**toe** NOUN le **doigt de pied** _masc_
**tongue** NOUN la **langue** _fem_
**tonsils** NOUN PL les **amygdales** _fem_ _pl_
**tooth** NOUN la **dent** _fem_
**tummy** NOUN le **ventre** _masc_
**waist** NOUN la **taille** _fem_
**wrist** NOUN le **poignet** _masc_
# **Clothes – Les vêtements**
**anorak** NOUN l' **anorak** _masc_
**apron** NOUN le **tablier** _masc_
**ballet shoes** NOUN PL les **chaussons de danse** _masc_ _pl_
**baseball cap** NOUN la **casquette de base-ball** _fem_
**belt** NOUN la **ceinture** _fem_
**bikini** NOUN le **bikini** _masc_
**blazer** NOUN le **blazer** _masc_
**blouse** NOUN le **chemisier** _masc_
**boots** NOUN les **bottes** _fem_ _pl_
**bow tie** NOUN le **nœud papillon** _masc_
**boxer shorts** NOUN PL le **caleçon** _masc_
**bra** NOUN le **soutien-gorge** _masc_
**cagoule** NOUN le **K-way** ® _masc_
**cap** NOUN la **casquette** _fem_
**cardigan** NOUN le **cardigan** _masc_
**clothes** NOUN PL les **vêtements** _masc_ _pl_
**coat** NOUN le **manteau** _masc_
**dinner jacket** NOUN le **smoking** _masc_
**dress** NOUN la **robe** _fem_
**dressing gown** NOUN la **robe de chambre** _fem_
**dungarees** NOUN la **salopette** _fem_
**fleece** NOUN la **laine polaire** _fem_
**flippers** NOUN PL les **palmes** _fem_ _pl_
**football boots** NOUN les **chaussures de foot** _fem_ _pl_
**football shirt** NOUN le **maillot de foot** _masc_
**glasses** NOUN PL les **lunettes** _fem_ _pl_
**glove** NOUN le **gant** _masc_
**goggles** NOUN PL les **lunettes de plongée** _fem_ _pl_
**hat** NOUN le **chapeau** _masc_
**helmet** NOUN le **casque** _masc_
**hood** NOUN la **capuche** _fem_
**jacket** NOUN la **veste** _fem_
**jeans** NOUN PL le **jean** _masc_
**jersey** NOUN le **pull-over** _masc_
**jumper** NOUN le **pull** _masc_
**kilt** NOUN le **kilt** _masc_
**knickers** NOUN PL la **culotte** _fem_
**leather jacket** NOUN la **veste en cuir** _fem_
**miniskirt** NOUN la **minijupe** _fem_
**nightdress** NOUN la **chemise de nuit** _fem_
**nightie** NOUN la **chemise de nuit** _fem_
**nightshirt** NOUN la **chemise de nuit** _fem_
**overalls** NOUN PL les **bleus de travail** _masc_ _pl_
**panties** NOUN PL le **slip** _masc_
**pants** NOUN PL le **slip** _masc_
**plimsolls** NOUN PL les **chaussons de gym** _masc_ _pl_
**polo-necked sweater** NOUN le **pull à col roulé** _masc_
**polo shirt** NOUN le **polo** _masc_
**pullover** NOUN le **pull** _masc_
**pyjamas** NOUN PL le **pyjama** _masc_
**raincoat** NOUN l' **imperméable** _masc_
**sandals** NOUN PL les **sandales** _fem_ _pl_
**scarf** NOUN l' **écharpe** _fem_
**shirt** NOUN la **chemise** _fem_
**shoes** NOUN PL les **chaussures** _fem_ _pl_
**shorts** NOUN PL le **short** _masc_
**ski boots** NOUN PL les **chaussures de ski** _fem_ _pl_
**skirt** NOUN la **jupe** _fem_
**slippers** NOUN PL les **chaussons** _masc_ _pl_
**sock** NOUN la **chaussette** _fem_
**suit** NOUN le **costume** _masc_ _(for a man)_ , le **tailleur** _masc_ _(for a woman)_
**sunglasses** NOUN PL les **lunettes de soleil** _fem_ _pl_
**sweater** NOUN le **pull** _masc_
**sweatshirt** NOUN le **sweat** _masc_
**swimming costume** NOUN le **maillot de bain** _masc_
**swimming trunks** NOUN PL le **maillot de bain** _masc_
**swimsuit** NOUN le **maillot de bain** _masc_
**tee-shirt** NOUN le **tee-shirt** _masc_
**tie** NOUN la **cravate** _fem_
**tights** NOUN PL le **collant** _masc_
**top** NOUN le **haut** _masc_
**tracksuit** NOUN le **jogging** _masc_
**trainers** NOUN PL les **baskets** _fem_ _pl_
**trousers** NOUN PL le **pantalon** _masc_
**trunks** NOUN PL le **maillot de bain** _masc_
**T-shirt** NOUN le **tee-shirt** _masc_
**underpants** NOUN PL le **slip** _masc_
**underskirt** NOUN le **jupon** _masc_
**underwear** NOUN les **sous-vêtements** _masc_ _pl_
**uniform** NOUN l' **uniforme** _masc_
**vest** NOUN le **maillot de corps** _masc_
**waistcoat** NOUN le **gilet** _masc_
**wellingtons** NOUN PL les **bottes en caoutchouc** _fem_ _pl_
**wetsuit** NOUN la **combinaison de plongée** _fem_
# **Colours – Les couleurs**
**beige** ADJECTIVE **beige**
**black** ADJECTIVE **noir** _masc_ , **noire** _fem_
**blue** ADJECTIVE **bleu** _masc_ , **bleue** _fem_
**brown** ADJECTIVE **marron** _masc_ , _fem_ , _pl_
**cream** ADJECTIVE **crème** _masc_ , _fem_ , _pl_
**green** ADJECTIVE **vert** _masc_ , **verte** _fem_
**grey** ADJECTIVE **gris** _masc_ , **grise** _fem_
**maroon** ADJECTIVE **bordeaux** _masc_ , _fem_ , _pl_
**navy** ADJECTIVE **bleu marine** _masc_ , _fem_ , _pl_
**navy blue** ADJECTIVE **bleu marine** _masc_ , _fem_ , _pl_
**orange** ADJECTIVE **orange** _masc_ , _fem_ , _pl_
**pink** ADJECTIVE **rose**
**purple** ADJECTIVE **violet** _masc_ , **violette** _fem_
**red** ADJECTIVE **rouge**
**turquoise** ADJECTIVE **turquoise**
**white** ADJECTIVE **blanc** _masc_ , **blanche** _fem_
**yellow** ADJECTIVE **jaune**
# **Family – La famille**
**aunt, aunty** NOUN la **tante** _fem_
**brother** NOUN le **frère** _masc_
**brother-in-law** NOUN le **beau-frère** _masc_
**cousin** NOUN le **cousin** _masc_ , la **cousine** _fem_
**dad** NOUN le **père** _masc_
**daddy** NOUN le **papa** _masc_
**daughter** NOUN la **fille** _fem_
**daughter-in-law** NOUN la **belle-fille** _fem_
**family** NOUN la **famille** _fem_
**father** NOUN le **père** _masc_
**father-in-law** NOUN le **beau-père** _masc_
**fiancé** NOUN le **fiancé** _masc_
**fiancée** NOUN la **fiancée** _fem_
**godfather** NOUN le **parrain** _masc_
**godmother** NOUN la **marraine** _fem_
**grandchildren** NOUN PL les **petits-enfants** _masc_ _pl_
**granddad** NOUN le **papi** _masc_
**granddaughter** NOUN la **petite-fille** _fem_
**grandfather** NOUN le **grand-père** _masc_
**grandma** NOUN la **mamie** _fem_
**grandmother** NOUN la **grand-mère** _fem_
**grandpa** NOUN le **papi** _masc_
**grandparents** NOUN PL les **grands-parents** _masc_ _pl_
**grandson** NOUN le **petit-fils** _masc_
**granny** NOUN la **mamie** _fem_
**half-brother** NOUN le **demi-frère** _masc_
**half-sister** NOUN la **demi-sœur** _fem_
**husband** NOUN le **mari** _masc_
**mother** NOUN la **mère** _fem_
**mother-in-law** NOUN la **belle-mère** _fem_
**mum** NOUN la **mère** _fem_
**mummy** NOUN la **maman** _fem_
**nephew** NOUN le **neveu** _masc_
**niece** NOUN la **nièce** _fem_
**parent** NOUN le **parent** _masc_
**sister** NOUN la **sœur** _fem_
**sister-in-law** NOUN la **belle-sœur** _fem_
**son** NOUN le **fils** _masc_
**son-in-law** NOUN le **gendre** _masc_
**stepbrother** NOUN le **demi-frère** _masc_
**stepdaughter** NOUN la **belle-fille** _fem_
**stepfather** NOUN le **beau-père** _masc_
**stepmother** NOUN la **belle-mère** _fem_
**stepsister** NOUN la **demi-sœur** _fem_
**stepson** NOUN le **beau-fils** _masc_
**uncle** NOUN l' **oncle** _masc_
**wife** NOUN la **femme** _fem_
# **Days and dates – Les jours et les dates**
**• Days of the week**
**Monday** **lundi**
**Tuesday** **mardi**
**Wednesday** **mercredi**
**Thursday** **jeudi**
**Friday** **vendredi**
**Saturday** **samedi**
**Sunday** **dimanche**
**• Months of the year**
**January** **janvier**
**February** **février**
**March** **mars**
**April** **avril**
**May** **mai**
**June** **juin**
**July** **juillet**
**August** **août**
**September** **septembre**
**October** **octobre**
**November** **novembre**
**December** **décembre**
**• Special days**
**April Fool's Day** NOUN le **premier avril** _masc_
**Boxing Day** NOUN le **lendemain de Noël** _masc_
**Christmas** NOUN **Noël** _masc_
**Christmas** **Day** NOUN le **jour de Noël** _masc_
**Christmas Eve** NOUN la **veille de Noël** _fem_
**Easter** NOUN **Pâques** _fem_ _pl_
**Father's Day** NOUN la **fête des Pères** _fem_
**Hallowe'en** NOUN la **veille de la Toussaint** _fem_
**Mother's Day** NOUN la **fête des Mères** _fem_
**New Year's Day** NOUN le **premier de l'An** _masc_
**New Year's Eve** NOUN la **Saint-Sylvestre** _fem_
**Pancake Day** NOUN le **mardi gras** _masc_
**Passover** NOUN la **Pâque juive** _fem_
**Ramadan** NOUN le **ramadan** _masc_
**Remembrance Day** NOUN le **jour de l'Armistice** _masc_
**Shrove Tuesday** NOUN le **mardi gras** _masc_
**Valentine's Day** NOUN la **Saint-Valentin** _fem_
**Whitsun** NOUN la **Pentecôte** _fem_
# **The weather – Le temps**
**It's chilly.** **Il fait froid.**
**It's cloudy.** **Il fait gris.**
**It's cold.** **Il fait froid.**
**It's dull.** **Il fait gris.**
**It's foggy.** **Il y a du** **brouillard.**
**It's freezing.** **Il gèle.**
**It's frosty.** **Il gèle.**
**It's icy.** **Il gèle.**
**It's misty.** **Le temps est brumeux.**
**It's nice.** **Il fait beau.**
**It's overcast.** **Le ciel est couvert.**
**It's raining.** **Il pleut.**
**It's snowing.** **Il neige.**
**It's stormy.** **Le temps est orageux.**
**It's sunny.** **Il fait du soleil.**
**It's warm.** **Il fait chaud.**
**It's windy.** **Il fait du vent.**
**• Seasons**
**winter** NOUN l' **hiver** _masc_
**spring** NOUN le **printemps** _masc_
**summer** NOUN l' **été** _masc_
**autumn** NOUN l' **automne** _masc_
# **Places – Les lieux**
**• Europe**
**Alps** NOUN PL les **Alpes** _fem_ _pl_
**Andorra** NOUN **Andorre** _fem_
**Atlantic** NOUN l' **Atlantique** _masc_
**Austria** NOUN l' **Autriche** _fem_
**Belgium** NOUN la **Belgique** _fem_
**Britain** NOUN la **Grande-Bretagne** _fem_
**British Isles** NOUN PL les **îles Britanniques** _fem_ _pl_
**Brittany** NOUN la **Bretagne** _fem_
**Brussels** NOUN **Bruxelles**
**Bulgaria** NOUN **Bulgarie** _fem_
**Channel** NOUN la **Manche** _fem_
**Channel Islands** NOUN PL les **îles Anglo-Normandes** _fem_ _pl_
**Cornwall** NOUN la **Cornouailles** _fem_
**Corsica** NOUN la **Corse** _fem_
**Cyprus** NOUN **Chypre** _fem_
**Czech Republic** NOUN la **République tchèque** _fem_
**Denmark** NOUN le **Danemark** _masc_
**Dover** NOUN **Douvres**
**Edinburgh** NOUN **Édimbourg**
**Eire** NOUN la **République d'Irlande** _fem_
**England** NOUN l' **Angleterre** _fem_
**Europe** NOUN l' **Europe** _fem_
**Finland** NOUN la **Finlande** _fem_
**France** NOUN la **France** _fem_
**French** **Riviera** NOUN la **Côte d'Azur** _fem_
**Germany** NOUN l' **Allemagne** _fem_
**Great Britain** NOUN la **Grande-Bretagne** _fem_
**Greece** NOUN la **Grèce** _fem_
**Greenland** NOUN le **Groenland** _masc_
**Holland** NOUN la **Hollande** _fem_
**Hungary** NOUN la **Hongrie** _fem_
**Iceland** NOUN l' **Islande** _fem_
**Ireland** NOUN l' **Irlande** _fem_
**Italy** NOUN l' **Italie** _fem_
**Lapland** NOUN la **Laponie** _fem_
**Liechtenstein** NOUN le **Liechtenstein** _masc_
**London** NOUN **Londres**
**Luxembourg** NOUN le **Luxembourg** _masc_
**Majorca** NOUN **Majorque** _fem_
**Malta** NOUN **Malte** _fem_
**Mediterranean** NOUN la **Méditerranée** _fem_
**Menorca** NOUN **Minorque** _fem_
**Monaco** NOUN **Monaco** _masc_
**Netherlands** NOUN PL les **Pays-Bas** _masc_ _pl_
**Normandy** NOUN la **Normandie** _fem_
**Northern Ireland** NOUN l' **Irlande du Nord** _fem_
**North Sea** NOUN la **mer du Nord** _fem_
**Norway** NOUN la **Norvège** _fem_
**Orkneys** NOUN PL les **Orcades** _fem_ _pl_
**Poland** NOUN la **Pologne** _fem_
**Portugal** NOUN le **Portugal** _masc_
**Pyrenees** NOUN PL les **Pyrénées** _fem_ _pl_
**Romania** NOUN la **Roumanie** _fem_
**Russia** NOUN la **Russie** _fem_
**Scandinavia** NOUN la **Scandinavie** _fem_
**Scotland** NOUN l' **Écosse** _fem_
**Shetland Islands** NOUN PL les **îles Shetland** _fem_ _pl_
**Sicily** NOUN la **Sicile** _fem_
**Spain** NOUN l' **Espagne** _fem_
**Sweden** NOUN la **Suède** _fem_
**Switzerland** NOUN la **Suisse** _fem_
**Turkey** NOUN la **Turquie** _fem_
**UK** NOUN le **Royaume-Uni** _masc_
**Ulster** NOUN l' **Irlande du Nord** _fem_
**United Kingdom** NOUN le **Royaume-Uni** _masc_
**Wales** NOUN le **pays de Galles** _masc_
**•** **Rest of the world**
**Africa** NOUN l' **Afrique** _fem_
**Algeria** NOUN l' **Algérie** _fem_
**America** NOUN l' **Amérique** _fem_
**Australia** NOUN l' **Australie** _fem_
**Brazil** NOUN le **Brésil** _masc_
**Canada** NOUN le **Canada** _masc_
**Caribbean** NOUN les **Caraïbes** _fem_ _pl_
**China** NOUN la **Chine** _fem_
**Egypt** NOUN l' **Égypte** _fem_
**Ethiopia** NOUN l' **Éthiopie** _fem_
**India** NOUN l' **Inde** _fem_
**Iran** NOUN l' **Iran** _masc_
**Iraq** NOUN l' **Iraq** _masc_
**Israel** NOUN **Israël** _masc_
**Japan** NOUN le **Japon** _masc_
**Jordan** NOUN la **Jordanie** _fem_
**Korea** NOUN la **Corée** _fem_
**Lebanon** NOUN le **Liban** _masc_
**Libya** NOUN la **Libye** _fem_
**Malaysia** NOUN la **Malaisie** _fem_
**Mexico** NOUN le **Mexique** _masc_
**Middle East** NOUN le **Moyen-Orient** _masc_
**Morocco** NOUN le **Maroc** _masc_
**New Zealand** NOUN la **Nouvelle-Zélande** _fem_
**Nigeria** NOUN le **Nigéria** _masc_
**North America** NOUN l' **Amérique du Nord** _fem_
**North Pole** NOUN le **pôle Nord** _masc_
**Pacific** NOUN le **Pacifique** _masc_
**Pakistan** NOUN le **Pakistan** _masc_
**Palestine** NOUN la **Palestine** _fem_
**Saudi Arabia** NOUN l' **Arabie Saoudite** _fem_
**South Africa** NOUN l' **Afrique du Sud** _fem_
**South America** NOUN l' **Amérique du Sud** _fem_
**South Pole** NOUN le **pôle Sud** _masc_
**Tunisia** NOUN la **Tunisie** _fem_
**United States** NOUN les **États-Unis** _masc_ _pl_
**USA** NOUN les **USA** _masc_ _pl_
**Vietnam** NOUN le **Viêt-Nam** _masc_
**West Indies** NOUN PL les **Antilles** _fem_ _pl_
# **Food – La nourriture**
**• Savoury**
**bacon** NOUN le **bacon** _masc_
**baked beans** NOUN PL les **haricots blancs à la sauce tomate** _masc_ _pl_
**baked potato** NOUN la **pomme de terre cuite au four** _fem_
**beans** NOUN PL les **haricots blancs à la sauce tomate** _masc_ _pl_
**beef** NOUN le **bœuf** _masc_
**boiled egg** NOUN l' **œuf à la coque** _masc_
**bread** NOUN le **pain** _masc_
**breakfast** NOUN le **petit déjeuner** _masc_
**brown bread** NOUN le **pain complet** _masc_
**bun** NOUN le **petit pain** _masc_
**burger** NOUN le **hamburger** _masc_
**butter** NOUN le **beurre** _masc_
**casserole** NOUN le **ragoût** _masc_
**cereal** NOUN les **céréales** _fem_ _pl_
**cheese** NOUN le **fromage** _masc_
**cheeseburger** NOUN le **cheeseburger** _masc_
**chicken** NOUN le **poulet** _masc_
**chips** NOUN les **frites** _fem_ _pl_
**chop** NOUN la **côte** _fem_
**cod** NOUN le **cabillaud** _masc_
**coleslaw** NOUN la **salade de chou cru à la mayonnaise** _fem_
**cornflakes** NOUN PL les **cornflakes** _masc_ _pl_
**cream cheese** NOUN le **fromage à tartiner** _masc_
**crisps** NOUN PL les **chips** _fem_ _pl_
**curry** NOUN le **curry** _masc_
**dinner** NOUN le **dîner** _masc_
**egg** NOUN l' **œuf** _masc_
**fish** NOUN le **poisson** _masc_
**fish fingers** NOUN PL les **bâtonnets de poisson** _masc_ _pl_
**flan** NOUN la **quiche** _fem_
**French fries** NOUN PL les **frites** _fem_ _pl_
**fried egg** NOUN l' **œuf sur le plat** _masc_
**garlic** NOUN l' **ail** _masc_
**gravy** NOUN la **sauce** _fem_
**haddock** NOUN l' **églefin** _masc_
**ham** NOUN le **jambon** _masc_
**hamburger** NOUN le **hamburger** _masc_
**hard-boiled egg** NOUN l' **œuf dur** _masc_
**herbs** NOUN PL les **fines herbes** _fem_ _pl_
**hot dog** NOUN le **hot-dog** _masc_
**jacket potato** NOUN la **pomme de terre cuite au four** _fem_
**ketchup** NOUN le **ketchup** _masc_
**lamb** NOUN l' **agneau** _masc_
**lentil** NOUN la **lentille** _fem_
**liver** NOUN le **foie** _masc_
**loaf** NOUN le **pain** _masc_
**lobster** NOUN le **homard** _masc_
**lunch** NOUN le **déjeuner** _masc_
**macaroni** NOUN les **macaronis** _masc_ _pl_
**margarine** NOUN la **margarine** _fem_
**mashed potatoes** NOUN PL la **purée** _fem_
**mayonnaise** NOUN la **mayonnaise** _fem_
**meat** NOUN la **viande** _fem_
**mince** NOUN la **viande hachée** _fem_
**muesli** NOUN le **muesli** _masc_
**mussel** NOUN la **moule** _fem_
**mustard** NOUN la **moutarde** _fem_
**noodles** NOUN PL les **nouilles** _fem_ _pl_
**olive** NOUN l' **olive** _fem_
**olive oil** NOUN l' **huile d'olive** _fem_
**omelette** NOUN l' **omelette** _fem_
**parsley** NOUN le **persil** _masc_
**pasta** NOUN les **pâtes** _fem_ _pl_
**pâté** NOUN le **pâté** _masc_
**peanut butter** NOUN le **beurre de cacahuètes** _masc_
**pepper** NOUN le **poivre** _masc_
**pie** NOUN la **tourte** _fem_
**pizza** NOUN la **pizza** _fem_
**poached egg** NOUN l' **œuf poché** _masc_
**pork** NOUN le **porc** _masc_
**porridge** NOUN le **porridge** _masc_
**prawn cocktail** NOUN le **cocktail de crevettes** _masc_
**prawns** NOUN PL les **crevettes** _fem_ _pl_
**rice** NOUN le **riz** _masc_
**roll** NOUN le **petit pain** _masc_
**salad** NOUN la **salade** _fem_
**salad cream** NOUN la **mayonnaise** _fem_
**salad dressing** NOUN la **vinaigrette** _fem_
**salami** NOUN le **salami** _masc_
**salmon** NOUN le **saumon** _masc_
**salt** NOUN le **sel** _masc_
**sandwich** NOUN le **sandwich** _masc_
**sardine** NOUN la **sardine** _fem_
**sauce** NOUN la **sauce** _fem_
**sausage** NOUN la **saucisse** _fem_
**scampi** NOUN PL les **scampi** _masc_ _pl_
**scrambled eggs** NOUN PL les **œufs brouillés** _masc_ _pl_
**seafood** NOUN les **fruits de mer** _masc_ _pl_
**shepherd's pie** NOUN le **hachis Parmentier** _masc_
**shrimps** NOUN PL les **crevettes** _fem_ _pl_
**soft-boiled egg** NOUN l' **œuf à la coque** _masc_
**soup** NOUN la **soupe** _fem_
**soy sauce** NOUN la **sauce de soja** _fem_
**spaghetti** NOUN les **spaghettis** _masc_ _pl_
**steak** NOUN le **steak** _masc_
**stew** NOUN le **ragoût** _masc_
**supper** NOUN le **dîner** _masc_
**toast** NOUN le **pain grillé** _masc_
**toastie** NOUN le **sandwich chaud** _masc_
**tuna** NOUN le **thon** _masc_
**turkey** NOUN la **dinde** _fem_
**vinegar** NOUN le **vinaigre** _masc_
**wholemeal bread** NOUN le **pain complet** _masc_
**• Sweet**
**afters** NOUN PL le **dessert** _masc_
**apple tart** NOUN la **tarte aux pommes** _fem_
**biscuit** NOUN le **gâteau sec** _masc_
**bubble gum** NOUN le **chewing-gum** _masc_
**cake** NOUN le **gâteau** _masc_
**candyfloss** NOUN la **barbe à papa** _fem_
**caramel** NOUN le **caramel** _masc_
**chewing gum** NOUN le **chewing-gum** _masc_
**chocolate** NOUN le **chocolat** _masc_
**cone** NOUN le **cornet** _masc_
**cream** NOUN la **crème** _fem_
**cream cake** NOUN le **gâteau à la crème** _masc_
**custard** NOUN la **crème anglaise** _fem_
**dessert** NOUN le **dessert** _masc_
**doughnut** NOUN le **beignet** _masc_
**flan** NOUN la **tarte** _fem_
**fruit salad** NOUN la **salade de fruits** _fem_
**honey** NOUN le **miel** _masc_
**ice cream** NOUN la **glace** _fem_
**ice lolly** NOUN la **glace à l'eau** _fem_
**jam** NOUN la **confiture** _fem_
**jelly** NOUN la **gelée** _fem_
**lollipop** NOUN la **sucette** _fem_
**marmalade** NOUN la **confiture d'oranges** _fem_
**marzipan** NOUN la **pâte d'amandes** _fem_
**meringue** NOUN la **meringue** _fem_
**mince pie** NOUN la **tartelette de Noël** _fem_
**mousse** NOUN la **mousse** _fem_
**pancake** NOUN la **crêpe** _fem_
**popcorn** NOUN le **pop-corn** _masc_
**pudding** NOUN le **dessert** _masc_
**rice pudding** NOUN le **riz au lait** _masc_
**scone** NOUN le **scone** _masc_
**sponge cake** NOUN le **biscuit de Savoie** _masc_
**sugar** NOUN le **sucre** _masc_
**tart** NOUN la **tarte** _fem_
**toffee** NOUN le **caramel** _masc_
**trifle** NOUN le **diplomate** _masc_
**vanilla** NOUN la **vanille** _fem_
**whipped cream** NOUN la **crème fouettée** _fem_
**yoghurt** NOUN le **yaourt** _masc_
# **Fruit and vegetables – Les fruits et légumes**
**apple** NOUN la **pomme** _fem_
**aubergine** NOUN l' **aubergine** _fem_
**avocado** NOUN l' **avocat** _masc_
**banana** NOUN la **banane** _fem_
**beetroot** NOUN la **betterave rouge** _fem_
**blackberry** NOUN la **mûre** _fem_
**blackcurrant** NOUN le **cassis** _masc_
**broccoli** NOUN les **brocolis** _masc_ _pl_
**Brussels sprouts** NOUN PL les **choux de Bruxelles** _masc_ _pl_
**cabbage** NOUN le **chou** _masc_
**carrot** NOUN la **carotte** _fem_
**cauliflower** NOUN le **chou-fleur** _masc_
**celery** NOUN le **céleri** _masc_
**cherry** NOUN la **cerise** _fem_
**coconut** NOUN la **noix de coco** _fem_
**corn on the cob** NOUN l' **épi de maïs** _masc_
**courgette** NOUN la **courgette** _fem_
**cress** NOUN le **cresson** _masc_
**cucumber** NOUN le **concombre** _masc_
**currant** NOUN le **raisin sec** _masc_
**gooseberry** NOUN la **groseille à maquereau** _fem_
**grapefruit** NOUN le **pamplemousse** _masc_
**grapes** NOUN PL le **raisin** _masc_
**green beans** NOUN PL les **haricots verts** _masc_ _pl_
**leek** NOUN le **poireau** _masc_
**lemon** NOUN le **citron** _masc_
**lettuce** NOUN la **salade** _fem_
**lime** NOUN le **citron vert** _masc_
**mango** NOUN la **mangue** _fem_
**melon** NOUN le **melon** _masc_
**mushrooom** NOUN le **champignon** _masc_
**onion** NOUN l' **oignon** _masc_
**orange** NOUN l' **orange** _fem_
**parsnip** NOUN le **panais** _masc_
**pea** NOUN le **petit pois** _masc_
**peach** NOUN la **pèche** _fem_
**pear** NOUN la **poire** _fem_
**pepper** NOUN le **poivron** _masc_
**pineapple** NOUN l' **ananas** _masc_
**plum** NOUN la **prune** _fem_
**potato** NOUN la **pomme de terre** _fem_
**pumpkin** NOUN le **potiron** _masc_
**radish** NOUN le **radis** _masc_
**raisin** NOUN le **raisin sec** _masc_
**raspberry** NOUN la **framboise** _fem_
**redcurrant** NOUN la **groseille** _fem_
**rhubarb** NOUN la **rhubarbe** _fem_
**satsuma** NOUN la **satsuma** _fem_
**spinach** NOUN les **épinards** _masc_ _pl_
**sprouts** NOUN PL les **choux de Bruxelles** _masc_ _pl_
**strawberry** NOUN la **fraise** _fem_
**sultana** NOUN le **raisin sec** _masc_
**sweetcorn** NOUN le **maïs** _masc_
**tangerine** NOUN la **mandarine** _fem_
**tomato** NOUN la **tomate** _fem_
**turnip** NOUN le **navet** _masc_
**watermelon** NOUN la **pastèque** _fem_
# **Drinks – Les boissons**
**apple juice** NOUN le **jus de pomme** _masc_
**beer** NOUN la **bière** _fem_
**black coffee** NOUN le **café** _masc_
**champagne** NOUN le **champagne** _masc_
**cider** NOUN le **cidre** _masc_
**cocoa** NOUN le **cacao** _masc_
**coffee** NOUN le **café** _masc_
**Coke** ® NOUN le **coca** _masc_
**decaffeinated coffee** NOUN le **café décaféiné** _masc_
**drink** NOUN la **boisson** _fem_
**fruit juice** NOUN le **jus de fruits** _masc_
**grapefruit juice** NOUN le **jus de pamplemousse** _masc_
**hot chocolate** NOUN le **chocolat chaud** _masc_
**juice** NOUN le **jus** _masc_
**lager** NOUN la **bière blonde** _fem_
**lemonade** NOUN la **limonade** _fem_
**milk** NOUN le **lait** _masc_
**milkshake** NOUN le **milk-shake** _masc_
**mineral water** NOUN l' **eau minérale** _fem_
**orange juice** NOUN le **jus d'orange** _masc_
**pineapple juice** NOUN le **jus d'ananas** _masc_
**red wine** NOUN le **vin rouge** _masc_
**shandy** NOUN le **panaché** _masc_
**soft drink** NOUN la **boisson non alcoolisée** _fem_
**sparkling wine** NOUN le **mousseau** _masc_
**tea** NOUN le **thé** _masc_
**tomato juice** NOUN le **jus de tomate** _masc_
**tonic** NOUN le **Schweppes** ® _masc_
**water** NOUN l' **eau** _fem_
**whisky** NOUN le **whisky** _masc_
**white coffee** NOUN le **café au lait** _masc_
**white wine** NOUN le **vin blanc** _masc_
**wine** NOUN le **vin** _masc_
# **Furniture – Les meubles**
**armchair** NOUN le **fauteuil** _masc_
**bath** NOUN la **baignoire** _fem_
**bed** NOUN le **lit** _masc_
**bench** NOUN le **banc** _masc_
**bookcase** NOUN la **bibliothèque** _fem_
**bookshelf** NOUN l' **étagère à livres** _fem_
**bunk beds** NOUN les **lits superposés** _masc_ _pl_
**CD player** NOUN la **platine laser** _fem_
**chair** NOUN la **chaise** _fem_
**chest of drawers** NOUN la **commode** _fem_
**coffee table** NOUN la **table basse** _fem_
**cooker** NOUN la **cuisinière** _fem_
**couch** NOUN le **canapé** _masc_
**cupboard** NOUN le **placard** _masc_
**curtain** NOUN le **rideau** _masc_
**cushion** NOUN le **coussin** _masc_
**deckchair** NOUN la **chaise longue** _fem_
**dishwasher** NOUN le **lave-vaisselle** _masc_
**double bed** NOUN le **grand lit** _masc_
**DVD player** NOUN le **lecteur de DVD** _masc_
**easy chair** NOUN le **fauteuil** _masc_
**freezer** NOUN le **congélateur** _masc_
**fridge** NOUN le **frigo** _masc_
**microwave oven** NOUN le **four à micro-ondes** _masc_
**oven** NOUN le **four** _masc_
**refrigerator** NOUN le **réfrigérateur** _masc_
**rug** NOUN le **tapis** _masc_
**settee** NOUN le **canapé** _masc_
**sink** NOUN l' **évier** _masc_
**sofa** NOUN le **canapé** _masc_
**table** NOUN la **table** _fem_
**television** NOUN la **télévision** _fem_
**tumble dryer** NOUN le **sèche-linge** _masc_
**video recorder** NOUN le **magnétoscope**
**wardrobe** NOUN l' **armoire** _fem_
**washing machine** NOUN la **machine à laver** _fem_
# **Instruments – Les instruments**
**accordion** NOUN l' **accordéon** _masc_
**bagpipes** NOUN PL la **cornemuse** _fem_
**bass drum** NOUN la **grosse caisse** _fem_
**bass guitar** NOUN la **guitare basse** _fem_
**bassoon** NOUN le **basson** _masc_
**cello** NOUN le **violoncelle** _masc_
**clarinet** NOUN la **clarinette** _fem_
**cornet** NOUN le **cornet à pistons** _masc_
**double bass** NOUN la **contrebasse** _fem_
**drum** NOUN le **tambour** _masc_
**drums** NOUN PL la **batterie** _fem_
**electric guitar** NOUN la **guitare électrique** _fem_
**flute** NOUN la **flûte** _fem_
**guitar** NOUN la **guitare** _fem_
**horn** NOUN le **cor** _masc_
**keyboards** NOUN PL le **synthétiseur** _masc_
**mouth organ** NOUN l' **harmonica** _masc_
**oboe** NOUN le **hautbois** _masc_
**organ** NOUN l' **orgue** _masc_
**percussion** NOUN la **percussion** _fem_
**piano** NOUN le **piano** _masc_
**pipes** NOUN PL la **cornemuse** _fem_
**recorder** NOUN la **flûte à bec** _fem_
**saxophone** NOUN le **saxophone** _masc_
**trombone** NOUN le **trombone** _masc_
**trumpet** NOUN la **trompette** _fem_
**tuba** NOUN le **tuba** _masc_
**viola** NOUN l' **alto** _masc_
**violin** NOUN le **violon** _masc_
# **Jobs – Les professions**
**accountant** NOUN le/la **comptable** _masc_ / _fem_
**actor** NOUN l' **acteur** _masc_
**actress** NOUN l' **actrice** _fem_
**architect** NOUN l' **architecte** _masc_ / _fem_
**artist** NOUN l' **artiste** _masc_ / _fem_
**athlete** NOUN l' **athlète** _masc_ / _fem_
**au pair** NOUN la **jeune fille au pair** _fem_
**author** NOUN l' **auteur** _masc_
**baker** NOUN le **boulanger** _masc_ , la **boulangère** _fem_
**barmaid** NOUN la **barmaid** _fem_
**barman** NOUN le **barman** _masc_
**builder** le **maçon** _masc_
**bus driver** NOUN le **conducteur d'autobus** _masc_
**butcher** NOUN le **boucher** _masc_
**caretaker** NOUN le **gardien** _masc_ , la **gardienne** _fem_
**carpenter** NOUN le **charpentier** _masc_
**chef** NOUN le **chef** _masc_
**child minder** NOUN la **nourrice** _fem_
**cleaner** NOUN la **femme de ménage** _fem_ , l' **agent d'entretien** _masc_
**computer programmer** NOUN le **programmeur** _masc_ , la **programmeuse** _fem_
**conductor** NOUN le **chef d'orchestre** _masc_
**cook** NOUN le **cuisinier** _masc_ , la **cuisinière** _fem_
**dancer** NOUN le **danseur** _masc_ , la **danseuse** _fem_
**dentist** NOUN le/la **dentiste** _masc_ / _fem_
**detective** NOUN l' **inspecteur de police** _masc_
**dinner lady** NOUN la **dame de service** _fem_
**disc jockey, DJ** NOUN le **disc-jockey** _masc_
**doctor** NOUN le **médecin** _masc_
**dustman** NOUN l' **éboueur** _masc_
**electrician** NOUN l' **électricien** _masc_
**engineer** NOUN l' **ingénieur** _masc_
**farmer** NOUN l' **agriculteur** _masc_ , l' **agricultrice** _fem_
**film star** NOUN la **vedette de cinéma** _fem_
**firefighter** NOUN le **pompier** _masc_
**fisherman** NOUN le **pêcheur** _masc_
**flight attendant** NOUN l' **hôtesse de l'air** _fem_ , le **steward** _masc_
**florist** NOUN le/la **fleuriste** _masc_ / _fem_
**footballer** NOUN le **footballeur** _masc_ , la **footballeuse** _fem_
**gardener** NOUN le **jardinier** _masc_
**goalkeeper** NOUN le **gardien de but** _masc_
**hairdresser** NOUN le **coiffeur** _masc_ , la **coiffeuse** _fem_
**headmaster** NOUN le **directeur** _masc_
**headmistress** NOUN la **directrice** _fem_
**housewife** NOUN la **femme au foyer** _fem_
**imam** NOUN l' **imam** _masc_
**instructor** NOUN le **moniteur** _masc_ , la **monitrice** _fem_
**interior designer** NOUN le/la **designer** _masc_ / _fem_
**interpreter** NOUN l' **interprète** _masc_ / _fem_
**janitor** NOUN le **concierge** _masc_
**jockey** NOUN le **jockey** _masc_
**joiner** NOUN le **menuisier** _masc_
**journalist** NOUN le/la **journaliste** _masc_ / _fem_
**judge** NOUN le **juge** _masc_
**lawyer** NOUN l' **avocat** _masc_ , l' **avocate** _fem_
**lecturer** NOUN le **professeur d'université** _masc_
**librarian** NOUN le/la **bibliothécaire** _masc_ / _fem_
**lorry driver** NOUN le **routier** _masc_
**matron** NOUN l' **infirmière-chef** _fem_
**mayor** NOUN le **maire** _masc_
**mechanic** NOUN le **mécanicien** _masc_
**midwife** NOUN la **sage-femme** _fem_
**milkman** NOUN le **laitier** _masc_
**miner** NOUN le **mineur** _masc_
**minister** NOUN le **pasteur** _masc_
**model** NOUN le **mannequin** _masc_
**MP** NOUN le **député** _masc_
**musician** NOUN le **musicien** _masc_ , la **musicienne** _fem_
**nanny** NOUN la **garde d'enfants** _fem_
**nurse** NOUN l' **infirmier** _masc_ , l' **infirmière** _fem_
**optician** NOUN l' **opticien** _masc_ , l' **opticienne** _fem_
**painter** NOUN le **peintre** _masc_
**paperboy** NOUN le **livreur de journaux** _masc_
**papergirl** NOUN la **livreuse de journaux** _fem_
**pharmacist** NOUN le **pharmacien** _masc_ , la **pharmacienne** _fem_
**physiotherapist** NOUN le/la **kinésithérapeute** _masc_ / _fem_
**pilot** NOUN le **pilote** _masc_
**plumber** NOUN le **plombier** _masc_
**policeman** NOUN le **policier** _masc_
**policewoman** NOUN la **femme policier** _fem_
**pop star** NOUN la **pop star** _fem_
**postman** NOUN le **facteur** _masc_
**priest** NOUN le **prêtre** _masc_
**professor** NOUN le **professeur d'université** _masc_
**programmer** NOUN le **programmeur** _masc_ , la **programmeuse** _fem_
**rabbi** NOUN le **rabbin** _masc_
**receptionist** NOUN le/la **réceptionniste** _masc_ / _fem_
**rep** NOUN le **représentant** _masc_ , la **représentante** _fem_
**reporter** NOUN le **reporter** _masc_
**sailor** NOUN le **marin** _masc_
**salesman** NOUN le **représentant** _masc_
**saleswoman** NOUN la **répresentante** _fem_
**scientist** NOUN le **chercheur** _masc_ , la **chercheuse** _fem_
**secretary** NOUN le/la **secrétaire** _masc_ / _fem_
**security guard** NOUN l' **agent de sécurité** _masc_
**shop assistant** NOUN le **vendeur** _masc_ , la **vendeuse** _fem_
**shopkeeper** NOUN le **commerçant** _masc_ , la **commerçante** _fem_
**social worker** NOUN l' **assistante sociale** _fem_ le **travailleur social** _masc_
**soldier** NOUN le **soldat** _masc_
**solicitor** NOUN l' **avocat** _masc_ / _fem_ , le **notaire** _masc_
**supply teacher** NOUN le **suppléant** _masc_ , la **suppléante** _fem_
**surgeon** NOUN le **chirurgien** _masc_
**surveyor** NOUN l' **expert en bâtiment** _masc_
**taxi driver** NOUN le **chauffeur de taxi** _masc_
**teacher** NOUN le **professeur des écoles** _masc_ _(in primary school)_ , le **professeur** _masc_ _(in secondary school)_
**technician** NOUN le **technicien** _masc_ la **technicienne** _fem_
**train driver** NOUN le **conducteur de train** _masc_
**translator** NOUN le **traducteur** _masc_ , la **traductrice** _fem_
**undertaker** NOUN l' **entrepreneur des pompes funèbres** _masc_
**vet** NOUN le/la **vétérinaire** _masc_ / _fem_
**vicar** NOUN le **pasteur** _masc_
**waiter** NOUN le **serveur** _masc_
**waitress** NOUN la **serveuse** _fem_
**writer** NOUN l' **écrivain** _masc_
# **Sports – Les sports**
**aerobics** NOUN l' **aérobic** _fem_
**athletics** NOUN l' **athlétisme** _masc_
**badminton** NOUN le **badminton** _masc_
**baseball** NOUN le **base-ball** _masc_
**basketball** NOUN le **basket** _masc_
**bowling** NOUN le **bowling** _masc_
**boxing** NOUN la **boxe** _fem_
**cricket** NOUN le **cricket** _masc_
**cycling** NOUN le **cyclisme** _masc_
**dancing** NOUN la **danse** _fem_
**fishing** NOUN la **pêche** _fem_
**football** NOUN le **football** _masc_
**golf** NOUN le **golf** _masc_
**gymnastics** NOUN la **gymnastique** _fem_
**handball** NOUN le **handball** _masc_
**high jump** NOUN le **saut en hauteur** _masc_
**hockey** NOUN le **hockey** _masc_
**ice hockey** NOUN le **hockey sur glace** _masc_
**ice-skating** NOUN le **patinage sur glace** _masc_
**judo** NOUN le **judo** _masc_
**karate** NOUN le **karaté** _masc_
**long jump** NOUN le **saut en longueur** _masc_
**motor racing** NOUN la **course automobile** _fem_
**mountaineering** NOUN l' **alpinisme** _masc_
**netball** NOUN le **netball** _masc_
**pool** NOUN le **billard américain** _masc_
**riding** NOUN l' **équitation** _fem_
**roller-blading** NOUN le **roller** _masc_
**roller-skating** NOUN le **patin à roulettes** _masc_
**rugby** NOUN le **rugby** _masc_
**running** NOUN la **course** _fem_
**sailing** NOUN la **voile** _fem_
**skateboarding** NOUN le **skateboard** _masc_
**skating** NOUN le **patin à glace** _masc_
**skiing** NOUN le **ski** _masc_
**snooker** NOUN le **billard** _masc_
**soccer** NOUN le **football** _masc_
**squash** NOUN le **squash** _masc_
**surfing** NOUN le **surf** _masc_
**swimming** NOUN la **natation** _fem_
**table tennis** NOUN le **ping-pong** _masc_
**tennis** NOUN le **tennis** _masc_
**tenpin bowling** NOUN le **bowling** _masc_
**trampolining** NOUN le **trampoline** _masc_
**volleyball** NOUN le **volley-ball** _masc_
**water-skiing** NOUN le **ski nautique** _masc_
**windsurfing** NOUN la **planche à voile** _fem_
**wrestling** NOUN la **lutte** _fem_
# **At school – À l'école**
**absent** ADJECTIVE **absent** _masc_ , **absente** _fem_
**assembly hall** NOUN la **salle de réunion** _fem_
**atlas** NOUN l' **atlas** _masc_
**bell** NOUN la **sonnerie** _fem_
**Biro** ® NOUN le **bic** ® _masc_
**blackboard** NOUN le **tableau** _masc_
**board** NOUN le **tableau** _masc_
**book** NOUN le **livre** _masc_
**break time** NOUN la **récréation** _fem_
**calculator** NOUN la **calculatrice** _fem_
**canteen** NOUN la **cantine** _fem_
**cassette player** NOUN le **lecteur de cassettes** _masc_
**CD player** NOUN la **platine laser** _fem_
**chair** NOUN la **chaise** _fem_
**chalk** NOUN la **craie** _fem_
**chart** NOUN le **tableau** _masc_
**class** NOUN la **classe** _fem_
**classroom** NOUN la **classe** _fem_
**classroom assistant** NOUN l' **aide-éducateur** _masc_ , l' **aide-éducatrice** _fem_
**cloakroom** NOUN le **vestiaire** _masc_
**computer** NOUN l' **ordinateur** _masc_
**computer room** NOUN la **salle d'informatique** _fem_
**corridor** NOUN le **couloir** _masc_
**curriculum** NOUN le **programme** _masc_
**deputy head** NOUN le **directeur adjoint** _masc_ , la **directrice adjointe** _fem_
**desk** NOUN le **pupitre** _masc_
**diagram** NOUN le **diagramme** _masc_
**dictionary** NOUN le **dictionnaire** _masc_
**dining room** NOUN le **réfectoire** _masc_
**dormitory** NOUN le **dortoir** _masc_
**drawing** NOUN le **dessin** _masc_
**drawing pin** NOUN la **punaise** _fem_
**essay** NOUN le **devoir** _masc_
**exam** NOUN l' **examen** _masc_
**exercise** NOUN l' **exercice** _masc_
**exercise book** NOUN le **cahier** _masc_
**felt-tip pen** NOUN le **stylo-feutre** _masc_
**folder** NOUN la **chemise** _fem_
**GCSE** NOUN le **brevet des collèges** _masc_
**general knowledge** NOUN les **connaissances générales** _fem_ _pl_
**grammar** NOUN la **grammaire** _fem_
**gym** **hall** NOUN la **salle de gym** _fem_
**gym kit** NOUN les **affaires de gym** _fem_ _pl_
**half term** NOUN les **petites vacances** _fem_ _pl_
**headmaster** NOUN le **directeur** _masc_
**headmistress** NOUN la **directrice** _fem_
**homework** NOUN les **devoirs** _masc_ _pl_
**interval** NOUN la **récréation** _fem_
**jotter** NOUN le **cahier** _masc_
**junior school** NOUN l' **école primaire** _fem_
**language laboratory** NOUN le **laboratoire de langues** _masc_
**lesson** NOUN la **leçon** _fem_
**library** NOUN la **bibliothèque** _fem_
**lower sixth** NOUN la **première** _fem_
**mouse** NOUN la **souris** _fem_
**mouse mat** NOUN le **tapis de souris** _masc_
**office** NOUN le **secrétariat** _masc_
**overhead projector** NOUN le **rétroprojecteur** _masc_
**packed lunch** NOUN le **casse-croûte** _masc_
**page** NOUN la **page** _fem_
**pen** NOUN le **stylo** _masc_
**pencil** NOUN le **crayon** _masc_
**pencil case** NOUN la **trousse** _fem_
**pencil sharpener** NOUN le **taille-crayon** _masc_
**photocopier** NOUN la **photocopieuse** _fem_
**photocopy** NOUN la **photocopie** _fem_
**playground** NOUN la **cour de récréation** _fem_
**playtime** NOUN la **récréation** _fem_
**poster** NOUN le **poster** _masc_
**primary school** NOUN l' **école primaire** _fem_
**printer** NOUN l' **imprimante** _fem_
**projector** NOUN le **projecteur** _masc_
**pupil** NOUN l' **élève** _masc_ / _fem_
**register** NOUN le **cahier d'appel** _masc_
**registration** NOUN l' **appel** _masc_
**rubber** NOUN la **gomme** _fem_
**ruler** NOUN la **règle** _fem_
**satchel** NOUN le **cartable** _masc_
**school** NOUN l' **école** _fem_
**school bag** NOUN le **cartable** _masc_
**schoolboy** NOUN l' **écolier** _masc_
**schoolchildren** NOUN les **écoliers** _masc_ _pl_
**schoolgirl** NOUN l' **écolière** _fem_
**school holidays** NOUN les **vacances scolaires** _fem_ _pl_
**school uniform** NOUN l' **uniforme scolaire** _masc_
**secondary school** NOUN le **collège** _masc_ _(for 11-15 year olds)_ , le **lycée** _masc_ _(for 15-18 year olds)_
**sharpener** NOUN le **taille-crayon** _masc_
**teacher** NOUN le **professeur des écoles** _masc_ _(in primary school)_ , le **professeur** _masc_ _(in secondary school)_
**team** NOUN l' **équipe** _fem_
**test** NOUN le **test** _masc_
**textbook** NOUN le **manuel** _masc_
**toilets** NOUN les **toilettes** _fem_ _pl_
**upper sixth** NOUN la **terminale** _fem_
**whiteboard** NOUN le **tableau** _masc_
**worksheet** NOUN la **feuille d'exercices** _fem_
**• School subjects**
**art** NOUN les **arts plastiques** _masc_ _pl_
**biology** NOUN la **biologie** _fem_
**chemistry** NOUN la **chimie** _fem_
**citizenship** NOUN la **citoyenneté** _fem_
**design and technology** NOUN la **technologie** _fem_
**drama** NOUN l' **art dramatique** _masc_
**English** NOUN l' **anglais** _masc_
**French** NOUN le **français** _masc_
**games** NOUN PL le **sport** _masc_
**geography** NOUN la **géographie** _fem_
**gym** NOUN la **gym** _fem_
**history** NOUN l' **histoire** _fem_
**ICT** NOUN l' **informatique** _fem_
**literacy** NOUN l' **apprentissage de la lecture** _masc_
**literature** NOUN la **littérature** _fem_
**maths** NOUN les **maths** _fem_ _pl_
**music** NOUN la **musique** _fem_
**PE** NOUN l' **EPS** _fem_
**physics** NOUN la **physique** _fem_
**RE** NOUN l' **éducation religieuse** _fem_
**science** NOUN les **sciences** _fem_ _pl_
**• School classes**
**Reception year/Primary 1** NOUN les **moyens** _masc_ _pl_
**Year 1/Primary 2** NOUN les **grands** _masc_ _pl_
**Year 2/Primary 3** NOUN le **CP** _masc_
**Year 3/Primary 4** NOUN le **CE1** _masc_
**Year 4/Primary 5** NOUN le **CE2** _masc_
**Year 5/Primary 6** NOUN le **CM1** _masc_
**Year 6/Primary 7** NOUN le **CM2** _masc_
**Year 7/S1** NOUN la **sixième** _fem_
# **Numbers and time – Les nombres et l'heure**
**1** un(une)
**2** deux
**3** trois
**4** quatre
**5** cinq
**6** six
**7** sept
**8** huit
**9** neuf
**10** dix
**11** onze
**12** douze
**13** treize
**14** quatorze
**15** quinze
**16** seize
**17** dix-sept
**18** dix-huit
**19** dix-neuf
**20** vingt
**21** vingt et un(une)
**22** vingt-deux
**30** trente
**40** quarante
**50** cinquante
**60** soixante
**70** soixante-dix
**71** soixante et onze
**72** soixante-douze
**80** quatre-vingts
**81** quatre-vingt-un(-une)
**82** quatre-vingt-deux
**90** quatre-vingt-dix
**91** quatre-vingt-onze
**100** cent
**101** cent un(une)
**200** deux cents
**250** deux cent cinquante
**1,000** mille
**2,000** deux mille
**1,000,000** un million
| **Quelle heure est-il?**
What time is it? | **Il est...**
It's...
---|---|---
**une heure**
one o'clock |
**une heure dix**
ten past one |
**une heure et quart**
quarter past one
---|---|---
**une heure et demie**
half past one |
**deux heures
moins vingt**
twenty to two |
**deux heures
moins le quart**
quarter to two
| **À quelle heure...?** | What time...?
---|---|---
**à minuit**
at midnight |
**à midi**
at midday |
**à une heure** (de l'après-midi) at one o'clock (in the afternoon)
---|---|---
**à huit heures**
(du soir) at eight o'clock (at night) |
**à 11h15** _or_ **onze heures quinze**
at quarter past eleven (in the morning) |
**à 20h45** _or_ **vingt heures quarante-cinq**
at quarter to nine (at night)
# **French verbs – Les verbes français**
In French, the ending of the verb varies according to the person – ie, the form of the verb that goes with **je** is different from the form that goes with **nous** , **vous** etc.
Here are the present tenses of some common verbs, with the endings highlighted.
We have also shown some useful phrases which require other tenses. As the examples make clear, a French verb may be translated in several different ways, depending on the context.
A verb form that is of particular interest to teachers is the imperative. In English, **Look!** , **Listen!** , **Don't do that!** can be used to a single child, or to the whole class, but in French there are always two different forms of the verb, depending on whether one, or more than one person is being spoken to. The plural form always ends in **-ez** , and this is also the polite form used to an adult. This dictionary contains many examples of imperatives that will be of use to teachers.
The dictionary also contains an explanation of the difference between the two words for **you** ( **tu** and **vous** ) – see the entry for **you**.
Some examples are given here to illustrate the past tense, and the dictionary includes translations for past tenses that children are very likely to want, such as **I got** , **I went** , **I've broken** , **it was** etc. Translations for these will be found at the entries for **get** , **go** , **break** , **be**.
**regarder** _to look_
je regard **e** | **Regarde** -moi, Emmanuelle. _Look at me Emmanuelle._
---|---
tu regard **es** | **Regardez** , les enfants! _Look, children!_
il regard **e** | **Regardez** le tableau! _Look at the board._
elle regard **e** | Je **regarde** la télé le samedi matin. _I watch TV on_ _Saturday morning._
nous regard **ons** |
vous regard **ez** | Il **a regardé** sa montre. _He looked at his watch._
ils regard **ent** | Elle aime regarder des films. _She likes watching films._
elles regard **ent** |
**finir** _to finish_
je fin **is** | J' **ai fini**! _I've finished!_
---|---
tu fin **is** | **Finis** tes devoirs! _Finish your homework!_
il fin **it** | Elle **a fini** sa soupe. _She's finished her soup._
elle fin **it** | Il n'a pas **fini** le livre. _He hasn't finished the book._
nous fin **issons** | Elle va **finir** ses devoirs demain. _She's going to finish_ _her homework tomorrow._
vous fin **issez** |
ils fi **nissent** |
elles fin **issent** |
**attendre** _to wait_
j'attend **s** | **Attends** -moi! _Wait for me!_
---|---
tu attend **s** | **Attendez** ici, les enfants! _Wait here, children!_
il attend | J' **ai attendu** deux heures. _I waited for two hours._
elle attend | Il m' **a attendu** à la gare. _He waited for me at the_ _station._
nous attend **ons** |
vous attend **ez** | Je vais **attendre** ici. _I'm going to wait here._
ils attend **ent** |
elles attend **ent**
**avoir** _to have_
j'ai | Je n' **ai** pas d'argent. _I haven't got any money._
---|---
tu as | J' **ai** les cheveux longs. _I've got long hair._
il a | Elle **a** un vélo. _She's got a bike._
elle a | Il **a eu** un accident. _He's had an accident._
nous av **ons** | J' **ai eu** beaucoup de cadeaux. _I got lots of presents._
vous av **ez** | Quel âge **as** -tu? _How old are you?_
ils ont | Elle **a** cinq ans. _She is five._
elles ont | Il y **a** un bon film à la télé. _There's a good film on TV._
| Qu'est-ce qu'il y **a**? _What's the matter?_
| Je n' **ai** pas fait mes devoirs. _I haven't done my homework._
| J' **ai** faim. _I'm hungry._
| J' **avais** faim. _I was hungry._
**être** _to be_
je suis | Ne **sois** pas effronté! _Don't be cheeky!_
---|---
tu es | Je **suis** fatigué. _I'm tired._
il est | Tu **es** en retard. _You're late._
elle est | C' **est** moi. _It's me._
nous sommes | Elle **est** anglaise. _She's English._
vous êtes | C' **était** difficile. _It was difficult._
ils sont | J' **étais** content. _I was happy._
elles sont | Nous **sommes** les gagnants! _We're the winners!_
| Vous **êtes** prêts? _Are you ready?_
| Nous **sommes** le premier mai. _It's the first of May._
| Mes parents **sont** au travail. _My parents are at work._
| Je **suis** allé à Paris. _I went to Paris._
| Où **es-tu** allé? _Where did you go?_
**aller** _to go_
je vais | Je ne **vais** pas à l'école le samedi. _I don't go to school_ _on Saturday._
---|---
tu vas |
il va | Je **vais** gagner. _I'm going to win._
elle va | Où **vas** -tu? _Where are you going?_
nous all **ons** | **Vas** -y! _Go on!_
vous all **ez** | Ça **va**? _Are you okay?_
ils vont | Il **va** pleuvoir. _It's going to rain._
elles vont | Je **suis allé** chez Luc. _I went to Luc's house._
| Où **es** -tu **allé** hier? _Where did you go yesterday?_
| Nous **sommes allés** en France. _We went to France._
**faire** _to do_
je fais | Je **fais** beaucoup de vélo. _I do a lot of cycling._
---|---
tu fais | Ne **fais** pas ça, chéri. _Don't do that, dear._
il fait | Qu'est-ce que tu **fais?** _What are you doing?_
elle fait | Mon frère **fait** du judo. _My brother does judo._
nous fais **ons** | Deux et deux **font** quatre. _Two and two make four._
vous faites | **Faites** les gestes! _Do the actions!_
ils font | Je n' **ai** pas **fait** mes devoirs. _I haven't done my homework._
elles font | Qui **a fait** ça? _Who did that?_
| Quel temps **fait** -il? _What's the weather like?_
| Il **fait** chaud. _It's hot._
| Il **faisait** froid. _It was cold._
| Je **fais** mon lit tous les matins. _I make my bed every morning._
| Ça ne **fait** rien. _It doesn't matter._
| Il va **faire** beau demain. _It's going to be nice weather tomorrow._
**s'appeler** _to be called_
je m'appell **e** | Je **m'appelle** Amélie. _My name is Amélie._
---|---
tu t'appell **es** | Comment ça **s'appelle?** _What is it called?_
il s'appell **e** | Comment tu **t'appelles?** _What are you called?_
elle s'appell **e** | Vous **vous appelez** comment? _What are you called?_
nous nous appel **ons** | Tes frères **s'appellent** comment? _What are your_ _brothers called?_
vous vous appel **ez** |
ils s'appell **ent** |
elles s'appell **ent** |
**pouvoir** _can_
je peux | Je ne **peux** pas venir. _I can't come._
---|---
tu peux | Vous **pouvez** vous asseoir là. _You can sit there._
il peut | Tu **peux** te pousser un peu? _Could you move over a bit?_
elle peut | Qui **peut** répondre à la question? _Who can answer_ _the question?_
nous pouv **ons** |
vous pouv **ez** | Je **peux** avoir un verre d'eau? _Could I have a glass_ _of water?_
ils peuv **ent** |
elles peuv **ent** | Tu **pourras** venir? _Will you be able to come?_
**vouloir** _to want_
je veux | Qu'est-ce que tu **veux** , Marie? _What do you want,_ _Marie?_
---|---
tu veux |
il veut | Qu'est-ce que vous **voulez** , les garçons? _What do_ _you want, boys?_
elle veut |
nous voul **ons** | Vous **voulez** du café, Madame? _Would you like some_ _coffee, Miss?_
vous voul **ez** |
ils veul **ent** | Tu **veux** un bonbon, Louis? _Would you like a sweet,_ _Louis?_
elles veul **ent** | Je **voudrais** une glace. _I'd like an ice cream._
| Qu'est-ce que ça **veut** dire? _What does that mean?_
# **English – French**
# **A a**
**a** ARTICLE
**_Language tip_**
_Use_ **un** _for masculine nouns,_ **une** _for feminine nouns._
**un** _masc_
**a book**
un livre
**une** _fem_
**a girl**
une fille
**ten kilometres an hour**
dix kilomètres à l'heure
**able** ADJECTIVE
**Will you be able to come?**
Est-ce que tu pourras venir?
**I won't be able to come.**
Je ne pourrai pas venir.
**about**
**about** _can be an adverb or a preposition._
**A** ADVERB
**environ** _(approximately)_
**about sixteen girls**
environ seize filles
**about fourteen euros**
environ quatorze euros
**at about eleven o'clock**
vers onze heures
**B** PREPOSITION
**sur** _(concerning)_
**about myself**
sur moi
**a letter about yourself**
une lettre sur toi
**a song about animals**
une chanson sur les animaux
**How about a game of cards?**
Tu veux jouer aux cartes?
**above** PREPOSITION
**1** **au-dessus de** _(higher than)_
**Hold the ball above your heads.**
Tenez la balle au-dessus de votre tête.
**2** **plus de** _(more than)_
**above thirty degrees**
plus de trente degrés
**abroad** ADVERB
**à l'étranger**
**We're going abroad this year.**
Nous partons à l'étranger cette année.
**absent** ADJECTIVE
**absent** _masc_
**absente** _fem_
**Who's absent today?**
Qui est absent aujourd'hui?
**absurd** ADJECTIVE
**absurde**
**That's absurd!**
C'est absurde!
**academy** NOUN
le **collège** _masc_
**accent** NOUN
l' **accent** _masc_
**He's got a good accent.**
Il a un bon accent.
**accident** NOUN
l' **accident** _masc_
**It was an accident.**
C'était un accident.
**ace** NOUN
l' **as** _masc_
**the ace of hearts**
l'as de cœur
**ache** VERB
**My leg's aching.**
J'ai mal à la jambe.
**across** PREPOSITION
**de l'autre côté de**
**It's across the road.**
C'est de l'autre côté de la rue.
**act** VERB
**jouer**
**He's acting in a play.**
Il joue dans une pièce.
**activity** NOUN
l' **activité** _fem_
**outdoor activities**
les activités de plein air
**actor** NOUN
l' **acteur** _masc_
**actress** NOUN
l' **actrice** _fem_
**actually** ADVERB
**en fait**
**Actually it's good fun.**
En fait, c'est bien amusant.
**AD** ABBREVIATION
**ap. J.-C.**
**in 800 AD**
en 800 ap. J.-C.
**add** VERB
**ajouter**
**Add some sugar.**
Ajoutez du sucre.
**add up** VERB
**additionner**
**Add the figures up.**
Additionnez les chiffres.
**address** NOUN
l' **adresse** _fem_
**What's your address?**
Quelle est votre adresse?
**What's your address, Charlotte?**
Quelle est ton adresse, Charlotte?
**_Language tip_**
**address** _in English is spelled with a double_ **d**. _The French word has only one_ **d** , _and an extra_ **e** _on the end._
**adjective** NOUN
l' **adjectif** _masc_
**admission** NOUN
l' **entrée** _fem_
**'admission free'**
'entrée gratuite'
**adopted** ADJECTIVE
**adopté** _masc_
**adoptée** _fem_
**adult** NOUN
l' **adulte** _masc/fem_
**two adults and one child**
deux adultes et un enfant
**advantage** NOUN
l' **avantage** _masc_
**It's an advantage to be able to speak French.**
C'est un avantage de savoir parler français.
**adventure** NOUN
l' **aventure** _fem_
**Harry has lots of adventures.**
Harry a beaucoup d'aventures.
**advice** NOUN
les **conseils** _masc pl_
**Could you give me some advice?**
Vous pouvez me donner des conseils?
**aerobics** PL NOUN
l' **aérobic** _fem_
**I'm going to aerobics tonight.**
Je vais au cours d'aérobic ce soir.
**aeroplane** NOUN
l' **avion** _masc_
**on an aeroplane**
en avion
**affectionate** ADJECTIVE
**affectueux** _masc_
**affectueuse** _fem_
**My cat is very affectionate.**
Mon chat est très affectueux
**afraid** ADJECTIVE
**to be afraid of...**
avoir peur de...
**I'm afraid of spiders.**
J'ai peur des araignées.
**Are you afraid of the dark?**
Tu as peur du noir?
**after** PREPOSITION
**après**
**after me**
après moi
**after you**
après toi
**after lunch**
après le déjeuner
**afternoon** NOUN
l' **après-midi** _masc/fem_
**In the morning or in the afternoon?**
Le matin ou l'après-midi?
**3 o'clock in the afternoon**
trois heures de l'après-midi
**I'm playing football on Saturday afternoon.**
Je joue au foot samedi après-midi.
**this afternoon**
cet après-midi
**in the afternoon**
l'après-midi
**afters** NOUN
le **dessert** _masc_
**What do you want for afters?**
Qu'est-ce que tu veux comme dessert?
**again** ADVERB
**1** **encore**
**Tamsin has won again.**
Tamsin a encore gagné.
**2** **encore une fois** _
(one more time)_
**Try again!**
Essaie encore une fois!
**_Language tip_**
_In French, you can also add_ **re-** _to verbs, to show you're doing something again. This is the same as English, for example,_ **re** _paint_ , **re** _write_.
**Let's begin again.**
Recommençons.
**Can you tell me again?**
Tu peux me le redire?
**Do it again!**
Refais-le!
**against** PREPOSITION
**contre**
**Don't put your chair against the wall.**
Ne mets pas ta chaise contre le mur.
**age** NOUN
l' **âge** _masc_
**Age: twelve**
Âge: douze ans
**your age**
ton âge
**at the age of thirteen**
à l'âge de treize ans
**Write your name and age.**
Écris ton nom et ton âge.
**I am the same age as you.**
J'ai le même âge que toi.
**ago** ADVERB
**two days ago**
il y a deux jours
**a week ago**
il y a une semaine
**a month ago**
il y a un mois
**a long time ago**
il y a longtemps
**agree** VERB
**être d'accord**
**I agree!**
Je suis d'accord!
**I agree with Carol.**
Je suis d'accord avec Carol.
**ahead** ADVERB
**devant**
**Look straight ahead!**
Regardez droit devant vous!
**The red team is five points ahead.**
L'équipe rouge a cinq points d'avance.
**air** NOUN
l' **air** _masc_
**Throw the ball into the air.**
Lance le ballon en l'air.
**I prefer to travel by air.**
Je préfère voyager en avion.
**air-conditioned** ADJECTIVE
**climatisé** _masc_
**climatisée** _fem_
**air hostess** NOUN
l' **hôtesse de l'air** _fem_
**airmail** NOUN
**by airmail**
par avion
**airport** NOUN
l' **aéroport**
_masc_
**alarm clock** NOUN
le **réveil** _masc_
**album** NOUN
l' **album** _masc_
**alcohol** NOUN
l' **alcool** _masc_
**I don't like alcohol.**
Je n'aime pas l'alcool.
**A levels** PL NOUN
le **baccalauréat** _masc_
**My brother is taking his A levels.**
Mon frère passe le baccalauréat.
**_Did you know...?_**
_In France, the_ **baccalauréat** ( _or_ **bac** _for short) is the equivalent of A levels in the UK._
**alien** NOUN
l' **extra-terrestre** _masc_
**alive** ADJECTIVE
**vivant** _masc_
**vivante** _fem_
**They're still alive.**
Ils sont encore vivants.
**all** ADJECTIVE, PRONOUN, ADVERB
**tout** _masc_
**toute** _fem_
**all the time**
tout le temps
**all day**
toute la journée
**all my friends**
tous mes amis
**all the girls**
toutes les filles
**The score is five all.**
Le score est de cinq partout.
**Is that all?**
C'est tout?
**allergic** ADJECTIVE
**allergique**
**I'm allergic to eggs.**
Je suis allergique aux œufs.
**allergy** NOUN
l' **allergie** _fem_
**Have you got any allergies?**
Tu as des allergies?
**allowed** ADJECTIVE
**It's not allowed.**
Ce n'est pas permis.
**all right** ADVERB
**1** **pas mal** _(not bad)_
**Great, or just all right?**
Super, ou seulement pas mal?
**Do you like school? — It's all right.**
Tu aimes l'école? — C'est pas mal.
**2** **d'accord** _(when agreeing)_
**I'd like a coke. — All right.**
Je voudrais un coca. — D'accord.
**Are you all right?**
Ça va?
**Is that all right?**
Ça va?
**almost** ADVERB
**presque**
**Are you ready? — Almost.**
Tu es prêt? — Presque.
**alone** ADJECTIVE, ADVERB
**seul** _masc_
**seule** _fem_
**She lives alone.**
Elle habite seule.
**Leave my things alone!**
Ne touche pas à mes affaires!
**Luc, leave Pierre alone!**
Luc, laisse Pierre tranquille!
**_Language tip_**
**le** _can mean 'him' and_ **la** _can mean 'her'._
**Leave him alone!**
Laisse-le tranquille!
**Leave her alone!**
Laisse-la tranquille!
**along** PREPOSITION
**le long de**
**a walk along the beach**
une promenade le long de la plage
**aloud** ADVERB
**à haute voix**
**Read the words aloud, children.**
Lisez les mots à haute voix, les enfants.
**Read the words aloud, Marcel.**
Lis les mots à haute voix, Marcel.
**alphabet** NOUN
l' **alphabet** _masc_
**alphabetical order** NOUN
**in alphabetical order**
par ordre alphabétique
**Alps** PL NOUN
les **Alpes** _fem pl_
**already** ADVERB
**déjà**
**Have you finished already?**
Tu as déjà fini?
**also** ADVERB
**aussi**
**alternate** ADJECTIVE
**on alternate days**
tous les deux jours
**alternative** NOUN
le **choix** _masc_
**You have no alternative.**
Tu n'as pas le choix.
**altogether** ADVERB
**en tout**
**That's £20 altogether.**
Ça fait vingt livres en tout.
**always** ADVERB
**toujours**
**The bus is always late.**
Le bus est toujours en retard.
**am** VERB _see_ **be**
**a.m.** ABBREVIATION
**du matin**
**at 4 a.m.**
à quatre heures du matin
**amazing** ADJECTIVE
**1** **incroyable** _(surprising)_
**That's amazing!**
C'est incroyable!
**2** **exceptionnel** _masc_ **exceptionnelle** _fem (excellent)_
**Vivian's an amazing cook.**
Vivian est une cuisinière exceptionnelle.
**amber** ADJECTIVE
**an amber light**
un feu orange
**ambition** NOUN
l' **ambition** _fem_
**It's my ambition.**
C'est mon ambition.
**ambulance** NOUN
l' **ambulance** _fem_
**America** NOUN
l' **Amérique** _fem_
**We're going to America.**
Nous allons en Amérique.
**American**
**American** _can be an adjective or a noun._
**A** ADJECTIVE
**américain** _masc_ **américaine** _fem_
**American food**
la cuisine américaine
**He's American.**
Il est américain.
**She's American.**
Elle est américaine.
**B** NOUN
l' **Américain** _masc_ l' **Américaine** _fem_
**the Americans**
les Américains
**_Language tip_**
**américain** _is not spelled with a capital letter except when it means an American person._
**amount** NOUN
**1** la **somme** _fem (sum of money)_
**a large amount of money**
une grosse somme d'argent
**2** la **quantité** _fem (quantity)_
**a huge amount of rice**
une énorme quantité de riz
**amusement arcade** NOUN
la **salle de jeux électroniques** _fem_
**an** ARTICLE
**_Language tip_**
_Use_ **un** _for masculine nouns,_ **une** _for feminine nouns._
**un** _masc_
**an animal**
un animal
**une** _fem_
**an apple**
une pomme
**and** CONJUNCTION
**et**
**you and me**
toi et moi
**Two and two are four.**
Deux et deux font quatre.
**angel** NOUN
l' **ange** _masc_
**You're an angel!**
Tu es un ange!
**angry** ADJECTIVE
**to get angry**
se fâcher
**Mum gets angry if I'm late.**
Maman se fâche si je suis en retard.
**animal** NOUN
l' **animal** _masc_ (PL les **animaux** _)_
**anniversary** NOUN
l' **anniversaire** _masc_
**my parents' wedding anniversary**
l'anniversaire de mariage de mes parents
**Happy anniversary!**
Joyeux anniversaire de mariage!
**announcement** NOUN
l' **annonce** _fem_
**an important announcement**
une annonce importante
**anorak** NOUN
l' **anorak** _masc_
**my new anorak**
mon nouvel anorak
**another** ADJECTIVE
**un autre** _masc_
**une autre** _fem_
**Would you like another sandwich?**
Tu veux un autre sandwich?
**Do you want another card?**
Tu veux une autre carte?
**answer**
**answer** _can be a verb or a noun._
**A** VERB
**répondre**
**Inès, you have to answer yes or no.**
Inès, tu dois répondre par oui ou par non.
**Think before you answer.**
Réfléchissez avant de répondre.
**to answer a question**
répondre à une question
**Who can answer the question?**
Qui peut répondre à la question?
**Can you answer my question?**
Peux-tu répondre à ma question?
**B** NOUN
la **réponse** _fem_
**the right answer**
la bonne réponse
**_Language tip_**
_The English words 'respond' and 'response' are related to_ **répondre** _and_ **réponse** _in French._
**ant** NOUN
la **fourmi** _
fem_
**anthem** NOUN
**the national anthem**
l'hymne national
**any** ADJECTIVE
**_Language tip_**
**any** _can be_ **du** , **de la** , **de l'** _or_ **des** , _in the same way that 'the' can be 'le', 'la', 'l' or 'les'._
**du**
**Do you want any bread?**
Voulez-vous du pain?
**de la**
**Would you like any salad?**
Voulez-vous de la salade?
**de l'**
**Have you got any mineral water?**
Avez-vous de l'eau minérale?
**des**
**Have you got any brothers or sisters?**
Tu as des frères et sœurs?
**_Language tip_**
_In negative phrases, the French for_ **any** _is_ **de** _or_ **d'**.
**de**
**I don't want any bread.**
Je ne veux pas de pain.
**d'**
**I haven't got any mineral water.**
Je n'ai pas d'eau minérale.
**I don't want any more.**
Je n'en veux plus.
**Have you got any money?**
Tu as de l'argent?
**Have you got any pets?**
Tu as des animaux?
**I haven't got any pets.**
Je n'ai pas d'animaux.
**anybody** PRONOUN
**1** **quelqu'un** _(in question)_
**Does anybody want a sweet?**
Quelqu'un veut un bonbon?
**2** **personne** _(in negative phrases)_
**I can't see anybody.**
Je ne vois personne.
**anyone** PRONOUN
**1** **quelqu'un** _(in question)_
**Does anyone want to try?**
Quelqu'un veut essayer?
**2** **personne** _(in negative phrases)_
**I can't see anyone.**
Je ne vois personne.
**anything** PRONOUN
**1** **quelque chose** _(in question)_
**Do you want anything to eat?**
Tu veux manger quelque chose?
**2** **rien** _(in negative phrases)_
**I don't want anything.**
Je ne veux rien.
**apart** ADVERB
**Stand with your feet apart.**
Tenez-vous debout, les pieds écartés.
**apartment** NOUN
l' **appartement** _masc_
**_Language tip_**
_What are the two differences in spelling between the French word and the English word?_
**apostrophe** NOUN
l' **apostrophe** _fem_
**Don't forget the apostrophe!**
N'oubliez pas l'apostrophe!
**app** NOUN
l' **appli** _fem (for phone)_
**apple** NOUN
la **pomme** _fem_
**a big red apple**
une grosse pomme rouge
**apple juice** NOUN
le **jus de pomme** _masc_
**apple tart** NOUN
la **tarte aux pommes** _fem_
**appointment** NOUN
le **rendez-vous** _masc_
**I've got a dental appointment.**
J'ai rendez-vous chez le dentiste.
**April** NOUN
**avril** _masc_
**April or May?**
Avril ou mai?
**My birthday's in April.**
Mon anniversaire est en avril.
**in April**
en avril
**the ninth of April**
le neuf avril
**_Language tip_**
_In French, the months are not spelled with a capital letter._
**April Fool** NOUN
le **poisson d'avril** _masc_
**_Did you know...?_**
_Pinning a paper fish to somebody's back is a traditional April Fool joke in France._
**April Fool's Day** NOUN
**le premier avril** _masc_
**apron** NOUN
le **tablier** _masc_
**a white apron**
un tablier blanc
**are** VERB _see_ **be**
**area** NOUN
la **région** _fem_
**She lives in the Paris area.**
Elle habite dans la région parisienne.
**argue** VERB
**se disputer**
**Stop arguing!**
Arrêtez de vous disputer!
**arm** NOUN
le **bras** _masc_
**Swing your arms!**
Balancez les bras!
**armchair** NOUN
le **fauteuil** _masc_
**army** NOUN
l' **armée** _fem_
**He's in the army.**
Il est dans l'armée.
**around** PREPOSITION
**1** **vers** _(date, time)_
**I go to bed around ten o'clock.**
Je me couche vers vingt-deux heures.
**2** _(nearby)_
**around here**
près d'ici
**Is there a chemist's around here?**
Il y a une pharmacie près d'ici?
**arrive** VERB
**arriver**
**What time does the train arrive?**
Le train arrive à quelle heure?
**arrow** NOUN
la **flèche** _fem_
**Follow the arrows.**
Suivez les flèches.
**art** NOUN
les **arts plastiques** _masc pl (at school)_
**Art is my favourite subject.**
Ma matière préférée, c'est les arts plastiques.
**art gallery** NOUN
le **musée** _masc_
**The art gallery is closed.**
Le musée est fermé.
**artist** NOUN
l' **artiste** _
masc/fem_
**as** CONJUNCTION, PREPOSITION
**puisque** _(since)_
**Alice, as it's your birthday you can choose.**
Alice, tu peux choisir, puisque c'est ton anniversaire.
**He works as a waiter in the holidays.**
Il travaille comme serveur pendant les vacances.
**as... as**
aussi... que
**Pierre's as tall as Michel.**
Pierre est aussi grand que Michel.
**Write to me as soon as possible.**
Écris-moi dès que possible.
**ashamed** ADJECTIVE
**to be ashamed**
avoir honte
**You should be ashamed of yourself!**
Tu devrais avoir honte!
**ashtray** NOUN
le **cendrier** _masc_
**Asian**
**Asian** _can be an adjective or a noun._
**A** ADJECTIVE
**indo-pakistanais** _masc_ **indo-pakistanaise** _fem_
**He's Asian.**
Il est indo-pakistanais.
**She's Asian.**
Elle est indo-pakistanaise.
**B** NOUN
l' **Indo-Pakistanais** _masc_
l' **Indo-Pakistanaise** _fem_
**_Language tip_**
**indo-pakistanais** _is not spelled with a capital letter except when it means an Asian person._
**ask** VERB
**1** **demander**
**If you need help, ask!**
Si tu as besoin d'aide, demande!
**Ask his name.**
Demande-lui son nom.
**Ask her age.**
Demande-lui son âge.
**_Language tip_**
_When_ **ask** _is followed by a person, use_ **demander à**.
**Ask your penfriend.**
Demande à ton correspondant.
**Ask your friends.**
Demande à tes amis.
**_Language tip_**
**to ask for** _is also_ **demander**.
**Ask for some chips and a drink.**
Demandez des frites et une boisson.
**Who wants to ask a question?**
Qui veut poser une question?
**Ask the question.**
Pose la question.
**2** **inviter** _(invite)_
**Are you going to ask Matthew to the party?**
Tu vas inviter Matthew à la fête?
**asleep** ADJECTIVE
**to be asleep**
dormir
**Are you asleep?**
Tu dors?
**assembly** NOUN
**_Did you know...?_**
_There is no assembly in French schools._
**assistant** NOUN
**1** le **vendeur** _masc_ la **vendeuse** _fem (shop assistant)_
**Ask the assistant.**
Demande à la vendeuse.
**2** l' **assistant** _masc_ l' **assistante** _fem (helper)_
**asthma** NOUN
l' **asthme** _masc_
**I've got asthma.**
J'ai de l'asthme.
**astronomy** NOUN
l' **astronomie** _fem_
**at**
**A** PREPOSITION
**à**
**at Christmas**
à Noël
**two at a time**
deux à la fois
**_Language tip_**
**à** \+ **le** _becomes_ **au** , **à** \+ **les** _becomes_ **aux**.
**au**
**at the café**
au café
**aux**
**at the races**
aux courses
**at night**
la nuit
**What are you doing at the weekend?**
Qu'est-ce que tu fais ce week-end?
**B** NOUN
l' **arobase** _fem
(symbol in email address)_
**at four o'clock**
à quatre heures
**at school**
à l'école
**at home**
à la maison
**athlete** NOUN
l' **athlète** _masc/fem_
**He's a good athlete.**
C'est un bon athlète.
**Atlantic** NOUN
l' **Atlantique** _masc_
**atlas** NOUN
l' **atlas** _masc_
**attention** NOUN
l' **attention** _fem_
**Pay attention!**
Faites attention!
**Pay attention, Léon!**
Fais attention, Léon!
**attic** NOUN
le **grenier** _masc_
**attractive** ADJECTIVE
**séduisant** _masc_
**séduisante** _fem_
**She's very attractive.**
Elle est très séduisante.
**August** NOUN
**août** _masc_
**August or September?**
Août ou septembre?
**My birthday's in August.**
Mon anniversaire est en août.
**in August**
en août
**the fifth of August**
le cinq août
**_Language tip_**
_The months are not spelled with a capital letter in French._
**aunt** NOUN
la **tante** _fem_
**my aunt**
ma tante
**au pair** NOUN
la **jeune fille au pair** _fem_
**She's an au pair.**
Elle est jeune fille au pair.
**_Language tip_**
_You do not translate_ **a** _when you say what someone's job is in French._
**Australia** NOUN
l' **Australie** _fem_
**Austria** NOUN
l' **Autriche** _fem_
**author** NOUN
l' **auteur** _masc_
**J. K. Rowling is a famous author.**
J. K. Rowling est un auteur connu.
**autumn** NOUN
l' **automne** _masc_
**in autumn**
_en automne_
**avenue** NOUN
l' **avenue** _fem_
**average**
**average** _can be a noun or an adjective._
**A** NOUN
la **moyenne** _fem_
**on average**
en moyenne
**above average**
au dessus de la moyenne
**B** ADJECTIVE
**moyen** _masc_ **moyenne** _fem_
**the average age**
l'âge moyen
**I'm average height.**
Je suis de taille moyenne.
**away** ADJECTIVE
**absent** _masc_
**absente** _fem (not here)_
**André's away today.**
André est absent aujourd'hui.
**He's away for a week.**
Il est parti pour une semaine.
**He's away.**
Il est absent.
**She's away.**
Elle est absente.
**awful** ADJECTIVE
**affreux** _masc_
**affreuse** _fem_
**That's awful!**
C'est affreux!
# **B b**
**baby** NOUN
le **bébé** _masc_
**We've got a new baby!**
On a un nouveau bébé!
**babysit** VERB
**faire du baby-sitting**
**I babysit at the weekend.**
Je fais du baby-sitting le weekend.
**babysitter** NOUN
le/la **baby-sitter** _masc/fem_
**back**
**back** _can be a noun or an adjective._
**A** NOUN
**1** le **dos** _masc (of person, horse, book)_
**Lie on your back!**
Couchez-vous sur le dos.
**2** le **fond** _masc (of room)_
**at the back**
au fond
**Luc and I sit at the back.**
Luc et moi, on s'assoit au fond.
**B** ADJECTIVE
**arrière** _masc, fem, pl_
**the back seat**
le siège arrière
**the back wheels of the car**
les roues arrière de la voiture
**the back door**
la porte de derrière
**background** NOUN
l' **arrière-plan** _masc_
**a house in the background**
une maison à l'arrière-plan
**backstroke** NOUN
le **dos crawlé** _masc_
**I do the backstroke.**
Je fais le dos crawlé.
**backwards** ADVERB
**en arrière**
**Take a step backwards!**
Faites un pas en arrière!
**bacon** NOUN
le **bacon** _masc_
**bacon and eggs**
des œufs au bacon
**bad** ADJECTIVE
**1** **mauvais** _masc_
**mauvaise** _fem (awful)_
**a bad film**
un mauvais film
**bad weather**
le mauvais temps
**That's not bad.**
Ce n'est pas mal.
**I'm bad at maths.**
Je suis mauvais en maths.
**_Language tip_**
_A boy is saying this. How can you tell?_
**2** **grave** _(serious)_
**a bad accident**
un accident grave
**3** **vilain** _masc_
**vilaine** _fem (naughty)_
**You bad boy!**
Vilain!
**not bad**
pas mal
**Bad luck!**
Pas de chance!
**badge** NOUN
le **badge** _masc_
**badly** ADVERB
**mal**
**He behaved badly.**
Il s'est mal comporté.
**badminton** NOUN
le **badminton** _masc_
**I play badminton.**
Je joue au badminton.
**bag** NOUN
le **sac** _masc_
**baggy** ADJECTIVE
**ample**
**baggy trousers**
un pantalon ample
**bagpipes** PL NOUN
la **cornemuse** _fem_
**Ed plays the bagpipes.**
Ed joue de la cornemuse.
**baked beans** PL NOUN
**les haricots blancs à la sauce tomate** _masc pl_
**_Language tip_**
_The literal translation of the French means 'white beans in tomato sauce'._
**baked potato** NOUN
la **pomme de terre cuite au four** _fem_
**two baked potatoes**
deux pommes de terre cuites au four
**baker** NOUN
le **boulanger** _masc_
la **boulangère** _fem_
**bakery** NOUN
la **boulangerie** _fem_
**balcony** NOUN
le **balcon** _masc_
**bald** ADJECTIVE
**chauve**
**My grandfather is bald.**
Mon grand-père est chauve.
**ball** NOUN
**1** la **balle** _fem (for tennis, golf, cricket)_
**Hit the ball!**
Frappe la balle!
**2** le **ballon** _
masc (for football, rugby)_
**Pass the ball!**
Passe le ballon!
**ballet** NOUN
la **danse classique** _fem_
**I do ballet.**
Je fais de la danse classique.
**_Language tip_**
_What's the difference in spelling between the English word_ **dance** _and the French word_ **danse**?
**ballet dancer** NOUN
le **danseur classique** _
masc_
la **danseuse classique** _fem_
**ballet shoes** PL NOUN
les **chaussons de danse** _
masc pl_
**balloon** NOUN
le **ballon** _masc_
**a red balloon**
un ballon rouge
**banana** NOUN
la **banane** _fem_
**band** NOUN
**1** le **groupe** _masc (rock band)_
**2** la **fanfare** _fem (brass band)_
**bandage** NOUN
le **bandage** _masc_
**He's got a bandage round his arm.**
Il a un bandage au bras.
**bang**
**bang** _can be a noun or a verb._
**A** NOUN
**Bang! Bang!**
Pan! Pan!
**B** VERB
**Don't bang the door!**
Ne claque pas la porte!
**banger** NOUN
**1** la **saucisse** _fem (sausage)_
**bangers and mash**
les saucisses à la purée
**2** le **pétard** _masc (firework)_
**Phyllis is scared of bangers.**
Phyllis a peur des pétards.
**bank** NOUN
**1** la **banque** _fem (for money)_
**2** le **bord** _masc (of river, lake)_
**bank holiday** NOUN
le **jour férié** _masc_
**bar** NOUN
**a bar of chocolate**
une barre de chocolat
**barbecue** NOUN
le **barbecue** _masc_
**bare** ADJECTIVE
**nu** _masc_
**nue** _fem_
**bare feet**
les pieds nus
**bargain** NOUN
l' **affaire** _fem_
**It's a bargain!**
C'est une affaire!
**barge** NOUN
la **péniche** _fem_
**bark** VERB
**aboyer**
**My dog barks a lot.**
Mon chien aboie beaucoup.
**baseball** NOUN
le **base-ball** _masc_
**I play baseball.**
Je joue au base-ball.
**baseball cap** NOUN
la **casquette de base-ball** _fem_
**basement** NOUN
le **sous-sol** _masc_
**basin** NOUN
le **lavabo** _masc_
**basket** NOUN
le **panier** _
masc_
**basketball** NOUN
le **basket** _masc_
**Do you play basketball?**
Tu joues au basket?
**bat** NOUN
**1** la **batte** _fem (for cricket, rounders)_
**2** la **raquette** _fem (for table tennis)_
**3** la **chauve-souris** _fem (animal)_
**two bats**
deux chauves-souris
**_Language tip_**
_Make sure you pick the word for the right sort of bat!_
**bath** NOUN
**1** le **bain** _masc (wash)_
**I have a bath every night.**
Je prends un bain tous les soirs.
**a hot bath**
un bain chaud
**2** la **baignoire** _fem (tub)_
**There's a spider in the bath!**
Il y a une araignée dans la baignoire!
**bathroom** NOUN
la **salle de bains** _fem_
**There are two bathrooms.**
Il y a deux salles de bains.
**baths** PL NOUN
la **piscine** _fem_
**battery** NOUN
la **pile** _fem (for torch, toy)_
**I need a battery.**
J'ai besoin d'une pile.
**battle** NOUN
la **bataille** _fem_
**the Battle of Hastings**
la bataille de Hastings
**battleships** NOUN
la **bataille navale** _fem_
**BC** ABBREVIATION
**av. J.-C.**
**in 200 BC**
en 200 av. J.-C.
**be** VERB
**1** **être**
**It's me.**
C'est moi.
**It's easy.**
C'est facile.
**It's not easy.**
Ce n'est pas facile.
**I'm tired.**
Je suis fatigué.
**You're late.**
Tu es en retard.
**She's English.**
Elle est anglaise.
**We're the winners!**
Nous sommes les gagnants!
**Are you ready?**
Vous êtes prêts?
**My parents are in Paris at the moment.**
Mes parents sont à Paris en ce moment.
**My name is not Inès, it's Fleur.**
Mon nom n'est pas Inès, c'est Fleur.
**_Language tip_**
_With certain adjectives, such as 'cold', 'hot', 'hungry' and 'thirsty', you use_ **avoir** _instead of_ **être**.
**I'm cold.**
J'ai froid.
**I'm hungry.**
J'ai faim.
**_Language tip_**
_When talking about ages, you use_ **avoir** , _not_ **être**.
**I'm eleven.**
J'ai onze ans.
**My brother is thirteen.**
Mon frère a treize ans.
**_Language tip_**
_When talking about the weather, you use_ **fait**.
**It's cold.**
Il fait froid.
**It's too hot.**
Il fait trop chaud.
**It's a nice day.**
Il fait beau.
**It's the twenty-eighth of October today.**
Aujourd'hui, nous sommes le vingt-huit octobre.
**_Language tip_**
_Another way of saying this date is_ **Aujourd'hui c'est le vingt-huit octobre**.
**2** **égaler** _(with totals)_
**Two times three is six.**
Deux fois trois égalent six.
**Ten divided by two is five.**
Dix divisé par deux égalent cinq.
**beach** NOUN
la **plage** _fem_
**beans** NOUN
**1** les **haricots blancs à la sauce tomate** _masc pl (baked beans)_
**Would you like some beans?**
Tu veux des haricots blancs à la sauce tomate?
**_Language tip_**
_Word for word this means 'white beans in tomato sauce'._
**2** **les haricots verts** _masc pl (green beans)_
**beard** NOUN
la **barbe** _fem_
**beat** VERB
**battre**
**We're going to beat you!**
Nous allons vous battre!
**beautiful** ADJECTIVE
**beau** _masc_
**belle** _fem_
**Your garden is beautiful.**
Votre jardin est beau.
**Delphine is very beautiful.**
Delphine est très belle.
**Your hair is beautiful.**
Tes cheveux sont beaux.
**because** CONJUNCTION
**parce que**
**Yvette is absent because she's ill.**
Yvette est absente parce qu'elle est malade.
**because of you**
à cause de toi
**because of the weather**
à cause du temps
**bed** NOUN
le **lit** _masc_
**in bed**
au lit
**It's time to go to bed.**
Il est temps de se coucher.
**I go to bed at ten o'clock.**
Je me couche à dix heures.
**What time do you go to bed?**
À quelle heure tu te couches?
**bed and breakfast** NOUN
la **chambre d'hôte** _fem_
**bedroom** NOUN
la **chambre** _fem_
**my bedroom**
ma chambre
**Alain's bedroom**
la chambre d'Alain
**bedtime** NOUN
**Ten o'clock is my usual bedtime.**
Je me couche généralement à dix heures.
**Bedtime!**
Au lit!
**bee** NOUN
l' **abeille** _fem_
**beef** NOUN
le **bœuf** _masc_
**Would you like beef or chicken?**
Tu veux du bœuf ou du poulet?
**roast beef**
le rôti de bœuf
**beefburger** NOUN
le **hamburger** _masc_
**beer** NOUN
la **bière** _fem_
**a can of beer**
une canette de bière
**beetle** NOUN
le **scarabée** _masc_
**beetroot** NOUN
la **betterave rouge** _fem_
**before** _preposition, conjunction_
**avant**
**before three o'clock**
avant trois heures
**Think before you answer, Noémie!**
Réfléchis avant de répondre, Noémie!
**begin** VERB
**commencer**
**It begins with 'b'.**
Ça commence par un 'b'.
**beginner** NOUN
le **débutant** _masc_
la **débutante** _fem_
**I'm a beginner.**
Je suis débutante.
**_Language tip_**
_In the example for_ **beginner** , _a girl is speaking. How can you tell?_
**beginning** NOUN
le **début** _masc_
**at the beginning**
au début
**behave** VERB
**se comporter**
**He behaves badly.**
Il se comporte mal.
**Behave!**
Sois sage!
**behind** PREPOSITION
**derrière**
**behind the television**
derrière la télévision
**one behind the other**
l'un derrière l'autre
**beige**
**beige** _can be an adjective or a noun._
**A** ADJECTIVE
**beige**
**a beige skirt**
une jupe beige
**_Language tip_**
_Colour adjectives come after the noun in French._
**B** NOUN
le **beige** _masc_
**Belgian**
**Belgian** _can be an adjective or a noun._
**A** ADJECTIVE
**belge**
**Belgian chocolate**
le chocolat belge
**Pauline is Belgian.**
Pauline est belge.
**_Language tip_**
**belge** _is not spelled with a capital letter except when it means a Belgian person._
**B** NOUN
le/la **Belge** _masc/fem_
**the Belgians**
les Belges
**Belgium** NOUN
la **Belgique** _fem_
**believe** VERB
**croire**
**I don't believe you.**
Je ne te crois pas.
**bell** NOUN
**1** la **sonnerie** _fem (at school)_
**There's the bell!**
C'est la sonnerie!
**2** la **clochette** _
fem (small bell)_
**My cat has a bell on its collar.**
Mon chat a une clochette à son collier.
**belong** VERB
**That belongs to me.**
C'est à moi.
**Does this belong to you?**
C'est à toi?
**Who does it belong to?**
C'est à qui?
**The ball belongs to Mathieu.**
Le ballon est à Mathieu.
**below** PREPOSITION
**au-dessous de**
**below ground**
au-dessous du sol
**ten degrees below freezing**
moins dix
**belt** NOUN
la **ceinture** _fem_
**bench** NOUN
le **banc** _masc_
**bend**
**bend** _can be a noun or a verb._
**A** NOUN
le **virage** _masc_
**a dangerous bend**
un virage dangereux
**B** VERB
**plier**
**Bend your leg!**
Pliez la jambe!
**beneath** PREPOSITION
**sous**
**beneath the table**
sous la table
**beret** NOUN
le **béret** _masc_
**a black beret**
un béret noir
**berth** NOUN
la **couchette** _fem_
**beside** PREPOSITION
**à côté de**
**Sit beside me.**
Assieds-toi à côté de moi.
**_Language tip_**
_To get the accents right in_ **à côté de** , _remember that they form a W: `^´._
**best**
**best** _can be an adjective, a noun or an adverb._
**A** ADJECTIVE
**meilleur** _masc_
**meilleure** _fem_
**Étienne is my best friend.**
Étienne est mon meilleur ami.
**Fleur and Roxanne are my best friends.**
Fleur et Roxanne sont mes meilleures amies.
**the best team in the world**
la meilleure équipe du monde
**B** NOUN
le **meilleur** _masc_
la **meilleure** _fem_
**He's the best in the class.**
C'est le meilleur de la classe.
**C** ADVERB
le **mieux** _masc_
**Emma sings best.**
C'est Emma qui chante le mieux.
**Best wishes!**
Meilleurs vœux!
**best man** NOUN
le **garçon d'honneur** _masc_
**better**
**better** _can be an adjective or an adverb._
**A** ADJECTIVE
**meilleur** _masc_
**meilleure** _fem_
**The ice cream is better than the cake.**
La glace est meilleure que le gâteau.
**B** ADVERB
**mieux**
**That's better!**
C'est mieux comme ça.
**Get better soon!**
Remets-toi vite!
**between** PREPOSITION
**entre**
**a number between one and twelve**
un nombre entre un et douze
**Bible** NOUN
la **Bible** _fem_
**bicycle** NOUN
le **vélo** _masc_
**by bicycle**
en vélo
**big** ADJECTIVE
**1** **grand** _masc_
**grande** _fem (garden, glass, plate, size)_
**a big garden**
un grand jardin
**a big house**
une grande maison
**my big brother**
mon grand frère
**her big sister**
sa grande sœur
**2** **gros** _masc_
**grosse** _fem (car, animal, book, parcel)_
**a big car**
une grosse voiture
**bike** NOUN
le **vélo** _masc_
**by bike**
en vélo
**bikini** NOUN
le **bikini** _masc_
**bill** NOUN
l' **addition** _fem_
**Can we have the bill, please?**
L'addition, s'il vous plaît.
**billion** NOUN
le **milliard** _masc_
**bin** NOUN
la **poubelle** _fem_
**Put your chewing gum in the bin.**
Mets ton chewing-gum à la poubelle.
**bingo** NOUN
le **loto** _masc_
**We're going to play bingo.**
On va jouer au loto.
**biology** NOUN
la **biologie** _fem_
**bird** NOUN
l' **oiseau** _masc_ (PL les **oiseaux** )
**My cat catches birds.**
Mon chat attrape des oiseaux.
**Biro** ® NOUN
le **bic** ® _masc_
**birthday** NOUN
l' **anniversaire** _masc_
**My birthday is the fifth of May.**
Mon anniversaire est le cinq mai.
**When's your birthday?**
Quelle est la date de ton anniversaire?
**Happy Birthday!**
Bon anniversaire!
**_Language tip_**
**anniversaire** _is related to_ **an** , _which is the French word for 'year', and to English words like 'annual' and 'anniversary'._
**birthday cake** NOUN
le **gâteau d'anniversaire** _masc_
**birthday card** NOUN
la **carte d'anniversaire** _fem_
**I got ten birthday cards.**
J'ai eu dix cartes d'anniversaire.
**birthday party** NOUN
la **fête d'anniversaire** _fem_
**Would you like to come to my birthday party?**
Tu veux venir à ma fête d'anniversaire?
**_Language tip_**
_In France, a children's party held in the afternoon is called_ **un goûter d'anniversaire**.
**biscuit** NOUN
le **biscuit** _masc_
**Would you like a biscuit?**
Tu veux un biscuit?
**bit** NOUN
**a bit**
un peu
**I'm a bit tired.**
Je suis un peu fatigué.
**Wait a bit!**
Attends un peu!
**bite** VERB
**mordre**
**My dog doesn't bite.**
Mon chien ne mord pas.
**black**
**black** _can be an adjective or a noun._
**A** ADJECTIVE
**noir** _masc_
**noire** _fem_
**She's black.**
Elle est noire.
**a black jacket**
une veste noire
**_Language tip_**
_Colour adjectives come after the noun in French._
**B** NOUN
le **noir** _masc_
**He is wearing black.**
Il est habillé en noir.
**blackberry** NOUN
la **mûre** _fem_
**We picked blackberries.**
Nous avons cueilli des mûres.
**blackboard** NOUN
le **tableau** _masc_ (PL les **tableaux** )
**Look at the blackboard!**
Regardez le tableau!
**black coffee** NOUN
le **café** _masc_
**blackcurrant** NOUN
le **cassis** _masc_
**blackcurrant jam**
la confiture de cassis
**blank**
**blank** _can be an adjective or a noun._
**A** ADJECTIVE
**blanc** _masc_ **blanche** _fem_
**a blank sheet of paper**
une feuille blanche
**B** NOUN
le **blanc** _masc_
**Fill in the blanks, everyone!**
Remplissez les blancs, tout le monde!
**blanket** NOUN
la **couverture** _fem_
**blazer** NOUN
le **blazer** _masc_
**a navy blazer**
un blazer bleu marine
**bless** VERB
**Bless you!**
À tes souhaits!
**blind**
**blind** _can be an adjective or a noun._
**A** ADJECTIVE
**aveugle**
**Are you blind?**
Tu es aveugle?
**B** NOUN
le **store** _masc_
**Open the blinds!**
Ouvrez les stores!
**blindfold** VERB
**I'm going to blindfold you.**
Je vais te bander les yeux.
**block** NOUN
**a block of flats**
un immeuble
**blog** NOUN
le **blog** _masc_
**blonde** ADJECTIVE
**blond** _masc_
**blonde** _fem_
**She's got blonde hair.**
Elle a les cheveux blonds.
**blood** NOUN
le **sang** _masc_
**blouse** NOUN
le **chemisier** _masc_
**a white blouse**
un chemisier blanc
**blow** VERB
**souffler**
**The wind is blowing.**
Le vent souffle.
**Stop when I blow the whistle!**
Arrêtez-vous quand je siffle!
**Blow your nose!**
Mouche-toi!
**Blow out the candles!**
Souffle sur les bougies!
**blue**
**blue** _can be an adjective or a noun._
**A** ADJECTIVE
**bleu** _masc_
**bleue** _fem_
**a blue dress**
une robe bleue
**_Language tip_**
_Colour adjectives come after the noun in French._
**B** NOUN
le **bleu** _masc_
**Blue is my favourite colour.**
Ma couleur préférée, c'est le bleu.
**board** NOUN
**1** le **tableau** _masc_
(PL les **tableaux** ) _(blackboard)_
**on the board**
au tableau
**Come to the board, Émilie.**
Viens au tableau, Émilie.
**2** le **jeu** _masc_ (PL les
**jeux** ) _
(for board games)_
**boarder** NOUN
l' **interne** _masc/fem_
**board game** NOUN
le **jeu de société** _masc_
**boarding school** NOUN
**I go to boarding school.**
Je suis interne dans une école privée.
**boat** NOUN
le **bateau** _masc_ (PL les
**bateaux** )
**body** NOUN
le **corps** _masc_
**boiled** ADJECTIVE
**à l'eau** _masc, fem, pl_
**boiled potatoes**
des pommes de terre à l'eau
**boiled egg** NOUN
l' **œuf à la coque** _masc_
**two boiled eggs**
deux œufs à la coque
**bomb** NOUN
la **bombe** _fem_
**bonfire** NOUN
le **feu** _masc_ (PL les **feux** )
**Bonfire Night** NOUN
**_Did you know...?_**
_In France, people do not celebrate_ **Bonfire Night** , _though they have fireworks displays on the fourteenth of July, Bastille Day._
**book**
**book** _can be a noun or a verb._
**A** NOUN
**1** le **livre** _masc (printed)_
**Open your books atpage 10.**
Ouvrez vos livres à la page 10.
**2** le **cahier** _masc (exercise book)_
**Write the words in your books.**
Écrivez les mots dans vos cahiers.
**B** VERB
**réserver**
**I want to book a seat.**
Je veux réserver une place.
**bookcase** NOUN
la **bibliothèque** _fem_
**booklet** NOUN
la **brochure** _fem_
**bookshelf** NOUN
l' **étagère à livres** _fem_
**on the bookshelves**
sur les étagères à livres
**bookshop** NOUN
la **librairie** _fem_
**_Language tip_**
**librairie** _is related to the English word 'library'. Both places contain books, but a_ **librairie** _sells them, and a 'library' lends them._
**boot** NOUN
**1** la **botte** _fem_
**I like your boots!**
J'aime bien tes bottes!
**football boots**
des chaussures de foot
**2** le **coffre** _masc (of car)_
**It's in the boot.**
C'est dans le coffre.
**border** NOUN
la **frontière** _fem_
**bored** ADJECTIVE
**I'm bored.**
Je m'ennuie.
**Are you bored?**
Tu t'ennuies?
**boring** ADJECTIVE
**ennuyeux** _masc_
**ennuyeuse** _fem_
**a boring programme**
une émission ennuyeuse
**born** ADJECTIVE
**I was born in 1996.**
Je suis né en 1996.
**She was born in 1998.**
Elle est née en 1998.
**borrow** VERB
**emprunter**
**Can I borrow your pen?**
Je peux emprunter ton stylo?
**boss** NOUN
le **patron** _masc_
la **patronne** _fem_
**bossy** ADJECTIVE
**autoritaire**
**both** PRONOUN
**tous les deux** _masc pl_
**toutes les deux** _fem pl_
**Louis and Daniel, you're both late!**
Louis et Daniel, vous êtes tous les deux en retard!
**Inès et Nadège have both got a rabbit.**
Inès et Nadège ont toutes les deux un lapin.
**bother** VERB
**déranger** _(disturb)_
**I'm sorry to bother you.**
Je suis désolé de vous déranger.
**no bother**
_aucun problème_
**Don't bother!**
_Ça n'est pas la peine!_
**bottle** NOUN
la **bouteille** _fem_
**bottom** NOUN
**1** le **bas** _masc (of page, list)_
**Look at the bottom of the page.**
Regardez le bas de la page.
**2** le **fond** _masc (of container, bag, sea)_
**My pen's in the bottom of my bag.**
Mon stylo est au fond de mon sac.
**bow** NOUN
**1** le **nœud** _masc (in ribbon)_
**Tie a bow!**
Fais un nœud!
**2** l' **arc** _masc (for archery)_
**a bow and arrows**
un arc et des flèches
**bowl** NOUN
le **bol** _masc_
**a bowl of soup**
un bol de soupe
**bowling** NOUN
le **bowling** _masc_
**Do you want to come bowling?**
Tu veux jouer au bowling?
**bowls** NOUN
les **boules** _fem pl_
**My grandfather plays bowls.**
Mon grand-père joue aux boules.
**_Did you know...?_**
**boules** _is played on rough ground, not smooth grass. The balls are smaller than those used in bowls, and are made of metal._
**box** NOUN
**1** la **boîte** _fem (container)_
**a box of matches**
une boîte d'allumettes
**a cardboard box**
un carton
**2** la **case** _fem (in questionnaire)_
**Tick the boxes.**
Cochez les cases.
**boxer** NOUN
le **boxeur** _masc_
**boxer shorts** PL NOUN
le **caleçon** _masc_
**_Language tip_**
**caleçon** _is a singular word._
**boxing** NOUN
la **boxe** _fem_
**I don't like boxing.**
Je n'aime pas la boxe.
**Boxing Day** NOUN
le **lendemain de Noël** _masc_
**on Boxing Day**
le lendemain de Noël
**_Language tip_**
_Word for word this means 'the day after Christmas'._
**boy** NOUN
le **garçon** _masc_
**Well done, boys!**
Bravo les garçons!
**boyfriend** NOUN
le **copain** _masc_
**Have you got a boyfriend?**
Tu as un copain?
**bra** NOUN
le **soutien-gorge** _masc_
**brace** NOUN
l' **appareil** _masc_
**She wears a brace.**
Elle a un appareil.
**bracelet** NOUN
le **bracelet** _masc_
**brain** NOUN
le **cerveau** _masc_ (PL les **cerveaux** )
**brainy** ADJECTIVE
**intelligent** _masc_
**intelligente** _fem_
**Sabine is very brainy.**
Sabine est très intelligente.
**branch** NOUN
la **branche** _fem_
**brand-new** ADJECTIVE
**tout neuf** _masc_
**toute neuve** _fem_
**I've got a brand-new computer.**
J'ai un ordinateur tout neuf.
**brass band** NOUN
la **fanfare** _fem_
**brave** ADJECTIVE
**courageux** _masc_
**courageuse** _fem_
**Be brave!**
Sois courageux!
**bread** NOUN
le **pain** _masc_
**Would you like some bread?**
Tu veux du pain?
**bread and butter**
les tartines de pain beurrées
**break**
**break** _can be a noun or a verb._
**A** NOUN
la **récréation** _fem_
**during morning break**
pendant la récréation du matin
**B** VERB
**casser**
**Michel has broken a window.**
Michel a cassé une fenêtre.
**Who broke the window?**
Qui a cassé la fenêtre?
**I have broken my leg.**
Je me suis cassé la jambe.
**Richard has broken his arm.**
Richard s'est cassé le bras.
**break down** VERB
**tomber en panne**
**Our car broke down.**
Notre voiture est tombée en panne.
**breakfast** NOUN
le **petit déjeuner** _masc_
**Breakfast is at eight o'clock.**
Le petit déjeuner est à huit heures.
**I have cereal for breakfast.**
Je prends des céréales au petit déjeuner.
**break time** NOUN
la **récréation** _fem_
**at break time**
à la récréation
**break up** VERB
**We break up next Wednesday.**
Nos vacances commencent mercredi.
**breaststroke** NOUN
la **brasse** _fem_
**I can do the breaststroke.**
Je sais faire la brasse.
**breath** NOUN
**Take a deep breath!**
Respirez à fond!
**brick** NOUN
la **brique** _fem_
**a brick wall**
un mur en brique
**bride** NOUN
la **mariée** _fem_
**bridegroom** NOUN
le **marié** _masc_
**bridesmaid** NOUN
la **demoiselle d'honneur** _fem_
**I'm going to be a bridesmaid.**
Je vais être demoiselle d'honneur.
**bridge** NOUN
le **pont** _masc_
**bright** ADJECTIVE
**vif** _masc_
**vive** _fem_
**a bright colour**
une couleur vive
**bright blue**
bleu vif
**a bright blue shirt**
une chemise bleu vif
**brilliant** ADJECTIVE
**génial** _masc_
**géniale** _fem_
**We're going to Paris. — Brilliant!**
On va à Paris. — Génial!
**bring** VERB
**apporter**
**Bring the money tomorrow.**
Apportez l'argent demain.
**Could you bring me a glass of water?**
Tu peux m'apporter un verre d'eau?
**bring back** VERB
**rapporter**
**Bring them back!**
Rapporte-les!
**Britain** NOUN
la **Grande-Bretagne** _fem_
**in Britain**
en Grande-Bretagne
**When are you coming to Britain?**
Quand est-ce que tu viens en Grande-Bretagne?
**British**
**British** _can be an adjective or a noun._
**A** ADJECTIVE
**britannique**
**I'm British.**
Je suis britannique.
**_Language tip_**
**britannique** _is not spelled with a capital letter except when it means a British person. Remember that it has two_ **n** _s._
**B** NOUN
**the British**
les Britanniques
**British Isles** PL NOUN
les **îles Britanniques** _fem pl_
**Brittany** NOUN
la **Bretagne** _fem_
**_Language tip_**
**Brittany** _has double_ **t** , **Bretagne** _has one_ **t**.
**broccoli** NOUN
les **brocolis** _masc pl_
**Would you like some broccoli?**
Tu veux des brocolis?
**_Language tip_**
_What are the two differences in spelling between the French word and the English word?_
**brochure** NOUN
la **brochure** _fem_
**broke** VERB _see_ **break**
**broken** ADJECTIVE
**cassé** _masc_
**cassée** _fem_
**It's broken.**
C'est cassé.
**a broken leg**
une jambe cassée
**He's got a broken arm.**
Il a le bras cassé.
**_Language tip_**
_If you want to say, for example, 'I have broken', look at the verb_ **to break**.
**bronze** NOUN
le **bronze** _masc_
**the bronze medal**
la médaille de bronze
**brother** NOUN
le **frère** _masc_
**my big brother**
mon grand frère
**I've got one brother.**
J'ai un frère.
**I haven't got a brother.**
Je n'ai pas de frère.
**Have you got any brothers or sisters?**
Tu as des frères et sœurs?
**brown**
**brown** _can be an adjective or a noun._
**A** ADJECTIVE
**1** **marron** _masc, fem, pl_
**I've got brown eyes.**
J'ai les yeux marron.
**My shoes are brown.**
Mes chaussures sont marron.
**2** **brun**
_masc_ **brune** _fem (hair)_
**I've got brown hair.**
J'ai les cheveux bruns.
**She's got light brown hair.**
Elle a les cheveux châtain.
**_Language tip_**
_Colour adjectives come after the noun in French._
**3** **bronzé** _masc_
**bronzée** _fem (tanned)_
**Nina is very brown.**
Nina est très bronzée.
**B** NOUN
le **marron** _masc_
**Do you have these shoes in brown?**
Vous avez ces chaussures en marron?
**brown bread** NOUN
le **pain complet** _masc_
**Brownie** NOUN
la **Jeannette** _fem_
**I'm a Brownie.**
Je suis Jeannette.
**I go to Brownies.**
Je vais au club des Jeannettes.
**_Did you know...?_**
_The brownies aren't as common in France as they are in Britain._
**bruise** NOUN
le **bleu** _masc_
**You've got a bruise.**
Tu as un bleu.
**_Language tip_**
**bleu** _is also the word for 'blue'. In English 'black and blue' means 'covered with bruises'._
**brush**
**brush** _can be a noun or a verb._
**A** NOUN
la **brosse** _fem_
**a brush and comb**
une brosse et un peigne
**B** VERB
**brosser**
**I brush my pony.**
Je brosse mon poney.
**I brush my hair.**
Je me brosse les cheveux.
**I brush my teeth every night.**
Je me brosse les dents tous les soirs.
**Brussels sprouts** PL NOUN
les **choux de Bruxelles** _masc pl_
**_Language tip_**
**Brussels** _has one_ **l** , **Bruxelles** _has two._
**bubble gum** NOUN
le **chewing-gum** _masc_
**bucket** NOUN
le **seau** _masc_ (PL les **seaux** )
**my bucket and spade**
mon seau et ma pelle
**budgie** NOUN
la **perruche** _fem_
**I've got a budgie.**
J'ai une perruche.
**buggy** NOUN
la **poussette** _fem_
**build** VERB
**construire**
**My dad is building a garage.**
Mon père construit un garage.
**building** NOUN
le **bâtiment** _masc_
**a tall building**
un grand bâtiment
**bull** NOUN
le **taureau** _masc_ (PL les **taureaux** )
**There's a bull in the field.**
Il y a un taureau dans le champ.
**bully** NOUN
**He's a big bully.**
Il joue les caïds.
**bum** NOUN
le **derrière** _masc_
**bum bag** NOUN
la **banane** _fem_
**bun** NOUN
le **petit pain au lait** _masc (roll)_
**I'd like a bun.**
Je voudrais un petit pain au lait.
**bunch** NOUN
**a bunch of flowers**
un bouquet de fleurs
**bunches** PL NOUN
les **couettes** _fem pl_
**She has bunches.**
Elle a des couettes.
**bungalow** NOUN
le **bungalow** _masc_
**bunk beds** PL NOUN
les **lits superposés** _masc pl_
**burger** NOUN
le **hamburger** _masc_
**a burger and chips**
un hamburger avec des frites
**bus** NOUN
le **bus** _masc_
**by bus**
en bus
**I go to school by bus.**
Je vais à l'école en bus.
**the school bus**
le car scolaire
**bus driver** NOUN
le **conducteur de bus** _masc_
**bus station** NOUN
la **gare routière** _fem_
**bus stop** NOUN
l' **arrêt de bus** _masc_
**business** NOUN
les **affaires** _fem pl_
**He's away on business.**
Il est en voyage d'affaires.
**a business trip**
un voyage d'affaires
**busy** ADJECTIVE
**occupé** _masc_
**occupée** _fem_
**My mother is always busy.**
Ma mère est toujours occupée.
**but** CONJUNCTION
**mais**
**Thanks, but I'm not hungry.**
Merci, mais je n'ai pas faim.
**butcher's** NOUN
la **boucherie** _fem_
**butter** NOUN
le **beurre** _masc_
**butterfly** NOUN
le **papillon** _
masc_
**button** NOUN
le **bouton** _masc_
**buy** VERB
**acheter**
**What are you going to buy?**
Qu'est-ce que tu vas acheter?
**I'm going to buy a present for Christophe.**
Je vais acheter un cadeau pour Christophe.
**by** PREPOSITION
**1** **par**
**a meal prepared by Pierre**
un repas préparé par Pierre
**2** **de** _(done by)_
**a painting by Picasso**
un tableau de Picasso
**a book by J.K. Rowling**
un livre de J.K. Rowling
**3** **à côté de** _(next to)_
**Where's the library? — It's by the post office.**
Où est la bibliothèque? — Elle est à côté de la poste.
**_Language tip_**
_To get the accents right in_ **à côté de** , _remember that they form a W: `^´._
**4** **en**
**We're going by car.**
On y va en voiture.
**by car**
en voiture
**by train**
en train
**by bus**
en bus
**bye** EXCLAMATION
**salut!**
# **C c**
**cab** NOUN
le **taxi** _masc_
**cabbage** NOUN
le **chou** _masc_ (PL les **choux** )
**cactus** NOUN
le **cactus** _masc_
**café** NOUN
le **café** _masc_
**_Did you know...?_**
_Cafés in France sell both alcoholic and non-alcoholic drinks._
**cafeteria** NOUN
la **cafétéria** _fem_
**cage** NOUN
la **cage** _fem_
**cagoule** NOUN
le **K-way** ® _masc_
**cake** NOUN
le **gâteau** _masc_
(PL les **gâteaux** )
**calculator** NOUN
la **calculatrice** _fem_
**calendar** NOUN
le **calendrier** _masc_
**calf** NOUN
le **veau** _masc_ (PL les **veaux** )
**call**
**call** _can be a verb or a noun._
**A** VERB
**appeler**
**Call this number.**
Appelez ce numéro.
**Call the police!**
Appelez la police!
**I am going to call the register.**
Je vais faire l'appel.
**_Language tip_**
_The_ **l** _of_ **appeler** _doubles when it is followed by_ **e** , **es** _and_ **ent**.
**Everyone calls him Matt.**
Tout le monde l'appelle Matt.
**My cat is called Fluffy.**
Mon chat s'appelle Fluffy.
**What's your cat called?**
Ton chat s'appelle comment?
**_Language tip_**
_The question word_ **comment** _can come at the beginning or end of a phrase._
**What's she called?**
Comment elle s'appelle?
**What are your brothers called?**
Tes frères s'appellent comment?
**What are you called?**
Comment tu t'appelles?/
Tu t'appelles comment?
**I'm called Helen.**
Je m'appelle Helen.
**B** NOUN
l' **appel** _masc_ **Thanks for your call.**
Merci de votre appel.
**Give me a call.**
Appelle-moi.
**call back** VERB
**rappeler**
**I'll call back at six o'clock.**
Je rappellerai à six heures.
**call centre** NOUN
le **centre d'appels** _masc_
**My sister works in a call centre in London.**
Ma sœur travaille dans un centre d'appels à Londres.
**calm** ADJECTIVE
**calme**
**calm down** VERB
**se calmer**
**Calm down, Hugo!**
Calme-toi, Hugo!
**Calm down, children!**
Calmez-vous, les enfants!
**calorie** NOUN
la **calorie** _fem_
**camcorder** NOUN
le **caméscope** _masc_
**came** VERB _see_ **come**
**camera** NOUN
**1** l' **appareil photo** _masc_
**I've got a new camera.**
J'ai un nouvel appareil photo.
**2** la **caméra** _fem (for filming, TV)_
**camera phone** NOUN
le **portable appareil photo** _masc_
**camp** NOUN
le **camp** _masc_ **a cub camp**
un camp de louveteaux
**camping** NOUN
le **camping** _masc_
**to go camping**
faire du camping
**We're going camping.**
Nous allons faire du camping.
**campsite** NOUN
le **terrain de camping** _masc_
**can**
**can** _can be a noun or a verb._
**A** NOUN
la **boîte** _fem_
**a can of coke**
une boîte de coca
**B** VERB
**1** **pouvoir** _(be able to)_
**I can't come.**
Je ne peux pas venir.
**Can I help you?**
Est-ce que je peux vous aider?
**_Language tip_**
**can** _is sometimes not translated into English._
**I can't see it.**
Je ne le vois pas.
**Can you speak French? — No, I can't.**
Parlez-vous français? — Non.
**I can.**
Je peux.
**I can't.**
Je ne peux pas.
**Can you?**
Tu peux?
**2** **savoir** _(know how to)_
**I can swim.**
Je sais nager.
**I can make pancakes.**
Je sais faire les crêpes.
**Canada** NOUN
le **Canada** _masc_
**Canada Day** NOUN _(Canada)_
la **Fête du Canada** _fem_
**canal** NOUN
le **canal** _masc_ (PL les **canaux** )
**cancel** VERB
**annuler**
**The match was cancelled.**
Le match a été annulé.
**cancer** NOUN
le **cancer** _masc_
**He's got cancer.**
Il a le cancer.
**candle** NOUN
la **bougie** _fem_
**candyfloss** NOUN
la **barbe à papa** _fem_
**canoe** NOUN
le **canoë** _masc_
**canoeing** NOUN
**to go canoeing**
faire du canoë
**We're going canoeing.**
Nous allons faire du canoë.
**can-opener** NOUN
l' **ouvre-boîte** _masc_
**a can-opener**
un ouvre-boîte
**can't** VERB _see_ **can**
**canteen** NOUN
la **cantine** _fem_
**I eat in the canteen.**
Je mange à la cantine.
**cap** NOUN
la **casquette** _fem_
**capital** NOUN
**1** la **capitale** _fem (city)_
**Cardiff is the capital of Wales.**
Cardiff est la capitale du pays de Galles.
**2** la **majuscule** _fem (letter)_
**Write your address in capitals.**
Écris ton adresse en majuscules.
**captain** NOUN
le **capitaine** _masc_
**She's captain of the hockey team.**
Elle est capitaine de l'équipe de hockey.
**caption** NOUN
la **légende** _fem_
**car** NOUN
la **voiture** _fem_
**We've got a new car.**
Nous avons une nouvelle voiture.
**by car**
en voiture
**We're going there by car.**
Nous y allons en voiture.
**caravan** NOUN
la **caravane** _fem_
**caravan site** NOUN
le **camping pour caravanes** _masc_
**car-boot sale** NOUN
la **brocante** _fem_
**car crash** NOUN
l' **accident de voiture** _masc_
**card** NOUN
**1** la **carte** _fem (playing card)_
**2** la **carte de vœux** _fem (for birthday, Christmas etc)_
**I got lots of cards.**
J'ai reçu beaucoup de cartes de vœux.
**_Did you know...?_**
_In France, people don't send as many cards as British people._
**cardboard** NOUN
le **carton** _masc_
**card game** NOUN
le **jeu de cartes** _masc_
**cardigan** NOUN
le **cardigan** _masc_
**a green cardigan**
un cardigan vert
**care**
**care** _can be a noun or a verb._
**A** NOUN
le **soin** _masc_
**with care**
avec soin
**B** VERB
**I don't care!**
Ça m'est égal!
**careful** ADJECTIVE
**Be careful, Gordon!**
Fais attention, Gordon!
**Be careful, children!**
Faites attention, les enfants!
**carefully** ADVERB
**Think carefully, Annick!**
Réfléchis bien, Annick!
**Listen carefully, children!**
Écoutez bien, les enfants!
**careless** ADJECTIVE
**a careless mistake**
une faute d'inattention
**caretaker** NOUN
le **gardien** _masc_
la **gardienne** _fem_
**My father's a caretaker.**
Mon père est gardien.
**_Language tip_**
_You do not translate_ **a** _when you say what someone's job is in French._
**car-ferry** NOUN
le **ferry** _masc_
**carol** NOUN
**a Christmas carol**
un chant de Noël
**car park** NOUN
le **parking** _masc_
**carpet** NOUN
la **moquette** _fem_
**My bedroom carpet is blue.**
La moquette de ma chambre est bleue.
**carriage** NOUN
la **voiture** _fem_
**carrier bag** NOUN
le **sac en plastique** _masc_
**carrot** NOUN
la **carotte** _fem_
**_Language tip_**
_The French word has only one_ **r** , _but two_ **t** _s_.
**carry** VERB
**porter**
**I'll carry your bag.**
Je vais porter ton sac.
**_Language tip_**
_The French word_ **porter** _is related to the English word 'portable', which describes something you can carry._
**carry on** VERB
**continuer**
**Carry on, Cécile!**
Continue, Cécile!
**carton** NOUN
la **brique** _fem_
**cartoon** NOUN
le **dessin animé** _masc_
**I watch cartoons on Saturdays.**
Je regarde les dessins animés le samedi.
**case** NOUN
la **valise** _fem_
**That's my case!**
C'est ma valise!
**casserole** NOUN
le **ragoût** _masc_
**I can make a casserole.**
Je sais faire le ragoût.
**cassette** NOUN
la **cassette** _fem_
**Listen to the cassette, children.**
Écoutez la cassette, les enfants.
**cassette player** NOUN
le **lecteur de cassettes** _masc_
**castle** NOUN
le **château** _masc_ (PL les **châteaux** )
**Dover Castle**
le château de Douvres
**_Language tip_**
_A few other British towns have French names. Can you recognize these:_ **Édimbourg** , **Cantorbéry** , **Londres**?
**casual** ADJECTIVE
**décontracté** _masc_
**décontractée** _fem_
**I prefer casual clothes.**
Je préfère les vêtements décontractés.
**cat** NOUN
le **chat** _masc_
la **chatte** _fem_
**Have you got a cat?**
Est-ce que tu as un chat?
**catch** VERB
**1** **attraper**
**Catch!**
Attrape!
**My cat catches birds.**
Mon chat attrape des oiseaux.
**2** **prendre** _(bus, train)_
**Which bus do you catch?**
Quel bus prends-tu?
**cathedral** NOUN
la **cathédrale** _fem_
**Catholic**
**Catholic** _can be an adjective or a noun._
**A** ADJECTIVE
**catholique**
**B** NOUN
le/la **catholique** _masc/fem_
**I'm a Catholic.**
Je suis catholique.
**_Language tip_**
**catholique** _is not spelled with a capital letter._
**cauliflower** NOUN
le **chou-fleur** _masc_
**two cauliflowers**
deux choux-fleurs
**cave** NOUN
la **grotte** _fem_
**CD** NOUN
le **CD** _masc_ (PL les **CD** )
**CD player** NOUN
la **platine laser** _fem_
**CD-ROM** NOUN
le **CD-ROM** _masc_
**ceiling** NOUN
le **plafond** _masc_
**celebrate** VERB
**fêter**
**Let's celebrate!**
Il faut fêter ça!
**celery** NOUN
le **céleri** _masc_
**I don't like celery.**
Je n'aime pas le céleri.
**cellar** NOUN
la **cave** _fem_
**a wine cellar**
une cave à vins
**_Language tip_**
**une cave** _is dark and underground, like an English_ **cave** , _but often contains bottles of wine._
**cello** NOUN
le **violoncelle** _masc_
**I play the cello.**
Je joue du violoncelle.
**cemetery** NOUN
le **cimetière** _masc_
**cent** NOUN
le **centime** _masc_
**two euros and twenty cents**
deux euros vingt centimes
**centigrade** ADJECTIVE
**centigrade**
**twenty degrees centigrade**
vingt degrés centigrade
**centimetre** NOUN
le **centimètre** _masc_
**central heating** NOUN
le **chauffage central** _masc_
**centre** NOUN
le **centre** _masc_
**in the centre**
au centre
**a sports centre**
un centre sportif
**The office is in the centre of town.**
Le bureau est en centre-ville.
**century** NOUN
le **siècle** _masc_
**the twenty-first century**
le vingt et unième siècle
**cereal** NOUN
les **céréales** _fem pl_
**I have cereal for breakfast.**
Je prends des céréales au petit déjeuner.
**certain** ADJECTIVE
**certain** _masc_
**certaine** _fem_
**a certain person**
une certaine personne
**I'm not certain.**
Je n'en suis pas certain.
**certainly** ADVERB
**Certainly not!**
Certainement pas!
**certificate** NOUN
le **certificat** _masc_
**chain** NOUN
la **chaîne** _fem_
**chair** NOUN
**1** la **chaise** _fem_
**There's a table and four chairs in the kitchen.**
Il y a une table et quatre chaises dans la cuisine.
**2** le **fauteuil** _masc (armchair)_
**There are two chairs and a sofa in the lounge.**
Il y a deux fauteuils et un canapé dans le salon.
**chalk** NOUN
la **craie** _fem_
**a stick of chalk**
une craie
**champagne** NOUN
le **champagne** _masc_
**a glass of champagne**
un verre de champagne
**champion** NOUN
le **champion** _masc_
la **championne** _fem_
**Anaïs is the champion!**
Anaïs est la championne!
**_Language tip_**
_Anaïs is a girl's name. How can you tell from this example?_
**championship** NOUN
le **championnat** _masc_
**chance** NOUN
**No chance!**
Pas question!
**You're taking a chance!**
Tu prends un risque!
**change**
**change** _can be a verb or a noun._
**A** VERB
**1** **changer**
**I'd like to change £50.**
Je voudrais changer cinquante livres.
**2** **changer de**
**_Language tip_**
_Use_ **changer de** _when you change one thing for another._
**Change places!**
Changez de place!
**I want to change my cards.**
Je veux changer de cartes.
**I've changed my mind.**
J'ai changé d'avis.
**B** NOUN
la **monnaie** _fem (money)_
**I haven't got any change.**
Je n'ai pas de monnaie.
**Keep the change!**
Gardez la monnaie!
**changeable** ADJECTIVE
**variable**
**The weather is changeable.**
Le temps est variable.
**changing room** NOUN
le **vestiaire** _masc_
**Channel** NOUN
la **Manche** _fem_
**_Language tip_**
**manche** _means 'sleeve' in French. Do you think the Channel is sleeve-shaped?_
**channel** NOUN
la **chaîne** _fem_
**There's football on the other channel.**
Il y a du football sur l'autre chaîne.
**Channel Islands** PL NOUN
les **îles Anglo-Normandes** _fem pl_
**Channel Tunnel** NOUN
le **tunnel sous la Manche** _masc_
**chapter** NOUN
le **chapitre** _masc_
**character** NOUN
le **personnage** _masc_
**Harry is the main character.**
Harry est le personnage principal.
**charge** NOUN
**an extra charge**
un supplément
**There's no charge.**
C'est gratuit.
**to be in charge**
être responsable
**Who is in charge?**
Qui est responsable?
**charity** NOUN
l' **association caritative** _fem_
**We give the money to charity.**
Nous donnons l'argent à une association caritative.
**chart** NOUN
le **tableau** _masc_ (PL les **tableaux** )
**We're making a chart.**
Nous faisons un tableau.
**charter flight** NOUN
le **charter** _masc_
**chase** VERB
**pourchasser**
**My dog chases cats.**
Mon chien pourchasse les chats.
**chat** VERB
**bavarder**
**Pauline chats a lot.**
Pauline bavarde beaucoup.
**cheap** ADJECTIVE
**bon marché** _masc, fem, pl_
**cheap T-shirts**
des T-shirts bon marché
**cheaper** ADJECTIVE
**moins cher** _masc_
**moins chère** _fem_
**It's cheaper by bus.**
C'est moins cher en bus.
**cheat**
**cheat** _can be a verb or a noun._
**A** VERB
**tricher**
**You're cheating!**
Tu triches!
**Don't cheat, children!**
Ne trichez pas, les enfants!
**B** NOUN
le **tricheur** _masc_
la **tricheuse** _fem_
**Isabelle, you're a cheat!**
Isabelle, tu es une tricheuse!
**check** VERB
**vérifier**
**Check the spelling.**
Vérifiez l'orthographe.
**check in** VERB
**se présenter à**
**l'enregistrement** _(at airport)_
**What time do I have to check in?**
À quelle heure je dois me présenter à l'enregistrement?
**checked** ADJECTIVE
**à carreaux** _masc, fem, pl_
**a checked shirt**
une chemise à carreaux
**checkout** NOUN
la **caisse** _fem_
**at the checkout**
à la caisse
**cheek** NOUN
la **joue** _fem_
**Yvette has got red cheeks.**
Yvette a les joues rouges.
**cheeky** ADJECTIVE
**effronté** _masc_
**effrontée** _fem_
**Don't be cheeky, Hugo!**
Ne sois pas effronté, Hugo!
**cheer**
**cheer** _can be a noun or a verb._
**A** NOUN
**Cheers!**
À la vôtre!
**B** VERB
**applaudir**
**Cheer your team!**
Applaudissez votre équipe!
**cheerful** ADJECTIVE
**gai** _masc_
**gaie** _fem_
**cheerio** EXCLAMATION
**salut!**
**cheese** NOUN
le **fromage** _masc_
**a cheese sandwich**
un sandwich au fromage
**chef** NOUN
le **chef** _masc_
**chemist** NOUN
la **pharmacie** _fem_
**You get it from the chemist.**
Ça s'achète en pharmacie.
**_Did you know...?_**
_Chemists in France have a big green cross on a sign outside the shop._
**chemistry** NOUN
la **chimie** _fem_
**the chemistry lab**
le laboratoire de chimie
**cherry** NOUN
la **cerise** _fem_
**I love cherries.**
J'adore les cerises.
**chess** NOUN
les **échecs** _masc pl_
**I can play chess.**
Je sais jouer aux échecs.
**chest** NOUN
la **poitrine** _fem_
**chest of drawers** NOUN
la **commode** _fem_
**chewing gum** NOUN
le **chewing-gum** _masc_
**Put your chewing gum in the bin!**
Mets ton chewing-gum à la poubelle!
**chick** NOUN
le **poussin** _masc_
**a hen and her chicks**
une poule et ses poussins
**chicken** NOUN
le **poulet** _masc_
**Chicken and chips, please.**
Un poulet frites, s'il vous plaît.
**chickenpox** NOUN
la **varicelle** _fem_
**Thibault has got chickenpox.**
Thibault a la varicelle.
**child** NOUN
l' **enfant** _masc/fem_
**a child**
un enfant
**all the children**
tous les enfants
**child minder** NOUN
la **nourrice** _fem_
**children** PL NOUN
les **enfants** _masc pl_
**Goodbye children!**
Au revoir, les enfants!
**chilly** ADJECTIVE
**froid** _masc_
**froide** _fem_
**It's chilly today.**
Il fait froid aujourd'hui.
**China** NOUN
la **Chine** _fem_
**Chinese**
**Chinese** _can be an adjective or a noun._
**A** ADJECTIVE
**chinois** _masc_
**chinoise** _fem_
**a Chinese restaurant**
un restaurant chinois
**a Chinese man**
un Chinois
**a Chinese woman**
une Chinoise
**Chinese people**
les Chinois
**_Language tip_**
**chinois** _is not spelled with a capital letter except when it means a Chinese person._
**B** NOUN
**the Chinese**
les Chinois
**chinook wind** NOUN _(Canada)_
le **chinook** _masc_
**chip** NOUN
la **frite** _fem_
**I'd like some chips.**
Je voudrais des frites.
**chocolate** NOUN
le **chocolat** _masc_
**I love chocolate.**
J'adore le chocolat.
**_Language tip_**
_Use_ **au chocolat** _when something is chocolate-flavoured._
**a chocolate cake**
un gâteau au chocolat
**a chocolate ice cream**
une glace au chocolat
**choice** NOUN
le **choix** _masc_
**There's lots of choice.**
Il y a beaucoup de choix.
**choir** NOUN
la **chorale** _fem_
**I sing in the school choir.**
Je chante dans la chorale de l'école.
**choose** VERB
**choisir**
**It's difficult to choose.**
C'est difficile de choisir.
**Choose the right answer.**
Choisissez la bonne réponse.
**chop** NOUN
la **côte** _fem_
**a pork chop**
une côte de porc
**chopsticks** PL NOUN
les **baguettes** _fem pl_
**christening** NOUN
le **baptême** _masc_
**Christian name** NOUN
le **prénom** _masc_
**Christmas** NOUN
**Noël** _masc_
**at Christmas**
à Noël
**Happy Christmas!**
Joyeux Noël!
**Christmas cake** NOUN
le **gâteau de Noël** _masc_
**_Did you know...?_**
_In France, people often eat Christmas log_ ( **la bûche de Noël** ) _instead of Christmas cake._
**Christmas card** NOUN
la **carte de Noël** _fem_
**_Did you know...?_**
_Christmas cards are not as common in France as they are in Britain. Instead, people sometimes send New Year cards in January._
**Christmas Day** NOUN
le **jour de Noël** _masc_
**Christmas Day is the twenty-fifth of December.**
Le jour de Noël est le vingt-cinq décembre.
**Christmas dinner** NOUN
le **repas de Noël** _masc_
**_Did you know...?_**
_In France, most people also have a Christmas meal_ ( **réveillon de Noël** ) _on Christmas Eve._
**Christmas Eve** NOUN
la **veille de Noël** _fem_
**Christmas Eve is the twenty-fourth of December.**
La veille de Noël est le vingt-quatre décembre.
**Christmas tree** NOUN
le **sapin de Noël** _masc_
**a big Christmas tree**
un grand sapin de Noël
**church** NOUN
l' **église** _fem_
**I don't go to church every Sunday.**
Je ne vais pas à l'église tous les dimanches.
**cider** NOUN
le **cidre** _masc_
**cigarette** NOUN
la **cigarette** _fem_
**cinema** NOUN
le **cinéma** _masc_
**I'm going to the cinema this evening.**
Je vais au cinéma ce soir.
**circle** NOUN
le **cercle** _masc_
**Stand in a cicle.**
Mettez-vous en cercle.
**circumflex** NOUN
l' **accent circonflexe** _masc_
**'Tête' has a circumflex.**
'Tête' a un accent circonflexe.
**circus** NOUN
le **cirque** _masc_
**citizenship** NOUN
la **citoyenneté** _fem_
**city** NOUN
la **grande ville** _fem_
**I live in a city.**
J'habite dans une grande ville.
**the city centre**
le centre-ville
**It's in the city centre.**
C'est au centre-ville.
**clap**
**clap** _can be a verb or a noun._
**A** VERB
**frapper dans ses mains**
**Sing and clap!**
Chantez et frappez dans vos mains!
**B** NOUN
**Give Delphine a clap.**
Applaudissez Delphine!
**clarinet** NOUN
la **clarinette** _fem_
**I play the clarinet.**
Je joue de la clarinette.
**class** NOUN
**1** la **classe** _fem (group)_
**Hermione is in my class.**
Hermione est dans ma classe.
**2** le **cours** _masc (lesson)_
**I go to dancing classes.**
Je vais à des cours de danse.
**classroom** NOUN
la **classe** _fem_
**classroom assistant** NOUN
l' **aide-éducateur** _masc_
l' **aide-éducatrice** _fem_
**clean**
**clean** _can be an adjective or a verb._
**A** ADJECTIVE
**propre**
**a clean shirt**
une chemise propre
**B** VERB
**nettoyer**
**Clean the board please!**
Nettoie le tableau s'il te plaît!
**cleaner** NOUN
**1** la **femme de ménage** _fem (woman)_
**2** l' **agent d'entretien** _masc (man)_
**clear** ADJECTIVE
**clair** _masc_
**claire** _fem_
**a clear explanation**
une explication claire
**clementine** NOUN
la **clémentine** _fem_
**clever** ADJECTIVE
**intelligent** _masc_
**intelligente** _fem_
**Sylvie is very clever.**
Sylvie est très intelligente.
**click** VERB
**cliquer**
**Click on the icon!**
Clique sur l'icône!
**climate** NOUN
le **climat** _masc_
**We have a terrible climate.**
Nous avons un climat terrible.
**cloakroom** NOUN
**1** le **vestiaire** _masc (for coats)_
**2** les **toilettes** _fem pl (toilet)_
**clock** NOUN
**1** l' **horloge** _fem (big)_
**the station clock**
l'horloge de la gare
**2** la **pendule** _fem (smaller)_
**Look at the clock.**
Regardez la pendule.
**close**
**close** _can be a verb, an adjective or an adverb._
**A** VERB
**fermer**
**Please close the door.**
Ferme la porte, s'il te plaît.
**Close your books, children.**
Fermez vos livres, les enfants.
**What time does the pool close?**
La piscine ferme à quelle heure?
**B** ADJECTIVE
**proche** _(near)_
**My house is close to the school.**
Ma maison est proche de l'école.
**C** ADVERB
**Come closer, Pierre.**
Rapproche-toi, Pierre.
**_Language tip_**
_The verb, adjective, and adverb_ **close** _have the same spelling, but one of them is pronounced 'cloze'. Which one?_
**closed** ADJECTIVE
**fermé** _masc_
**fermée** _fem_
**The door's closed.**
La porte est fermée.
**clothes** PL NOUN
les **vêtements** _masc pl_
**I'd like some new clothes.**
Je voudrais de nouveaux vêtements.
**cloud** NOUN
le **nuage** _masc_
**There are black clouds.**
Il y a des nuages noirs.
**cloudy** ADJECTIVE
**It's cloudy today.**
Il fait gris aujourd'hui.
**_Language tip_**
**gris** _means 'grey'. It is rather grey when it's cloudy._
**clown** NOUN
le **clown** _
masc_
**club** NOUN
**1** le **club** _masc_
**a football club**
un club de football
**2** _(in cards)_
**clubs**
le trèfle
**the ace of clubs**
l'as de trèfle
**coach** NOUN
le **car** _masc_
**by coach**
en car
**We're going by coach.**
Nous y allons en car.
**_Language tip_**
_Be careful! The French word_ **car** _doesn't mean the same as the English word_ **car**.
**coach station** NOUN
la **gare routière** _fem_
**coal** NOUN
le **charbon** _masc_
**coast** NOUN
la **côte** _fem_
**It's on the west coast of Scotland.**
C'est sur la côte ouest de l'Écosse.
**coat** NOUN
le **manteau** _masc_
(PL les **manteaux** )
**I'm wearing a warm coat.**
Je porte un manteau chaud.
**cocoa** NOUN
le **cacao** _masc_
**coconut** NOUN
la **noix de coco** _fem_
**coffee** NOUN
le **café** _masc_
**I like coffee.**
J'aime le café.
**A cup of coffee, please.**
Un café, s'il vous plaît.
**coffee table** NOUN
la **table basse** _fem_
**coin** NOUN
la **pièce de monnaie** _fem_
**a two euro coin**
une pièce de deux euros
**Coke** ® NOUN
le **coca** _masc_
**a can of Coke** ®
une boîte de coca
**cold**
**cold** _can be an adjective or a noun._
**A** ADJECTIVE
**froid** _masc_
**froide** _fem_
**The water's cold.**
L'eau est froide.
**It's cold today.**
Il fait froid aujourd'hui.
**I'm cold.**
J'ai froid.
**I'm not cold.**
Je n'ai pas froid.
**Are you cold?**
Tu as froid?
**B** NOUN
le **rhume** _masc (illness)_
**I've got a cold.**
J'ai un rhume.
**Ron's got a cold.**
Ron a un rhume.
**coleslaw** NOUN
la **salade de chou cru à la mayonnaise** _fem_
**collar** NOUN
le **col** _masc_
**a white collar**
un col blanc
**collect** VERB
**1** **ramasser** _(pick up)_
**Collect the books please, Natasha.**
Ramasse les livres s'il te plaît, Natasha.
**2** **faire collection de** _(as hobby)_
**I collect stamps.**
Je fais collection de timbres.
**collection** NOUN
la **collection** _fem_
**college** NOUN
le **lycée** _masc_
**a technical college**
un lycée technique
**colour**
**colour** _can be a noun or a verb._
**A** NOUN
la **couleur** _fem_
**What colour eyes has he got?**
Il a les yeux de quelle couleur?
**What colour is it?**
C'est de quelle couleur?
**B** VERB
**colorier**
**Colour it blue, children.**
Coloriez en bleu, les enfants.
**comb** NOUN
le **peigne** _masc_
**come** VERB
**1** **venir**
**Come with me, Jean.**
Viens avec moi, Jean.
**Can I come too?**
Est-ce que je peux venir aussi?
**I'll come with you.**
Je viens avec toi.
**2** **arriver** _(arrive)_
**The bus is coming.**
Le bus arrive.
**The letter came this morning.**
La lettre est arrivée ce matin.
**I'm coming!**
J'arrive!
**Come on!**
Allez!
**come back** VERB
**revenir**
**Come back, Louise!**
Reviens, Louise!
**come from** VERB
**venir de**
**Where do you come from?**
Tu viens d'où?
**come in** VERB
**entrer**
**Can I come in?**
Je peux entrer?
**Come in!**
Entrez!
**comfortable** ADJECTIVE
**1** **à l'aise** _(person)_
**Are you comfortable?**
Tu es à l'aise?
**2** **confortable** _(bed, chair)_
**a comfortable bed**
un lit confortable
**comic** NOUN
l' **illustré** _masc_
**a comic**
un illustré
**comma** NOUN
la **virgule** _fem_
**common** ADJECTIVE
**courant** _masc_
**courante** _fem_
**'Smith' is a very common surname.**
'Smith' est un nom de famille très courant.
**communion** NOUN
la **communion** _fem_
**my First Communion**
ma première communion
**compared** ADJECTIVE
**Oxford is small compared with London.**
Oxford est une petite ville en comparaison de Londres.
**competition** NOUN
le **concours** _
masc_
**competitor** NOUN
le **concurrent** _masc_
la **concurrente** _fem_
**complete**
**complete** _can be an adjective or a verb._
**A** ADJECTIVE
**complet** _masc_
**complète** _fem_
**B** VERB
**finir**
**You must complete your homework by Friday.**
Il faut finir vos devoirs pour vendredi.
**completely** ADVERB
**complètement**
**complicated** ADJECTIVE
**compliqué** _masc_
**compliquée** _fem_
**comprehension** NOUN
l' **exercice de compréhension** _masc (exercise)_
**comprehensive school** NOUN
**1** le **collège** _masc (for pupils 11–15)_
**2** le **lycée** _masc (for pupils 15–18)_
**_Did you know...?_**
_In France, pupils go to a_ **collège** _between the ages of 11 and 15, and then to a_ **lycée** _until the age of 18._
**computer** NOUN
l' **ordinateur** _masc_
**computer game** NOUN
le **jeu électronique** _masc_
**I like computer games.**
J'aime les jeux électroniques.
**computer room** NOUN
la **salle d'informatique** _fem_
**concert** NOUN
le **concert** _masc_
**cone** NOUN
le **cornet** _masc_
**an ice-cream cone**
un cornet de glace
**congratulations** PL NOUN
les **félicitations** _fem pl_
**Congratulations!**
Félicitations!
**conjurer** NOUN
le **prestidigitateur** _masc_
**conservatory** NOUN
le **jardin d'hiver** _masc_
**constant** ADJECTIVE
**constant** _masc_
**constante** _fem_
**contact lenses** PL NOUN
les **verres de contact** _masc pl_
**container** NOUN
le **récipient** _masc_
**a plastic container**
un récipient en plastique
**contest** NOUN
le **concours** _masc_
**contestant** NOUN
le **concurrent** _masc_
la **concurrente** _fem_
**continent** NOUN
le **continent** _masc_
**How many continents are there?**
Il y a combien de continents?
**the Continent**
l'Europe
**on the Continent**
en Europe
**continental breakfast** NOUN
le **petit déjeuner à la française** _masc_
**continue** VERB
**continuer**
**Continue with your work, children!**
Continuez à travailler, les enfants!
**convent school** NOUN
le **couvent** _masc_
**She goes to a convent school.**
Elle va au couvent.
**conversation** NOUN
la **conversation** _fem_
**cook**
**cook** _can be a verb or a noun._
**A** VERB
**1** **cuisiner**
**I can cook.**
Je sais cuisiner.
**I can't cook.**
Je ne sais pas cuisiner.
**2** **faire cuire** _(potatoes, rice etc)_
**Cook the pasta for ten minutes.**
Faites cuire les pâtes pendant dix minutes.
**B** NOUN
le **cuisinier** _masc_
la **cuisinière** _fem_
**Matthew's an excellent cook.**
Matthew est un excellent cuisinier.
**cookbook** NOUN
le **livre de cuisine** _masc_
**cooked** ADJECTIVE
**cuit** _masc_
**cuite** _fem_
**I don't like cooked tomatoes.**
Je n'aime pas les tomates cuites.
**cooker** NOUN
la **cuisinière** _fem_
**a gas cooker**
une cuisinière à gaz
**cooking** NOUN
la **cuisine** _fem_
**I like cooking.**
J'aime bien cuisiner.
**cool** ADJECTIVE
**1** **frais** _masc_
**fraîche** _fem (quite cold)_
**a cool place**
un endroit frais
**2** **super** _(great)_
**copy**
**copy** _can be a noun or a verb._
**A** NOUN
la **copie** _fem_
**Make a copy.**
Faites une copie.
**B** VERB
**copier**
**Copy the words off the board.**
Copiez les mots au tableau.
**cork** NOUN
le **bouchon** _masc_
**corkscrew** NOUN
le **tire-bouchon** _masc_
**corner** NOUN
le **coin** _masc_
**in a corner of the room**
dans un coin de la pièce
**cornflakes** PL NOUN
les **corn-flakes** _masc pl_
**Cornwall** NOUN
la **Cornouailles** _fem_
**correct**
**correct** _can be an adjective or a verb._
**A** ADJECTIVE
**exact** _masc_ **exacte** _fem_
**That's correct.**
C'est exact.
**the correct answer**
la bonne réponse
**B** VERB
**corriger**
**Correct the spelling.**
Corrigez l'orthographe.
**correction** NOUN
la **correction** _fem_
**correctly** ADVERB
**correctement**
**corridor** NOUN
le **couloir** _masc_
**in the corridor**
dans le couloir
**Corsica** NOUN
la **Corse** _fem_
**cost** VERB
**coûter**
**A coke costs two euros.**
Un coca coûte deux euros.
**How much does it cost?**
Ça coûte combien?
**costume** NOUN
le **costume**
_masc_
**cottage** NOUN
le **cottage** _masc_
**cotton** NOUN
le **coton** _masc_
**a cotton shirt**
une chemise en coton
**_Language tip_**
_The French word only has one_ **t**.
**couch** NOUN
le **canapé** _masc_
**cough**
**cough** _can be a noun or a verb._
**A** NOUN
la **toux** _fem_
**a bad cough**
une mauvaise toux
**I've got a cough.**
Je tousse.
**B** VERB
**tousser**
**I can't stop coughing.**
Je n'arrête pas de tousser.
**could** VERB
**Could I have a glass of water?**
Je peux avoir un verre d'eau?
**Could you move a bit?**
Tu peux te pousser un peu?
**Could you move a bit, boys?**
Vous pouvez vous pousser un peu, les garçons?
**Could I...?**
Je peux...?
**Could you...?**
Tu peux...?
**count** VERB
**compter**
**Count from one to twenty!**
Comptez de un à vingt!
**counter** NOUN
**1** le **comptoir** _masc (in shop)_
**2** le **jeton** _masc (in game)_
**country** NOUN
**1** le **pays** _masc (France, Britain etc)_
**France is a big country.**
La France est un grand pays.
**2** la **campagne** _fem (countryside)_
**I live in the country.**
J'habite à la campagne.
**country dancing** NOUN
la **danse folklorique** _fem_
**countryside** NOUN
la **campagne** _fem_
**in the countryside**
à la campagne
**couple** NOUN
**a couple of days**
deux jours
**a couple of hours**
deux heures
**a young couple**
un jeune couple
**courgette** NOUN
la **courgette** _fem_
**course** NOUN
**1** le **plat** _masc (of meal)_
**the main course**
le plat principal
**the first course**
l'entrée
**2** le **cours** _masc (lessons)_
**a French course**
un cours de français
**Do you love me? — Of course I do!**
Tu m'aimes? — Bien sûr que oui!
**of course**
bien sûr
**court** NOUN
le **court** _masc_
**There are tennis courts.**
Il y a des courts de tennis.
**cousin** NOUN
le **cousin** _masc_
la **cousine** _fem_
**Jo is my favourite cousin.**
Jo est ma cousine préférée.
**_Language tip_**
_Is Jo a boy or a girl? What are the three clues in the French sentence?_
**cover** NOUN
la **couverture** _fem_
**cow** NOUN
la **vache** _fem_
**a big black cow**
une grosse vache noire
**crab** NOUN
le **crabe** _masc_
**cracker** NOUN
**1** le **cracker** _masc (biscuit)_
**2** la **papillote** _fem (Christmas cracker)_
**_Did you know...?_**
**papillotes** _are different from crackers in Britain. They consist of a sweet with a joke and a banger wrapped round it, covered in foil. You unwrap them and pull the banger._
**crash** NOUN
l' **accident** _masc_
**a crash**
un accident
**crawl** NOUN
le **crawl** _masc_
**I can do the crawl.**
Je sais nager le crawl.
**crazy** ADJECTIVE
**fou** _masc_
**folle** _fem_
**cream**
**cream** _can be a noun or an adjective._
**A** NOUN
la **crème** _fem_
**strawberries and cream**
les fraises à la crème
**B** ADJECTIVE
**crème** _masc, fem, pl (colour)_
**a cream shirt**
une chemise crème
**_Language tip_**
_Colour adjectives come after the noun in French._
**cream cake** NOUN
le **gâteau à la crème** _masc_
**two cream cakes**
deux gâteaux à la crème
**credit card** NOUN
la **carte de crédit** _fem_
**cress** NOUN
le **cresson** _masc_
**I'm growing cress.**
Je fais pousser du cresson.
**crew cut** NOUN
les **cheveux en brosse** _
masc pl_
**He's got a crew cut.**
Il a les cheveux en brosse.
**cricket** NOUN
le **cricket** _masc_
**I play cricket.**
Je joue au cricket.
**_Did you know...?_**
**Cricket** _is not played in France._
**cricket bat** NOUN
la **batte de cricket** _fem_
**crisps** PL NOUN
les **chips** _fem pl_
**a bag of crisps**
un paquet de chips
**cross**
**cross** _can be a verb, a noun or an adjective._
**A** VERB
**traverser**
**Cross the road at the lights.**
Traversez la rue aux feux.
**B** NOUN
la **croix** _fem_
**Put a tick or a cross.**
Cochez ou mettez une croix.
**C** ADJECTIVE
**pas content** _masc_
**pas contente** _fem_
**She is cross.**
Elle n'est pas contente.
**crossing** NOUN
la **traversée** _fem_
**the crossing from Dover to Calais**
la traversée de Douvres à Calais
**crossroads** NOUN
le **carrefour** _masc_
**at the crossroads**
au carrefour
**crossword** NOUN
les **mots croisés** _masc pl_
**I like doing crosswords.**
J'aime faire les mots croisés.
**crowd** NOUN
la **foule** _fem_
**crowded** ADJECTIVE
**bondé** _masc_
**bondée** _fem_
**The pool is crowded on Saturdays.**
La piscine est bondée le samedi.
**crown** NOUN
la **couronne** _fem_
**crutch** NOUN
la **béquille** _fem_
**cry** VERB
**pleurer**
**Why are you crying?**
Pourquoi tu pleures?
**cub** NOUN
**1** le **louveteau** _masc_ (PL les **louveteaux** ) _(scout)_
**_Did you know...?_**
_Cubs and scouts are not as common in France as they are in Britain._
**2** le **petit** _masc (young animal)_
**cube** NOUN
le **cube** _masc_
**cucumber** NOUN
le **concombre** _masc_
**cup** NOUN
la **tasse** _fem_
**a cup of tea**
une tasse de thé
**a cup of coffee**
un café
**cupboard** NOUN
le **placard** _masc_
**What's in the cupboard?**
Qu'est-ce qu'il y a dans le placard?
**curious** ADJECTIVE
**curieux** _masc_
**curieuse** _fem_
**curly** ADJECTIVE
**1** **bouclé** _masc_
**bouclée** _fem (wavy)_
**2** **frisé** _masc_
**frisée** _fem (tightly curled)_
**currant** NOUN
le **raisin sec** _masc_
**I don't like currants.**
Je n'aime pas les raisins secs.
**_Language tip_**
**raisin sec** _means 'dried grape', which is what a currant is._
**curriculum** NOUN
le **programme** _masc_
**curry** NOUN
le **curry** _masc_
**curtain** NOUN
le **rideau** _masc_ (PL les **rideaux** )
**The curtains are green and white.**
Les rideaux sont verts et blancs.
**Draw the curtains, please.**
Tirez les rideaux, s'il vous plaît.
**cushion** NOUN
le **coussin** _masc_
**custard** NOUN
la **crème anglaise** _fem_
**custom** NOUN
la **coutume** _fem_
**It's an old custom.**
C'est une ancienne coutume.
**customer** NOUN
le **client** _masc_
la **cliente** _fem_
**cut** VERB
**couper**
**I'll cut the cake.**
Je vais couper le gâteau.
**Mind you don't cut yourself!**
Attention à ne pas te couper!
**cutlery** NOUN
les **couverts** _masc pl_
**cycle** VERB
**faire du vélo**
**I like cycling.**
J'aime faire du vélo.
**I cycle to school.**
Je vais à l'école à vélo.
**cycle lane** NOUN
la **piste cyclable** _fem_
**cycling** NOUN
le **cyclisme** _masc_
**cyclist** NOUN
le/la **cycliste** _masc/fem_
# **D d**
**dad** NOUN
**1** le **père** _masc_
**my dad**
mon père
**his dad**
son père
**2** le **papa** _masc (used as a name)_
**Dad!**
Papa!
**Let's ask Dad.**
On va demander à papa.
**daddy** NOUN
le **papa** _masc_
**Hello Daddy!**
Bonjour Papa!
**daffodil** NOUN
la **jonquille** _fem_
**daily** ADVERB
**tous les jours**
**The pool is open daily from 9 a.m. to 6 p.m.**
La piscine est ouverte tous les jours de neuf heures à dix-huit heures.
**damn** EXCLAMATION
**Zut!**
**damp** ADJECTIVE
**humide**
**dance**
**dance** _can be a noun or a verb._
**A** NOUN
**1** la **danse** _fem_
**It's a new dance.**
C'est une nouvelle danse.
**2** le **bal** _masc_
**Are you going to the dance tonight, Marie-Thérèse?**
Tu vas au bal ce soir, Marie-Thérèse?
**B** VERB
**danser**
**Can you dance?**
Tu sais danser?
**I like dancing.**
J'aime danser.
**dancer** NOUN
le **danseur** _masc_
la **danseuse** _fem_
**dandelion** NOUN
le **pissenlit** _masc_
**danger** NOUN
le **danger** _masc_
**in danger**
en danger
**His life is in danger.**
Sa vie est en danger.
**dangerous** ADJECTIVE
**dangereux** _masc_
**dangereuse** _fem_
**dark**
**dark** _can be an adjective or a noun._
**A** ADJECTIVE
**1** **foncé** _masc_ **foncée** _fem (colour)_
**a dark green sweater**
un pull vert foncé
**She's got dark hair.**
Elle a les cheveux bruns.
**2** _(at night)_
**It's dark at six o'clock.**
Il fait nuit à six heures.
**It's getting dark.**
Il commence à faire nuit.
**B** NOUN
le **noir** _masc_
**I'm afraid of the dark.**
J'ai peur du noir.
**darling** NOUN
le **chéri** _masc_
la **chérie** _fem_
**Thank you, darling!**
Merci, chéri!
**dart** NOUN
la **fléchette** _fem_
**Do you want to play darts?**
Tu veux jouer aux fléchettes?
**date** NOUN
la **date** _fem_
**my date of birth**
ma date de naissance
**What date is your birthday?**
Quelle est la date de ton anniversaire?
**What's the date today?**
Quelle est la date aujourd'hui?
**daughter** NOUN
la **fille** _fem_
**day** NOUN
**_Language tip_**
_There are two words for_ **day** : **un jour** _is the whole 24 hours_ , **une journée** _is the time you're awake._
**1** le **jour** _masc_
**I am going to Paris for three days.**
Je vais à Paris pour trois jours.
**2** la **journée** _fem_
**during the day**
dans la journée
**Marc watches TV all day.**
Marc regarde la télé toute la journée.
**the day before my birthday**
la veille de mon anniversaire
**It's Richard's birthday the day after tomorrow.**
C'est l'anniversaire de Richard après-demain.
**It's my day off.**
C'est mon jour de congé.
**the days of the week**
les jours de la semaine
**every day**
tous les jours
**all day**
toute la journée
**What day is it today?**
Quel jour sommes-nous?
**the day after tomorrow**
après-demain
**dead** ADJECTIVE
**mort** _masc_
**morte** _fem_
**deaf** ADJECTIVE
**sourd** _masc_
**sourde** _fem_
**deal**
**deal** _can be a noun or a verb._
**A** NOUN
le **marché** _masc_
**It's a deal!**
Marché conclu!
**a great deal**
beaucoup
**a great deal of money**
beaucoup d'argent
**B** VERB
**donner** _(cards)_
**It's your turn to deal.**
C'est à toi de donner.
**dear** ADJECTIVE
**cher** _masc_
**chère** _fem_
**Dear Mrs Duval**
Chère Madame Duval
**death** NOUN
la **mort** _fem_
**after his death**
après sa mort
**_Language tip_**
**mort** _is related to the words 'mortal' and 'mortality' in English._
**December** NOUN
**décembre** _masc_
**December or January?**
Décembre ou janvier?
**My birthday's in December.**
Mon anniversaire est en décembre.
**in December**
en décembre
**the fifth of December**
le cinq décembre
**_Language tip_**
_The months are not spelled with capital letters in French._
**decide** VERB
**décider**
**I have decided to go to the party.**
J'ai décidé d'aller à la fête.
**I can't decide.**
Je n'arrive pas à me décider.
**decision** NOUN
la **décision** _fem_
**What's your decision?**
Quelle est ta décision?
**We need to make a decision.**
On doit prendre une décision.
**deck** NOUN
le **pont** _masc_
**on deck**
sur le pont
**deckchair** NOUN
la **chaise longue** _fem_
**decorate** VERB
**1** **décorer**
**We decorate the classroom for Christmas.**
Nous décorons la classe pour Noël.
**2** **peindre et tapisser**
_(a room)_
**Mum's going to decorate my bedroom.**
Maman va peindre et tapisser ma chambre.
**_Language tip_**
_Use_ **peindre** _alone, if you just mean 'paint'. Use_ **tapisser** _alone, if you just mean 'wallpaper'._
**decorations** PL NOUN
les **décorations** _fem pl_
**Christmas decorations**
les décorations de Noël
**deep** ADJECTIVE
**1** **profond** _masc_ **profonde** _fem (water, hole, cut)_
**Is it deep?**
Est-ce que c'est profond?
**2** **épais** _masc_ **épaisse** _fem (snow, mud)_
**The snow is deep.**
La neige est épaisse.
**Take a deep breath, girls!**
Respirez à fond, les filles!
**deer** NOUN
**1** le **cerf** _masc (red deer)_
**2** le **daim** _masc (fallow deer)_
**3** le **chevreuil** _
masc (roe deer)_
**_Language tip_**
_In French, you have to say which kind of deer you are talking about!_
**defence** NOUN
la **défense** _fem_
**I play in defence.**
Je joue en défense.
**_Language tip_**
_What are the two differences in spelling between the French word and the English word?_
**defender** NOUN
le **défenseur** _masc_
**definite** ADJECTIVE
**1** **précis** _masc_ **précise** _fem (precise)_
**I haven't got any definite plans.**
Je n'ai pas de projets précis.
**2** **sûr** _masc_ **sûre** _fem (certain)_
**Maybe, it's not definite.**
Peut-être, ce n'est pas sûr.
**definitely** ADVERB
**vraiment**
**He's definitely the best player.**
C'est vraiment lui le meilleur joueur.
**Definitely!**
C'est sûr!
**degree** NOUN
**1** le **degré** _masc (measurement)_
**a temperature of thirty degrees**
une température de trente degrés
**2** la **licence** _fem (qualification)_
**a degree in English**
une licence d'anglais
**delayed** ADJECTIVE
**retardé** _masc_
**retardée** _fem_
**All flights are delayed.**
Tous les vols sont retardés.
**delicatessen** NOUN
l' **épicerie fine** _fem_
**a delicatessen**
une épicerie fine
**delicious** ADJECTIVE
**délicieux** _masc_
**délicieuse** _fem_
**The chocolate mousse is delicious!**
La mousse au chocolat est délicieuse!
**deliver** VERB
**1** **livrer**
**I deliver newspapers.**
Je livre les journaux.
**2** **distribuer** _(letters)_
**The postman delivers our mail.**
Le facteur distribue notre courrier.
**denim** NOUN
le **jean** _masc_
**a denim jacket**
une veste en jean
**Denmark** NOUN
le **Danemark** _masc_
**dentist** NOUN
le/la **dentiste** _masc/fem_
**I'm going to the dentist.**
Je vais chez le dentiste.
**Catherine is a dentist.**
Catherine est dentiste.
**_Language tip_**
_You do not translate_ ' **a** ' _when you say what someone's job is in French._
**department** NOUN
**1** le **rayon** _masc (in shop)_
**the shoe department**
le rayon chaussures
**2** le **département** _masc (of university, school)_
**He works in the English department.**
Il travaille dans le département d'anglais.
**department store** NOUN
le **grand magasin** _masc_
**departure** NOUN
le **départ** _masc_
**departure lounge** NOUN
le **hall des départs** _masc_
**depend** VERB
**It depends.**
Ça dépend.
**depending on the weather**
selon le temps
**deposit** NOUN
**1** les **arrhes** _fem pl (part payment)_
**You have to pay a deposit when you book.**
Il faut verser des arrhes lors de la réservation.
**2** la **caution** _fem (when hiring something)_
**You get the deposit back when you return the bike.**
On vous remboursera la caution quand vous ramènerez le vélo.
**depressed** ADJECTIVE
**déprimé** _masc_
**déprimée** _fem_
**I feel depressed.**
Je suis déprimé.
**deputy head** NOUN
le **directeur adjoint** _
masc_
la **directrice adjointe** _
fem_
**describe** VERB
**décrire**
**Describe yourself.**
Décris-toi.
**description** NOUN
la **description** _fem_
**desert** NOUN
le **désert** _masc_
**desert island** NOUN
l' **île déserte** _fem_
**deserve** VERB
**mériter**
**You deserve a prize, Marie.**
Tu mérites un prix, Marie.
**design**
**design** _can be a noun or a verb._
**A** NOUN
le **motif** _masc (pattern)_
**a simple design**
un motif simple
**B** VERB
**dessiner**
**We're going to design a birthday card.**
On va dessiner une carte d'anniversaire.
**designer clothes** PL NOUN
les **vêtements griffés** _masc pl_
**desk** NOUN
**1** le **pupitre** _masc (in school)_
**my desk**
mon pupitre
**2** le **bureau** _masc_
(PL les **bureaux** ) _(in office)_
**dessert** NOUN
le **dessert** _masc_
**for dessert**
comme dessert
**destination** NOUN
la **destination** _fem_
**detached house** NOUN
le **pavillon** _masc_
**detail** NOUN
le **détail** _masc_
**in detail**
en détail
**detective** NOUN
l' **inspecteur de police** _masc_
**He's a detective.**
Il est inspecteur de police.
**_Language tip_**
_When you say what someone's job is in French, you do not translate_ **a**.
**detective story** NOUN
le **roman policier** _masc_
**detention** NOUN
**You'll get a detention!**
Tu vas avoir une retenue!
**develop** VERB
**développer**
**I want to get this film developed.**
Je veux faire développer ce film.
**_Language tip_**
_The French word_ **développer** _has double_ **p**.
**diabetic** NOUN
le/la **diabétique** _masc/fem_
**I'm a diabetic.**
Je suis diabétique.
**diagonal** ADJECTIVE
**diagonal** _masc_
**diagonale** _fem_
**diagram** NOUN
le **diagramme** _masc_
**dial** VERB
**composer**
**Dial the number.**
Composez le numéro.
**dialogue** NOUN
le **dialogue** _masc_
**diamond** NOUN
**1** le **diamant** _masc_
**a diamond ring**
une bague en diamant
**2** _(cards)_
**diamonds**
le carreau
**the ace of diamonds**
l'as de carreau
**diary** NOUN
**1** l' **agenda** _masc_
**I've got her phone number in my diary.**
J'ai son numéro de téléphone dans mon agenda.
**2** le **journal** _masc_
(PL les **journaux** )
**I keep a diary.**
Je tiens un journal.
**_Language tip_**
_The French word_ **journal** _is related to the word 'jour', which means 'day'_. **Journal** _also means 'newspaper'. Newspapers come out every day, and people write in their diaries every day._
**dice** NOUN
le **dé** _masc_
**Throw the dice, Leah.**
Jette le dé, Leah.
**dictionary** NOUN
le **dictionnaire** _masc_
**Look in the dictionary.**
Cherchez dans le dictionnaire.
**_Language tip_**
_The French word_ **dictionnaire** _has a double_ **n**.
**did** VERB _see_ **do**
**die** VERB
**mourir**
**He died last year.**
Il est mort l'année dernière.
**She died in 2002.**
Elle est morte en deux mille deux.
**diesel** NOUN
**1** le **gazole** _masc (fuel)_
**2** la **voiture diesel** _fem (car)_
**diet**
**diet** _can be a noun or a verb._
**A** NOUN
**1** l' **alimentation** _fem_
**a healthy diet**
une alimentation saine
**2** le **régime** _masc (for slimming)_
**My dad's on a diet.**
Mon père est au régime.
**Are you on a diet?**
Tu es au régime?
**B** VERB
**faire un régime**
**My mum's dieting.**
Ma mère fait un régime.
**difference** NOUN
la **différence** _fem_
**What's the difference?**
Quelle est la différence?
**different** ADJECTIVE
**différent** _masc_
**différente** _fem_
**We are very different.**
Nous sommes très différents.
**Paris is different from London.**
Paris est différent de Londres.
**difficult** ADJECTIVE
**difficile**
**It's difficult.**
C'est difficile.
**difficulty** NOUN
la **difficulté** _fem_
**without difficulty**
sans difficulté
**dig** VERB
**creuser**
**My rabbit digs lots of holes.**
Mon lapin creuse beaucoup de trous.
**digital camera** NOUN
l' **appareil photo
numérique** _masc_
**digital radio** NOUN
la **radio numérique** _fem_
**digital television** NOUN
la **télévision numérique** _fem_
**dinghy** NOUN
**a rubber dinghy**
un canot pneumatique
**dining room** NOUN
la **salle à manger** _fem_
**_Language tip_**
**manger** _means ' to eat', so the French literally means 'the room for eating'._
**dinner** NOUN
**1** le **déjeuner** _masc (midday meal)_
**2** le **dîner** _masc (evening meal)_
**dinner lady** NOUN
la **dame de service** _fem_
**dinner time** NOUN
**1** l' **heure du déjeuner** _fem (midday meal)_
**2** l' **heure du dîner** _fem (evening meal)_
**dinosaur** NOUN
le **dinosaure**
_masc_
**direct** ADJECTIVE
**direct** _masc_
**directe** _fem_
**the most direct route**
le chemin le plus direct
**direction** NOUN
la **direction** _fem_
**You're going in the wrong direction.**
Vous allez dans la mauvaise direction.
**dirty** ADJECTIVE
**sale**
**My shoes are dirty.**
Mes chaussures sont sales.
**disabled** ADJECTIVE
**handicapé** _masc_
**handicapée** _fem_
**disabled people**
les handicapés
**disagree** VERB
**I disagree!**
Je ne suis pas d'accord!
**disappointed** ADJECTIVE
**déçu** _masc_
**déçue** _fem_
**disappointment** NOUN
la **déception** _fem_
**disaster** NOUN
le **désastre** _masc_
**It's a disaster!**
C'est un désastre!
**discipline** NOUN
la **discipline** _fem_
**disc jockey** NOUN
le **disc-jockey** _masc_
**disco** NOUN
la **soirée disco** _fem_
**There's a disco at the school tonight.**
Il y a une soirée disco à l'école ce soir.
**discussion** NOUN
la **discussion** _fem_
**disguise** VERB
**déguiser**
**He was disguised as a policeman.**
Il était déguisé en policier.
**_Language tip_**
_Which consonant is different from the English in the French word_ **déguiser**?
**disgusting** ADJECTIVE
**dégoûtant** _masc_
**dégoûtante** _fem_
**It looks disgusting.**
Ça a l'air dégoûtant.
**dish** NOUN
le **plat** _masc_
**a vegetarian dish**
un plat végétarien
**I always do the dishes.**
Je fais toujours la vaisselle.
**dishwasher** NOUN
le **lave-vaisselle** _masc_
**disk** NOUN
le **disque** _masc_
**dislike** NOUN
**my likes and dislikes**
ce que j'aime et ce que je n'aime pas
**distance** NOUN
la **distance** _fem_
**a distance of ten kilometres**
une distance de dix kilomètres
**in the distance**
au loin
**distract** VERB
**distraire**
**Don't distract him, Lulu.**
Ne le distraie pas, Lulu.
**district** NOUN
**1** le **quartier** _masc (of town)_
**2** la **région** _fem (of country)_
**disturb** VERB
**déranger**
**I'm sorry to disturb you.**
Je suis désolé de vous déranger.
**dive** VERB
**plonger**
**I like diving.**
J'aime plonger.
**_Language tip_**
**plonger** _is related to the English word 'plunge'. When you dive, you plunge into the pool._
**divide** VERB
**diviser**
**Divide the pastry in half.**
Divisez la pâte en deux.
**Twelve divided by three is four.**
Douze divisé par trois égale quatre.
**Divide into two groups!**
Divisez-vous en deux groupes!
**diving board** NOUN
le **plongeoir** _masc_
**divorced** ADJECTIVE
**divorcé** _masc_
**divorcée** _fem_
**My parents are divorced.**
Mes parents sont divorcés.
**Diwali** NOUN
le **Dipavali** _masc_
**DIY** NOUN
le **bricolage** _masc_
**He likes doing DIY.**
Il aime faire du bricolage.
**dizzy** ADJECTIVE
**I feel dizzy.**
J'ai la tête qui tourne.
**DJ** NOUN
le **disc-jockey** _masc_
**do** VERB
**_Language tip_**
_Look carefully through the entry for_ **do** _to find what you want to say._
**faire**
**I do a lot of cycling.**
Je fais beaucoup de vélo.
**What are you doing this evening?**
Qu'est-ce que tu fais ce soir?
**My brother does judo.**
Mon frère fait du judo.
**Do the actions.**
Faites les gestes!
**I haven't done my homework.**
Je n'ai pas fait mes devoirs.
**Who did that?**
Qui a fait ça?
**That'll do, thanks.**
Ça ira, merci.
**_Language tip_**
_In English_ , **do** _is often used to make questions. In French, questions are made either with_ **est-ce que**.
**Do you like French food?**
Est-ce que vous aimez la cuisine française?
**Where does he live?**
Où est-ce qu'il habite?
**What do you do in your free time?**
Qu'est-ce que vous faites pendant vos loisirs?
**_Language tip_**
_... or by reversing the order of verb and subject..._
**Do you speak English?**
Parlez-vous anglais?
**_Language tip_**
_... or by adding a question mark._
**Do you speak French, Kevin?**
Tu parles français, Kevin?
**_Language tip_**
_Use **ne... pas** in negative sentences._
**I don't understand.**
Je ne comprends pas.
**She doesn't like dogs.**
Elle n'aime pas les chiens.
**You go swimming on Fridays, don't you?**
Tu fais de la natation le vendredi, n'est-ce pas?
**What are you doing?**
Qu'est-ce que tu fais?
**I'm not doing anything.**
Je ne fais rien.
**... don't you?**
... n'est-ce pas?
**do up** VERB
**1** **lacer** _(tie)_
**Do up your shoes!**
Lace tes chaussures!
**2** **boutonner** _(button up)_
**Do up your coat!**
Boutonne ton manteau!
**Do up your zip!** _(on trousers)_
Ferme ta braguette!
**doctor** NOUN
le **médecin** _masc_
**I'm going to the doctor.**
Je vais chez le médecin.
**I'd like to be a doctor.**
Je voudrais être médecin.
**She's a doctor.**
Elle est médecin.
**_Language tip_**
_You do not translate_ ' **a** ' _when you say what someone's job is in French._
**dodgems** PL NOUN
les **autos tamponneuses** _fem pl_
**does** VERB _see_ **do**
**dog** NOUN
le **chien** _masc_
la **chienne** _fem_
**Have you got a dog?**
Tu as un chien?
**doll** NOUN
la **poupée** _fem_
**dolphin** NOUN
le **dauphin**
_masc_
**dominoes** PL NOUN
**Let's have a game of dominoes.**
Faisons une partie de dominos.
**done** VERB _see_ **do**
**donkey** NOUN
l' **âne** _masc_
**Pin the tail on the donkey!**
Accroche la queue à l'âne.
**door** NOUN
**1** la **porte** _fem_
**the first door on the right**
la première porte à droite
**2** la **portière** _fem (of car, train)_
**dormitory** NOUN
le **dortoir** _masc_
**_Language tip_**
**dormitory** _is related to the verb_ **dormir** , _which means 'to sleep'. A_ **dormitory** _is a place where you sleep._
**dot** NOUN
le **point** _masc_
**double** ADJECTIVE
**double**
**a double helping**
une double portion
**double bed** NOUN
le **grand lit** _masc_
**double room** NOUN
la **chambre pour deux personnes** _fem_
**double-decker bus** NOUN
le **bus à impériale** _masc_
**doubt** VERB
**I doubt it.**
J'en doute.
**doughnut** NOUN
le **beignet** _masc_
**a jam doughnut**
un beignet à la confiture
**Dover** NOUN
**Douvres**
**from Dover to Boulogne**
de Douvres à Boulogne
**in Dover**
à Douvres
**down**
**down** _can be an adverb, a preposition, or an adjective._
**A** ADVERB
**en bas**
**Don't look down!**
Ne regarde pas en bas!
**It's down in the cellar.**
C'est dans la cave.
**It's down there.**
C'est là-bas.
**B** PREPOSITION
**I live just down the road.**
J'habite tout à côté.
**C** ADJECTIVE
**I'm feeling a bit down.**
J'ai un peu le cafard.
**The computer's down.**
L'ordinateur est en panne.
**download** VERB
**télécharger**
**You can download the file.**
Tu peux télécharger le fichier.
**downstairs** ADVERB
**au rez-de-chaussée**
**The bathroom's downstairs.**
La salle de bain est au rez-de-chaussée.
**I'm downstairs!**
Je suis en bas!
**dozen** NOUN
la **douzaine** _fem_
**two dozen**
deux douzaines
**a dozen eggs**
une douzaine d'œufs
**_Language tip_**
**douzaine** _is related to the French word_ **douze** , _which means 'twelve'. A_ **dozen** _means twelve._
**dragon** NOUN
le **dragon** _masc_
**drama** NOUN
l' **art dramatique** _masc_
**Drama is my favourite subject.**
Ma matière préférée, c'est l'art dramatique.
**drank** VERB _see_ **drink**
**draughts** NOUN
les **dames** _fem pl_
**Do you want to play draughts?**
Tu veux jouer aux dames?
**draw**
**draw** _can be a verb or a noun._
**A** VERB
**1** **dessiner** _(with pencil)_
**I can't draw.**
Je ne sais pas dessiner.
**Draw a house, everyone.**
Dessinez une maison, tout le monde.
**Draw a picture.**
Faites un dessin.
**2** **faire match nul** _(in game)_
**We drew 2–2.**
Nous avons fait match nul deux à deux.
**B** NOUN
le **match nul** _masc (in game)_
**It's a draw between the boys and the girls.**
Match nul entre les garçons et les filles.
**drawer** NOUN
le **tiroir** _masc_
**_Language tip_**
_You see_ **'Tirez'** _on doors in France. It means 'pull'._
**Un tiroir** _is something you pull out._
**drawing** NOUN
le **dessin** _masc_
**drawing pin** NOUN
la **punaise** _fem_
**dream** NOUN
le **rêve** _masc_
**Sweet dreams, darling!**
Fais de beaux rêves, chérie!
**a bad dream**
un cauchemar
**dress**
**dress** _can be a noun or a verb._
**A** NOUN
la **robe** _fem_
**Élodie is wearing a white dress.**
Élodie porte une robe blanche.
**B** VERB
**to get dressed**
s'habiller
**I'm getting dressed.**
Je m'habille.
**Go and get dressed.**
Va t'habiller.
**dress up** VERB
**se déguiser**
**I'm going to dress up as a princess.**
Je vais me déguiser en princesse.
**dressed** ADJECTIVE
**habillé** _masc_
**habillée** _fem_
**I'm not dressed yet.**
Je ne suis pas encore habillé.
**How was she dressed?**
Comment est-ce qu'elle était habillée?
**She was dressed in a green sweater and jeans.**
Elle portait un pull vert et un jean.
**drew** VERB _see_ **draw**
**drink**
**drink** _can be a verb or a noun._
**A** VERB
**boire**
**What would you like to drink?**
Qu'est-ce que vous voulez boire?
**She drank three cups of tea.**
Elle a bu trois tasses de thé.
**B** NOUN
**1** la **boisson** _fem_
**a cold drink**
une boisson fraîche
**a hot drink**
une boisson chaude
**2** le **verre** _masc (alcoholic)_
**Would you like a drink?**
Vous prenez un verre?
**drive**
**drive** _can be a noun or a verb._
**A** NOUN
**1** le **tour en voiture** _masc_
**Let's go for a drive.**
Allons faire un tour en voiture.
**2** l' **allée** _fem (of house)_
**You can park your car in the drive.**
Vous pouvez garer votre voiture dans l'allée.
**B** VERB
**1** **conduire** _(car)_
**She's learning to drive.**
Elle apprend à conduire.
**Can you drive?**
Tu sais conduire?
**2** **aller en voiture** _(go by car)_
**Are you going by train? — No, we're driving.**
Vous prenez le train? — Non, nous y allons en voiture.
**3** **emmener en voiture** _(take by car)_
**My mother drives me to school.**
Ma mère m'emmène à l'école en voiture.
**driver** NOUN
**1** le **conducteur** _masc_ la **conductrice** _fem (of car)_
**She's an excellent driver.**
C'est une excellente conductrice.
**2** le **chauffeur** _masc (of taxi, bus)_
**driving licence** NOUN
le **permis de conduire** _masc_
**drop**
**drop** _can be a noun or a verb._
**A** NOUN
la **goutte** _fem_
**a drop of water**
une goutte d'eau
**B** VERB
**laisser tomber**
**Drop the ball!**
Laisse tomber la balle!
**drug** NOUN
**1** le **médicament** _masc (medicine)_
**They need food and drugs.**
Ils ont besoin de nourriture et de médicaments.
**2** la **drogue** _fem (illegal)_
**hard drugs**
les drogues dures
**Don't take drugs.**
Ne vous droguez pas.
**drum** NOUN
le **tambour** _masc_
**an African drum**
un tambour africain
**I play drums.**
Je joue de la batterie.
**drum kit** NOUN
la **batterie** _fem_
**drummer** NOUN
le **batteur** _masc_
la **batteuse** _fem_
**drunk** ADJECTIVE
**ivre**
**dry**
**dry** _can be an adjective or a verb._
**A** ADJECTIVE
**1** **sec** _masc_ **sèche** _fem (not wet)_
**The paint isn't dry yet.**
La peinture n'est pas encore sèche.
**2** **sans pluie** _(weather)_
**a long dry period**
une longue période sans pluie
**B** VERB
**sécher**
**Let the glue dry.**
Laissez sécher la colle.
**I need to dry my hair.**
Je dois me sécher les cheveux.
**duck** NOUN
le **canard** _masc_
**due** ADJECTIVE
**The plane's due in half an hour.**
L'avion doit arriver dans une demi-heure.
**When's the baby due?**
Le bébé est prévu pour quand?
**dull** ADJECTIVE
**It's dull today.**
Il fait gris aujourd'hui.
**dummy** NOUN
la **tétine** _fem_
**dump** NOUN
**It's a real dump!**
C'est un endroit minable!
**dungarees** PL NOUN
la **salopette** _fem_
**_Language tip_**
**salopette** _is a singular word._
**dungeon** NOUN
le **cachot** _masc_
**during** PREPOSITION
**pendant**
**during the day**
pendant la journée
**dustbin** NOUN
la **poubelle** _fem_
**duty-free shop** NOUN
**la boutique hors taxes** _fem_
**duvet** NOUN
la **couette** _fem_
**DVD** NOUN
le **DVD** _masc_
**I've got that film on DVD.**
J'ai ce film en DVD.
**DVD player** NOUN
le **lecteur de DVD** _masc_
**dwarf** NOUN
le **nain** _masc_
la **naine** _fem_
# **E e**
**each**
**each** _can be an adjective or a pronoun._
**A** ADJECTIVE
**chaque**
**each day**
chaque jour
**B** PRONOUN
**chacun** _masc_ **chacune** _fem_
**They have ten points each.**
Ils ont dix points chacun.
**The plates cost £5 each.**
Les assiettes coûtent cinq livres chacune.
**Take one card each.**
Prenez une carte chacun.
**We write to each other.**
Nous nous écrivons.
**ear** NOUN
l' **oreille** _fem_
**earache** NOUN
**I've got earache.**
J'ai mal aux oreilles.
**early** ADVERB
**1** **tôt** _(early in the day)_
**I get up early.**
Je me lève tôt.
**I go to bed early.**
Je me couche tôt.
**2** **en avance** _(ahead of time)_
**Come early to get a good seat.**
Venez en avance pour avoir une bonne place.
**earn** VERB
**gagner**
**She earns £5 an hour.**
Elle gagne cinq livres de l'heure.
**earring** NOUN
la **boucle d'oreille** _fem_
**diamond earrings**
des boucles d'oreille en diamant
**earth** NOUN
la **terre** _fem_
**east**
**east** _can be an adjective or a noun._
**A** ADJECTIVE
**est** _masc, fem, pl_
**the east coast**
la côte est
**B** NOUN
l' **est** _masc_
**in the east**
dans l'est
**Easter** NOUN
**Pâques** _fem pl_
**at Easter**
à Pâques
**the Easter holidays**
les vacances de Pâques
**Happy Easter!**
Joyeuses Pâques!
**Easter egg** NOUN
l' **œuf de Pâques** _masc_
**a big Easter egg**
un gros œuf de Pâques
**_Did you know...?_**
_In France, Easter eggs are said to be brought by the Easter bells or_ **cloches de Pâques** _which fly from Rome and drop them in people's gardens._
**easy** ADJECTIVE
**facile**
**It's easy!**
C'est facile!
**eat** VERB
**manger**
**I eat a lot of sweets.**
Je mange beaucoup de bonbons.
**Would you like something to eat?**
Est-ce que tu veux manger quelque chose?
**edge** NOUN
le **bord** _masc_
**on the edge of the table**
au bord de la table
**Edinburgh** NOUN
**Édimbourg**
**Andrew lives in Edinburgh.**
Andrew habite à Édimbourg.
**_Did you know...?_**
_A few British towns have French names. Can you recognise these:_ **Douvres** , **Cantorbéry** , **Londres**?
**education** NOUN
l' **éducation** _fem_
**effect** NOUN
l' **effet** _masc_
**special effects**
les effets spéciaux
**effort** NOUN
l' **effort** _masc_
**You have to make an effort.**
Tu dois faire un effort.
**e.g.** ABBREVIATION
**p. ex.**
**egg** NOUN
l' **œuf** _masc_
**a hard-boiled egg**
un œuf dur
**a soft-boiled egg**
un œuf à la coque
**a fried egg**
un œuf sur le plat
**scrambled eggs**
les œufs brouillés
**Eiffel Tower** NOUN
la **tour Eiffel** _fem_
**eight** NUMBER
**huit**
**eight euros**
huit euros
**She's eight.**
Elle a huit ans.
**_Language tip_**
_In English, you can say_ **eight** _or_ **eight years old**. _In French, you can only say_ **huit ans**.
**eighteen** NUMBER
**dix-huit**
**eighteen euros**
dix-huit euros
**He is eighteen.**
Il a dix-huit ans.
**_Language tip_**
_In English, you can say_ **eighteen** _or_ **eighteen years old**. _In French, you can only say_ **dix-huit ans**.
**eighteenth** ADJECTIVE
**dix-huitième**
**on the eighteenth floor**
au dix-huitième étage
**the eighteenth of August**
le dix-huit août
**eighth** ADJECTIVE
**huitième**
**on the eighth floor**
au huitième étage
**the eighth of August**
le huit août
**eighty** NUMBER
**quatre-vingts**
**_Language tip_**
**quatre-vingts** _is made up of two words. What does each one mean?_
**Eire** NOUN
la **République d'Irlande** _fem_
**either** ADVERB, CONJUNCTION, PRONOUN
**non plus**
**I don't like milk, and I don't like eggs either.**
Je n'aime pas le lait, et je n'aime pas les œufs non plus.
**I haven't got any money. — I haven't either.**
Je n'ai pas d'argent. — Moi non plus.
**I don't like either of them.**
Je n'aime ni l'un ni l'autre.
**either... or...**
soit... soit...
**You can have either ice cream or yoghurt.**
Tu peux prendre soit une glace soit un yaourt.
**elastic band** NOUN
l' **élastique** _masc_
**an elastic band**
un élastique
**elder** ADJECTIVE
**aîné** _masc_
**aînée** _fem_
**my elder sister**
ma sœur aînée
**elderly** ADJECTIVE
**âgé** _masc_
**âgée** _fem_
**the elderly**
les personnes âgées
**eldest** ADJECTIVE
**aîné** _masc_
**aînée** _fem_
**my eldest sister**
ma sœur aînée
**He's the eldest.**
C'est l'aîné.
**election** NOUN
l' **élection** _fem_
**an election**
une élection
**electric** ADJECTIVE
**électrique**
**an electric guitar**
une guitare électrique
**electricity** NOUN
l' **électricité** _fem_
**electronic** ADJECTIVE
**électronique**
**elegant** ADJECTIVE
**élégant** _masc_
**élégante** _fem_
**elephant** NOUN
l' **éléphant** _masc_
**_Language tip_**
_What is the difference in spelling between the French word and the English word?_
**eleven** NUMBER
**onze**
**eleven euros**
onze euros
**I'm eleven.**
J'ai onze ans.
**_Language tip_**
_In English, you can say_ **eleven** _or_ **eleven years old**. _In French, you can only say_ **onze ans**.
**eleventh** ADJECTIVE
**onzième**
**on the eleventh floor**
au onzième étage
**the eleventh of August**
le onze août
**else** ADVERB
**d'autre**
**somebody else**
quelqu'un d'autre
**nobody else**
personne d'autre
**nothing else**
rien d'autre
**anything else**
autre chose
**Would you like anything else?**
Désirez-vous autre chose?
**I don't want anything else.**
Je ne veux rien d'autre.
**email**
**email** _can be a noun or a verb._
**A** NOUN
l' **e-mail** _masc_
**by email**
par e-mail
**Send your penfriend an email.**
Envoie un e-mail à ton correspondant.
**B** VERB
**envoyer un e-mail à**
**I'll email you.**
Je vais t'envoyer un e-mail.
**email address** NOUN
l' **adresse e-mail** _fem_
**My email address is:...**
Mon adresse e-mail, c'est:...
**_Language tip_**
**adresse** _in French has one_ **d** , **address** _in English has two_ **d** _s._
**embarrassed** ADJECTIVE
**gêné** _masc_
**gênée** _fem_
**I was really embarrassed.**
J'étais vraiment gêné.
**emergency** NOUN
l' **urgence** _fem_
**This is an emergency!**
C'est une urgence!
**in an emergency**
en cas d'urgence
**emergency exit** NOUN
la **sortie de secours** _fem_
**empty**
**empty** _can be an adjective or a verb._
**A** ADJECTIVE
**vide**
**The bottle is empty.**
La bouteille est vide.
**B** VERB
**vider**
**Empty your pockets!**
Vide tes poches!
**encourage** VERB
**encourager**
**Encourage your team!**
Encouragez votre équipe!
**_Language tip_**
_Some French words are very like English words!_
**encyclopedia** NOUN
l' **encyclopédie** _fem_
**end**
**end** _can be a noun or a verb._
**A** NOUN
**1** la **fin** _fem (final part)_
**the end of the lesson**
la fin du cours
**2** le **bout** _masc (of place)_
**at the end of the street**
au bout de la rue
**B** VERB
**finir**
**What time does the lesson end?**
À quelle heure est-ce que le cours finit?
**_Language tip_**
**fin** _and_ **finir** _in French and_ **finish** _and_ **final** _in English are related words. What do they have in common?_
**ending** NOUN
la **fin** _fem_
**It's a great film, especially the ending.**
C'est un film génial, surtout la fin.
**enemy** NOUN
l' **ennemi** _masc_
l' **ennemie** _fem_
**_Language tip_**
_The French word has double_ **n**.
**energetic** ADJECTIVE
**énergique**
**energy** NOUN
l' **énergie** _fem_
**engaged** ADJECTIVE
**1** **occupé** _masc_ **occupée** _fem (busy)_
**Her phone is always engaged.**
Son téléphone est toujours occupé.
**2** **fiancé** _masc_ **fiancée** _fem (to be married)_
**My brother is engaged.**
Mon frère est fiancé.
**My sister is engaged.**
Ma sœur est fiancée.
**She's engaged to Ron.**
Elle est fiancée à Ron.
**engagement** NOUN
les **fiançailles** _fem pl_
**engagement ring**
la **bague de fiançailles** _fem_
**engine** NOUN
le **moteur** _masc_
**_Language tip_**
_Be careful not to translate_ **engine** _by the French word_ **engin** , _which is a slang word for 'thing'._
**England** NOUN
l' **Angleterre** _fem_
**I live in England.**
J'habite en Angleterre.
**to England**
_en Angleterre_
**Are you coming to England?**
_Tu viens en Angleterre?_
**English**
**English** _can be an adjective or a noun._
**A** ADJECTIVE
**anglais** _masc_ **anglaise** _fem_
**I am English.**
Je suis anglais.
**English food is different.**
La cuisine anglaise est différente.
**English people**
les Anglais
**B** NOUN
l' **anglais** _masc (language)_
**Do you speak English?**
Est-ce que vous parlez anglais?
**the English**
les Anglais
**He's English.**
Il est anglais.
**She's English.**
Elle est anglaise.
**_Language tip_**
**anglais** _is not spelled with a capital letter except when it means an English person._
**Englishman** NOUN
l' **Anglais** _masc_
**an Englishman**
un Anglais
**Englishwoman** NOUN
l' **Anglaise** _fem_
**a Englishwoman**
une Anglaise
**enjoy** VERB
**aimer**
**I enjoy learning French.**
J'aime apprendre le français.
**Did you enjoy the film?**
Est-ce que vous avez aimé le film?
**enjoyable** ADJECTIVE
**agréable**
**enormous** ADJECTIVE
**énorme**
**Benoît has got enormous feet.**
Benoît a des pieds énormes.
**enough**
**enough** _can be an adjective or a pronoun._
**A** ADJECTIVE
**assez de**
**enough time**
assez de temps
**I haven't got enough money.**
Je n'ai pas assez d'argent.
**B** PRONOUN
**assez**
**Have you got enough?**
Tu en as assez?
**I've had enough!**
J'en ai assez!
**That's enough.**
Ça suffit.
**enter** VERB
**I'm going to enter the competition.**
Je vais m'inscrire à la compétition.
**enthusiasm** NOUN
l' **enthousiasme** _masc_
**_Language tip_**
_Which letters does the French word have that the English word doesn't?_
**enthusiastic** ADJECTIVE
**enthousiaste**
**entrance** NOUN
l' **entrée** _fem_
**by the entrance**
à l'entrée
**entrance exam** NOUN
le **concours d'entrée** _masc_
**entry** NOUN
**'no entry'**
'défense d'entrer'
**entry phone** NOUN
l' **interphone** _masc_
**envelope** NOUN
l' **enveloppe** _fem_
**_Language tip_**
_The English word has one_ **p** , _and the French word has two_ **p** _s._
**envious** ADJECTIVE
**envieux** _masc_
**envieuse** _fem_
**environment** NOUN
l' **environnement** _masc_
**_Language tip_**
_What are the differences in spelling between the French word and the English word?_
**episode** NOUN
l' **épisode** _masc_
**equal**
**equal** _can be an adjective or a verb._
**A** ADJECTIVE
**égal** _masc_ **égale** _fem_
**Divide the map into six equal squares.**
Divisez la carte en six carrés égaux.
**B** VERB
**égaler**
**Two times three equals six.**
Deux fois trois égalent six.
**equality** NOUN
l' **égalité** _fem_
**_Language tip_**
_What letter does the French word have instead of_ **qu**?
**equalize** VERB
**égaliser**
**Thierry Henry has equalized.**
Thierry Henry a égalisé.
**equipment** NOUN
l' **équipement** _masc_
**lots of equipment**
beaucoup d'équipement
**_Language tip_**
_The French word has one more letter than the English word. What is it?_
**error** NOUN
l' **erreur** _fem_
**a small error**
une petite erreur
**escalator** NOUN
l' **escalier roulant** _masc_
**Is there an escalator?**
Est-ce qu'il y a un escalier roulant?
**escape** VERB
**s'échapper**
**A lion has escaped.**
Un lion s'est échappé.
**especially** ADVERB
**surtout**
**It's very hot there, especially in summer.**
Il fait très chaud là-bas, surtout en été.
**essay** NOUN
le **devoir** _masc_
**a history essay**
un devoir d'histoire
**essential** ADJECTIVE
**essentiel** _masc_
**essentielle** _fem_
**It's essential to bring warm clothes.**
Il est essentiel d'apporter des vêtements chauds.
**_Language tip_**
_What is the difference in spelling between the French word and the English word?_
**euro** NOUN
l' **euro** _masc_
**one euro**
un euro
**Europe** NOUN
l' **Europe** _fem_
**even**
**even** _can be an adverb or an adjective._
**A** ADVERB
**même**
**I like all animals, even snakes.**
J'aime tous les animaux, même les serpents.
**B** ADJECTIVE
**an even number**
un nombre pair
**evening** NOUN
le **soir** _masc_
**at seven o'clock in the evening**
à sept heures du soir
**this evening**
ce soir
**in the evening**
le soir
**yesterday evening**
hier soir
**tomorrow evening**
demain soir
**Good evening!**
Bonsoir!
**evening class** NOUN
le **cours du soir** _masc_
**My mother goes to an evening class.**
Ma mère va à un cours du soir.
**event** NOUN
l' **événement** _masc_
**an important event**
un événement important
**ever** ADVERB
**Have you ever been to France?**
Est-ce que tu es déjà allé en France?
**for the first time ever**
pour la première fois
**every** ADJECTIVE
**chaque**
**every pupil**
chaque élève
**every time**
chaque fois
**I talk to her every day.**
Je parle avec elle tous les jours.
**I do judo every week.**
Je fais du judo toutes les semaines.
**every day**
tous les jours
**every night**
tous les soirs
**every week**
toutes les semaines
**everybody** PRONOUN
**tout le monde**
**Good morning everybody!**
Bonjour tout le monde!
**Everybody likes sweets.**
Tout le monde aime les bonbons.
**everyone** PRONOUN
**tout le monde**
**Is everyone here?**
Tout le monde est là?
**_Language tip_**
**everyone** _is the same as_ **everybody**.
**everything** PRONOUN
**tout**
**Everything's fine!**
Tout va bien!
**Is that everything?**
C'est tout?
**everywhere** ADVERB
**partout**
**There are cats everywhere!**
Il y a des chats partout!
**exact** ADJECTIVE
**exact** _masc_
**exacte** _fem_
**exactly** ADVERB
**exactement**
**Our trainers are exactly the same.**
Nos baskets sont exactement les mêmes.
**not exactly**
pas exactement
**_Language tip_**
_In English_ , - **ly** _is added to_ **exact**. _What is added to_ **exact** _in French?_
**It's exactly 1 o'clock.**
Il est une heure précise.
**exam** NOUN
l' **examen** _masc_
**a French exam**
un examen de français
**example** NOUN
l' **exemple** _masc_
**an example**
un exemple
**for example**
par exemple
**_Language tip_**
_What is the difference in spelling between the French word and the English word?_
**excellent** ADJECTIVE
**excellent** _masc_
**excellente** _fem_
**Excellent!**
Excellent!
**It was excellent fun.**
C'était vraiment super.
**except** PREPOSITION
**sauf**
**everyone except me**
tout le monde sauf moi
**exchange** VERB
**échanger**
**I want to exchange the book for a video.**
Je veux échanger le livre contre une vidéo.
**exchange rate** NOUN
le **taux de change** _masc_
**excited** ADJECTIVE **excité** _masc_
**excitée** _fem_
**exciting** ADJECTIVE
**passionnant** _masc_
**passionnante** _fem_
**an exciting film**
un film passionnant
**excuse** VERB
**Excuse me!**
Pardon!
**exercise** NOUN
l' **exercice** _masc_
**an exercise**
un exercice
**_Language tip_**
_What is the difference in spelling between the French word and the English word?_
**exercise book** NOUN
le **cahier** _masc_
**exhausted** ADJECTIVE
**épuisé** _masc_
**épuisée** _fem_
**Fabrice is exhausted.**
Fabrice est épuisé.
**_Language tip_**
_Fabrice is a boy's name. How can you tell that by looking at the example sentence?_
**exhibition** NOUN
l' **exposition** _fem_
**an exhibition**
une exposition
**exit** NOUN
la **sortie** _fem_
**Where is the exit?**
Où est la sortie?
**expect** VERB
**1** **attendre** _(wait for)_
**I'm expecting a phone call.**
J'attends un coup de téléphone.
**She's expecting a baby.**
Elle attend un enfant.
**2** **supposer** _(suppose)_
**I expect he wants a coke.**
Je suppose qu'il veut un coca.
**expedition** NOUN
l' **expédition** _fem_
**an expedition**
une expédition
**expensive** ADJECTIVE
**cher** _masc_
**chère** _fem_
**It's too expensive.**
C'est trop cher.
**experience** NOUN
l' **expérience** _fem_
**an interesting experience**
une expérience intéressante
**experiment** NOUN
l' **expérience** _fem_
**expert** NOUN
le **spécialiste** _masc_
la **spécialiste** _fem_
**She's a computer expert.**
C'est une spécialiste en informatique.
**Matthew is an expert cook.**
Matthew cuisine très bien.
**explain** VERB
**expliquer**
**I'll explain in English.**
Je vais expliquer en Anglais.
**explanation** NOUN
l' **explication** _fem_
**a clear explanation**
une explication claire
**explode** VERB
**exploser**
**It's going to explode!**
Ça va exploser!
**explosion** NOUN
l' **explosion** _fem_
**an explosion**
une explosion
**extension** NOUN
**1** l' **annexe** _fem (of a public building)_
**2** le **poste** _masc (phone)_
**Extension 3137, please.**
Poste 3137, s'il vous plaît.
**_Language tip_**
_In France, phone numbers are broken into pairs, so a French person would say this example as 'trente et un, trente-sept'._
**extra** ADJECTIVE, PRONOUN, ADVERB
**supplémentaire**
**an extra blanket**
une couverture supplémentaire
**Breakfast is extra.**
Il y a un supplément pour le petit déjeuner.
**to pay extra**
payer un supplément
**It costs extra.**
Il y a un supplément.
**extremely** ADVERB
**extrêmement**
**_Language tip_**
_In English_ , - **ly** _is added to_ **extreme**. _What is added to_ **extrême** _in French?_
**eye** NOUN
l' **œil** _masc_ (PL les **yeux** )
**I've got blue eyes.**
J'ai les yeux bleus.
**She's got green eyes.**
Elle a les yeux verts.
**What colour eyes has he got?**
Il a les yeux de quelle couleur?
**eyesight** NOUN
la **vue** _fem_
# **F f**
**fabulous** ADJECTIVE
**formidable**
**A fabulous show.**
Un spectacle formidable.
**face** NOUN
la **figure** _fem_
**His face is red.**
Il a la figure rouge.
**face cloth** NOUN
le **gant de toilette** _masc_
**_Language tip_**
**gant** _means 'glove'. A_ **gant de toilette** _is a glove-shaped face cloth._
**facilities** PL NOUN
l' **équipement** _masc_
**_Language tip_**
**équipement** _is a singular word._
**factory** NOUN
l' **usine** _fem_
**My mum works in a factory.**
Ma mère travaille dans une usine.
**fail** VERB
**rater**
**She's going to fail her exams.**
Elle va rater ses examens.
**fair**
**fair** _can be an adjective or a noun._
**A** ADJECTIVE
**1** **juste**
**That's not fair.**
Ce n'est pas juste.
**2** **blond** _masc_ **blonde** _fem_
**He's got fair hair.**
Il a les cheveux blonds.
**B** NOUN
la **foire** _fem_
**Are you going to the fair?**
Est-ce que tu vas à la foire?
**fairground** NOUN
le **champ de foire** _masc_
**fair-haired** ADJECTIVE
**Hélène is fair-haired.**
Hélène a les cheveux blonds.
**fairly** ADVERB
**assez**
**That's fairly good.**
C'est assez bien.
**fairy** NOUN
la **fée**
_fem_
**fairy tale** NOUN
le **conte de fées** _masc_
**fall** VERB
**tomber**
**Mind you don't fall!**
Fais attention de ne pas tomber!
**fall off** VERB
**tomber de**
**He's going to fall off the wall.**
Il va tomber du mur.
**false** ADJECTIVE
**True or false?**
Vrai ou faux?
**family** NOUN
la **famille** _fem_
**my family**
ma famille
**the whole family**
toute la famille
**the Cooke family**
la famille Cooke
**_Language tip_**
**family** _has one_ **l** , _how many has_ **famille** _got?_
**famous** ADJECTIVE
**célèbre**
**_Language tip_**
_There are two different accents for two different sounds in this word._
**fan** NOUN
le/la **supporter** _masc/fem_
**football fans**
les supporters de football
**fantastic** ADJECTIVE
**fantastique**
**far**
**far** _can be an adjective or an adverb._
**A** ADJECTIVE
**loin** _(a long way)_
**It's not very far.**
Ce n'est pas très loin.
**far from**
loin de
**It's not far from here.**
Ce n'est pas loin d'ici.
**B** ADVERB
**beaucoup** _(much)_
**That's far better!**
C'est beaucoup mieux!
**Is it far?**
C'est loin?
**No, it's not far.**
Non, ce n'est pas loin.
**It's too far.**
C'est trop loin.
**farm** NOUN
la **ferme** _fem_
**farmer** NOUN
l' **agriculteur** _masc_
l' **agricultrice** _fem_
**He's a farmer.**
Il est agriculteur.
**_Language tip_**
_When you say what someone's job is in French, you do not translate_ **a**.
**farmhouse** NOUN
la **ferme** _fem_
**fashion** NOUN
la **mode** _fem_
**fashionable** ADJECTIVE
**à la mode** _masc, fem, pl_
**Jane wears fashionable clothes.**
Jane porte des vêtements à la mode.
**fashion show** NOUN
le **défilé** _masc_
**fast**
**fast** _can be an adverb or an adjective._
**A** ADVERB
**vite**
**You walk fast.**
Tu marches vite.
**B** ADJECTIVE
**rapide**
**a fast car**
une voiture rapide
**fat** ADJECTIVE
**gros** _masc_
**grosse** _fem_
**They're both fat.**
Ils sont gros tous les deux.
**father** NOUN
le **père** _masc_
**my father**
mon père
**your father**
ton père
**Father Christmas** NOUN
le **père Noël** _masc_
**Father's Day** NOUN
la **fête des pères** _fem_
**favourite** ADJECTIVE
**préféré** _masc_
**préférée** _fem_
**David is my favourite cousin.**
David est mon cousin préféré.
**Blue's my favourite colour.**
Ma couleur préférée, c'est le bleu.
**February** NOUN
**février** _masc_
**next February**
en février
**in February**
en février
**the fifth of February**
le cinq février
**_Language tip_**
_The months are not spelled with a capital letter in French._
**feed** VERB
**donner à manger à**
**I'm going to feed the cat.**
Je vais donner à manger au chat.
**feel** VERB
**se sentir**
**I don't feel well.**
Je ne me sens pas bien.
**I feel like...**
J'ai envie de...
**Do you feel like an ice cream?**
Tu as envie d'une glace?
**feet** PL NOUN
les **pieds** _masc pl_
**My feet are cold.**
J'ai froid aux pieds.
**felt-tip pen** NOUN
le **stylo-feutre** _masc_
**Can I borrow your felt-tip pens?**
Je peux emprunter tes stylos-feutres?
**female** NOUN
la **femelle** _fem_
**Is it a male or a female?**
C'est un mâle ou une femelle?
**feminine** ADJECTIVE
**féminin** _masc_
**féminine** _fem_
**fence** NOUN
la **barrière** _fem_
**ferret** NOUN
le **furet** _masc_
**ferry** NOUN
le **ferry** _masc_
**fetch** VERB
**aller chercher**
**Can you fetch my bag?**
Tu peux aller chercher mon sac?
**few**
**few** _can be an adjective or a pronoun._
**A** ADJECTIVE
**a few**
quelques
**a few hours**
quelques heures
**quite a few people**
pas mal de monde
**B** PRONOUN
**a few**
quelques-uns _masc pl_
quelques-unes _fem pl_
**How many chips do you want? — Just a few.**
Tu veux combien de frites? — Seulement quelques-unes.
**fiancé** NOUN
le **fiancé** _masc_
**He's her fiancé.**
C'est son fiancé.
**fiancée** NOUN
la **fiancée** _fem_
**She's his fiancée.**
C'est sa fiancée.
**field** NOUN
**1** le **champ** _masc (in countryside)_
**a field of wheat**
un champ de blé
**2** le **terrain** _masc (for sport)_
**a football field**
un terrain de football
**fifteen** NUMBER
**quinze**
**fifteen euros**
quinze euros
**I am fifteen.**
J'ai quinze ans.
**_Language tip_**
_In English, you can say_ **fifteen** _or_ **fifteen years old**. _In French, you can only say_ **quinze ans**.
**fifteenth** ADJECTIVE
**quinzième**
**on the fifteenth floor**
au quinzième étage
**the fifteenth of August**
le quinze août
**fifth** ADJECTIVE
**cinquième**
**on the fifth floor**
au cinquième étage
**the fifth of August**
le cinq août
**fifty** NUMBER
**cinquante**
**My aunt is fifty.**
Ma tante a cinquante ans.
**_Language tip_**
_In English, you can say_ **fifty** _or_ **fifty years old**. _In French, you can only say_ **cinquante ans**.
**fight**
**fight** _can be a noun or a verb._
**A** NOUN
la **bagarre** _fem_
**B** VERB
**se battre**
**Two boys are fighting.**
Deux garçons se battent.
**figure** NOUN
le **chiffre** _masc_
**Write down the figures.**
Écrivez les chiffres.
**file** NOUN
**1** la **chemise** _fem (folder)_
**Keep the leaflets in your files.**
Gardez les brochures dans vos chemises.
**2** le **fichier** _masc (on computer)_
**fill** VERB
**remplir**
**Can you fill the glasses?**
Tu peux remplir les verres?
**fill in** VERB
**remplir**
**Fill in the gaps in the sentences.**
Remplissez les blancs dans les phrases.
**film** NOUN
**1** le **film** _masc_
**Is it a good film?**
C'est un bon film?
**2** la **pellicule** _fem (for camera)_
**film star** NOUN
la **vedette de cinéma** _fem_
**Johnny Depp is a film star.**
Johnny Depp est une vedette de cinéma.
**final**
**final** _can be an adjective or a noun._
**A** ADJECTIVE
**dernier** _masc_ **dernière** _fem_
**the final minutes**
les dernières minutes
**B** NOUN
la **finale** _fem_
**The final is tomorrow.**
Demain, c'est la finale.
**find** VERB
**trouver**
**My brother wants to find a job.**
Mon frère veut trouver du travail.
**Find page fifteen.**
Trouvez la page quinze.
**fine** ADJECTIVE
**That's fine, thanks.**
C'est très bien, merci.
**How are you? — I'm fine.**
Comment ça va? — Ça va bien.
**finger** NOUN
le **doigt** _masc_
**my little finger**
mon petit doigt
**My finger is hurting.**
J'ai mal au doigt.
**finish**
**finish** _can be a verb or a noun._
**A** VERB
**finir**
**I've got to finish my homework.**
Je dois finir mes devoirs.
**I've finished!**
J'ai fini!
**Is it finished?**
Ça y est?
**_Language tip_**
**finir** _and_ **finish** _are related words. What do they have in common?_
**B** NOUN
**la case 'Arrivée'** _(in board game)_
**fire** NOUN
**1** le **feu** _masc_ (PL les **feux** )
**There's a nice fire in the sitting room.**
Il y a un bon feu dans le salon.
**2** l' **incendie** _masc (accidental)_
**There's a fire in the wood.**
Il y a un incendie dans le bois.
**fire engine** NOUN
la **voiture de pompiers** _fem_
**two fire engines**
deux voitures de pompiers
**fire fighter** NOUN
le **pompier** _masc_
**He's a fire fighter.**
Il est pompier.
**_Language tip_**
_You do not translate_ **a** _when you say what someone's job is in French._
**fire station** NOUN
la **caserne de pompiers** _fem_
**fireworks** PL NOUN
le **feu d'artifice** _masc_
**There are fireworks this evening.**
Il y a un feu d'artifice ce soir.
**first**
**first** _can be an adjective, a noun or an adverb._
**A** ADJECTIVE
**premier** _masc_
**première** _fem_
**the first day**
le premier jour
**the first time**
la première fois
**to come first**
arriver premier
**Who came first?**
Qui est arrivé premier?
**Who wants to be first?**
Qui veut commencer?
**Who's first?**
Qui commence?
**Me first!**
C'est moi qui commence!
**B** NOUN
**at first**
au début
**It's easy at first.**
Au début c'est facile.
**the first of September**
le premier septembre
**C** ADVERB
**d'abord**
**First write your names.**
D'abord écrivez vos noms.
**first of all**
tout d'abord
**first aid** NOUN
les **premiers secours** _masc pl_
**fir tree** NOUN
le **sapin** _masc_
**fish**
**fish** _can be a noun or a verb._
**A** NOUN
le **poisson** _masc_
**I don't like fish.**
Je n'aime pas le poisson.
**B** VERB
**to go fishing**
aller à la pêche
**Let's go fishing.**
On va à la pêche?
**fish fingers** PL NOUN
les **bâtonnets de poisson** _masc pl_
**fishing** NOUN
la **pêche** _fem_
**I like fishing.**
J'aime la pêche.
**fishing boat** NOUN
le **bateau de pêche** _masc_
**fish tank** NOUN
l' **aquarium** _masc_
**fit**
**fit** _can be a verb or an adjective._
**A** VERB
**être la bonne taille**
**It doesn't fit.**
Ce n'est pas la bonne taille.
**B** ADJECTIVE
**en forme**
**She's fit.**
Elle est en forme.
**five** NUMBER
**cinq**
**five euros**
cinq euros
**She is five.**
Elle a cinq ans.
**_Language tip_**
_In English, you can say_ **five** _or_ **five years old**. _In French, you can only say_ **cinq ans**.
**fix** VERB
**réparer**
**Can you fix my bike?**
Vous pouvez réparer mon vélo?
**fizzy** ADJECTIVE
**gazeux** _masc_
**gazeuse** _fem_
**I don't like fizzy drinks.**
Je n'aime pas les boissons gazeuses.
**flag** NOUN
le **drapeau** _masc_ (PL les **drapeaux** )
**flame** NOUN
la **flamme** _fem_
**flan** NOUN
**1** la **tarte** _fem (sweet)_
**a raspberry flan**
une tarte aux framboises
**2** la **quiche** _fem (savoury)_
**a cheese and onion flan**
une quiche au fromage et aux oignons
**flannel** NOUN
le **gant de toilette** _masc_
**_Language tip_**
**gant** _means 'glove'. A_ **gant de toilette** _is a glove-shaped face cloth._
**flash** NOUN
le **flash** _masc_ (PL les **flashes** )
**Has your camera got a flash?**
Est-ce que ton appareil photo a un flash?
**a flash of lightning**
un éclair
**flask** NOUN
le **thermos** _masc_
**flat**
**flat** _can be an adjective or a noun._
**A** ADJECTIVE
**1** **plat** _masc_
**plate** _fem (level)_
**a flat roof**
un toit plat
**flat shoes**
des chaussures plates
**2** **crevé** _masc_ **crevée** _fem (tyre)_
**I've got a flat tyre.**
J'ai un pneu crevé.
**B** NOUN
l' **appartement** _masc_
**She lives in a flat.**
Elle habite un appartement.
**_Language tip_**
_The English word_ **apartment** _has one_ **p** , _how many has_ **appartement** _got?_
**flavour** NOUN
le **parfum** _masc_
**Which flavour of ice cream would you like?**
Quel parfum de glace est-ce que tu veux?
**flight** NOUN
le **vol** _masc_
**What time is the flight to Paris?**
À quelle heure est le vol pour Paris?
**flippers** PL NOUN
les **palmes** _fem pl_
**floor** NOUN
**1** le **sol** _masc_
**a tiled floor**
un sol carrelé
**on the floor**
par terre
**Sit on the floor.**
Asseyez-vous par terre.
**2** l' **étage** _masc (storey)_
**the first floor**
le premier étage
**the ground floor**
le rez-de-chaussée
**on the third floor**
au troisième étage
**floppy disk** NOUN
la **disquette** _fem_
**florist** NOUN
le/la **fleuriste** _masc/fem_
**flour** NOUN
la **farine** _fem_
**flower** NOUN
la **fleur** _fem_
**flu** NOUN
la **grippe** _fem_
**Jean-Louis has got flu.**
Jean-Louis a la grippe.
**fluent** ADJECTIVE
**My sister speaks fluent French.**
Ma sœur parle couramment le français.
**flute** NOUN
la **flûte** _fem_
**I play the flute.**
Je joue de la flûte.
**_Language tip_**
_There's an extra word in the French example sentence. What is it?_
**fly**
**fly** _can be a verb or a noun._
**A** VERB
**aller en avion** _(go by plane)_
**I'm going to fly to Florida.**
Je vais aller en Floride en avion.
**B** NOUN
la **mouche** _
fem (insect)_
**fog** NOUN
le **brouillard** _masc_
**foggy** ADJECTIVE
**a foggy day**
un jour de brouillard
**It's foggy.**
Il y a du brouillard.
**fold** VERB
**plier**
**Fold the paper in half.**
Pliez la feuille en deux.
**folder** NOUN
la **chemise** _fem_
**follow** VERB
**suivre**
**Follow me.**
Suivez-moi.
**food** NOUN
**I like French food.**
J'aime la cuisine française.
**Bring some food.**
Apportez à manger.
**We need to buy some food.**
Nous devons acheter à manger.
**food processor** NOUN
le **robot** _masc_
**foot** NOUN
le **pied** _masc_
**My feet are hurting.**
J'ai mal aux pieds.
**on foot**
à pied
**Richard is 6 foot tall.**
Richard mesure un mètre quatre-vingt.
**_Did you know...?_**
_In France, measurements are always in metres and centimetres, rather than feet and inches._
**football** NOUN
**1** le **football** _masc (game)_
**I like playing football.**
J'aime jouer au football.
**_Language tip_**
_You can also say_ **J'aime jouer au foot** , _which is more slang._
**Do you want to play football, Pascal?**
Tu veux jouer au foot, Pascal?
**Do you want to play football, boys?**
Vous voulez jouer au foot, les garçons?
**2** le **ballon de foot** _masc (ball)_
**Jason's got a new football.**
Jason a un nouveau ballon de foot.
**football boots** PL NOUN
les **chaussures de foot** _fem pl_
**footballer** NOUN
le **footballeur** _masc_
la **footballeuse** _fem_
**football player** NOUN
le **joueur de football** _masc_
la **joueuse de football** _fem_
**David Beckham is a famous football player.**
David Beckham est un joueur de football célèbre.
**football shirt** NOUN
le **maillot de foot** _masc_
**footpath** NOUN
le **sentier** _masc_
**for** PREPOSITION
**pour**
**a present for me**
un cadeau pour moi
**I'll do it for you.**
Je vais le faire pour toi.
**What's it for?**
Ça sert à quoi?
**What's the French for 'lion'?**
Comment dit-on 'lion' en français?
**I have been learning French for six months.**
J'apprends le français depuis six mois.
**forbidden** ADJECTIVE
**défendu** _masc_
**défendue** _fem_
**forecast** NOUN
**the weather forecast**
la météo
**What's the forecast for today?**
Il va faire quel temps aujourd'hui?
**foreign** ADJECTIVE
**étranger** _masc_
**étrangère** _fem_
**foreigner** NOUN
l' **étranger** _masc_
l' **étrangère** _fem_
**He's a foreigner.**
C'est un étranger.
**forest** NOUN
la **forêt** _fem_
**forget** VERB
**oublier**
**Don't forget!**
N'oubliez pas!
**fork** NOUN
la **fourchette** _
fem_
**form** NOUN
le **formulaire** _
masc_
**You have to fill in the form.**
Vous devez remplir le formulaire.
**fortnight** NOUN
**a fortnight**
quinze jours
**I'm going on holiday for a fortnight.**
Je pars en vacances pendant quinze jours.
**_Language tip_**
**quinze jours** _actually means 15 days._
**forty** NUMBER
**quarante**
**My father is forty.**
Mon père a quarante ans.
**_Language tip_**
_In English, you can say_ **forty** _or_ **forty years old**. _In French, you can only say_ **quarante ans**.
**forward** ADVERB
**en avant**
**a step forward**
un pas en avant
**to move forward**
avancer
**Move forward two spaces.**
Avancez de deux cases.
**foster child** NOUN
l' **enfant adoptif** _masc_
l' **enfant adoptive** _fem_
**fountain** NOUN
la **fontaine** _fem_
**four** NUMBER
**quatre**
**four euros**
quatre euros
**He is four.**
Il a quatre ans.
**_Language tip_**
_In English, you can say_ **four** _or_ **four years old**. _In French, you can only say_ **quatre ans**.
**fourteen** NUMBER
**quatorze**
**fourteen euros**
quatorze euros
**I'm fourteen.**
J'ai quatorze ans.
**_Language tip_**
_In English, you can say_ **fourteen** _or_ **fourteen years old**. _In French, you can only say_ **quatorze ans**.
**fourteenth** ADJECTIVE
**quatorzième**
**on the fourteenth floor**
au quatorzième étage
**the fourteenth of August**
le quatorze août
**fourth** ADJECTIVE
**quatrième**
**on the fourth floor**
au quatrième étage
**the fourth of July**
le quatre juillet
**fox** NOUN
le **renard** _masc_
**France** NOUN
la **France** _fem_
**I like France.**
J'aime la France.
**Cannes is in France.**
Cannes est en France.
**We're going to France.**
Nous allons en France.
**to France**
en France
**He lives in France.**
Il habite en France.
**They are from France.**
Ils sont français.
**freckles** PL NOUN
les **taches de rousseur** _fem pl_
**free** ADJECTIVE
**1** **gratuit** _masc_ **gratuite** _fem (free of charge)_
**a free brochure**
une brochure gratuite
**2** **libre** _(not taken)_
**Excuse me, is this seat free?**
Excusez-moi, la place est libre?
**freezer** NOUN
le **congélateur** _masc_
**freezing** ADJECTIVE
**I'm freezing!**
Je suis gelé!
**It's absolutely freezing!**
Il fait un froid de canard!
**French**
**French** _can be an adjective or a noun._
**A** ADJECTIVE
**français** _masc_ **française** _fem_
**a French name**
un nom français
**a French school**
une école française
**our French friends**
nos amis français
**our French teacher**
notre professeur de français
**my French book**
mon livre de français
**French people**
les Français
**He's French.**
Il est français.
**She's French.**
Elle est française.
**B** NOUN
le **français** _masc (language)_
**Do you speak French?**
Est-ce que tu parles français?
**the French**
les Français
**_Language tip_**
**français** _is not spelled with a capital letter except when it means a French person._
**French beans** PL NOUN
les **haricots verts** _masc pl_
**French fries** PL NOUN
les **frites** _fem pl_
**Frenchman** NOUN
le **Français** _masc_
**Frenchwoman** NOUN
la **Française** _fem_
**Friday** NOUN
le **vendredi** _masc_
**It's Friday today.**
Aujourd'hui c'est vendredi.
**on Friday**
vendredi
**on Fridays**
le vendredi
**every Friday**
tous les vendredis
**last Friday**
vendredi dernier
**next Friday**
vendredi prochain
**_Language tip_**
_Days of the week are not spelled with a capital letter in French._
**fridge** NOUN
le **frigo** _masc_
**friend** NOUN
l' **ami** _masc_
l' **amie** _fem_
**my friend Paul**
mon ami Paul
**my friend Gaëlle**
mon amie Gaëlle
**friendly** ADJECTIVE
**gentil** _masc_
**gentille** _fem_
**She's very friendly.**
Elle est très gentille.
**frightened** ADJECTIVE
**to be frightened**
avoir peur
**Anna's frightened of spiders.**
Anna a peur des araignées.
**I'm frightened!**
J'ai peur!
**fringe** NOUN
la **frange** _fem_
**She's got a fringe.**
Elle a une frange.
**Frisbee** ® NOUN
le **Frisbee** ® _masc_
**frog** NOUN
la **grenouille** _
fem_
**frogs' legs**
les cuisses de grenouille
**from** PREPOSITION
**de**
**She comes from Perth.**
Elle vient de Perth.
**a letter from my penfriend**
une lettre de mon correspondant
**from... to...**
de... à...
**from London to Paris**
de Londres à Paris
**the numbers from 1 to 39**
les nombres de un à trente-neuf
**Where do you come from?**
Tu viens d'où?
**I come from Birmingham.**
Je viens de Birmingham.
**front**
**front** _can be a noun or an adjective._
**A** NOUN
le **devant** _masc_
**the front of the house**
le devant de la maison
**in front of**
devant
**in front of the house**
devant la maison
**B** ADJECTIVE
**de devant**
**the front row**
la rangée de devant
**front door** NOUN
la **porte d'entrée** _fem_
**frost** NOUN
le **gel** _masc_
**frosty** ADJECTIVE
**a frosty morning**
un matin glacial
**It's frosty today.**
Il gèle aujourd'hui.
**frozen** ADJECTIVE
**1** **gelé** _masc_ **gelée** _fem (fingers, lake)_
**2** **surgelé** _masc_ **surgelée** _fem (food)_
**fruit** NOUN
**I like fruit.**
J'aime les fruits.
**a piece of fruit**
un fruit
**fruit juice** NOUN
le **jus de fruits** _masc_
**fruit salad** NOUN
la **salade de fruits** _fem_
**frying pan** NOUN
la **poêle** _fem_
**full** ADJECTIVE
**plein** _masc_
**pleine** _fem_
**The bottle's full.**
La bouteille est pleine.
**I'm full.**
J'ai bien mangé.
**full stop** NOUN
le **point** _masc_
**fun** NOUN
**to have fun**
s'amuser
**Are you having fun?**
Tu t'amuses?
**It's fun!**
C'est chouette!
**Have fun!**
Amuse-toi bien!
**funfair** NOUN
la **fête foraine** _fem_
**funny** ADJECTIVE
**drôle**
**It was very funny.**
C'était très drôle.
**fur** NOUN
**1** la **fourrure** _fem_
**a fur coat**
un manteau de fourrure
**2** le **poil** _masc_
**the dog's fur**
le poil du chien
**furious** ADJECTIVE
**furieux** _masc_
**furieuse** _fem_
**Dad was furious with me.**
Papa était furieux contre moi.
**The girls are furious.**
Les filles sont furieuses.
**furniture** NOUN
les **meubles** _masc pl_
**We've got new furniture.**
Nous avons de nouveaux meubles.
**a piece of furniture**
un meuble
**future** NOUN
l' **avenir** _masc_
**Be more careful in future.**
Sois plus prudent à l'avenir.
# **G g**
**game** NOUN
**1** le **jeu** _masc_ (PL les **jeux** ) _(hangman, marbles, bingo etc)_
**It's a new game.**
C'est un nouveau jeu.
**Let's play a game.**
On joue à un jeu?
**2** le **match** _masc (match)_
**The game is tomorrow.**
Le match, c'est demain.
**a game of football**
un match de foot
**games** PL NOUN
le **sport** _masc (at school)_
**I like games.**
J'aime le sport.
**gang** NOUN
la **bande** _fem_
**garage** NOUN
le **garage** _masc_
**garden** NOUN
le **jardin** _masc_
**We haven't got a garden.**
Nous n'avons pas de jardin.
**garden centre** NOUN
la **jardinerie** _fem_
**gardening** NOUN
le **jardinage** _masc_
**garlic** NOUN
l' **ail** _masc_
**I don't like garlic.**
Je n'aime pas l'ail.
**gas** NOUN
le **gaz** _masc_
**gas cooker** NOUN
la **cuisinière à gaz** _fem_
**gate** NOUN
**1** le **portail** _masc (of garden, of school)_
**Please close the gate.**
Fermez le portail s'il vous plaît.
**2** la **barrière** _fem (of field)_
**There's a cow by the gate.**
Il y a une vache près de la barrière.
**gave** VERB _see_ **give**
**GCSE** NOUN
le **brevet des collèges** _masc_
**_Did you know...?_**
_Exams in France are different from exams in Britain_. **Le brevet des collèges** _is an exam you take at the end of the fourth year in secondary school._
**geese** PL NOUN
les **oies** _fem pl_
**general knowledge** NOUN
les **connaissances générales** _fem pl_
**a general knowledge quiz**
un quiz de connaissances générales
**generous** ADJECTIVE
**généreux** _masc_
**généreuse** _fem_
**That's very generous of you.**
C'est très généreux de ta part.
**genius** NOUN
le **génie** _masc_
**She's a genius!**
C'est un génie!
**gents** NOUN
les **toilettes** _
fem pl_
**Where is the gents, please?**
Où sont les toilettes, s'il vous plaît?
**geography** NOUN
la **géographie** _fem_
**I like geography.**
J'aime la géographie.
**gerbil** NOUN
la **gerbille** _fem_
**German**
**German** _can be an adjective or a noun._
**A** ADJECTIVE
**allemand**
_masc_ **allemande** _fem_
**a German car**
une voiture allemande
**German people**
les Allemands
**B** NOUN
l' **allemand** _masc_
**I can speak German.**
Je parle allemand.
**_Language tip_**
**allemand** _is not spelled with a capital letter except when it means a German person._
**German measles** NOUN
la **rubéole** _fem_
**He's got German measles.**
Il a la rubéole.
**Germany** NOUN
l' **Allemagne** _fem_
**get** VERB
**1** **avoir** _(receive)_
**He always gets lots of presents.**
Il a toujours plein de cadeaux.
**What did you get for your birthday?**
Qu'est-ce que tu as eu pour ton anniversaire?
**I got lots of presents.**
J'ai eu beaucoup de cadeaux.
**How much pocket money do you get?**
Tu reçois combien d'argent de poche?
**I get £5 a week.**
Je reçois cinq livres par semaine.
**_Language tip_**
_When_ **I've got** _means_ **I have** _it is translated by the verb_ **avoir**.
**I've got a dog and two cats.**
J'ai un chien et deux chats.
**I haven't got a mobile phone.**
Je n'ai pas de portable.
**Marie hasn't got long hair.**
Marie n'a pas les cheveux longs.
**How many have you got?**
Combien en avez-vous?
**2** **acheter** _(buy)_
**Can you get me a coke?**
Tu peux m'acheter un coca?
**Mum's getting me a playstation.**
Maman m'achète une play station.
**3** **aller chercher** _(fetch)_
**Get your coats.**
Allez chercher vos manteaux.
**4** **aller** _(go)_
**How do you get to the castle, please?**
Pour aller au château, s'il vous plaît?
**5** **arriver** _(arrive)_
**What time do we get there?**
À quelle heure est-ce qu'on arrive?
**_Language tip_**
_When_ **I've got to** _means_ **I must** , _it is translated by the verb_ **devoir**.
**I've got to go to the dentist.**
Je dois aller chez le dentiste.
**You've got to take a card, Michel.**
Tu dois prendre une carte, Michel.
**You've got to be careful, children.**
Vous devez faire attention, les enfants.
**I've got a cat.**
J'ai un chat.
**I haven't got a dog.**
Je n'ai pas de chien.
**Have you got a sister?**
Tu as une sœur?
**She's got long hair.**
Elle a les cheveux longs.
**get away** VERB
**s'échapper**
**Quick! He's getting away!**
Vite! Il s'échappe!
**get back** VERB
**rentrer**
**What time will you get back?**
Tu rentres à quelle heure?
**get in** VERB
**monter**
**Get in, boys!**
Montez, les garçons!
**Get in the car, Charlotte.**
Monte dans la voiture, Charlotte.
**get off** VERB
**descendre de**
**Where do we get off the train?**
Où est-ce que nous descendons du train?
**get on** VERB
**1** **prendre** _(bus, train)_
**I get on the bus at the station.**
Je prends le bus à la gare.
**2** **monter sur** _(bike)_
**I got on my bike.**
Je suis monté sur mon vélo.
**How are you getting on?**
Comment ça marche?
**get out** VERB
**sortir**
**Get out!**
Sortez!
**Get your book out, André.**
Sors ton livre, André.
**Get your things out!**
Sortez vos affaires!
**get up** VERB
**se lever**
**What time do you get up?**
Tu te lèves à quelle heure?
**I get up early.**
Je me lève tôt.
**ghost** NOUN
le **fantôme** _masc_
**giant** NOUN
le **géant** _masc_
la **géante** _fem_
**gift** NOUN
le **cadeau** _masc_ (PL les **cadeaux** )
**Christmas gifts**
les cadeaux de Noël
**gift shop** NOUN
la **boutique de cadeaux** _fem_
**gigantic** ADJECTIVE
**gigantesque**
**ginger** ADJECTIVE
**I've got ginger hair.**
J'ai les cheveux roux.
**giraffe** NOUN
la **girafe** _fem_
**girl** NOUN
**1** la **fille** _fem_
**Come on girls!**
Allez les filles!
**2** la **petite fille** _fem (little girl)_
**a five-year-old girl**
une petite fille de cinq ans
**3** la **jeune fille** _fem (teenager)_
**a sixteen-year-old girl**
une jeune fille de seize ans
**girlfriend** NOUN
la **copine** _fem_
**She's his girlfriend.**
C'est sa copine.
**give** VERB
**1** **donner**
**Give me the book, please.**
Donne-moi le livre, s'il te plaît.
**Give the books to Adam.**
Donne les livres à Adam.
**2** **offrir** _(gift)_
**What are you giving Luc?**
Qu'est-ce que tu vas offrir à Luc?
**My parents gave me a bike.**
Mes parents m'ont offert un vélo.
**give out** VERB
**distribuer**
**Will you give out the books, please, Christine?**
Tu peux distribuer les livres, s'il te plaît, Christine?
**glad** ADJECTIVE
**content** _masc_
**contente** _fem_
**I was glad to get your letter.**
J'étais content de recevoir ta lettre.
**glass** NOUN
le **verre** _masc_
**I'd like a glass of milk.**
Je voudrais un verre de lait.
**glasses** PL NOUN
les **lunettes** _fem pl_
**I wear glasses.**
Je porte des lunettes.
**globe** NOUN
le **globe** _masc_
**We've got a globe in the classroom.**
Nous avons un globe dans la classe.
**glove** NOUN
le **gant** _masc_
**I've got red gloves.**
J'ai des gants rouges.
**glue** NOUN
la **colle** _fem_
**go**
**go** _can be a noun or a verb._
**A** NOUN
le **tour** _masc_
**It's my go.**
C'est mon tour.
**Whose go is it?**
À qui le tour?
**B** VERB
**1** **aller**
**I don't want to go to school.**
Je ne veux pas aller à l'école.
**I don't go to school on Saturday.**
Je ne vais pas à l'école le samedi.
**Where are you going?**
Où vas-tu?
**2** _(talking about the future)_
**I'm going to win.**
Je vais gagner.
**We're going to visit our cousins on Friday.**
On va rendre visite à nos cousins vendredi.
**I'm not going to play.**
Je ne vais pas jouer.
**3** _(talking about the past)_
**I went to London.**
Je suis allé à Londres.
**Where did you go yesterday?**
Où es-tu allé hier?
**I went to Luc's house.**
Je suis allé chez Luc.
**He's gone.**
Il est parti.
**She's gone.**
Elle est partie.
**go away** VERB
**s'en aller**
**Go away, Sophie!**
Va-t'en, Sophie!
**Go away!**
Allez-vous-en!
**go back** VERB
**1** _(in game)_
**Go back three spaces.**
Recule de trois cases.
**2** **retourner** _(return)_
**Go back to your seat, Colette!**
Retourne à ta place, Colette!
**Go back to your seats, boys!**
Retournez à vos places, les garçons!
**Let's go back to the beginning.**
Recommençons.
**go down** VERB
**descendre**
**Let's go down to the cellar.**
Descendons à la cave.
**go forward** VERB
**Go forward three spaces, Alain.**
Avance de trois cases, Alain.
**go in** VERB
**entrer**
**Let's go in.**
Entrons.
**go on** VERB
**1** **continuer** _(continue)_
**Shall I go on?**
Je continue?
**Go on, don't stop.**
Vas-y, ne t'arrête pas.
**2** **se passer** _(happen)_
**What's going on?**
Qu'est-ce qui se passe?
**go out** VERB
**sortir**
**Are you going out tonight?**
Tu sors ce soir?
**Melanie's going out with Matt.**
Melanie sort avec Matt.
**go past** VERB
**passer devant**
**We're going past the cathedral.**
Nous passons devant la cathédrale.
**Go past the post office and turn right.**
Passe devant la poste et tourne à droite.
**go up** VERB
**monter**
**I'm going up to my room.**
Je monte dans ma chambre.
**goal** NOUN
le **but** _masc_
**It's a goal!**
C'est un but!
**He's scored a goal!**
Il a marqué un but!
**goalkeeper** NOUN
le **gardien de but** _masc_
**He's the goalkeeper.**
C'est le gardien de but.
**goat** NOUN
la **chèvre** _fem_
**God** NOUN
**Dieu** _masc_
**godfather** NOUN
le **parrain** _masc_
**my godfather**
mon parrain
**godmother** NOUN
la **marraine** _fem_
**my godmother**
ma marraine
**goggles** PL NOUN
les **lunettes de plongée** _
fem pl_
**I've got new goggles.**
J'ai de nouvelles lunettes de plongée.
**gold** ADJECTIVE
**a gold necklace**
un collier en or
**goldfish** NOUN
le **poisson rouge** _masc_
**I've got five goldfish.**
J'ai cinq poissons rouges.
**golf** NOUN
le **golf** _masc_
**My dad plays golf.**
Mon père joue au golf.
**golf club** NOUN
le **club de golf** _masc_
**golf course** NOUN
le **terrain de golf** _masc_
**gone** VERB _see_ **go**
**good** ADJECTIVE
**1** **bon** _masc_ **bonne** _fem (great)_
**It's a very good film.**
C'est un très bon film.
**We've got a good teacher.**
Nous avons une bonne maîtresse.
**That's a good idea.**
C'est une bonne idée.
**Jane's very good at French.**
Jane est très bonne en français.
**2** **sage** _(not naughty)_
**Marcel is always good.**
Marcel est toujours sage.
**It's good.**
C'est bon.
**Good morning!**
Bonjour!
**Good morning everyone!**
Bonjour tout le monde!
**Good afternoon!**
Bonjour!
**Good evening!**
Bonsoir!
**Good night!**
Bonne nuit!
**Good luck!**
Bonne chance!
**Be good, André!**
Sois sage, André!
**goodbye** EXCLAMATION
**au revoir!**
**Good Friday** NOUN
le **Vendredi saint** _masc_
**good-looking** ADJECTIVE
**beau** _masc_
**belle** _fem_
**Yann is very good-looking.**
Yann est très beau.
**_Language tip_**
_When_ **beau** _comes before a vowel sound, it changes to_ **bel**.
**a good-looking man**
un bel homme
**goose** NOUN
l' **oie** _fem_
**gorgeous** ADJECTIVE
**1** **beau** _masc_ **belle** _fem (person)_
**Isn't she gorgeous!**
Qu'elle est belle!
**2** **splendide** _(weather)_
**The weather's gorgeous.**
Il fait un temps splendide.
**got** VERB _see_ **get**
**gradually** ADVERB
**peu à peu**
**graffiti** PL NOUN
les **graffiti** _masc pl_
**There's a lot of graffiti.**
Il y a beaucoup de graffiti.
**gram** NOUN
le **gramme** _masc_
**two hundred grams of cheese**
deux cents grammes de fromage
**grammar** NOUN
la **grammaire** _fem_
**I like grammar.**
J'aime la grammaire.
**grandchildren** PL NOUN
les **petits-enfants** _masc pl_
**her grandchildren**
ses petits-enfants
**granddad** NOUN
le **papi** _masc_
**my granddad**
mon papi
**granddaughter** NOUN
la **petite-fille** _fem_
**He has two granddaughters.**
Il a deux petites-filles.
**grandfather** NOUN
le **grand-père** _masc_
**my grandfather**
mon grand-père
**grandma** NOUN
la **mamie** _fem_
**her grandma**
sa mamie
**grandmother** NOUN
la **grand-mère** _fem_
**his grandmother**
sa grand-mère
**grandpa** NOUN
le **papi** _masc_
**my grandpa**
mon papi
**grandparents** PL NOUN
les **grands-parents** _masc pl_
**my grandparents**
mes grands-parents
**grandson** NOUN
le **petit-fils** _masc_
**her grandsons**
ses petits-fils
**granny** NOUN
la **mamie** _fem_
**my granny**
ma mamie
**grapefruit** NOUN
le **pamplemousse** _masc_
**I don't like grapefruit.**
Je n'aime pas le pamplemousse.
**grapefruit juice** NOUN
le **jus de pamplemousse** _masc_
**grapes** PL NOUN
le **raisin** _masc_
**a kilo of grapes**
un kilo de raisin
**_Language tip_**
**raisin** _is a singular word. In English_ , **raisins** _are dried grapes._
**grass** NOUN
l' **herbe** _fem_
**The children are playing on the grass.**
Les enfants jouent dans l'herbe.
**grated** ADJECTIVE
**râpé** _masc_
**râpée** _fem_
**grated cheese**
du fromage râpé
**gravy** NOUN
**I'd like some gravy.**
Je voudrais de la sauce.
**great** ADJECTIVE
**génial** _masc_
**géniale** _fem_
**We're going to France. — Great!**
Nous allons en France. — Génial!
**That's great!**
C'est génial!
**Great Britain** NOUN
la **Grande-Bretagne** _fem_
**We live in Great Britain.**
Nous habitons en Grande-Bretagne.
**greedy** ADJECTIVE
**gourmand** _masc_
**gourmande** _fem_
**Don't be so greedy Émmeline.**
Ne sois pas si gourmande, Émmeline!
**green**
**green** _can be an adjective or a noun._
**A** ADJECTIVE
**vert** _masc_
**verte** _fem_
**a green sweater**
un pull vert
**a green car**
une voiture verte
**I've got green eyes.**
J'ai les yeux verts.
**_Language tip_**
_Colour adjectives come after the noun in French._
**B** NOUN
le **vert** _masc_
**Green is my favourite colour.**
Ma couleur préférée, c'est le vert.
**greengrocer's** NOUN
le **marchand de fruits et légumes** _masc_
**at the greengrocer's**
chez le marchand de fruits et légumes
**greenhouse** NOUN
la **serre** _fem_
**greetings card** NOUN
la **carte de vœux** _fem_
**grey**
**grey** _can be an adjective or a noun._
**A** ADJECTIVE
**gris** _masc_ **grise** _fem_
**a grey sweater**
un pull gris
**a grey skirt**
une jupe grise
**She's got grey hair.**
Elle a les cheveux gris.
**_Language tip_**
_Colour adjectives come after the noun in French._
**B** NOUN
le **gris** _masc_
**He is dressed in grey.**
Il est habillé en gris.
**grin** VERB
**sourire**
**Why are you grinning like that?**
Pourquoi tu souris comme ça?
**grocer's** NOUN
l' **épicerie** _fem_
**I'm going to the grocer's.**
Je vais à l'épicerie.
**groom** NOUN
le **marié** _masc_
**ground** NOUN
**1** la **terre** _fem_
**We sat on the ground.**
Nous nous sommes assis par terre.
**2** le **sol** _masc (earth)_
**The ground is wet.**
Le sol est mouillé.
**3** le **terrain** _masc (sports ground)_
**Where's the football ground?**
Où est le terrain de football?
**on the ground**
par terre
**ground floor** NOUN
le **rez-de-chaussée** _masc_
**This is the ground floor.**
C'est le rez-de-chaussée.
**The toilets are on the ground floor.**
Les toilettes sont au rez-de-chaussée.
**on the ground floor**
au rez-de-chaussée
**group** NOUN
le **groupe** _masc_
**Get into groups of four.**
Mettez-vous en groupes de quatre.
**grow** VERB
**1** **pousser** _(plant)_
**Grass grows fast.**
L'herbe pousse vite.
**2** **faire pousser** _(gardener)_
**I'm growing a sunflower.**
Je fais pousser un tournesol.
**3** **grandir** _(get bigger)_
**My feet have grown.**
Mes pieds ont grandi.
**grow up** VERB
**What do you want to be when you grow up, Samir?**
Samir, qu'est ce que tu veux faire quand tu seras grand?
**What do want to be when you grow up, Céline?**
Céline, qu'est ce que tu veux faire quand tu seras grande?
**_Language tip_**
_One example question is to a boy, the other to a girl. How can you tell?_
**growl** VERB
**grogner**
**My dog growls a lot.**
Mon chien grogne beaucoup.
**grown** VERB _see_ **grow**
**grown-up** NOUN
la **grande personne** _fem_
**the grown-ups**
les grandes personnes
**guard dog** NOUN
le **chien de garde** _masc_
**guess** VERB
**deviner**
**Guess what this is!**
Devine ce que c'est!
**guest** NOUN
l' **invité** _masc_
l' **invitée** _fem_
**our French guests**
nos invités français
**guide** NOUN
**1** le **guide** _masc_
la **guide** _fem (tourist guide)_
**He works as a guide at the castle.**
Il travaille comme guide au château.
**2** l' **éclaireuse** _fem (girl guide)_
**I'm a guide.**
Je suis éclaireuse.
**_Did you know...?_**
_Guides and scouts are not as common in France as they are in Britain._
**guidebook** NOUN
le **guide** _masc_
**guide dog** NOUN
le **chien d'aveugle** _masc_
**guinea pig** NOUN
le **cochon d'Inde** _masc_
**I've got a guinea pig.**
J'ai un cochon d'Inde.
**guitar** NOUN
la **guitare** _fem_
**I play the guitar.**
Je joue de la guitare.
**_Language tip_**
_There is one letter in the French word_ **guitare** _that isn't in the English word. What is it?_
**gun** NOUN
le **pistolet** _masc_
**guy** NOUN
**you guys**
les gars
**Hurry up you guys!**
Dépêchez-vous les gars!
**gym** NOUN
**1** la **gym** _fem (school subject)_
**We've got gym today.**
On a gym aujourd'hui.
**2** la **salle de gym** _fem (place)_
**My mum goes to the gym.**
Ma mère va à la salle de gym.
**gymnastics** NOUN
la **gymnastique** _fem_
**I like gymnastics.**
J'aime la gymnastique.
**I do gymnastics.**
Je fais de la gymnastique.
# **H h**
**had** VERB _see_ **have**
**hadn't** = **had not** _see_ **have**
**hail**
**hail** _can be a noun or a verb._
**A** NOUN
la **grêle** _fem_
**B** VERB
**grêler**
**It's hailing.**
Il grêle.
**hair** NOUN
**1** les **cheveux** _masc pl_
**_Language tip_**
**cheveux** _is a plural word, so you have to use a plural adjective with it._
**He's got black hair.**
Il a les cheveux noirs.
**I've got long hair.**
J'ai les cheveux longs.
**I want to wash my hair.**
Je veux me laver les cheveux.
**You've had your hair cut!**
Tu t'es fait couper les cheveux!
**2** le **poil** _masc (fur)_
**My cat has long hair.**
Mon chat a le poil long.
**hairbrush** NOUN
la **brosse à cheveux** _fem_
**hairdresser** NOUN
le **coiffeur** _masc_
la **coiffeuse** _fem_
**He's a hairdresser.**
Il est coiffeur.
**_Language tip_**
_You do not translate_ **'a'** _when you say what someone's job is in French._
**hairdresser's** NOUN
le **coiffeur** _masc_
**at the hairdresser's**
chez le coiffeur
**hairstyle** NOUN
la **coiffure** _fem_
**You've got a new hairstyle.**
Tu as une nouvelle coiffure.
**hairy** ADJECTIVE
**poilu** _masc_
**poilue** _fem_
**half**
**half** _can be a noun, an adjective or an adverb._
**A** NOUN
**1** la **moitié** _fem (fraction)_
**half of the class**
la moitié de la classe
**to cut something in half**
couper quelque chose en deux
**2** le **billet demi-tarif** _masc (ticket)_
**A half single to York, please.**
Un billet aller simple demi-tarif pour York, s'il vous plaît.
**two and a half**
deux et demi
**half an hour**
une demi-heure
**half past ten**
dix heures et demie
**half a kilo**
un demi kilo
**B** ADJECTIVE
**a half portion**
une demi-portion
**C** ADVERB
**à moitié**
**I'm half Scottish.**
Je suis à moitié écossais.
**half-brother** NOUN
le **demi-frère** _masc_
**my half-brother**
mon demi-frère
**half-sister** NOUN
la **demi-sœur** _fem_
**my half-sister**
ma demi-sœur
**half-term** NOUN
les **vacances** _fem pl_
**What are you doing at half-term?**
Qu'est-ce que tu fais pendant les vacances?
_**Did you know...?**_
_There are two half-term holidays in France:_ **les vacances de la Toussaint** _(in October/November) and_ **les vacances de février** _(in February)._
**half-time** NOUN
la **mi-temps** _fem_
**hall** NOUN
**1** le **hall** _masc (of school)_
**We have gym in the hall.**
On a gym dans le hall.
**2** l' **entrée** _fem (entrance hall)_
**Hallowe'en** NOUN
la **veille de la Toussaint** _fem_
_**Did you know...?**_
_The French means 'Eve of All Saints' Day'._ **Hallowe'en** _is not traditionally celebrated in France, but All Saints' Day (the first of November) is a public holiday, and is the day when people often visit family graves._
**ham** NOUN
le **jambon** _masc_
**a ham sandwich**
un sandwich au jambon
**hamburger** NOUN
le **hamburger**
_masc_
**hamster** NOUN
le **hamster**
_masc_
**hand** NOUN
**1** la **main** _fem (of person)_
**Put up your hands.**
Levez la main.
**Can you give me a hand?**
Tu peux me donner un coup de main?
**2** l' **aiguille** _fem (of clock)_
**hand in** VERB
**rendre**
**Hand in your books.**
Rendez vos cahiers.
**hand out** VERB
**distribuer**
**Hand out the books, Ahmed.**
Distribue les livres, Ahmed.
**handbag** NOUN
le **sac à main** _masc_
**handball** NOUN
le **handball** _masc_
**Can we play handball?**
On peut jouer au handball?
**handkerchief** NOUN
le **mouchoir** _masc_
**Have you got a handkerchief?**
Tu as un mouchoir?
**handle** NOUN
la **poignée** _fem_
**handlebars** PL NOUN
le **guidon** _masc_
**_Language tip_**
**guidon** _is a singular word._
**handsome** ADJECTIVE
**beau** _masc_
**belle** _fem_
**Gaston is very handsome.**
Gaston est très beau.
**_Language tip_**
**beau** _changes to_ **bel** _before a vowel sound._
**a handsome man**
un bel homme
**handwriting** NOUN
l' **écriture** _fem_
**He has nice handwriting.**
Il a une belle écriture.
**_Language tip_**
**écriture** _is related to the French verb_ **écrire** , _which means 'to write'._
**hangman** NOUN
le **pendu** _masc_
**hang on** VERB
**patienter**
**Hang on a minute please.**
Patientez une minute, s'il vous plaît.
**happen** VERB
**se passer**
**What's happening?**
Qu'est-ce qui se passe?
**happy** ADJECTIVE
**heureux** _masc_
**heureuse** _fem_
**Joséphine is happy.**
Joséphine est heureuse.
**The children are happy.**
Les enfants sont heureux.
**Happy birthday!**
Bon anniversaire!
**Happy Mother's Day!**
Bonne Fête Maman!
**Happy Christmas!**
Joyeux Noël!
**Happy New Year!**
Bonne année!
**Happy Families** NOUN
le **jeu des sept familles** _masc_
**harbour** NOUN
le **port** _masc_
**hard**
**hard** _can be an adjective or an adverb._
**A** ADJECTIVE
**1** **difficile** _(difficult)_
**This question's too hard for me.**
Cette question est trop difficile pour moi.
**2** **dur** _masc_ **dure** _fem (not soft)_
**This cheese is very hard.**
Ce fromage est très dur.
**B** ADVERB
**dur**
**Colette works hard.**
Colette travaille dur.
**has** VERB _see_ **have**
**hasn't** = **has not** _see_ **have**
**hat** NOUN
le **chapeau** _masc_
(PL les **chapeaux** )
**hate** VERB
**détester**
**I hate maths.**
Je déteste les maths.
**_Language tip_**
_There is an extra word in the French example sentence. What is it?_
**have** VERB
**1** **avoir**
**I've got a bike.**
J'ai un vélo.
**Have you got a sister?**
Tu as une sœur?
**No, I haven't got a sister.**
Non, je n'ai pas de sœur.
**He's got blue eyes.**
Il a les yeux bleus.
**I have...**
J'ai...
**I have got...**
J'ai...
**_Language tip_**
**have** _and_ **have got** _are the same in French._
**2** **prendre** _(eat)_
**What time do you have breakfast?**
À quelle heure tu prends le petit déjeuner?
**What are you going to have?**
Qu'est-ce que tu prends?
**3** **devoir** _(must)_
**You have to be careful.**
Tu dois faire attention.
**Do I have to choose a card?**
Est-ce que je dois choisir une carte?
**Do I have to?**
Est-ce que je suis vraiment obligé?
**You have to...**
Tu dois...
**You have got to...**
Tu dois...
**_Language tip_**
**have** _and_ **have got** _are the same in French._
**haven't** = **have not** _see_ **have**
**hay fever** NOUN
le **rhume des foins** _masc_
**he** PRONOUN
**il**
**He loves dogs.**
Il aime les chiens.
**head** NOUN
**1** la **tête** _fem (of person)_
**Mind your head!**
Attention à la tête!
**Heads or tails? — Heads.**
Pile ou face? — Face.
**2** le **directeur** _masc_
la **directrice** _fem (headteacher)_
**headache** NOUN
**I've got a headache.**
J'ai mal à la tête.
**headmaster** NOUN
le **directeur** _masc_
**headmistress** NOUN
la **directrice** _fem_
**health** NOUN
la **santé** _fem_
**healthy** ADJECTIVE
**sain** _masc_
**saine** _fem_
**a healthy diet**
une alimentation saine
**hear** VERB
**entendre**
**I can't hear.**
Je n'entends pas.
**I can't hear you.**
Je ne vous entends pas.
**Can you hear the difference?**
Vous entendez la différence?
**heart** NOUN
**1** le **cœur** _masc_
**2** _(in cards)_
**hearts**
le cœur
**the ace of hearts**
l'as de cœur
**heater** NOUN
le **radiateur** _masc_
**an electric heater**
un radiateur électrique
**heather** NOUN
la **bruyère** _fem_
**heavy** ADJECTIVE
**lourd** _masc_
**lourde** _fem_
**This bag's very heavy.**
Ce sac est très lourd.
**hedgehog** NOUN
le **hérisson** _masc_
**height** NOUN
la **taille** _fem_
**held** VERB _see_ **hold**
**helicopter** NOUN
l' **hélicoptère** _masc_
**hello** EXCLAMATION
**bonjour!**
**helmet** NOUN
le **casque** _masc_
**help**
**help** _can be a verb or a noun._
**A** VERB
**aider**
**Can you help me?**
Vous pouvez m'aider?
**Help yourself!**
Servez-vous!
**Help!**
Au secours!
**B** NOUN
l' **aide** _fem_
**Do you need any help?**
Vous avez besoin d'aide?
**hen** NOUN
la **poule** _fem_
**her**
**her** _can be an adjective or a pronoun._
**A** ADJECTIVE
**_Language tip_**
_When you want to say something like 'her name', 'her house', or 'her hair' in French, you need to know if 'name', 'house', and 'hair' are masculine, feminine, or plural, because there are three possible words for_ **her**.
**son** _masc_
**her name**
son nom **sa** _fem_
**her house**
sa maison **ses** _pl_
**her hair**
ses cheveux
**_Language tip_**
**sa** _changes to_ **son** _before a vowel sound._
**her address**
son adresse
**B** PRONOUN _(object of the verb)_
**1** **la**
**I hate her.**
Je la déteste.
**Do you know her?**
Tu la connais?
**Look at her!**
Regarde-la!
**_Language tip_**
**la** _changes to_ **l'** _before a vowel sound._
**I love her.**
Je l'aime.
**2** **elle**
**I'm going with her.**
Je vais avec elle.
**It's for her.**
C'est pour elle.
**He's next to her.**
Il est à côté d'elle.
**I'm older than her.**
Je suis plus âgé qu'elle.
**here** ADVERB
**ici**
**I live here.**
J'habite ici.
**Here's Helen.**
Voici Helen.
**Here are the books.**
Voici les livres.
**Here he is!**
Le voici!
**here is...**
voici...
**here are...**
voici...
**_Language tip_**
**here is** _and_ **here are** _are the same in French._
**hers** PRONOUN
**à elle**
**Is this hers?**
C'est à elle?
**This book is hers.**
Ce livre est à elle.
**Whose is this? — It's hers.**
C'est à qui? — À elle.
**herself** PRONOUN
**se**
**My cat washes herself a lot.**
Ma chatte se lave beaucoup.
**She lives by herself.**
Elle habite toute seule.
**by herself**
toute seule
**he's** = **he is, he has** _see_ **have**
**hi** EXCLAMATION
**salut!**
**hide** VERB
**se cacher**
**Daniel is hiding under the bed.**
Daniel se cache sous le lit.
**Hide!**
Cache-toi!
**Mum hides the biscuits.**
Maman cache les biscuits.
**hide-and-seek** NOUN
**cache-cache** _masc_
**high** ADJECTIVE
**haut** _masc_
**haute** _fem_
**It's too high.**
C'est trop haut.
**Higher!**
Plus haut!
**high jump** NOUN
le **saut en hauteur** _masc_
**high-rise** NOUN
la **tour** _fem_
**I live in a high-rise.**
J'habite dans une tour.
**high school** NOUN
**1** le **collège** _masc (for pupils 11–15)_
**2** le **lycée** _masc (for pupils 15–18)_
_**Did you know...?**_
_In France, pupils go to a_ **collège** _between the ages of 11 and 15, and then to a_ **lycée** _until the age of 18._
**hiking** NOUN
**We're going to go hiking.**
Nous allons faire une randonnée.
**hill** NOUN
la **colline** _fem_
**him** PRONOUN
**1** **le** _(object of the verb)_
**I hate him.**
Je le déteste.
**Look at him!**
Regarde-le!
**_Language tip_**
**le** _changes to_ **l'** _before a vowel sound._
**I love him.**
Je l'aime.
**2** **lui**
**I'm going with him.**
Je vais avec lui.
**It's for him.**
C'est pour lui.
**She's next to him.**
Elle est à côté de lui.
**I'm older than him.**
Je suis plus âgé que lui.
**himself** PRONOUN
**se**
**The cat is washing himself.**
Le chat se lave.
**He lives by himself.**
Il habite tout seul.
**by himself**
tout seul
**hippo** NOUN
l' **hippopotame** _masc_
**hire** VERB
**louer**
**You can hire bikes.**
On peut louer des vélos.
**his**
**his** _can be an adjective or a pronoun._
**A** ADJECTIVE
**_Language tip_**
_When you want to say something like 'his name', 'his house', or 'his hair' in French, you need to know if 'name', 'house', 'hair' are masculine, feminine or plural, because there are three possible words for_ **his**.
**son** _masc_
**his name**
son nom **sa** _fem_
**his house**
sa maison **ses** _pl_
**his hair**
ses cheveux
**_Language tip_**
**sa** _changes to_ **son** _before a vowel sound._
**his address**
son adresse
**B** PRONOUN
**à lui**
**Is this his?**
C'est à lui?
**This book is his.**
Ce livre est à lui.
**Whose is this? — It's his.**
C'est à qui? — À lui.
**history** NOUN
l' **histoire** _fem_
**hit**
**hit** _can be a verb or a noun._
**A** VERB
**frapper**
**Don't hit Luc, Pascal!**
Ne frappe pas Luc, Pascal!
**B** NOUN
le **tube** _masc (song)_
**Westlife's latest hit**
le dernier tube de Westlife
**hobby** NOUN
le **passe-temps** _masc_
**What are your favourite hobbies?**
Quels sont tes passe-temps favoris?
**hockey** NOUN
le **hockey** _masc_
**I play hockey.**
Je joue au hockey.
**hold** VERB
**tenir**
**Can you hold the baby?**
Tu peux tenir le bébé?
**Hold hands!**
Donnez-vous la main!
**hold on** VERB
**Hold on a minute!**
Attends un peu!
**hold up** VERB
**Hold up your hands.**
Levez la main.
**hole** NOUN
le **trou** _masc_
**holiday** NOUN
**1** les **vacances** _fem pl_
**our holiday in France**
nos vacances en France
**When are you going on holiday?**
Quand pars-tu en vacances?
**We are on holiday.**
Nous sommes en vacances.
**in the school holidays**
pendant les vacances scolaires
**on holiday**
en vacances
**the school holidays**
les vacances scolaires
**2** le **jour férié** _masc (public holiday)_
**Monday is a holiday.**
Lundi, c'est un jour férié.
**holiday home** NOUN
la **résidence secondaire** _fem_
**Holland** NOUN
la **Hollande** _fem_
**holly** NOUN
le **houx** _masc_
**a sprig of holly**
un brin de houx
**home** NOUN
la **maison** _fem_
**Is Charlotte at home?**
Est-ce que Charlotte est à la maison?
**What time do you get home?**
Tu rentres à quelle heure?
**I get home at five o'clock.**
Je rentre à cinq heures.
**to go home**
rentrer à la maison
**I want to go home.**
Je veux rentrer à la maison.
**at home**
à la maison
**homeless** PL NOUN
**the homeless**
les sans-abri
**home page** NOUN
la **page d'accueil** _fem_
**homework** NOUN
les **devoirs** _masc pl_
**We have too much homework.**
Nous avons trop de devoirs.
**my geography homework**
mes devoirs de géographie
**honey** NOUN
le **miel** _masc_
**honeymoon** NOUN
la **lune de miel** _fem_
**hood** NOUN
la **capuche** _fem_
**hooray** EXCLAMATION
**hourra!**
**hop** VERB
**sauter à cloche-pied**
**Hop!**
Sautez à cloche-pied!
**hope** VERB
**espérer**
**I hope that's okay.**
J'espère que ça ira.
**I'm hoping to go to France.**
J'espère aller en France.
**I hope so.**
Je l'espère.
**I hope not.**
J'espère que non.
**hopeless** ADJECTIVE
**nul** _masc_
**nulle** _fem_
**I'm hopeless at maths.**
Je suis nul en maths.
**You're hopeless, Martine!**
Martine, tu es nulle!
**horrible** ADJECTIVE
**horrible**
**horror film** NOUN
le **film d'horreur** _masc_
**horse** NOUN
le **cheval** _masc_ (PL les **chevaux** )
**hospital** NOUN
l' **hôpital** _masc_ (PL les **hôpitaux** )
**My grandmother is in hospital**
Ma grand-mère est à l'hôpital.
**hot** ADJECTIVE
**1** **chaud** _masc_
**chaude** _fem (very warm)_
**a hot bath**
un bain chaud
**I'm too hot.**
J'ai trop chaud.
**It's very hot today.**
Il fait très chaud aujourd'hui.
**I'm hot.**
J'ai chaud.
**It's hot.**
Il fait chaud.
**2** **épicé** _masc_
**épicée** _fem (spicy)_
**a very hot curry**
un curry très épicé
**hot chocolate** NOUN
le **chocolat chaud** _masc_
**hot dog** NOUN
le **hot-dog** _masc_
**hotel** NOUN
l' **hôtel** _masc_
**hour** NOUN
l' **heure** _fem_
**an hour and ten minutes**
une heure dix
**a quarter of an hour**
un quart d'heure
**half an hour**
une demi-heure
**two and a half hours**
deux heures et demie
**house** NOUN
**1** la **maison** _fem (building)_
**You've got a nice house.**
Vous avez une belle maison.
**Do you want to play at my house?**
Tu veux jouer chez moi?
**at my house**
chez moi
**2** le **groupe** _masc (at school)_
**Skye house has 180 points.**
Le groupe Skye a 180 points.
**housewife** NOUN
la **femme au foyer** _fem_
**She's a housewife.**
Elle est femme au foyer.
**_Language tip_**
_You do not translate **'a'** when you say what someone's job is in French._
**how** ADVERB
**comment**
**How do you say 'apple' in French?**
Comment dit-on 'apple' en français?
**How many...?**
Combien de...?
**How many pupils are there in the class?**
Il y a combien d'élèves dans la classe?
**How much is it?**
C'est combien?
**How old is your brother?**
Ton frère a quel âge?
**How are you?**
Comment allez-vous?
**How old are you?**
Tu as quel âge?
**How many?**
Combien?
**How much?**
Combien?
**huge** ADJECTIVE
**immense**
**humidex** NOUN _(Canada)_
l' **humidex** _masc_
**hundred** NUMBER
**a hundred**
cent
**a hundred euros**
cent euros
**_Language tip_**
**cent** _is spelled with an_ **s** _when there are two or more hundreds, but not when it is followed by another number, as in 'six hundred and two'._
**five hundred**
cinq cents
**five hundred and one**
cinq cent un
**hundreds of people**
des centaines de personnes
**hungry** ADJECTIVE
**Are you hungry?**
Tu as faim?
**I'm hungry.**
J'ai faim.
**I'm not hungry.**
Je n'ai pas faim.
**hunting** NOUN
la **chasse** _fem_
**I'm against hunting.**
Je suis contre la chasse.
**fox-hunting**
la chasse au renard
**hurry up** VERB
**Hurry up, Gavin!**
Dépêche-toi, Gavin!
**Hurry up, children!**
Dépêchez-vous, les enfants!
**hurt** VERB
**You're hurting me!**
Tu me fais mal!
**My leg hurts.**
J'ai mal à la jambe.
**Have you hurt yourself?**
Tu t'es fait mal?
**That hurts.**
Ça fait mal.
**husband** NOUN
le **mari** _masc_
**hydro** NOUN _(Canada)_
l' **électricité** _fem_
**hymn** NOUN
le **cantique** _masc_
**hyphen** NOUN
le **trait d'union** _masc_
# **I i**
**I** PRONOUN
**1** **je**
**I speak French.**
Je parle français.
**_Language tip_**
**je** _changes to_ **j'** _before a vowel sound._
**I love cats.**
J'aime les chats.
**2** **moi**
**Ann and I**
Ann et moi
**ice** NOUN
la **glace** _fem_
**There is ice on the lake.**
Il y a de la glace sur le lac.
**ice cream** NOUN
la **glace** _fem_
**Would you like an ice cream?**
Tu veux une glace?
**vanilla ice cream**
la glace à la vanille
**chocolate ice cream**
la glace au chocolat
**_Language tip_**
_The French is 'à la vanille' because_ **vanille** _is feminine, and 'au chocolat' because_ **chocolat** _is masculine._
**ice cube** NOUN
le **glaçon** _masc_
**ice lolly** NOUN
la **glace à l'eau** _fem_
**two ice lollies**
deux glaces à l'eau
**ice rink** NOUN
la **patinoire** _fem_
**ice-skating** NOUN
le **patin à glace** _masc_
**I go ice-skating.**
Je fais du patin à glace.
**ICT** PL NOUN
les **TIC** _fem pl_
**icy** ADJECTIVE
**The roads are icy.**
Il y a du verglas sur les routes.
**idea** NOUN
l' **idée** _fem_
**Good idea!**
Bonne idée!
**identical** ADJECTIVE
**identique**
**The twins are identical.**
Ces jumeaux sont identiques.
**if** CONJUNCTION
**si**
**You can have it if you like.**
Tu peux le prendre si tu veux.
**_Language tip_**
**si** _changes to_ **s'** _before_ **il** _and_ **ils**.
**Do you know if he's there?**
Savez-vous s'il est là?
**ill** ADJECTIVE
**malade**
**Christelle is ill.**
Christelle est malade.
**imagination** NOUN
l' **imagination** _fem_
**imagine** VERB
**imaginer**
**Imagine you have lots of money.**
Imagine que tu as beaucoup d'argent.
**imitate** VERB
**imiter**
**Imitate the sound.**
Imitez le son.
**immediately** ADVERB
**immédiatement**
**I'll do it immediately.**
Je vais le faire immédiatement.
**immigrant** NOUN
l' **immigré** _masc_
l' **immigrée** _fem_
**impatient** ADJECTIVE
**impatient** _masc_
**impatiente** _fem_
**Don't be so impatient, Édith.**
Ne sois pas si impatiente Édith.
**important** ADJECTIVE
**important** _masc_
**importante** _fem_
**This is an important letter.**
C'est une lettre importante.
**Today's an important day.**
Aujourd'hui est un grand jour.
**impossible** ADJECTIVE
**impossible**
**Sorry, it's impossible.**
Désolée, c'est impossible.
**in**
**in** _can be a preposition or an adverb._
**A** PREPOSITION
**_Language tip_**
_There are several ways of translating_ **in**. _Scan the examples for one that is similar to what you want to say._
**1** **dans**
**in the house**
dans la maison
**in my bag**
dans mon sac
**What can you see in the picture?**
Que voyez-vous sur l'image?
**2** **à**
**in the country**
à la campagne
**in school**
à l'école
**in hospital**
à l'hôpital
**in London**
à Londres
**the boy in the blue shirt**
le garçon à la chemise bleue
**3** **en**
**in English**
en anglais
**in summer**
en été
**in May**
en mai
**in 2008**
en deux mille huit
**_Language tip_**
_When_ **in** _refers to a country which is feminine, use_ **en** ; _when the country is masculine, use_ **au** ; _when the country is plural, use_ **aux**.
**in England**
en Angleterre
**in Portugal**
au Portugal
**in the United States**
aux États-Unis
**4** **de**
**the tallest person in the family**
le plus grand de la famille
**at 6 o'clock in the morning**
à six heures du matin
**She's the oldest in the class.**
C'est la plus vieille de la classe.
**in my class**
dans ma classe
**in Paris**
à Paris
**in France**
en France
**in French**
en français
**B** ADVERB
**to be in**
être là
**He isn't in.**
Il n'est pas là.
**inch** NOUN
**6 inches**
quinze centimètres
_**Did you know...?**_
_In France, measurements are always in metres and centimetres rather than feet and inches. An inch is about 2.5 centimetres._
**incident** NOUN
l' **incident** _masc_
**an incident**
un incident
**included** ADJECTIVE
**compris** _masc_
**comprise** _fem_
**Service is not included.**
Le service n'est pas compris.
**incredible** ADJECTIVE
**incroyable**
**That's incredible!**
C'est incroyable!
**indeed** ADVERB
**Thank you very much indeed!**
Merci beaucoup!
**Indian** ADJECTIVE
**indien** _masc_
**indienne** _fem_
**an Indian restaurant**
un restaurant indien
**_Language tip_**
_The adjective_ **Indian** _is spelled with a capital letter, but_ **indien** _is not._
**indoor** ADJECTIVE
**an indoor swimming pool**
une piscine couverte
**indoors** ADVERB
**à l'intérieur**
**They're indoors.**
Ils sont à l'intérieur.
**inexpensive** ADJECTIVE
**bon marché** _masc, fem, pl_
**an inexpensive hotel**
un hôtel bon marché
**infant school** NOUN
**He's going to start at infant school.**
Il va entrer en cours préparatoire.
_**Did you know...?**_
**CP (cours préparatoire)** _is the equivalent of first-year infants, and_ **CE1 (cours élémentaire de première année)** _is the equivalent of second-year infants in schools in the UK._
**infection** NOUN
**an ear infection**
une otite
**a throat infection**
une angine
**information** NOUN
les **renseignements** _masc pl_
**I need some information.**
J'ai besoin de renseignements.
**important information**
des renseignements importants
**information about France**
des renseignements sur la France
**_Language tip_**
**information** _is a singular word in English, but a plural word in French._
**ingredient** NOUN
l' **ingrédient** _masc_
**a list of ingredients**
une liste d'ingrédients
**inhabitant** NOUN
l' **habitant** _masc_
l' **habitante** _fem_
**inhaler** NOUN
l' **inhalateur** _masc_
**initials** PL NOUN
les **initiales** _fem pl_
**My initials are GAC.**
Mes initiales sont GAC.
**injection** NOUN
la **piqûre** _fem_
**injure** VERB
**blesser**
**Was anyone injured?**
Est-ce que quelqu'un a été blessé?
**injury** NOUN
la **blessure** _fem_
**a serious injury**
une blessure grave
**ink** NOUN
l' **encre** _fem_
**inquire** VERB
**to inquire about something**
se renseigner sur quelque chose
**I'm going to inquire about train times.**
Je vais me renseigner sur les horaires des trains.
**inquiries** PL NOUN
les **renseignements** _masc pl_
**inquisitive** ADJECTIVE
**curieux** _masc_
**curieuse** _fem_
**insect** NOUN
l' **insecte** _masc_
**in-service day** NOUN
la **journée de formation** _fem_
**inside**
**inside** _can be an adverb or a preposition._
**A** ADVERB
**à l'intérieur**
**They're inside.**
Ils sont à l'intérieur.
**Do you want a table inside or outside?**
Vous voulez une table à l'intérieur ou à l'extérieur?
**B** PREPOSITION
**à l'intérieur de**
**inside the house**
à l'intérieur de la maison
**inspector** NOUN
le **contrôleur** _masc_
**instance** NOUN
**for instance**
par exemple
**instantly** ADVERB
**tout de suite**
**instead** ADVERB
**à la place**
**There's no coke. Do you want orange juice instead?**
Il n'y a pas de coca. Tu veux du jus d'orange à la place?
**instead of**
au lieu de
**Eat fruit instead of sweets.**
Mangez des fruits au lieu de bonbons.
**instead of me**
à ma place
**instead of Manon**
à la place de Manon
**instructions** PL NOUN
les **instructions** _fem pl_
**Follow the instructions.**
Suivez les instructions.
**instructor** NOUN
le **moniteur** _masc_
la **monitrice** _fem_
**a skiing instructor**
un moniteur de ski
**instrument** NOUN
l' **instrument** _masc_
**Do you play an instrument?**
Est-ce que tu joues d'un instrument?
**intelligent** ADJECTIVE
**intelligent** _masc_
**intelligente** _fem_
**You're very intelligent.**
Tu es très intelligente.
**_Language tip_**
_The person being spoken to in the example is a girl. How can you tell?_
**interest** NOUN
**My main interest is music.**
Ce qui m'intéresse le plus c'est la musique.
**interested** ADJECTIVE
**I'm not interested.**
Ça ne m'intéresse pas.
**I'm not interested in football.**
Le football ne m'intéresse pas.
**Are you interested?**
Ça t'intéresse?
**interesting** ADJECTIVE
**intéressant** _masc_
**intéressante** _fem_
**It's a very interesting story.**
C'est une histoire très intéressante.
**international** ADJECTIVE
**international** _masc_
**internationale** _fem_
**an international school**
une école internationale
**internet** NOUN
l' **Internet** _masc_
**on the internet**
sur Internet
**_Language tip_**
_There's one more word in the English example sentence than there is in the French sentence. What is it?_
**internet café** NOUN
le **cybercafé** _masc_
**interrupt** VERB
**interrompre**
**Don't interrupt Hugues!**
N'interromps pas, Hugues!
**interval** NOUN
**1** l' **entracte** _masc (cinema, theatre)_
**during the interval**
pendant l'entracte
**2** la **récréation** _fem (school)_
**interview** NOUN
l' **interview** _fem_
**interviewer** NOUN
l' **interviewer** _masc_
**into** PREPOSITION
**1** **en**
**I'm going into town.**
Je vais en ville.
**Translate it into French.**
Traduisez ça en français.
**Divide into two groups.**
Répartissez-vous en deux groupes.
**2** **dans** _(inside)_
**He got into the car.**
Il est monté dans la voiture.
**introduce** VERB
**présenter**
**Introduce yourselves.**
Présentez-vous.
**I'd like to introduce Michelle Davies.**
Je vous présente Michelle Davies.
**Inuit**
**Inuit** _can be an adjective or a noun._
**A** ADJECTIVE
**inuit** _masc_
**inuite** _fem_
**B** PL NOUN
les **Inuits** _masc pl_
**invalid** NOUN
le/la **malade** _masc/fem_
**inventor** NOUN
l' **inventeur** _masc_
l' **inventrice** _fem_
**invisible** ADJECTIVE
**invisible**
**invitation** NOUN
l' **invitation** _fem_
**Thank you for the invitation.**
Merci pour l'invitation.
**invite** VERB
**inviter**
**I'm going to invite Léon to my party.**
Je vais inviter Léon à ma fête.
**iPod** ® NOUN
l' **iPod** ® _masc_
**Ireland** NOUN
l' **Irlande** _fem_
**I live in Ireland.**
J'habite en Irlande.
**When are you coming to Ireland?**
Quand est-ce que tu viens en Irlande?
**I'm from Ireland.**
Je suis irlandaise.
**in Ireland**
en Irlande
**I'm going to Ireland.**
Je vais en Irlande.
**Irish**
**Irish** _can be an adjective or a noun._
**A** ADJECTIVE
**irlandais** _masc_
**irlandaise** _fem_
**I am Irish.**
Je suis irlandais.
**_Language tip_**
_Is a boy or a girl speaking in the example sentence? How can you tell?_
**I like Irish music.**
J'aime la musique irlandaise.
**Irish people**
les Irlandais
**He's Irish.**
Il est irlandais.
**She's Irish.**
Elle est irlandaise.
**B** NOUN
l' **irlandais** _masc (language)_
**Do you speak Irish?**
Est-ce que tu parles irlandais?
**the Irish**
les Irlandais
**_Language tip_**
**irlandais** _is not spelled with a capital letter except when it means an Irish person._
**Irishman** NOUN
l' **Irlandais** _masc_
**Irishwoman** NOUN
l' **Irlandaise** _fem_
**iron**
**iron** _can be a noun or a verb._
**A** NOUN
**1** le **fer** _masc (metal)_
**an iron gate**
un portail en fer
**2** le **fer à repasser** _masc (for clothes)_
**B** VERB
**repasser**
**I can iron a shirt.**
Je sais repasser une chemise.
**irritating** ADJECTIVE
**irritant** _masc_
**irritante** _fem_
**is** VERB _see_ **be**
**Islam** NOUN
l' **Islam** _masc_
**island** NOUN
l' **île** _fem_
**isle** NOUN
**the Isle of Man**
l'île de Man
**the Isle of Wight**
l'île de Wight
**it** PRONOUN
**_Language tip_**
_You need to know if_ **it** _stands for a masculine noun or a feminine noun, so that you can choose_ **il** _or_ **elle**.
**il**
**Where's my book? — It's on the table.**
Où est mon livre? — Il est sur la table.
**elle**
**Where's my pencil case? — It's in your bag.**
Où est ma trousse? — Elle est dans ton sac.
**_Language tip_**
_Use_ **le** _or_ **la** _when_ **it** _is the object of the sentence_.
**le** _and_ **la** _change to_ **l'** _before a vowel sound._
**le**
**There's a croissant left. Do you want it?**
Il reste un croissant. Tu le veux?
**la**
**I don't want this apple. You can have it.**
Je ne veux pas de cette pomme. Tu peux la prendre.
**l'**
**This is my new jumper. Do you like it?**
C'est mon nouveau pull. Tu l'aimes?
**It's me.**
C'est moi.
**It's you.**
C'est toi.
**It's expensive.**
C'est cher.
**It's delicious.**
C'est délicieux.
**Italian**
**Italian** _can be an adjective or a noun._
**A** ADJECTIVE
**italien** _masc_
**italienne** _fem_
**an Italian restaurant**
un restaurant italien
**B** NOUN
l' **italien** _masc (language)_
**_Language tip_**
**italien** _is not spelt with a capital letter except when it means an Italian person._
**Italy** NOUN
l' **Italie** _fem_
**item** NOUN
l' **article** _masc_
**its** ADJECTIVE
**_Language tip_**
_To say something like 'its name', 'its place', or 'its hair' in French, you need to know if 'name', 'place', and 'hair' are masculine, feminine or plural, because there are three possible words for_ **its**.
**son** _masc_
**What's its name?**
Quel est son nom?
**sa** _fem_
**Everything is in its place.**
Chaque chose est à sa place.
**ses** _pl_
**The dog is losing its hair.**
Le chien perd ses poils.
# **J j**
**jab** NOUN
la **piqûre** _fem_
**jack** NOUN
le **valet** _masc_
**the jack of hearts**
le valet de cœur
**jacket** NOUN
la **veste** _fem_
**a white jacket**
une veste blanche
**jacket potato** NOUN
la **pomme de terre cuite au four** _fem_
**There are chips and jacket potatoes.**
Il y a des frites et des pommes de terre cuites au four.
**jam** NOUN
la **confiture** _fem_
**strawberry jam**
la confiture de fraises
**jam jar** NOUN
le **pot à confiture** _masc_
**janitor** NOUN
le **concierge** _masc_
**He's a janitor.**
Il est concierge.
**_Language tip_**
_You do not translate_ **'a'** _when you say what someone's job is in French._
**January** NOUN
**janvier** _masc_
**January or February?**
Janvier ou février?
**My birthday's in January.**
Mon anniversaire est en janvier.
**in January**
en janvier
**the fifth of January**
le cinq janvier
**_Language tip_**
_The months are not spelled with a capital letter in French._
**jealous** ADJECTIVE
**jaloux** _masc_
**jalouse** _fem_
**Aline is jealous.**
Aline est jalouse.
**jeans** PL NOUN
le **jean** _masc_
**I've got new jeans.**
J'ai un jean neuf.
**_Language tip_**
**jeans** _is plural in English, but the French word is singular._
**jelly** NOUN
la **gelée** _fem_
**jersey** NOUN
le **pull-over** _masc_
**Jew** NOUN
le **Juif** _masc_
la **Juive** _fem_
**jewellery** NOUN
les **bijoux** _masc pl_
**Jewish** ADJECTIVE
**juif** _masc_
**juive** _fem_
**_Language tip_**
**Jewish** _has a capital letter, but_ **juif** _does not._
**jigsaw** NOUN
le **puzzle** _masc_
**I like doing jigsaws.**
J'aime faire des puzzles.
**job** NOUN
l' **emploi** _masc_
**She's looking for a job.**
Elle cherche un emploi.
**I've got a Saturday job.**
Je travaille le samedi.
**jogging** NOUN
**She goes jogging.**
Elle fait du jogging.
**joke** NOUN
la **plaisanterie** _fem_
**jotter** NOUN
le **cahier** _masc_
**journey** NOUN
le **voyage** _masc_
**I don't like long journeys.**
Je n'aime pas les longs voyages.
**judge**
**judge** _can be a noun or a verb._
**A** NOUN
le **juge** _masc_
**She's a judge.**
Elle est juge.
**_Language tip_**
_You do not translate_ **'a'** _when you say what someone's job is in French._
**B** VERB
**juger**
**Who's going to judge the competition?**
Qui va juger le concours?
**judo** NOUN
le **judo** _masc_ **I do judo.**
Je fais du judo.
**juggler** NOUN
le **jongleur** _masc_
la **jongleuse** _fem_
**juice** NOUN
le **jus** _masc_
**I'd like some orange juice.**
Je voudrais du jus d'orange.
**July** NOUN
**juillet** _masc_
**July or August?**
Juillet ou août?
**My birthday is in July.**
Mon anniversaire est en juillet.
**in July**
en juillet
**the fourteenth of July**
le quatorze juillet
**_Language tip_**
_Months are not written with a capital letter in French._
_**Did you know...?**_
_The fourteenth of July_ ( **la fête nationale** ) _is the French national holiday. There's a firework display and a military parade in Paris._
**jump** VERB
**sauter**
**Jump!**
Saute!
**jumper** NOUN
le **pull** _masc_
**a dark green jumper**
un pull vert foncé
**June** NOUN
**juin** _masc_
**June or July?**
Juin ou juillet?
**My birthday is in June.**
Mon anniversaire est en juin.
**in June**
en juin
**the fourth of June**
le quatre juin
**_Language tip_**
_Months are not written with a capital letter in French._
**junior** NOUN
**the juniors**
les élèves des petites classes
**junior school** NOUN
l' **école primaire** _fem_
**just** ADVERB
**juste**
**just after Christmas**
juste après Noël
**just now**
en ce moment
**I'm busy just now.**
Je suis occupé en ce moment.
**I'm just coming!**
J'arrive!
**Just a moment, please.**
Un moment, s'il vous plaît.
# **K k**
**karaoke** NOUN
le **karaoké** _masc_
**karate** NOUN
le **karaté** _masc_
**I do karate.**
Je fais du karaté.
**keen** ADJECTIVE
**enthousiaste**
**He's not very keen.**
Il n'est pas très enthousiaste.
**keep** VERB
**1** **garder** _(have)_
**You can keep it.**
Tu peux le garder.
**2** **rester** _(stay)_
**Keep still!**
Reste tranquille!
**Keep quiet!**
Tais-toi!
**keep on** VERB
**continuer**
**Keep on singing.**
Continuez de chanter.
**keep-fit** NOUN
**The keep-fit class is on Tuesday.**
Le cours de gym, c'est mardi.
**key** NOUN
la **clé** _fem_
**Where are my keys?**
Où sont mes clés?
**kick**
**kick** _can be a noun or a verb._
**A** NOUN
le **coup de pied** _masc_
**B** VERB
**donner un coup de pied**
**He kicked me!**
Il m'a donné un coup de pied!
**kid** NOUN
le/la **gosse** _masc/fem (child)_
**the kids**
les gosses
**kill** VERB
**tuer**
**My cat kills birds.**
Mon chat tue les oiseaux.
**kilo** NOUN
le **kilo** _masc_
**two euros a kilo**
deux euros le kilo
**kilometre** NOUN
le **kilomètre** _masc_
**kilt** NOUN
le **kilt** _masc_
**kind**
**kind** _can be an adjective or a noun._
**A** ADJECTIVE
**gentil** _masc_
**gentille** _fem_
**That's very kind of you.**
C'est très gentil.
**B** NOUN
la **sorte** _fem_
**'Saucisson' is a kind of sausage.**
Le saucisson est une sorte de saucisse.
**kindergarten** NOUN
l' **école maternelle** _fem_
**king** NOUN
le **roi** _masc_
**the king of hearts**
le roi de cœur
**kiss**
**kiss** _can be a noun or a verb._
**A** NOUN
le **baiser** _masc_
**Give me a kiss.**
Donne-moi un baiser.
**_Language tip_**
**bisou** _and_ **bise** _are two other words meaning_ **kiss**. _At the end of a letter to a friend you could write_ **Bisous** _or_ **Grosses bises**.
**B** VERB
**embrasser**
**Kiss me.**
Embrasse-moi.
_**Did you know...?**_
_Between girls and boys, and between girls, the normal French way of saying hello and goodbye is with kisses, usually one on each cheek. Boys shake hands with each other instead._
**kit** NOUN
les **affaires** _fem pl_
**Don't forget your gym kit.**
N'oublie pas tes affaires de gym.
**kitchen** NOUN
la **cuisine** _fem_
**She's in the kitchen.**
Elle est dans la cuisine.
**kite** NOUN
le **cerf-volant**
_masc_ **two kites**
deux cerfs-volants
**kitten** NOUN
le **chaton** _masc_
**knee** NOUN
le **genou** _masc_ (PL les **genoux** )
**knickers** PL NOUN
la **culotte** _fem_
**I can see your knickers!**
Je vois ta culotte!
**a pair of knickers**
une culotte
**_Language tip_**
**culotte** _is a singular word._
**knife** NOUN
le **couteau** _masc_ (PL
les **couteaux** )
**knit** VERB
**tricoter**
**I can knit.**
Je sais tricoter.
**knives** PL NOUN
les **couteaux** _masc pl_
**knives, forks and spoons**
les couteaux, les fourchettes et les cuillères
**knob** NOUN
le **bouton** _masc_
**knock** VERB
**frapper**
**Someone's knocking at the door.**
Quelqu'un frappe à la porte.
**know** VERB
**1** **savoir** _(know something)_
**It's a long way. — Yes, I know.**
C'est loin. — Oui, je sais.
**Who knows the answer?**
Qui sait la réponse?
**I don't know.**
Je ne sais pas.
**2** **connaître** _(know someone)_
**I know her.**
Je la connais.
**I don't know him.**
Je ne le connais pas.
**Do you know Louise?**
Tu connais Louise?
**Koran** NOUN
le **Coran** _masc_
# **L l**
**label** NOUN
l' **étiquette** _fem_
**lace** NOUN
le **lacet** _masc_
**lacrosse** NOUN
la **crosse** _fem_ **a lacrosse stick**
une crosse
_**Did you know...?**_
**lacrosse** _is Canada's official summer sport._
**ladder** NOUN
l' **échelle** _fem_
**lady** NOUN
la **dame** _fem_
**a young lady**
une jeune fille
**Ladies and gentlemen...**
Mesdames et messieurs...
**Where is the 'ladies'?**
Où sont les toilettes?
**lake** NOUN
le **lac** _masc_
**lamb** NOUN
l' **agneau** _masc_ (PL les **agneaux** )
**a lamb chop**
une côtelette d'agneau
**land**
**land** _can be a verb or a noun._
**A** NOUN
la **terre** _fem_
**on land**
sur terre
**B** VERB
**atterrir**
**The plane lands at nine o'clock.**
L'avion atterrit à neuf heures.
**lane** NOUN
le **chemin** _masc_
**a country lane**
un chemin de campagne
**the fast lane**
la voie rapide
**language** NOUN
la **langue** _fem_
**French isn't a difficult language.**
Le français n'est pas une langue difficile.
**language laboratory** NOUN
le **laboratoire de langues** _masc_
**lap** NOUN
**on my lap**
sur mes genoux
**laptop** NOUN
l' **ordinateur portable** _masc_
**large** ADJECTIVE
**1** **grand** _masc_
**grande** _fem (size, glass, plate, garden)_
**a large house**
une grande maison
**2** **gros** _masc_
**grosse** _fem (car, animal, book, parcel)_
**a large dog**
un gros chien
**last**
**last** _can be an adjective or an adverb._
**A** ADJECTIVE
**dernier** _masc_
**dernière** _fem_
**the last time**
la dernière fois
**tonight and last night**
ce soir et hier soir
**last Friday**
vendredi dernier
**last week**
la semaine dernière
**last summer**
l'été dernier
**last night**
hier soir
**at last**
enfin
**B** ADVERB
**en dernier**
**He always comes last.**
Il arrive toujours en dernier.
**late** ADJECTIVE, ADVERB
**1** **en retard**
**You're going to be late!**
Tu vas être en retard!
**I'm late for school.**
Je suis en retard pour l'école.
**Sorry I'm late!**
Désolé d'être en retard!
**2** **tard** _(late at night)_
**I go to bed late.**
Je me couche tard.
**later** ADVERB
**plus tard**
**I'll do it later.**
Je ferai ça plus tard.
**See you later!**
À tout à l'heure!
**latest** ADJECTIVE
**dernier** _masc_
**dernière** _fem_
**their latest album**
leur dernier album
**Latin** NOUN
le **latin** _masc_
**I do Latin.**
Je fais du latin.
**laugh** VERB
**rire**
**Why are you laughing?**
Pourquoi tu ris?
**lawn** NOUN
la **pelouse** _fem_
**lawnmower** NOUN
la **tondeuse à gazon** _fem_
**lawyer** NOUN
l' **avocat** _masc_
l' **avocate** _fem_
**My mother's a lawyer.**
Ma mère est avocate.
**_Language tip_**
_You do not translate **'a'** when you say what someone's job is in French._
**lay** VERB
**poser**
**Lay your cards on the table**
Posez vos cartes sur la table.
**to lay the table**
mettre la table
**It's André's turn to lay the table.**
C'est à André de mettre la table.
**lazy** ADJECTIVE
**paresseux** _masc_
**paresseuse** _fem_
**My sister is very lazy.**
Ma sœur est très paresseuse.
**lead**
**lead** _can be a noun or a verb._
**A** NOUN
**to be in the lead**
être en tête
**Our team is in the lead.**
Notre équipe est en tête.
**B** VERB
**mener**
**This street leads to the station.**
Cette rue mène à la gare.
**leaf** NOUN
la **feuille**
_fem_
**lean out** VERB
**se pencher**
**Don't lean out of the window.**
Ne te penche pas par la fenêtre.
**lean over** VERB
**se pencher**
**Don't lean over too far.**
Ne te penche pas trop.
**leap year** NOUN
l' **année bissextile** _fem_
**learn** VERB
**apprendre**
**I'm learning to ski.**
J'apprends à skier.
**We're learning a lot.**
Nous apprenons beaucoup.
**I'm learning French.**
J'apprends le français.
**least** ADVERB, ADJECTIVE, PRONOUN
**the least**
le moins de
**Who's got the least cards?**
Qui a le moins de cartes?
**_Language tip_**
_When_ **the least** _is followed by an adjective, it is translated as_ **le moins** , **la moins** , _or_ **les moins** , _depending on the following noun._
**the least expensive hotel**
l'hôtel le moins cher
**the least expensive seat**
la place la moins chère
**the least expensive hotels**
les hôtels les moins chers
**It'll cost at least £200.**
Ça va coûter au moins deux cents livres.
**at least**
au moins
**leather** NOUN
le **cuir** _masc_
**It's made of leather.**
C'est en cuir.
**leave** VERB
**1** **laisser** _(on purpose)_
**Don't leave your bag in the car.**
Ne laisse pas ton sac dans la voiture.
**2** **oublier** _(by mistake)_
**I've left my book at home.**
J'ai oublié mon livre à la maison.
**3** **partir** _(depart)_
**The bus leaves at 8.**
Le car part à huit heures.
**leaves** PL NOUN
les **feuilles** _fem pl_
**leek** NOUN
le **poireau** _masc_
(PL les **poireaux** )
**left** VERB _see_ **leave**
**left**
**left** _can be an adjective, an adverb or a noun._
**A** ADJECTIVE
**1** **gauche** _(not right)_
**my left hand**
ma main gauche
**on the left side of the road**
sur le côté gauche de la route
**2** _(remaining)_
**How many cards have you got left?**
Il te reste combien de cartes?
**I haven't got any money left.**
Il ne me reste plus d'argent.
**B** ADVERB
**à gauche**
**Turn left.**
Tournez à gauche.
**Take the next left.**
Prenez la prochaine à gauche.
**C** NOUN
la **gauche** _fem_
**on the left**
à gauche
**the house on the left**
la maison à gauche
**left-hand** ADJECTIVE
**the left-hand side**
la gauche
**It's on the left-hand side.**
C'est à gauche.
**left-handed** ADJECTIVE
**gaucher** _masc_
**gauchère** _fem_
**Annick is left-handed.**
Annick est gauchère.
**_Language tip_**
_Annick is a girl's name. How can you tell from the translation in the example sentence?_
**left-luggage office** NOUN
la **consigne** _fem_
**leg** NOUN
la **jambe** _fem_
**She has a broken leg.**
Elle a une jambe cassée.
**a chicken leg**
une cuisse de poulet
**leisure centre** NOUN
le **centre de loisirs** _masc_
**lemon** NOUN
le **citron** _masc_
**lemonade** NOUN
la **limonade** _fem_
**lend** VERB
**prêter**
**Can you lend me a pencil?**
Tu peux me prêter un crayon?
**less**
**less** _can be an adjective or a pronoun._
**A** ADJECTIVE
**moins de**
**Less noise, please!**
Moins de bruit, s'il vous plaît!
**B** PRONOUN
**moins**
**A bit less, please.**
Un peu moins, s'il vous plaît.
**I've got less than him!**
J'en ai moins que lui!
**_Language tip_**
_When_ **less than** _is followed by a number, the translation is_ **moins de**.
**It costs less than £10.**
Ça coûte moins de dix livres.
**lesson** NOUN
**1** la **leçon** _fem_
**a French lesson**
une leçon de français
**2** le **cours** _masc (class)_
**Each lesson lasts forty minutes.**
Chaque cours dure quarante minutes.
**let** VERB
**1** **laisser** _(allow)_
**Let me have a look.**
Laisse-moi voir.
**2** _(shall we)_
**Let's go to the park!**
Allons au parc!
**Let's go!**
Allons-y!
**Let's start now!**
Commençons maintenant!
**letter** NOUN
la **lettre** _fem_
**I'm writing a letter to my penfriend.**
J'écris une lettre à ma correspondante.
**It's a ten-letter word.**
C'est un mot en dix lettres.
**letterbox** NOUN
la **boîte à lettres** _fem_
_**Did you know...?**_
_In France, people don't usually have letterboxes in their front doors. More often, they have a box outside or, in a block of flats, on the ground floor._
**lettuce** NOUN
la **salade** _fem_
**liar** NOUN
le **menteur** _masc_
la **menteuse** _fem_
**library** NOUN
la **bibliothèque** _fem_
**licence** NOUN
le **permis** _masc_
**a driving licence**
un permis de conduire
**lick** VERB
**lécher**
**The dog is licking me.**
Le chien me lèche.
**lid** NOUN
le **couvercle** _masc_
**lie** VERB
**lie** _can be a verb or a noun._
**A** VERB
**1** **mentir** _(tell lies)_
**She's lying.**
Elle ment.
**2** _(lie down)_
**He is lying on the sofa.**
Il est allongé sur le canapé.
**B** NOUN
le **mensonge** _masc_
**That's a lie!**
C'est un mensonge!
**life** NOUN
la **vie** _fem_
**life-saving** NOUN
le **sauvetage** _masc_
**I'm doing a course in life-saving.**
Je prends des cours de sauvetage.
**lift**
**lift** _can be a verb or a noun._
**A** VERB
**soulever**
**It's too heavy, I can't lift it.**
C'est trop lourd, je ne peux pas le soulever.
**B** NOUN
l' **ascenseur** _masc_
**The lift isn't working.**
L'ascenseur est en panne.
**light**
**light** _can be an adjective, a noun or a verb._
**A** ADJECTIVE
**1** **léger** _masc_
**légère** _fem (not heavy)_
**as light as a feather**
léger comme une plume
**2** **clair** _masc, fem, pl (colours)_
**light blue socks**
des chaussettes bleu clair
**B** NOUN
la **lumière** _fem_
**Switch on the light.**
Allume la lumière.
**Switch off the light.**
Éteins la lumière.
**C** VERB
**allumer**
**Let's light the fire.**
Allumons le feu.
**light bulb** NOUN
l' **ampoule** _fem_
**lightning** NOUN
les **éclairs** _masc pl_
**a flash of lightning**
un éclair
**like**
**like** _can be a verb or a preposition._
**A** VERB
**1** **aimer** _(enjoy)_
**I like cherries.**
J'aime les cerises.
**_Language tip_**
_There's an extra word in the French example sentence that isn't in the English. What is it?_
**I don't like mustard.**
Je n'aime pas la moutarde.
**I like riding.**
J'aime faire du cheval.
**2** **bien aimer** _(be fond of)_
**I like Paul.**
J'aime bien Paul.
**3** **vouloir** _(want)_
**Yes, if you like.**
Oui, si tu veux.
**_Language tip_**
_If you want to say that you'd like something, use_ **je voudrais**.
**I'd like an orange juice, please.**
Je voudrais un jus d'orange, s'il vous plaît.
**I'd like some chips.**
Je voudrais des frites.
**_Language tip_**
_To ask what somebody would like, use_ **vous voulez** _or_ **tu veux**.
**What would you like, Miss?**
Qu'est-ce que vous voulez, Madame?
**What would you like, dear?**
Qu'est-ce que tu veux, mon chéri?
**Would you like some tea, Miss?**
Vous voulez du thé, Madame?
**Would you like a coke, Louis?**
Tu veux un coca, Louis?
**_Language tip_**
_Another way to ask_ **would you like** _is to put the verb first._
**Would you like a coke?**
Veux-tu un coca?
**I'd like...**
Je voudrais...
**B** PREPOSITION
**comme**
**a city like Paris**
une ville comme Paris
**I look like my brother.**
Je ressemble à mon frère.
**What's the weather like?**
Quel temps fait-il?
**likely** ADJECTIVE
**probable**
**That's not very likely.**
C'est peu probable.
**lily of the valley** NOUN
le **muguet** _masc_
_**Did you know...?**_
_On the first of May or May Day, people in France celebrate by giving each other small bunches of lily of the valley._
**line** NOUN
la **ligne** _fem_
**a straight line**
une ligne droite
**to draw a line**
tirer un trait
**Draw a line under each answer.**
Tirez un trait après chaque réponse.
**lion** NOUN
le **lion** _masc_
**lip** NOUN
la **lèvre** _fem_
**lipstick** NOUN
le **rouge à lèvres** _masc_
**_Language tip_**
_Word for word this means 'red for lips'._
**liquid** NOUN
le **liquide** _masc_
**list**
**list** _can be a noun or a verb._
**A** NOUN
la **liste** _fem_ **a shopping list**
une liste de courses
**B** VERB
**faire une liste de**
**List your hobbies!**
Fais une liste de tes hobbies!
**listen** VERB
**écouter**
**Are you listening, Gaëlle?**
Tu écoutes, Gaëlle?
**Listen to this, everybody!**
Écoutez ça, tout le monde!
**Listen to me, children!**
Écoutez-moi, les enfants!
**litre** NOUN
le **litre** _masc_
**litter** NOUN
les **détritus** _masc pl_
**Don't leave litter.**
Ne laissez pas de détritus.
**litter bin** NOUN
la **poubelle** _fem_
**little** ADJECTIVE
**petit** _masc_
**petite** _fem_
**a little girl**
une petite fille
**very little**
très peu
**We've got very little time.**
Nous avons très peu de temps.
**a little**
un peu
**How much would you like? — Just a little.**
Combien en voulez-vous? — Juste un peu.
**_Language tip_**
_The word_ **en** _means 'of it'._
**live** VERB
**1** **habiter**
**Where do you live?**
Où est-ce que tu habites?
**I live here.**
J'habite ici.
**I live in Edinburgh.**
J'habite à Édimbourg.
**2** **vivre**
**I live with my grandmother.**
Je vis avec ma grand-mère.
**to live together**
vivre ensemble
**My parents don't live together anymore.**
Mes parents ne vivent plus ensemble.
**living room** NOUN
la **salle de séjour** _fem_
**load** NOUN
**loads of**
un tas de
**loads of people**
un tas de gens
**loads of money**
un tas d'argent
**loaf** NOUN
le **pain** _masc_
**a loaf of bread**
un pain
**loaves** PL NOUN
les **pains** _masc pl_
**lock**
**lock** _can be a noun or a verb._
**A** NOUN
la **serrure** _fem_
**The lock is broken.**
La serrure est cassée.
**B** VERB
**fermer à clé**
**Lock your door.**
Fermez votre porte à clé.
**locker** NOUN
le **casier** _masc_
**Leave your books in your locker.**
Laissez vos livres dans votre casier.
**log** NOUN
la **bûche** _fem_
**log in** VERB
**se connecter**
**I can't log in.**
Je n'arrive pas à me connecter.
**log off** VERB
**se déconnecter**
**I've forgotten how to log off.**
J'ai oublié comment on se déconnecte.
**log on** VERB
**se connecter**
**Have you logged on yet?**
Ça y est, tu t'es connecté?
**log out** VERB
**se déconnecter**
**Please log out now.**
Déconnectez-vous maintenant, s'il vous plaît.
**lollipop** NOUN
la **sucette** _fem_
**lollipop lady** NOUN
la **dame qui aide à traverser** _fem_
**London** NOUN
**Londres**
**in London**
à Londres
**to London**
à Londres
**I'm from London.**
Je suis de Londres.
**_Language tip_**
_A few British towns have French names. Can you recognize these:_ **Douvres** ,
**Cantorbéry** , **Édimbourg**?
**lonely** ADJECTIVE
**seul** _masc_
**seule** _fem_
**to feel lonely**
se sentir seul
**She feels lonely.**
Elle se sent seule.
**long** ADJECTIVE
**long** _masc_
**longue** _fem_
**There's a long queue.**
Il y a une longue queue.
**She's got long hair.**
Elle a les cheveux longs.
**_Language tip_**
_Hair is plural in French so the adjective has to be plural too._
**How long is the flight?**
Combien de temps dure le vol?
**how long?**
combien de temps?
**It takes a long time.**
Ça prend du temps.
**loo** NOUN
les **toilettes** _fem pl_
**Where's the loo?**
Où sont les toilettes?
**May I go to the loo?**
Je peux aller aux toilettes?
**look**
**look** _can be a noun or a verb._
**A** NOUN
**to have a look**
regarder
**Have a look at this!**
Regardez ça!
**B** VERB
**1** **regarder**
**Look, children!**
Regardez, les enfants!
**Look Olivier, you've broken it.**
Regarde Olivier, tu l'as cassé.
**_Language tip_**
**to look at** _is also_
**regarder**.
**Look at the picture.**
Regardez cette image.
**Look at me, Stéphane.**
Regarde-moi, Stéphane.
**2** **avoir l'air** _(seem)_
**That cake looks nice.**
Ce gâteau a l'air bon.
**Look!**
Regarde!
**Look at the board.**
Regardez le tableau.
**Look out!**
Attention!
**look after** VERB
**s'occuper de**
**I look after my little sister.**
Je m'occupe de ma petite sœur.
**look for** VERB
**chercher**
**I'm looking for my rubber.**
Je cherche ma gomme.
**What are you looking for?**
Qu'est-ce que tu cherches?
**look up** VERB
**chercher**
**Look up the words in the dictionary.**
Cherchez les mots dans le dictionnaire.
**loonie** NOUN _(Canada)_
le **huard** _masc_
**lorry** NOUN
le **camion** _masc_
**lorry driver** NOUN
le **routier** _masc_
**He's a lorry driver.**
Il est routier.
**_Language tip_**
_When you say what someone's job is in French, you do not translate_ **a**.
**lose** VERB
**perdre**
**I've lost my purse.**
J'ai perdu mon porte-monnaie.
**Our team always loses.**
Notre équipe perd toujours.
**loser** NOUN
le **perdant** _masc_
la **perdante** _fem_
**lost** VERB _see_ **lose**
**lost property office** NOUN
les **objets trouvés** _masc pl_
**_Language tip_**
_The French word literally means 'things that have been found'._
**lot** NOUN
**a lot**
beaucoup
**not a lot**
pas beaucoup
**That's a lot.**
C'est beaucoup.
**a lot of**
beaucoup de
**She has a lot of books.**
Elle a beaucoup de livres.
**lots of**
un tas de
**He's got lots of friends.**
Il a un tas d'amis.
**lottery** NOUN
le **loto** _masc_
**I hope I win the lottery.**
J'espère que je vais gagner au loto.
**loud** ADJECTIVE
**fort** _masc_
**forte** _fem_
**The television is too loud.**
La télévision est trop forte.
**Speak louder!**
Parle plus fort!
**lounge** NOUN
le **salon** _masc_
**love**
**love** _can be a noun or a verb._
**A** NOUN
l' **amour** _masc_
**She's in love.**
Elle est amoureuse.
**She's in love with Paul.**
Elle est amoureuse de Paul.
**Give Delphine my love.**
Embrasse Delphine pour moi.
**Love, Rosemary.**
Amitiés, Rosemary.
**B** VERB
**1** **aimer**
**Do you love me?**
Tu m'aimes?
**2** **beaucoup aimer** _(be very fond of)_
**Everybody loves her.**
Tout le monde l'aime beaucoup.
**3** **adorer** _(enjoy)_
**I love chocolate.**
J'adore le chocolat.
**_Language tip_**
_There is an extra word in the French sentence that isn't in the English. What is it?_
**I love skiing.**
J'adore le ski.
**I love you.**
Je t'aime.
**Love from...**
Amitiés...
**lovely** ADJECTIVE
**It's a lovely day.**
Il fait très beau aujourd'hui.
**They've got a lovely house.**
Ils ont une très belle maison.
**Have a lovely time!**
Amusez-vous bien!
**low** ADJECTIVE
**bas** _masc_
**basse** _fem_
**a low price**
un prix bas
**lower sixth** NOUN
la **première** _fem_
**He's in the lower sixth.**
Il est en première.
_**Did you know...?**_
_In French secondary schools, the years are counted from the_ **sixième** _(youngest) to_ **première** _and_ **terminale** _(oldest)._
**luck** NOUN
la **chance** _fem_
**She doesn't have much luck.**
Elle n'a pas beaucoup de chance.
**Good luck!**
Bonne chance!
**Bad luck!**
Pas de chance!
**luckily** ADVERB
**heureusement**
**lucky** ADJECTIVE
**You're lucky!**
Tu as de la chance!
**Leah is lucky, she's going to France.**
Leah a de la chance, elle va en France.
**_Language tip_**
_When you talk about things that are lucky, use_ **porter bonheur**.
**Black cats are lucky.**
Les chats noirs portent bonheur.
**a lucky horseshoe**
un fer à cheval porte-bonheur
_**Did you know...?**_
_In France, a black cat crossing your path is unlucky._
**luggage** NOUN
les **bagages** _masc pl_
**Have you got any luggage?**
Vous avez des bagages?
**lump** NOUN
la **bosse** _fem_
**He's got a lump on his forehead.**
Il a une bosse sur le front.
**lunch** NOUN
le **déjeuner** _masc_
**I go home for lunch.**
Je rentre à la maison pour le déjeuner.
**It's time for lunch.**
C'est l'heure du déjeuner.
**to have lunch**
déjeuner
**We have lunch at 12.30.**
Nous déjeunons à midi et demi.
**Luxembourg** NOUN
le **Luxembourg** _masc_
**lying** VERB _see_ **lie**
# **M m**
**machine** NOUN
la **machine** _fem_
**mad** ADJECTIVE
**1** **fou** _masc_
**folle** _fem (insane)_
**You're mad!**
Tu es fou!
**He's mad about football.**
Il est dingue de foot.
**She's mad about horses.**
Elle adore les chevaux.
**2** **furieux** _masc_
**furieuse** _fem (angry)_
**If you don't invite her she'll be mad.**
Elle sera furieuse si tu ne l'invites pas.
**madam** NOUN
**madame** _fem_
**Would you like to order, Madam?**
Désirez-vous commander, Madame?
**made** VERB _see_ **make**
**magazine** NOUN
le **magazine** _masc_
**magic**
**magic** _can be an adjective or a noun._
**A** ADJECTIVE
**1** **magique** _(magical)_
**a magic wand**
une baguette magique
**a magic trick**
un tour de magie
**2** **super** _(brilliant)_
**It was magic!**
C'était super!
**B** NOUN
la **magie** _fem_
**by magic**
par magie
**magician** NOUN
le **prestidigitateur** _masc_
**magnifying glass** NOUN
la **loupe** _fem_
**mail**
**mail** _can be a noun or a verb._
**A** NOUN
le **courrier** _masc_
**You've got some mail.**
Tu as du courrier.
**B** VERB
**envoyer un e-mail à**
**I'll mail my friend.**
Je vais envoyer un e-mail à mon copain.
**main** ADJECTIVE
**principal** _masc_
**principale** _fem_
**the main problem**
le principal problème
**main road** NOUN
la **grande route** _fem_
**The hotel is on the main road.**
L'hôtel est sur la grande route.
**Majorca** NOUN
**Majorque** _fem_
**make**
**make** _can be a noun or a verb._
**A** NOUN
la **marque** _fem_
**What make is that car?**
De quelle marque est cette voiture?
**B** VERB
**1** **faire**
**I'm going to make a cake.**
Je vais faire un gâteau.
**Make a sentence, everyone.**
Faites une phrase, tout le monde.
**I make my bed every morning.**
Je fais mon lit tous les matins.
**2 and 2 make 4.**
Deux et deux font quatre.
**4 take away 2, what does that make?**
Quatre moins deux, ça fait combien?
**He made it himself.**
Il l'a fait lui-même.
**2** **fabriquer** _(manufacture)_
**made in France**
fabriqué en France
**3** **gagner** _(earn)_
**He makes a lot of money.**
Il gagne beaucoup d'argent.
**4** **préparer** _(prepare)_
**She's making lunch.**
Elle prépare le déjeuner.
**make up** VERB
**inventer**
**You're making it up!**
Tu inventes!
**make-up** NOUN
le **maquillage** _masc_
**male** ADJECTIVE
**1** **mâle** _(animal)_
**a male kitten**
un chaton mâle
**2** **masculin** _(person, on official forms)_
**Sex: male.**
Sexe: masculin.
**man** NOUN
l' **homme** _masc_
**an old man**
un vieil homme
**manage** VERB
**se débrouiller**
**It's okay, I can manage.**
Ça va, je me débrouille.
**I can't manage all that.**
C'est trop pour moi.
**manager** NOUN
**1** le **directeur** _masc_
la **directrice** _fem (of company)_
**2** le **gérant** _masc_
la **gérante** _fem (of shop, restaurant)_
**3** le **manager** _masc (of team)_
**manageress** NOUN
la **gérante** _fem_
**manners** PL NOUN
les **manières** _fem pl_
**good manners**
les bonnes manières
**Her manners are appalling.**
Elle a de très mauvaises manières.
**It's bad manners to speak with your mouth full.**
Ce n'est pas poli de parler la bouche pleine.
**many** ADJECTIVE, PRONOUN
**beaucoup de**
**He hasn't got many friends.**
Il n'a pas beaucoup d'amis.
**Are many people absent?**
Est-ce qu'il y a beaucoup d'absents?
**How many?**
Combien?
**_Language tip_**
_When_ **how many** _is followed by a noun, it is translated by_
**combien de**.
**How many sisters have you got?**
Tu as combien de sœurs?
**How many girls are there?**
Il y a combien de filles?
**How many euros do you get for £10?**
Combien d'euros a-t-on pour dix livres?
**How many do you want?**
Combien en veux-tu?
**_Language tip_**
**en** _means 'of them'._
**That's too many.**
C'est trop.
**You ask too many questions!**
Tu poses trop de questions!
**How many?**
Combien?
**Not many.**
Pas beaucoup.
**too many**
trop
**map** NOUN
**1** la **carte** _fem (of country, area)_
**a map of France**
une carte de France
**2** le **plan** _masc (of town)_
**a map of Paris**
un plan de Paris
**marathon** NOUN
le **marathon** _masc_
**the London marathon**
le marathon de Londres
**marbles** NOUN
les **billes** _fem pl_
**Do you want to play marbles?**
Tu veux jouer aux billes?
**March** NOUN
**mars** _masc_
**March or April?**
Mars ou avril?
**My birthday's in March**
Mon anniversaire est en mars.
**in March**
en mars
**the fifth of March**
le cinq mars
**_Language tip_**
_The months in French are not spelled with a capital letter._
**margarine** NOUN
la **margarine** _fem_
**margin** NOUN
la **marge** _fem_
**Write notes in the margin.**
Écrivez vos notes dans la marge.
**mark**
**mark** _can be a noun or a verb._
**A** NOUN
la **note** _fem (in school)_
**I get good marks for French.**
J'ai de bonnes notes en français.
**B** VERB
**corriger**
**She's got books to mark.**
Elle a des cahiers à corriger.
**market** NOUN
le **marché** _masc_
**marmalade** NOUN
la **confiture d'oranges** _fem_
**marriage** NOUN
le **mariage** _masc_
**_Language tip_**
_The English word has one more letter than the French word. What is it?_
**married** ADJECTIVE
**marié** _masc_
**mariée** _fem_
**They are not married.**
Ils ne sont pas mariés.
**a married couple**
un couple marié
**marry** VERB
**épouser**
**He wants to marry her.**
Il veut l'épouser.
**They want to get married.**
Ils veulent se marier.
**My sister's getting married in June.**
Ma sœur se marie en juin.
**marvellous** ADJECTIVE
**1** **excellent** _masc_
**excellente** _fem_
**She's a marvellous cook.**
C'est une excellente cuisinière.
**2** **superbe**
**The weather was marvellous.**
Il a fait un temps superbe.
**masculine** ADJECTIVE
**masculin** _masc_
**masculine** _fem_
**mashed potatoes** PL NOUN
la **purée** _fem_
**sausages and mashed potatoes**
des saucisses avec de la purée
**_Language tip_**
**purée** _is a singular word._
**mask** NOUN
le **masque**
_masc_
**mass** NOUN
**1** la **multitude** _fem_
**a mass of books and papers**
une multitude de livres et de papiers
**2** la **messe** _fem (in church)_
**We go to mass on Sunday.**
Nous allons à la messe le dimanche.
**massive** ADJECTIVE
**énorme**
**masterpiece** NOUN
le **chef-d'œuvre** _masc_
**mat** NOUN
le **paillasson** _masc_
**a table mat**
un set de table
**match**
**match** _can be a noun or a verb._
**A** NOUN
**1** l' **allumette** _fem_
**a box of matches**
une boîte d'allumettes
**2** le **match** _masc_ (PL les **matchs** ) _(game)_
**a football match**
un match de foot
**B** VERB
**1** **être assorti à** _(go with)_
**The jacket matches the trousers.**
La veste est assortie au pantalon.
**2** **faire correspondre à** _(put with)_
**Match the names to the pictures.**
Faites correspondre les noms aux images.
**matching** ADJECTIVE
**assorti** _masc_
**assortie** _fem_
**My bedroom has matching wallpaper and curtains.**
Ma chambre a du papier peint et des rideaux assortis.
**mate** NOUN
le **pote** _masc_
**He's my mate.**
C'est mon pote.
**material** NOUN
le **tissu** _masc_
**It's made of red material.**
C'est fait en tissu rouge.
**maths** NOUN
les **maths**
_fem pl_
**matter**
**matter** _can be a noun or a verb._
**A** NOUN
**What's the matter? Why are you crying?**
Qu'est-ce que tu as? Pourquoi tu pleures?
**What's the matter with him?**
Qu'est-ce qu'il a?
**B** VERB
**It doesn't matter.**
Ça ne fait rien.
**mattress** NOUN
le **matelas** _masc_
**maximum** ADJECTIVE
**maximum** _masc, fem, pl_
**May** NOUN
**mai** _masc_
**May or June?**
Mai ou juin?
**My birthday's in May.**
Mon anniversaire est en mai.
**in May**
en mai
**the fifth of May**
le cinq mai
**_Language tip_**
_The months in French are not spelled with a capital letter._
**May Day** NOUN
**le Premier Mai** _masc_
_**Did you know...?**_
_In France, people give friends little bunches of lily of the valley_ ( **muguet** ) _on May Day._
**maybe** ADVERB
**peut-être**
**maybe not**
peut-être pas
**Maybe she's at home.**
Elle est peut-être chez elle.
**mayonnaise** NOUN
la **mayonnaise** _fem_
**mayor** NOUN
le **maire** _masc_
**maze** NOUN
le **labyrinthe** _masc_
**me** PRONOUN
**1** **me**
**Could you lend me your pen, Rachid?**
Tu peux me prêter ton stylo, Rachid?
**Are you looking for me?**
Tu me cherches?
**_Language tip_**
**me** _changes to_ **m'** _before a vowel sound._
**Do you love me?**
Tu m'aimes?
**Can you help me?**
Est-ce que tu peux m'aider?
**2** **moi**
**_Language tip_**
_The French word_ **me** _cannot come at the end of a sentence. Use_ **moi** _instead._
**Wait for me!**
Attends-moi!
**Look at me, children!**
Regardez-moi, les enfants!
**You're after me.**
Tu es après moi.
**Is it for me?**
C'est pour moi?
**Me too!**
Moi aussi!
**Excuse me!**
Excusez-moi!
**meal** NOUN
le **repas** _masc_
**mean**
**mean** _can be a verb or an adjective._
**A** VERB
**vouloir dire**
**What does 'complet' mean?**
Qu'est-ce que 'complet' veut dire?
**I don't know what it means.**
Je ne sais pas ce que ça veut dire.
**What do you mean?**
Qu'est que vous voulez dire?
**That's not what I meant.**
Ce n'est pas ce que je voulais dire.
**What does it mean?**
Qu'est-ce que ça veut dire?
**B** ADJECTIVE
**1** **radin** _masc_
**radine** _fem (with money)_
**He's too mean to buy presents.**
Il est trop radin pour acheter des cadeaux.
**2** **méchant**
_masc_ **méchante** _fem (unkind)_
**You're being mean to me.**
Tu es méchant avec moi.
**meaning** NOUN
le **sens** _masc_
**measles** NOUN
la **rougeole** _fem_
**measure** VERB
**mesurer**
**Measure the length.**
Mesurez la longueur.
**meat** NOUN
la **viande** _fem_
**I don't eat meat.**
Je ne mange pas de viande.
**Mecca** NOUN
**La Mecque** _fem_
**medal** NOUN
la **médaille** _fem_
**the gold medal**
la médaille d'or
**medical**
**medical** _can be an adjective or a noun._
**A** ADJECTIVE
**She's a medical student.**
Elle est étudiante en médecine.
**B** NOUN
**You have to have a medical.**
Tu dois passer une visite médicale.
**medicine** NOUN
le **médicament**
_masc_ **I need some medicine.**
J'ai besoin d'un médicament.
**Mediterranean** NOUN
**the Mediterranean**
la Méditerranée
**medium** ADJECTIVE
**moyen** _masc_
**moyenne** _fem_
**a man of medium height**
un homme de taille moyenne
**medium-sized** ADJECTIVE
**de taille moyenne**
**a medium-sized town**
une ville de taille moyenne
**meet** VERB
**1** **retrouver** _(by arrangement)_
**I'm meeting my friends at the swimming pool.**
Je retrouve mes amis à la piscine.
**Let's meet in front of the tourist office.**
Retrouvons-nous devant l'office de tourisme.
**2** **rencontrer** _(by chance)_
**I met some French people.**
J'ai rencontré des Français.
**3** **aller chercher** _(pick up)_
**I'll meet you at the station.**
J'irai te chercher à la gare.
**meeting** NOUN
**1** la **rencontre** _fem_
**their first meeting**
leur première rencontre
**2** la **réunion** _fem_
**There's a meeting at school tonight.**
Il y a une réunion à l'école ce soir.
**melon** NOUN
le **melon** _masc_
**melt** VERB
**fondre**
**The snow is melting.**
La neige est en train de fondre.
**member** NOUN
le **membre** _masc_
**a member of our club**
un membre de notre club
**memory** NOUN
la **mémoire** _fem_
**I haven't got a good memory.**
Je n'ai pas une bonne mémoire.
**memory game** NOUN
le **jeu de mémoire** _masc_
**men** PL NOUN _see_ **man**
les **hommes** _masc pl_
**mend** VERB
**réparer**
**Can you mend it?**
Vous pouvez le réparer?
**mention** VERB
**Thank you! — Don't mention it!**
Merci! — Il n'y a pas de quoi!
**menu** NOUN
le **menu** _masc_
**merry** ADJECTIVE
**Merry Christmas!**
Joyeux Noël!
**merry-go-round** NOUN
le **manège** _masc_
**mess** NOUN
le **bazar** _masc_
**My bedroom's in a mess.**
C'est le bazar dans ma chambre.
**message** NOUN
le **message** _masc_
**met** VERB _see_ **meet**
**metal** NOUN
le **métal** _masc_ (PL les **métaux** )
**method** NOUN
la **méthode** _fem_
**metre** NOUN
le **mètre** _masc_
**I'm one metre thirty tall.**
Je mesure un mètre trente.
_**Did you know...?**_
_In France, measurements are always in metres and centimetres, rather than feet and inches._
**metric** ADJECTIVE
**métrique**
**Mexican wave** NOUN
la **hola** _fem_
**mice** PL NOUN
les **souris** _fem pl_
**microphone** NOUN
le **microphone** _masc_
**microwave** NOUN
le **four à micro-ondes** _masc_
**midday** NOUN
le **midi** _masc_
**It's midday.**
Il est midi.
**at midday**
à midi
**middle** NOUN
le **milieu** _masc_
**Come into the middle, Hugo.**
Viens au milieu, Hugo.
**in the middle of the road**
au milieu de la route
**in the middle of the night**
au milieu de la nuit
**middle-aged** ADJECTIVE
**d'un certain âge**
**a middle-aged man**
un homme d'un certain âge
**middle name** NOUN
le **deuxième prénom** _masc_
**It's my middle name.**
C'est mon deuxième prénom.
**midge** NOUN
le **moucheron** _masc_
**midnight** NOUN
**minuit** _masc_
**It's midnight.**
Il est minuit.
**at midnight**
à minuit
**might** VERB
**I might, I might not.**
Peut-être, peut-être pas.
**_Language tip_**
**peut-être** _means 'maybe'. You're really saying 'maybe, maybe not'._
**migraine** NOUN
la **migraine** _fem_
**I've got a migraine.**
J'ai la migraine.
**mild** ADJECTIVE
**doux** _masc_
**douce** _fem_
**The winters are quite mild.**
Les hivers sont assez doux.
**mile** NOUN
_**Did you know...?**_
_In France, distances are always measured in kilometres. A mile is about 1.6 kilometres._
**It's five miles from here.**
C'est à huit kilomètres d'ici.
**We walked miles!**
Nous avons marché pendant des kilomètres!
**milk** NOUN
le **lait** _masc_
**tea with milk**
du thé au lait
**milkman** NOUN
**He's a milkman.**
Il livre le lait à domicile.
**milk shake** NOUN
le **milk-shake** _masc_
**millimetre** NOUN
le **millimètre** _masc_
**million** NOUN
le **million** _masc_
**two million**
deux millions
**millionaire** NOUN
le **millionnaire** _masc_
**mince** NOUN
la **viande hachée** _fem_
**mince pie** NOUN
la **tartelette de Noël** _fem_
_**Did you know...?**_
**Mince pies** _are not eaten in France, instead French people eat_ **papillotes** , _which are chocolates wrapped in foil._
**mind**
**mind** _can be a verb or a noun._
**A** VERB
**Do you mind if I open the window?**
Est-ce que je peux ouvrir la fenêtre?
**Mind the step!**
Attention à la marche!
**I don't mind.**
Ça ne me dérange pas.
**Never mind!**
Ça ne fait rien!
**B** NOUN
**I've changed my mind.**
J'ai changé d'avis.
**mine**
**mine** _can be a pronoun or a noun._
**A** PRONOUN
**This book is mine.**
Ce livre est à moi.
**It's mine.**
C'est à moi.
**B** NOUN
la **mine** _fem_
**a coal mine**
une mine de charbon
**mineral**
**water**
NOUN
l' **eau**
**minérale**
_fem_
**minibus** NOUN
le **minibus** _masc_
**Minidisc** ® NOUN
le **minidisque** _masc_
**minimum** ADJECTIVE
**minimum** _masc, fem, pl_
**miniskirt** NOUN
la **mini-jupe** _fem_
**minister** NOUN
**1** le **pasteur** _masc_
_(of church)_
**2** le **ministre** _masc_
_(in government)_
**minor** ADJECTIVE
**mineur** _masc_
**mineure** _fem_
**a minor problem**
un problème mineur
**mint** NOUN
**1** le **bonbon à la**
**menthe** _masc (sweet)_
**2** la **menthe** _fem (plant)_
**mint sauce**
la sauce à la menthe
**minus** PREPOSITION
**moins**
**16 minus 3 is 13.**
Seize moins trois égale treize.
**It's minus two degrees outside.**
Il fait moins deux dehors.
**minute** NOUN
la **minute** _fem_
**Wait a minute!**
Attends une minute!
**mirror** NOUN
le **miroir** _masc_
**misbehave** VERB
**Don't misbehave, Pierre!**
Sois sage, Pierre!
**mischief** NOUN
les **bêtises** _fem pl_
**My little sister's always up to mischief.**
Ma petite sœur fait constamment des bêtises.
**miserable** ADJECTIVE
**1** **malheureux** _masc_
**malheureuse** _fem (person)_
**You're looking miserable.**
Tu as l'air malheureux.
**2** **épouvantable** _(weather)_
**The weather was miserable.**
Il faisait un temps épouvantable.
**Miss** NOUN
**1** **maîtresse** _fem (teacher)_
**Yes, Miss.**
Oui, maîtresse.
**2** **Mademoiselle** _fem_
**Miss Jones**
Mademoiselle Jones
**_Language tip_**
_In addresses_ , **Miss** _is_ **Mlle**.
**miss** VERB
**rater**
**Hurry or you'll miss the bus.**
Dépêche-toi ou tu vas rater le bus.
**I miss you.**
Tu me manques.
**Miss a turn.**
Passe un tour.
**missing** ADJECTIVE
**manquant** _masc_
**manquante** _fem_
**the missing piece**
la pièce manquante
**My rucksack is missing.**
Mon sac à dos a disparu.
**Two children are missing.**
Deux enfants ont disparu.
**mist** NOUN
la **brume** _fem_
**mistake** NOUN
la **faute** _fem_
**Only one mistake!**
Une faute seulement!
**a spelling mistake**
une faute d'orthographe
**Be careful not to make any mistakes, Luc.**
Fais attention à ne pas faire de fautes, Luc.
**by mistake**
par erreur
**I took his bag by mistake.**
J'ai pris son sac par erreur.
**mistletoe** NOUN
le **gui** _masc_
**misty** ADJECTIVE
**brumeux** _masc_
**brumeuse** _fem_
**a misty morning**
un matin brumeux
**It's misty.**
Le temps est brumeux.
**mix** VERB
**mélanger**
**Mix the flour with the sugar.**
Mélangez la farine au sucre.
**mix up** VERB
**confondre**
**He always mixes me up with my sister.**
Il me confond toujours avec ma sœur.
**mixed** ADJECTIVE
**a mixed salad**
une salade composée
**a mixed school**
une école mixte
**mixture** NOUN
le **mélange** _masc_
**mix-up** NOUN
la **confusion** _fem_
**mobile** NOUN
le **portable** _masc_
**I haven't got a mobile.**
Je n'ai pas de portable.
**mobile phone** NOUN
le **portable** _masc_
**Have you got a mobile phone?**
Tu as un portable?
**model**
**model** _can be a noun or an adjective._
**A** NOUN
**1** la **maquette** _fem (small version)_
**I'm making a model of the castle.**
Je fais une maquette du château.
**2** le **mannequin** _masc (person)_
**She's a famous model.**
C'est un mannequin célèbre.
**B** ADJECTIVE
**a model plane**
un modèle réduit d'avion
**a model railway**
un modèle réduit de voie ferrée
**modern** ADJECTIVE
**moderne**
**_Language tip_**
_What is the difference in spelling between the French word and the English word?_
**moment** NOUN
l' **instant** _masc_
**Wait a moment, Alain.**
Attends un instant, Alain.
**Could you wait a moment?**
Pouvez-vous attendre un instant?
**in a moment**
dans un instant
**Just a moment!**
Un instant!
**at the moment**
en ce moment
**Monday** NOUN
le **lundi** _masc_
**It's Monday today.**
Aujourd'hui c'est lundi.
**on Monday**
lundi
**on Mondays**
le lundi
**every Monday**
tous les lundis
**last Monday**
lundi dernier
**next Monday**
lundi prochain
**_Language tip_**
_Days of the week are not written with a capital letter in French._
**money** NOUN
l' **argent** _masc_ **I haven't got enough money.**
Je n'ai pas assez d'argent.
**I need to change some money.**
J'ai besoin de changer de l'argent.
**monitor** NOUN
le **moniteur** _masc_
**monk** NOUN
le **moine** _masc_
**monkey** NOUN
le **singe** _masc_
**monster** NOUN
le **monstre** _masc_
**month** NOUN
le **mois** _masc_
**two months**
deux mois
**at the end of the month**
à la fin du mois
**this month**
ce mois-ci
**next month**
le mois prochain
**last month**
le mois dernier
**every month**
tous les mois
**What month is it?**
Quel mois sommes-nous?
**mood** NOUN
l' **humeur** _fem_
**She's in a bad mood.**
Elle est de mauvaise humeur.
**moon** NOUN
la **lune** _fem_
**the moon and the stars**
la lune et les étoiles
**moped** NOUN
le **cyclomoteur** _masc_
**more** ADJECTIVE, PRONOUN, ADVERB
**1** **plus**
**_Language tip_**
_When comparing one thing with another, you usually use_ **plus**.
**more difficult**
plus difficile
**This model is more expensive.**
Ce modèle est plus cher.
**Could you speak more slowly?**
Vous pourriez parler plus lentement?
**more than me**
plus que moi
**more than that**
plus que ça
**He's more intelligent than me.**
Il est plus intelligent que moi.
**_Language tip_**
_When **plus** is followed by a noun, it becomes **plus de**._
**There are more girls in the class.**
Il y a plus de filles dans la classe.
**I've got more than 50 euros.**
J'ai plus de cinquante euros.
**There isn't any more.**
Il n'y en a plus.
**a bit more**
un peu plus
**more... than**
plus... que
**2** **encore**
**_Language tip_**
_When you are talking about second helpings, or extra time, you use_ **encore**.
**Do you want some more, André?**
Tu en veux encore, André?
**Would you like some more, Mr Gautier?**
Vous en voulez encore, M. Gautier?
**Two minutes more!**
Encore deux minutes!
**_Language tip_**
_When_ **encore** _is followed by a noun, it becomes_ **encore de**.
**Could I have some more chips?**
Est-ce que je pourrais avoir encore des frites?
**Do you want some more tea?**
Voulez-vous encore du thé?
**morning** NOUN
le **matin** _masc_
**on Saturday morning**
le samedi matin
**all morning**
toute la matinée
**Are they staying all morning?**
Est-ce qu'ils vont rester toute la matinée?
**this morning**
ce matin
**tomorrow morning**
demain matin
**every morning**
tous les matins
**in the morning**
le matin
**at 7 o'clock in the morning**
à sept heures du matin
**mosque** NOUN
la **mosquée** _fem_
**mosquito** NOUN
le **moustique** _masc_
**a mosquito bite**
une piqûre de moustique
**most** ADVERB, ADJECTIVE, PRONOUN
**_Language tip_**
**most of** _can be translated by_ **la plupart de** , **la plupart du** , **la plupart de la** , **la plupart des** , _depending on the following noun._
**most of my friends**
la plupart de mes amis
**most of the time**
la plupart du temps
**most French people**
la plupart des Français
**most of the class**
la majeure partie de la classe
**the most**
le plus
**Chantal talks the most.**
C'est Chantal qui parle le plus.
**_Language tip_**
_When_ **the most** _is followed by an adjective, it is translated_ **le plus** , **la plus** , _or_ **les plus** , _depending on the following noun._
**the most expensive restaurant**
le restaurant le plus cher
**the most expensive seat**
la place la plus chère
**the most expensive restaurants**
les restaurants les plus chers
**the most expensive seats**
les places les plus chères
**at the most**
au maximum
**two hours at the most**
deux heures au maximum
**motel** NOUN
le **motel** _masc_
**moth** NOUN
le **papillon de nuit** _masc_
**_Language tip_**
_The French word for moth literally means 'butterfly of the night'._
**mother** NOUN
la **mère** _fem_
**my mother**
ma mère
**your mother**
ta mère
**Mother's Day** NOUN
la **fête des Mères** _fem_
**It's Mother's Day on Sunday.**
Dimanche, c'est la fête des Mères.
**Happy Mother's Day!**
Bonne Fête, Maman!
_**Did you know...?**_
_Mother's Day is usually on the last Sunday of May in France._
**motor** NOUN
le **moteur** _masc_
**motorbike** NOUN
la **moto** _fem_
**motorboat** NOUN
le **bateau à moteur** _masc_
**motorcycle** NOUN
le **vélomoteur** _masc_
**motorcyclist** NOUN
le **motard** _masc_
**motorist** NOUN
l' **automobiliste** _masc/fem_
**motorway** NOUN
l' **autoroute** _fem_
**on the motorway**
sur l'autoroute
**mountain** NOUN
la **montagne** _fem_
**mountain bike** NOUN
le **VTT** _masc_
**I've got a mountain bike.**
J'ai un VTT.
**mouse** NOUN
la **souris** _fem_
**two white mice**
deux souris blanches
**mouse mat** NOUN
le **tapis de souris** _masc_
**mousse** NOUN
la **mousse** _fem_
**chocolate mousse**
la mousse au chocolat
**moustache** NOUN
la **moustache** _fem_
**He's got a moustache.**
Il a une moustache.
**mouth** NOUN
la **bouche** _fem_
**move**
**move** _can be a noun or a verb._
**A** NOUN
le **tour** _masc_
**It's your move.**
C'est ton tour.
**Get a move on, Marcel!**
Remue-toi, Marcel!
**B** VERB
**bouger**
**Don't move!**
Ne bouge pas!
**You moved!**
Tu as bougé!
**Could you move your stuff please?**
Tu peux pousser tes affaires, s'il te plaît?
**Move forward two spaces!**
Avance de deux cases!
**move over** VERB
**se pousser**
**Could you move over a bit?**
Tu peux te pousser un peu?
**movement** NOUN
le **mouvement** _masc_
**MP** NOUN
le **député** _masc_
**She's an MP.**
Elle est député.
**_Language tip_**
_You do not translate_ **'a'** _when you say what someone's job is in French._
**MP3 player** NOUN
le **baladeur numérique** _masc_
**mph** ABBREVIATION
**km/h**
_**Did you know...?**_
_In France, speed is measured in kilometres per hour, so 50 mph is about 80 km/h._
**Mr** NOUN
**Monsieur** _masc_
**_Language tip_**
_In addresses_ , **Mr** _is_ **M.**
**Mrs** NOUN
**Madame** _fem_
**_Language tip_**
_In addresses_ , **Mrs** _is_ **Mme.**
**Ms** NOUN
**Madame** _fem_
**_Language tip_**
_In addresses, **Ms** is **Mme.**_
_**Did you know...?**_
_There isn't a specific word for_ **Ms** _in French. If you are writing to somebody and don't know whether she is married, use_ **Madame**.
**much** ADJECTIVE, ADVERB, PRONOUN
**1** **beaucoup** _(a lot)_
**not much**
pas beaucoup
**I don't like sport much.**
Je n'aime pas beaucoup le sport.
**I don't want much.**
Je n'en veux pas beaucoup.
**_Language tip_**
_You can also use_ **beaucoup** _to say 'very much'._
**I like France very much.**
J'aime beaucoup la France.
**2** **beaucoup de** _(a lot of)_
**I haven't got much money.**
Je n'ai pas beaucoup d'argent.
**_Language tip_**
_You can also use_ **beaucoup de** _to say 'very much'._
**I don't want very much rice.**
Je ne veux pas beaucoup de riz.
**How much?**
Combien?
**How much does it cost?**
C'est combien?
**How much do you want?**
Tu en veux combien?
**How much is it all together?**
Ça fait combien en tout?
**_Language tip_**
_When_ **how much** _is followed by a noun, it is translated by_ **combien de**.
**How much money have you got?**
Tu as combien d'argent?
**too much**
trop
**That's too much!**
C'est trop!
**It costs too much.**
Ça coûte trop cher.
**How much?**
Combien?
**not much**
pas beaucoup
**too much**
trop
**Thank you very much.**
Merci beaucoup.
**mud** NOUN
la **boue** _fem_
**muesli** NOUN
le **muesli** _masc_
**mug** NOUN
la **grande tasse** _fem_
**Do you want a cup or a mug?**
Est-ce que vous voulez une tasse normale ou une grande tasse?
**multiply** VERB
**multiplier**
**Multiply six by three.**
Multipliez six par trois.
**Two multiplied by three is six.**
Deux multiplié par trois égale six.
**mum** NOUN
**1** la **mère** _fem_
**my mum**
ma mère
**2** la **maman** _fem (used as a name)_
**Mum!**
Maman!
**I'll ask Mum.**
Je vais demander à maman.
**mummy** NOUN
la **maman** _fem_
**Hello Mummy!**
Bonjour maman!
**mumps** NOUN
les **oreillons** _masc pl_
**Thérèse has got mumps.**
Thérèse a les oreillons.
**murder** NOUN
le **meurtre** _masc_
**muscle** NOUN
le **muscle** _masc_
**museum** NOUN
le **musée** _masc_
**mushroom** NOUN
le **champignon** _masc_
**music** NOUN
la **musique** _fem_
**I like listening to music.**
J'aime écouter de la musique.
**musical** ADJECTIVE
**a musical instrument**
un instrument de musique
**musician** NOUN
le **musicien** _masc_
la **musicienne** _fem_
**Muslim** NOUN
le **musulman** _masc_
la **musulmane** _fem_
**He's a Muslim.**
Il est musulman.
**_Language tip_**
_The French word is not spelled with a capital letter._
**mussel** NOUN
la **moule** _fem_
**must** VERB
**You must be careful, Gaëlle.**
Tu dois faire attention, Gaëlle.
**You must listen, children.**
Vous devez écouter, les enfants.
**mustard** NOUN
la **moutarde** _fem_
**my** ADJECTIVE
**_Language tip_**
_When you want to say something like 'my name', 'my house', or 'my hair' in French, you need to know if 'name', 'house', 'hair' are masculine, feminine, or plural, because there are three possible words for_ **my**.
**mon** _masc_
**my father**
mon père
**ma** _fem_
**my aunt**
ma tante
**mes** _pl_
**my parents**
mes parents
**_Language tip_**
**ma** _changes to_ **mon** _before a vowel sound._
**my friend Alice**
mon amie Alice
**_Language tip_**
**my** _is not always_ **mon** , **ma** , _or_ **mes**. _Notice how_ **my** _is translated in the next example._
**I wash my face in the morning.**
Je me lave le visage le matin.
**myself** PRONOUN
**1** **me**
**I've hurt myself.**
Je me suis fait mal.
**I like to look at myself in the mirror.**
J'aime me regarder dans la glace.
**_Language tip_**
**me** _changes to_ **m'** _before a vowel sound._
**I'm enjoying myself.**
Je m'amuse.
**2** **moi**
**_Language tip_**
_After a preposition, use_ **moi** _instead of_ **me**.
**I'll tell you about myself.**
Je vais te parler de moi.
**3** **moi-même**
**I made it myself.**
Je l'ai fait moi-même.
**by myself**
tout seul
**_Language tip_**
_Use_ **toute seule** _if you are a girl._
**I don't like travelling by myself.**
Je n'aime pas voyager toute seule.
**mystery** NOUN
le **mystère** _masc_
# **N n**
**nail** NOUN
**1** l' **ongle** _masc_
**Don't bite your nails!**
Ne te ronge pas les ongles!
**2** le **clou** _masc_
**a hammer and some nails**
un marteau et des clous
**nailfile** NOUN
la **lime à ongles** _fem_
**nail varnish** NOUN
le **vernis à ongles** _masc_
**naked** ADJECTIVE
**nu** _masc_
**nue** _fem_
**name** NOUN
le **nom** _masc_
**What's your cat's name?**
Comment s'appelle ton chat?
**His name's Max.**
Il s'appelle Max.
**What's your name?**
Comment tu t'appelles?
**_Language tip_**
_There are two other ways of asking this question:_ **Tu t'appelles comment?** _and_ **Comment t'appelles-tu?**
**What's her name?**
Comment elle s'appelle?
**What are their names?**
Ils s'appellent comment?
**What's your name?**
Comment tu t'appelles?
**My name is Natasha.**
Je m'appelle Natasha.
**nanny** NOUN
la **garde d'enfants** _fem_
**She's a nanny.**
C'est une garde d'enfants.
**napkin** NOUN
la **serviette** _fem_
**narrow** ADJECTIVE
**étroit** _masc_
**étroite** _fem_
**a narrow street**
une rue étroite
**nasty** ADJECTIVE
**1** **mauvais** _masc_
**mauvaise** _fem (unpleasant)_
**a nasty cold**
un mauvais rhume
**a nasty smell**
une mauvaise odeur
**2** **méchant** _masc_
**méchante** _fem (evil)_
**He's a nasty man.**
C'est un homme méchant.
**nationality** NOUN
la **nationalité** _fem_
**natural** ADJECTIVE
**naturel** _masc_
**naturelle** _fem_
**nature** NOUN
la **nature** _fem_
**naughty** ADJECTIVE
**vilain** _masc_
**vilaine** _fem_
**Naughty girl!**
Vilaine!
**navy** NOUN
la **marine** _fem_
**He's in the navy.**
Il est dans la marine.
**navy-blue**
**navy-blue** _can be an adjective or a noun._
**A** ADJECTIVE
**bleu marine** _masc, fem, pl_
**a navy-blue skirt**
une jupe bleu marine
**_Language tip_**
_Colour adjectives come after the noun in French._
**B** NOUN
le **bleu marine** _masc_
**near**
**near** _can be an adjective or a preposition._
**A** ADJECTIVE
**proche**
**It's fairly near.**
C'est assez proche.
**_Language tip_**
**the nearest** _can be translated by_ **le plus proche** , **la plus proche** _or_ **les plus proches** , _depending on the following noun._
**the nearest village**
le village le plus proche
**Where's the nearest service station?**
Où est la station-service la plus proche?
**The nearest shops are three kilometres away.**
Les magasins les plus proches sont à trois kilomètres.
**B** PREPOSITION
**près de**
**I live near Liverpool.**
J'habite près de Liverpool.
**near my house**
près de chez moi
**near here**
près d'ici
**Is there a bank near here?**
Est-ce qu'il y a une banque près d'ici?
**nearby** ADVERB
**à proximité**
**There's a supermarket nearby.**
Il y a un supermarché à proximité.
**nearly** ADVERB
**presque**
**Dinner's nearly ready.**
Le dîner est presque prêt.
**I'm nearly ten.**
J'ai presque dix ans.
**neat** ADJECTIVE
**soigné** _masc_
**soignée** _fem_
**She has very neat writing.**
Elle a une écriture très soignée.
**necessary** ADJECTIVE
**nécessaire**
**neck** NOUN
le **cou** _masc_
**necklace** NOUN
le **collier** _masc_
**need** VERB
**avoir besoin de**
**I need a rubber.**
J'ai besoin d'une gomme.
**needle** NOUN
l' **aiguille** _fem_
**neighbour** NOUN
le **voisin** _masc_
la **voisine** _fem_
**the neighbours' garden**
le jardin des voisins
**neighbourhood** NOUN
le **quartier** _masc_
**neither** PRONOUN, CONJUNCTION, ADVERB
**aucun des deux** _masc_
**aucune des deux** _fem_
**Carrots or peas? — Neither, thanks.**
Des carottes ou des petits pois? — Aucun des deux merci.
**neither... nor...**
ni... ni...
**Neither Sarah nor Tamsin is coming to the party.**
Ni Sarah ni Tamsin ne vient à la soirée.
**Neither do I.**
Moi non plus.
**Neither have I.**
Moi non plus.
**nephew** NOUN
le **neveu** _masc_ (PL les **neveux** )
**her nephew**
son neveu
**nerve** NOUN
le **nerf** _masc_
**She gets on my nerves.**
Elle me tape sur les nerfs.
**Net** NOUN
le **Net** _masc_
**I like to surf the Net.**
J'aime surfer sur le Net.
**netball** NOUN
le **netball** _masc_
_**Did you know...?**_
_Netball is not played in France. Both boys and girls play basketball or volleyball instead._
**Netherlands** PL NOUN
les **Pays-Bas** _masc pl_
**never** ADVERB
**1** **jamais**
**When are you going to phone him? — Never!**
Quand est-ce que tu vas l'appeler? — Jamais!
**2** **ne... jamais**
**_Language tip_**
_Add_ **ne** _if the sentence contains a verb._
**I never go to the cinema.**
Je ne vais jamais au cinéma.
**new** ADJECTIVE
**1** **nouveau** _masc_
**nouvelle** _fem_
**a new jumper**
un nouveau pull
**a new dress**
une nouvelle robe
**2** **neuf** _masc_
**neuve** _fem (brand new)_
**We've got a new car.**
Nous avons une voiture neuve.
**news** NOUN
**1** les **nouvelles** _fem pl_
**good news**
de bonnes nouvelles
**2** la **nouvelle** _fem (single piece of news)_
**That's wonderful news!**
Quelle bonne nouvelle!
**3** les **informations** _fem pl (on TV)_
**It was on the news.**
C'était aux informations.
**newsagent** NOUN
le **marchand de journaux** _masc_
**newspaper** NOUN
le **journal**
_masc_ (PL les **
journaux** )
**New Year** NOUN
**New Year's Day**
le premier de l'An
**New Year's Eve**
la Saint-Sylvestre
**Happy New Year!**
Bonne Année!
**next**
**next** _can be an adjective, an adverb or a preposition._
**A** ADJECTIVE
**prochain** _masc_
**prochaine** _fem (in time)_
**the next time**
la prochaine fois
**Who's next?**
C'est à qui, maintenant?
**I'm next.**
C'est à moi, maintenant.
**next door**
à côté
**They live next door.**
Ils habitent à côté.
**next Saturday**
samedi prochain
**next year**
l'année prochaine
**next summer**
l'été prochain
**B** ADVERB
**ensuite** _(after this)_
**What shall I do next?**
Qu'est-ce que je fais ensuite?
**C** PREPOSITION
**next to**
à côté de
**next to the bank**
à côté de la banque
**I sit next to my friend.**
Je m'asseois à côté de mon copain.
**_Language tip_**
_To get the accents right in_ **à côté de** , _remember that they form a W: `^´._
**nice** ADJECTIVE
**1** **gentil** _masc_
**gentille** _fem (kind)_
**Your parents are very nice.**
Tes parents sont très gentils.
**2** **joli** _masc_
**jolie** _fem (pretty)_
**Aix is a nice town.**
Aix est une jolie ville.
**3** **bon** _masc_
**bonne** _fem (food)_
**The soup is very nice.**
La soupe est très bonne.
**Have a nice time!**
Amuse-toi bien!
**Have a nice time, girls!**
Amusez-vous bien, les filles!
**It's a nice day.**
Il fait beau.
**niece** NOUN
la **nièce** _fem_
**his niece**
sa nièce
**night** NOUN
**1** la **nuit** _fem_
**I want a room for two nights.**
Je veux une chambre pour deux nuits.
**2** le **soir** _masc (evening)_
**What are you doing tonight?**
Qu'est-ce que tu fais ce soir?
**last night**
hier soir
**nightie** NOUN
la **chemise de nuit** _fem_
**nightmare** NOUN
le **cauchemar** _masc_
**I have nightmares.**
Je fais des cauchemars.
**nightshirt** NOUN
la **chemise de nuit** _fem_
**nil** NOUN
le **zéro** _masc_
**We won one-nil.**
Nous avons gagné un à zéro.
**nine** NUMBER
**neuf**
**nine euros**
neuf euros
**She's nine.**
Elle a neuf ans.
**_Language tip_**
_In English, you can say_ **nine** _or_ **nine years old**. _In French, you can only say_ **neuf ans**.
**nineteen** NUMBER
**dix-neuf**
**nineteen euros**
dix-neuf euros
**She's nineteen.**
Elle a dix-neuf ans.
**_Language tip_**
_In English, you can say_ **nineteen**
_or_ **nineteen years old**. _In French, you can only say_ **dix-neuf ans**.
**nineteenth** ADJECTIVE
**dix-neuvième**
**on the nineteenth floor**
au dix-neuvième étage
**the nineteenth of August**
le dix-neuf août
**ninety** NUMBER
**quatre-vingt-dix**
**My gran is ninety.**
Ma grand-mère a quatre-vingt-dix ans.
**_Language tip_**
**quatre-vingt-dix** _is made up of three words in French. What do you think they mean?_
**ninth** ADJECTIVE
**neuvième**
**on the ninth floor**
au neuvième étage
**the ninth of August**
le neuf août
**no** ADVERB
**1** **non**
**Are you coming? — No.**
Est-ce que tu viens? — Non.
**2** **pas de** _(not any)_
**There are no trains on Sundays.**
Il n'y a pas de trains le dimanche.
**'no smoking'**
'défense de fumer'
**nobody** PRONOUN
**1** **personne**
**Who's going with you? — Nobody.**
Qui t'accompagne? — Personne.
**2** **ne... personne**
**_Language tip_**
_Add_ **ne** _if the sentence contains a verb._
**There's nobody in the classroom.**
Il n'y a personne dans la classe.
**noise** NOUN
le **bruit** _masc_ **Please make less noise.**
Faites moins de bruit s'il vous plaît.
**noisy** ADJECTIVE
**bruyant** _masc_
**bruyante** _fem_
**none** PRONOUN
**aucun** _masc_
**aucune** _fem_
**How many girls? — None.**
Combien de filles? — Aucune.
**There's none left.**
Il n'y en a plus.
**There are none left.**
Il n'y en a plus.
**nonsense** NOUN
les **bêtises** _fem pl_
**She talks a lot of nonsense.**
Elle dit beaucoup de bêtises.
**noodles** PL NOUN
les **nouilles** _fem pl_
**noon** NOUN
le **midi** _masc_
**It's noon.**
Il est midi.
**at noon**
à midi
**no one** PRONOUN
**1** **personne**
**Who's going with you? — No one.**
Qui t'accompagne? — Personne.
**2** **ne... personne**
**_Language tip_**
_Add_ **ne** _if the sentence contains a verb._
**There's no one in the classroom.**
Il n'y a personne dans la classe.
**nor** CONJUNCTION
**neither... nor**
ni... ni
**neither Pascal nor Yann**
ni Pascal, ni Yann
**Nor do I.**
Moi non plus.
**Nor have I.**
Moi non plus.
**normal** ADJECTIVE
**habituel** _masc_
**habituelle** _fem_
**at the normal time**
à l'heure habituelle
**Normandy** NOUN
la **Normandie** _fem_
**in Normandy**
en Normandie
**to Normandy**
en Normandie
**Alain is from Normandy.**
Alain vient de la Normandie.
**north**
**north** _can be an adjective or a noun._
**A** ADJECTIVE
**nord** _masc, fem, pl_
**the north coast**
la côte nord
**B** NOUN
le **nord** _masc_
**in the north**
dans le nord
**Northern Ireland** NOUN
l' **Irlande du Nord** _fem_
**in Northern Ireland**
en Irlande du Nord
**to Northern Ireland**
en Irlande du Nord
**I'm from Northern Ireland.**
Je viens de l'Irlande du Nord.
**North Pole** NOUN
le **pôle Nord** _masc_
**North Sea** NOUN
la **mer du Nord** _fem_
**nose** NOUN
le **nez** _masc_ (PL les **nez** )
**nosy** ADJECTIVE
**fouineur** _masc_ (FEM
**fouineuse** )
**not** ADVERB
**1** **pas**
**Are you coming or not?**
Est-ce que tu viens ou pas?
**not really**
pas vraiment
**Do you like him? — Not at all.**
Tu l'aimes bien? — Pas du tout.
**Have you finished? — Not yet.**
As-tu fini? — Pas encore.
**2** **ne... pas**
**_Language tip_**
_Add_ **ne** _if_ **not** _comes before a verb._
**It's not raining.**
Il ne pleut pas.
**not yet**
pas encore
**not you**
pas toi
**note** NOUN
le **mot** _masc_
**I'll write her a note.**
Je vais lui écrire un mot.
**notebook** NOUN
le **carnet** _masc_
**notepad** NOUN
le **bloc-notes** _masc_
**notepaper** NOUN
le **papier à lettres** _masc_
**nothing** NOUN
**1** **rien** _masc_
**What's wrong? — Nothing.**
Qu'est-ce qui ne va pas? — Rien.
**2** **ne... rien**
**He does nothing.**
Il ne fait rien.
**_Language tip_**
_Add_ **ne** _if the sentence contains a verb._
**notice** NOUN
l' **affiche** _fem_
**notice board** NOUN
le **panneau d'affichage** _masc_
**novel** NOUN
le **roman** _masc_
**November** NOUN
**novembre** _masc_
**October or November?**
Octobre ou novembre?
**My birthday's in November.**
Mon anniversaire est en novembre.
**in November**
en novembre
**the fifth of November**
le cinq novembre
**_Language tip_**
_The months in French are not spelled with a capital letter._
**now** ADVERB
**maintenant**
**What are you doing now?**
Qu'est-ce que tu fais maintenant?
**I'm rather busy just now.**
Je suis très occupé en ce moment.
**not now**
pas maintenant
**just now**
en ce moment
**nowhere** ADVERB
**nulle part**
**number** NOUN
**1** le **nombre** _masc_
**a large number of people**
un grand nombre de gens
**2** le **numéro** _masc (of house, telephone)_
**They live at number 5.**
Ils habitent au numéro cinq.
**What's your phone number?**
Quel est votre numéro de téléphone?
**3** le **chiffre** _masc (figure)_
**the second number**
le deuxième chiffre
**nun** NOUN
la **religieuse** _fem_
**I want to be a nun.**
Je veux être religieuse.
**nurse** NOUN
l' **infirmier** _masc_
l' **infirmière** _fem_
**She's a nurse.**
Elle est infirmière.
**_Language tip_**
_You do not translate_ **'a'** _when you say what someone's job is in French._
**nursery** NOUN
la **crèche** _fem_
**My sister goes to nursery.**
Ma sœur va à la crèche.
**nursery school** NOUN
l' **école maternelle** _fem_
**My little sister goes to nursery school.**
Ma petite sœur va à l'école maternelle.
_**Did you know...?**_
_The_ **école maternelle** _is a state school for children between the ages of three and six._
**nut** NOUN
**1** la **cacahuète** _fem (peanut)_
**2** la **noisette** _fem (hazelnut)_
**3** la **noix** _fem_ (PL les **noix** ) _(walnut)_
**_Language tip_**
_You have to say which kind of nut you mean, because there is no general word for_ **nut** _in French._
# **O o**
**oats** NOUN
l' **avoine** _fem_
**_Language tip_**
**avoine** _is a singular word._
**obedient** ADJECTIVE
**obéissant** _masc_
**obéissante** _fem_
**obey** VERB
**You must obey the rules of the game.**
Vous devez respecter les règles du jeu.
**object** NOUN
l' **objet** _masc_
**classroom objects**
les objets de la classe
**obvious** ADJECTIVE
**évident** _masc_
**évidente** _fem_
**That's obvious!**
C'est évident!
**occasion** NOUN
l' **occasion** _fem_
**a special occasion**
une occasion spéciale
**on several occasions**
à plusieurs reprises
**occasionally** ADVERB
**de temps en temps**
**occupation** NOUN
la **profession** _fem_
**ocean** NOUN
l' **océan** _masc_
**o'clock** ADVERB
**at four o'clock**
à quatre heures
**It's five o'clock.**
Il est cinq heures.
**October** NOUN
**octobre** _masc_
**October or November?**
Octobre ou novembre?
**My birthday's in October.**
Mon anniversaire est en octobre.
**in October**
en octobre
**the fifth of October**
le cinq octobre
**_Language tip_**
_The months in French are not spelled with a capital letter._
**odd** ADJECTIVE
**bizarre**
**That's odd!**
C'est bizarre!
**of** PREPOSITION
**de**
**some photos of my family**
des photos de ma famille
**a boy of ten**
un garçon de dix ans
**a picture of the school**
une photo de l'école
**a friend of mine**
un de mes amis
**That's very kind of you.**
C'est très gentil de votre part.
**_Language tip_**
**de** _changes to_ **d'** _before a vowel sound._
**a kilo of oranges**
un kilo d'oranges
**_Language tip_**
**de** _+_ **le** _changes to_ **du** , _and_ **de** \+ **les** _changes to_ **des**.
**the end of the film**
la fin du film
**the end of the holidays**
la fin des vacances
**_Language tip_**
**of it** , **of that** _and_ **of them** _is translated by **en**._
**Do you want half of it?**
Tu en veux la moitié?
**Can I have half of that?**
Je peux en avoir la moitié?
**Do you want some of them?**
Tu en veux?
**off**
**off** _can be an adjective, a preposition or an adverb._
**A** ADJECTIVE
**1** **éteint** _masc_
**éteinte** _fem (switched off)_
**The light is off.**
La lumière est éteinte.
**2** **fermé** _masc_
**fermée** _fem (turned off)_
**Is the tap off?**
Est-ce que le robinet est fermé?
**3** **annulé** _masc_
**annulée** _fem (cancelled)_
**The match is off.**
Le match est annulé.
**4** **absent** _masc_
**absente** _fem (absent)_
**He's off today.**
Il est absent aujourd'hui.
**B** PREPOSITION
**She's off school today.**
Elle n'est pas à l'école aujourd'hui.
**C** ADVERB
**Off you go, Jack!**
Vas-y, Jack!
**offer** VERB
**offrir**
**Offer Melanie something to drink.**
Offre quelque chose à boire à Melanie.
**office** NOUN
le **bureau** _masc_
(PL les **bureaux** )
**She works in an office.**
Elle travaille dans un bureau.
**often** ADVERB
**souvent**
**We often go to London.**
Nous allons souvent à Londres.
**It often rains.**
Il pleut souvent.
**oil** NOUN
l' **huile** _fem_
**okay** EXCLAMATION, ADJECTIVE
**1** **d'accord** _(in agreement)_
**I'll come tomorrow. — Okay!**
Je viens demain. — D'accord!
**Is that okay?**
C'est d'accord?
**2** **pas mal** _(not bad)_
**Do you like school? — It's okay.**
Tu aimes l'école? — C'est pas mal.
**I'm okay thanks.**
Ça va, merci.
**Is everything okay?**
Tout va bien?
**Okay!**
D'accord!
**Are you okay?**
Ça va?
**old** ADJECTIVE
**vieux** _masc_
**vieille** _fem_
**an old dog**
un vieux chien
**an old house**
une vieille maison
**old clothes**
des vieux vêtements
**old shoes**
des vieilles chaussures
**_Language tip_**
_In the singular_ , **vieux** _changes to_ **vieil** _before a vowel sound._
**an old man**
un vieil homme
**_Language tip_**
**âgé** _and_ **âgée** _are more polite than **vieux** and **vieille**._
**old people**
les personnes âgées
**I am older than you.**
Je suis plus âgée que toi.
**Léa is older than Richard.**
Léa est plus âgée que Richard.
**She's two years older than me.**
Elle a deux ans de plus que moi.
**How old are you, Max?**
Tu as quel âge, Max?
**_Language tip_**
_Another way of asking this question is_ **Quel âge as-tu, Max?**
**How old are you?**
Quel âge as-tu?
**How old are you, Miss?**
Quel âge avez-vous, Maîtresse?
**He's ten years old.**
Il a dix ans.
**old age pensioner** NOUN
le **retraité** _masc_
la **retraitée** _fem_
**She's an old age pensioner.**
Elle est retraitée.
**oldest** ADJECTIVE
**aîné** _masc_
**aînée** _fem_
**my oldest brother**
mon frère aîné
**_Language tip_**
_To say that someone is the oldest use_ **le plus âgé** _for a boy and_ **la plus âgée** _for a girl._
**Hugo's the oldest in the class.**
Hugo est le plus âgé de la classe.
**She's the oldest.**
C'est la plus âgée.
**Olympic** ADJECTIVE
**olympique**
**the Olympics**
les Jeux olympiques
**omelette** NOUN
l' **omelette** _fem_
**on**
**on** _can be an adjective or a preposition. There are a lot of translations. Skim down the page for the one you need._
**A** ADJECTIVE
**1** **allumé** _masc_
**allumée** _fem (switched on)_
**The light is on.**
La lumière est allumée.
**2** **ouvert** _masc_
**ouverte** _fem (turned on)_
**The tap is on.**
Le robinet est ouvert.
**B** PREPOSITION
**1** **à**
**on the left**
à gauche
**I go to school on my bike.**
Je vais à l'école à vélo.
**on TV**
à la télé
**_Language tip_**
**à + le** _changes to_ **au**.
**on the phone**
au téléphone
**on the 2nd floor**
au deuxième étage
**2** **sur** _(on top of)_
**on the table**
sur la table
**3** **en**
**They're on holiday.**
Ils sont en vacances.
**_Language tip_**
_Notice how_ **on** _is translated in days and dates._
**on Christmas Day**
le jour de Noël
**on my birthday**
le jour de mon anniversaire
**on Friday**
vendredi
**on Fridays**
le vendredi
**on the twentieth of June**
le vingt juin
**on holiday**
en vacances
**once** ADVERB
**une fois**
**once a week**
une fois par semaine
**only once**
juste une fois
**at once**
tout de suite
**once more**
encore une fois
**one** NUMBER
**_Language tip_**
_Use_ **un** _for masculine nouns and_ **une** _for feminine nouns._
**un** _masc_
**one day**
un jour
**une** _fem_
**one minute**
une minute
**I've got one brother and one sister.**
J'ai un frère et une sœur.
**onion** NOUN
l' **oignon** _masc_
**only**
**only** _can be an adjective or an adverb._
**A** ADJECTIVE
**seul** _masc_
**seule** _fem_
**my only clean T-shirt**
mon seul tee-shirt propre
**my only dress**
ma seule robe
**I'm an only child.**
Je suis fils unique.
**Danielle is an only child.**
Danielle est fille unique.
**B** ADVERB
**1** **seulement**
**only ten euros**
seulement dix euros
**2** **ne... que** _(with a verb)_
**I've only got two cards.**
Je n'ai que deux cartes.
**He's only three.**
Il n'a que trois ans.
**open**
**open** _can be an adjective or a verb._
**A** ADJECTIVE
**ouvert** _masc_ **ouverte** _fem_
**The baker's is open on Sunday morning.**
La boulangerie est ouverte le dimanche matin.
**B** VERB
**ouvrir**
**Can I open the window?**
Est-ce que je peux ouvrir la fenêtre?
**Open your books.**
Ouvrez vos livres.
**opening hours** PL NOUN
les **heures d'ouverture** _fem pl_
**opinion** NOUN
l' **avis** _masc_
**in my opinion**
à mon avis
**What's your opinion?**
Qu'est-ce que vous en pensez?
**opinion poll** NOUN
le **sondage** _masc_
**opponent** NOUN
l' **adversaire** _masc/fem_
**opportunity** NOUN
l' **occasion** _fem_
**It's a good opportunity.**
C'est une bonne occasion.
**opposite**
**opposite** _can be an adjective, an adverb or a preposition._
**A** ADJECTIVE
**opposé** _masc_ **opposée** _fem_
**It's in the opposite direction.**
C'est dans la direction opposée.
**B** ADVERB
**en face**
**They live opposite.**
Ils habitent en face.
**C** PREPOSITION
**en face de**
**the girl sitting opposite me**
la fille assise en face de moi
**optimistic** ADJECTIVE
**optimiste**
**or** CONJUNCTION
**1** **ou**
**Would you like tea or coffee?**
Tu veux du thé ou du café?
**2** **ni... ni**
**_Language tip_**
_Use_ **ni... ni** _in negative sentences._
**I don't eat meat or fish.**
Je ne mange ni viande, ni poisson.
**3** **sinon** _(otherwise)_
**Hurry up or you'll miss the bus.**
Dépêche-toi, sinon tu vas rater le bus.
**oral** NOUN
l' **oral** _masc_ (PL les **oraux** )
**I've got my French oral soon.**
Je vais bientôt passer mon oral de français.
**orange**
**orange** _can be a noun or an adjective._
**A** NOUN
**1** l' **orange** _fem_
**a big orange**
une grosse orange
**2** l' **orange** _masc_
**Orange is my favourite colour.**
Ma couleur préférée, c'est l'orange.
**B** ADJECTIVE
**orange** _masc, fem, pl_
**orange curtains**
des rideaux orange
**_Language tip_**
_Colour adjectives come after the noun in French._
**orange juice** NOUN
le **jus d'orange** _masc_
**orchard** NOUN
le **verger** _masc_
**orchestra** NOUN
l' **orchestre** _masc_
**I play in the school orchestra.**
Je joue dans l'orchestre de l'école.
**order**
**order** _can be a noun or a verb._
**A** NOUN
**1** l' **ordre** _masc (sequence)_
**Put the words in alphabetical order, children.**
Rangez ces mots par ordre alphabétique, les enfants.
**The words are not in the right order.**
Les mots ne sont pas dans le bon ordre.
**2** la **commande** _fem_
_(in restaurant)_
**The waiter took our order.**
Le serveur a pris notre commande.
**'out of order'**
'en panne'
**B** VERB
**commander**
**Are you ready to order?**
Vous êtes prêt à commander?
**ordinary** ADJECTIVE
**ordinaire**
**an ordinary day**
une journée ordinaire
**organ** NOUN
l' **orgue** _masc_
**I play the organ.**
Je joue de l'orgue.
**organize** VERB
**organiser**
**Could you help to organize the party?**
Vous pouvez aider à organiser la fête?
**original** ADJECTIVE
**original** _masc_
**originale** _fem_
**It's a very original idea.**
C'est une idée très originale.
**Orkneys** PL NOUN
les **Orcades** _fem pl_
**orphan** NOUN
l' **orphelin** _masc_
l' **orpheline** _fem_
**other**
**other** _can be an adjective or a pronoun._
**A** ADJECTIVE
**autre**
**on the other side of the street**
de l'autre côté de la rue
**the other day**
l'autre jour
**the other one**
l'autre
**This one? — No, the other one.**
Celui-ci? — Non, l'autre.
**B** PRONOUN
l' **autre** _masc/fem_
**Get into twos, one behind the other.**
Mettez-vous par deux, l'un derrière l'autre.
**Where are the others?**
Où sont les autres?
**our** ADJECTIVE
**notre** _masc/fem_ (PL
**nos** )
**Our house is quite big.**
Notre maison est plutôt grande.
**They are our friends.**
Ce sont nos amis.
**ours** PRONOUN
**à nous**
**Is this ours?**
C'est à nous?
**Whose is this? — It's ours.**
C'est à qui? — À nous.
**out**
**out** _can be an adverb or an adjective._
**A** ADVERB
**1** **sorti** _masc_
**sortie** _fem (not at home)_
**Gaston's out.**
Gaston est sorti.
**I'm going out.**
Je sors.
**2** **éliminé** _masc_
**éliminée** _fem (in game)_
**You're out Lucie!**
Tu es éliminée, Lucie!
**'way out'**
'sortie'
**B** ADJECTIVE
**éteint** _masc_
**éteinte** _fem (turned off)_
**All the lights are out.**
Toutes les lumières sont éteintes.
**outdoor** ADJECTIVE
**en plein air**
**an outdoor swimming pool**
une piscine en plein air
**outdoor activities**
les activités de plein air
**outdoors** ADVERB
**au grand air**
**outer space** NOUN
l' **espace** _masc_
**a monster from outer space**
un monstre de l'espace
**outside**
**outside** _can be an adverb or a preposition._
**A** ADVERB
**dehors**
**It's very cold outside.**
Il fait très froid dehors.
**B** PREPOSITION
**en dehors de**
**outside the school**
en dehors de l'école
**oven** NOUN
le **four** _masc_
**over**
**over** _can be a preposition or an adjective._
**A** PREPOSITION
**1** **plus de** _(more than)_
**Are you over ten?**
Tu as plus de dix ans?
**The temperature is over 30 degrees.**
Il fait une température de plus de trente degrés.
**2** **pendant** _(during)_
**over Christmas**
pendant les fêtes de Noël
**3** **de l'autre côté de** _(across)_
**The baker's is over the road.**
La boulangerie est de l'autre côté de la rue.
**over here**
ici
**over there**
là-bas
**all over Scotland**
dans toute l'Écosse
**B** ADJECTIVE
**terminé** _masc_
**terminée** _fem (finished)_
**The match is over.**
Le match est terminé.
**overcast** ADJECTIVE
**couvert** _masc_
**couverte** _fem_
**The sky was overcast.**
Le ciel était couvert.
**overhead projector** NOUN
le **rétroprojecteur** _masc_
**owl** NOUN
le **hibou** _masc_ (PL les **hiboux** )
**own** ADJECTIVE
**propre**
**I've got my own bathroom.**
J'ai ma propre salle de bain.
**I'd like a room of my own.**
J'aimerais avoir une chambre à moi.
**on his own**
tout seul
**on her own**
toute seule
**owner** NOUN
le/la **propriétaire** _masc/fem_
# **P p**
**pack**
**pack** _can be a verb or a noun._
**A** VERB
**faire ses bagages**
**I need to pack.**
Je dois faire mes bagages.
**B** NOUN
**a pack of cards**
un jeu de cartes
**packed lunch** NOUN
le **casse-croûte** _masc_
**I take a packed lunch to school.**
J'apporte un casse-croûte à l'école pour le déjeuner.
_**Did you know...?**_
_French schoolchildren do not take packed lunches to school. They either eat at the canteen or go home for lunch._
**packet** NOUN
le **paquet** _masc_
**a packet of crisps**
un paquet de chips
**page** NOUN
la **page** _fem_
**on page ten**
page dix
**Look at page six, everyone.**
Regardez page six, tout le monde.
**paid** VERB _see_ **pay**
**pain** NOUN
la **douleur** _fem_
**a terrible pain**
une douleur insupportable
**I've got a pain in my stomach.**
J'ai mal à l'estomac.
**2** le/la **casse-pieds** _masc/fem (a nuisance)_
**My little sister is a pain.**
Ma petite sœur est casse-pieds.
**paint**
**paint** _can be a noun or a verb._
**A** NOUN
la **peinture** _fem_
**'wet paint'**
'attention, peinture fraîche'
**B** VERB
**peindre**
**I'm going to paint it green.**
Je vais le peindre en vert.
**painting** NOUN
le **tableau** _masc_ (PL les
**tableaux** ) **a painting by Picasso**
un tableau de Picasso
**I like painting.**
J'aime faire de la peinture.
**pair** NOUN
la **paire** _fem_
**a pair of shoes**
une paire de chaussures
**a pair of trousers**
un pantalon
**a pair of jeans**
un jean
**in pairs**
deux par deux
**We work in pairs.**
Nous travaillons deux par deux.
**Pakistan** NOUN
le **Pakistan** _masc_
**Pakistani**
**Pakistani** _can be a noun or an adjective._
**A** NOUN
le **Pakistanais** _masc_
la **Pakistanaise** _fem_
**B** ADJECTIVE
**pakistanais** _masc_
**pakistanaise** _fem_
**_Language tip_**
**pakistanais** _is not spelled with a capital letter when it is an adjective._
**pal** NOUN
le **copain** _masc_
la **copine** _fem_
**my pal Ronan**
mon copain Ronan
**my pal Elsa**
ma copine Elsa
**You're my best pal.**
Tu es monmeilleur copain.
**_Language tip_**
_This 'best pal' in the example sentence is a boy. How can you tell?_
**palace** NOUN
le **palais** _masc_
**pale** ADJECTIVE
**pâle**
**a pale blue shirt**
une chemise bleu pâle
**pan** NOUN
**1** la **casserole** _fem (saucepan)_
**2** la **poêle** _fem (frying pan)_
**pancake** NOUN
la **crêpe** _fem_
**Pancake Day** NOUN
le **mardi gras** _masc_
_**Did you know...?**_
**Pancake Day** _is celebrated in France as well. Children dress up and eat pancakes_ ( **crêpes** ).
**panic** VERB
**Don't panic!**
Pas de panique!
**pantomime** NOUN
le **spectacle de Noël pour enfants** _masc_
_**Did you know...?**_
_There is no such thing as a_ **pantomime** _in France._
**pants** PL NOUN
le **slip** _masc_
**a pair of pants**
un slip
**paper** NOUN
**1** le **papier** _masc_
**Have you got a pencil and some paper?**
Tu as un crayon et du papier?
**a piece of paper**
du papier
**a paper towel**
une serviette en papier
**2** le **journal** _masc_ (PL les
**journaux** ) _(newspaper)_
**paper boy** NOUN
le **livreur de journaux** _masc_
**paper girl** NOUN
la **livreuse de journaux** _fem_
**paper round** NOUN
la **tournée de distribution de journaux** _fem_
**parade** NOUN
le **défilé** _masc_
**paragraph** NOUN
le **paragraphe** _masc_
**parcel** NOUN
le **colis** _masc_
**pardon** NOUN
**Pardon?**
Pardon?
**parent** NOUN
**parent** _masc_
**my parents**
mes parents
**Paris** NOUN
**Paris**
**in Paris**
à Paris
**to Paris**
à Paris
**Gilles is from Paris.**
Gilles est parisien.
**Inès is from Paris.**
Inès est parisienne.
**Parisian** NOUN
le **Parisien** _masc_
la **Parisienne** _fem_
**park**
**park** _can be a noun or a verb._
**A** NOUN
le **parc** _masc_
**There's a nice park.**
Il y a un beau parc.
**B** VERB
**se garer**
**It's difficult to park.**
C'est difficile de se garer.
**parking** NOUN
**'no parking'**
'stationnement interdit'
**parrot** NOUN
le **perroquet** _masc_
**part** NOUN
la **partie** _fem_
**The first part is easy.**
La première partie est facile.
**partly** ADVERB
**en partie**
**partner** NOUN
**1** le/la **partenaire** _masc/fem (in game, role play)_
**2** le **cavalier** _masc_ la **cavalière** _fem (in dance)_
**part-time** ADJECTIVE, ADVERB
**à temps partiel**
**a part-time job**
un travail à temps partiel
**She works part-time.**
Elle travaille à temps partiel.
**party** NOUN
**1** la **fête** _fem_
**a birthday party**
une fête d'anniversaire
**_Language tip_**
_In France, a children's birthday party held in the afternoon is called_ **un goûter d'anniversaire**.
**a Christmas party**
une fête de Noël
**a New Year party**
une fête du Nouvel An
**2** la **soirée** _fem (more formal)_
**I'm going to a party on Saturday.**
Je vais à une soirée samedi.
**pass** VERB
**1** **passer** _(hand)_
**Pass the ball, Nina!**
Passe le ballon, Nina!
**Could you pass me the salt?**
Vous pouvez me passer le sel?
**2** **passer devant** _(go)_
**You pass the post office.**
Vous passez devant la poste.
**passenger** NOUN
le **passager** _masc_
la **passagère** _fem_
**Passover** NOUN
la **Pâque juive** _fem_
**at Passover**
à la Pâque juive
**passport** NOUN
le **passeport** _masc_
**password** NOUN
le **mot de passe** _masc_
**past**
**past** _can be a preposition or a noun._
**A** PREPOSITION
**1** **après** _(after)_
**It's on the right, just past the station.**
C'est sur la droite, juste après la gare.
**2** _(with times)_
**It's half past ten exactly.**
Il est exactement dix heures et demie.
**It's quarter past nine.**
Il est neuf heures et quart.
**It's ten past eight.**
Il est huit heures dix.
**half past eight**
huit heures et demie
**quarter past ten**
dix heures et quart
**B** NOUN
le **passé** _masc_
**in the past**
dans le passé
**pasta** NOUN
les **pâtes** _fem pl_
**Pasta is easy to cook.**
Les pâtes sont faciles à préparer.
**pâté** NOUN
le **pâté** _masc_
**path** NOUN
**1** le **chemin** _masc (footpath)_
**Follow the path.**
Suivez le chemin.
**2** l' **allée** _fem (in garden, park)_
**patience** NOUN
**1** la **patience** _fem_
**He hasn't got much patience.**
Il n'a pas beaucoup de patience.
**2** la **réussite** _fem (card game)_
**I sometimes play patience.**
Quelquefois je fais une réussite.
**patient**
**patient** _can be a noun or an adjective._
**A** NOUN
le **patient** _masc_
la **patiente** _fem_
**B** ADJECTIVE
**patient** _masc_
**patiente** _fem_
**The teacher is very patient.**
La maîtresse est très patiente.
**patio** NOUN
le **patio** _masc_
**pattern** NOUN
le **motif** _masc_
**a simple pattern**
un motif simple
**pause** NOUN
la **pause** _fem_
**pavement** NOUN
le **trottoir** _masc_
**on the pavement**
sur le trottoir
**paw** NOUN
la **patte** _fem_
**pay**
**pay** _can be a noun or a verb._
**A** NOUN
le **salaire** _masc_
**What is the pay?**
Le salaire est de combien?
**B** VERB
**payer**
**Who's going to pay?**
Qui va payer?
**Where do I pay?**
Où est-ce que je dois payer?
**_Language tip_**
**pay for** _is also translated by_ **payer**.
**I've paid for my ticket.**
J'ai payé mon billet.
**I paid ten euros for it.**
Je l'ai payé dix euros.
**Pay attention, Christophe!**
Fais attention, Christophe!
**Pay attention, everybody!**
Faites attention, tout le monde!
**PC** NOUN
le **PC** _masc_
**I have a PC at home.**
J'ai un PC chez moi.
**PE** NOUN
l' **EPS** _fem_
**We do PE twice a week.**
Nous avons EPS deux fois par semaine.
**pea** NOUN
le **petit pois** _masc_
**Peas or beans?**
Des petits pois ou des haricots?
**peach** NOUN
la **pêche** _fem_
**a kilo of peaches**
un kilo de pêches
**peanut** NOUN
la **cacahuète** _fem_
**a packet of peanuts**
un paquet de cacahuètes
**peanut butter** NOUN
le **beurre de cacahuètes** _masc_
**a peanut-butter sandwich**
un sandwich au beurre de cacahuètes
**pear** NOUN
la **poire** _fem_
**Which would you like, a pear or an apple?**
Qu'est-ce que tu veux: une poire ou une pomme?
**pebble** NOUN
le **galet** _masc_
**a pebble beach**
une plage de galets
**pedal** NOUN
la **pédale** _fem_
**pedigree** ADJECTIVE
**de race**
**a pedigree dog**
un chien de race
**peg** NOUN
**1** le **portemanteau** _masc_ (PL les
**portemanteaux** ) _(for coats)_
**2** l' **épingle à linge** _fem (clothes peg)_
**pen** NOUN
le **stylo** _masc_
**Can I borrow your pen?**
Je peux emprunter ton stylo?
**pencil** NOUN
le **crayon** _masc_
**in pencil**
au crayon
**coloured pencils**
les crayons de couleur
**pencil case** NOUN
la **trousse** _fem_
**pencil sharpener** NOUN
le **taille-crayon** _masc_
**penfriend** NOUN
le **correspondant** _masc_
la **correspondante** _fem_
**I'm Emma, your English penfriend.**
Je suis Emma, ta correspondante anglaise.
**_Language tip_**
_What is the difference between the English word_ **correspondent** _and the French word_ **correspondant**?
**penknife** NOUN
le **canif** _masc_
**pensioner** NOUN
le **retraité** _masc_
la **retraitée** _fem_
**people** PL NOUN
**1** les **gens** _masc pl_
**The people are nice.**
Les gens sont sympathiques.
**a lot of people**
beaucoup de gens
**2** les **personnes** _fem pl (individuals)_
**Four people can play.**
Quatre personnes peuvent jouer.
**How many people are there in your family?**
Vous êtes combien dans votre famille?
**_Language tip_**
_In English, you usually say 'tall people', 'rich people', etc. In French, you say 'the tall', 'the rich', etc._
**tall people**
les grands
**French people**
les Français
**pepper** NOUN
**1** le **poivre** _masc (spice)_
**Pass the pepper, please.**
Passez-moi le poivre, s'il vous plaît.
**2** le **poivron** _masc (vegetable)_
**a green pepper**
un poivron vert
**per** PREPOSITION
**par**
**per day**
par jour
**per cent** ADVERB
**pour cent**
**fifty per cent**
cinquante pour cent
**perfect** ADJECTIVE
**parfait** _masc_
**parfaite** _fem_
**Chantal speaks perfect English.**
Chantal parle un anglais parfait.
**performance** NOUN
le **spectacle** _masc (show)_
**The performance starts at two o'clock.**
Le spectacle commence à deux heures.
**perfume** NOUN
le **parfum** _masc_
**perhaps** ADVERB
**peut-être**
**Perhaps he's ill.**
Il est peut-être malade.
**period** NOUN
la **période** _fem_
**the holiday period**
la période des vacances
**permission** NOUN
la **permission** _fem_
**Have you got permission?**
Tu as la permission?
**person** NOUN
la **personne** _fem_
**She's a very nice person.**
C'est une personne très sympathique.
**_Language tip_**
_There are two more letters in the French word. What are they?_
**personality** NOUN
la **personnalité** _fem_
**personal stereo** NOUN
le **walkman** ® _masc_
**pessimistic** ADJECTIVE
**pessimiste**
**pet** NOUN
l' **animal** _masc_ (PL les
**animaux** )
**Have you got a pet?**
Tu as un animal?
**petrol** NOUN
l' **essence** _fem_
**unleaded petrol**
l'essence sans plomb
**phone**
**phone** _can be a noun or a verb._
**A** NOUN
le **téléphone** _masc_
**Where's the phone?**
Où est le téléphone?
**by phone**
par téléphone
**on the phone**
au téléphone
**Can I use the phone, please?**
Je peux téléphoner, s'il vous plaît?
**B** VERB
**téléphoner à**
**I have to phone my Mum.**
Je dois téléphoner à ma mère.
**phone box** NOUN
la **cabine téléphonique** _fem_
**phone call** NOUN
l' **appel** _masc_
**She gets lots of phone calls.**
Elle reçoit beaucoup d'appels.
**Can I make a phone call?**
Est-ce que peux téléphoner?
**phonecard** NOUN
la **carte de téléphone** _fem_
**phone number** NOUN
le **numéro de téléphone** _masc_
**What's your phone number?**
Quel est ton numéro de téléphone?
**photo** NOUN
la **photo** _fem_
**This is a photo of my family.**
Voici une photo de ma famille.
**I want to take some photos.**
Je veux prendre des photos.
**I want to take a photo of you.**
Je veux te prendre en photo.
**photocopier** NOUN
la **photocopieuse** _fem_
**photocopy**
**photocopy** _can be a noun or a verb._
**A** NOUN
la **photocopie** _fem_
**It's only a photocopy.**
Ce n'est qu'une photocopie.
**B** VERB
**photocopier**
**You can photocopy it.**
Vous pouvez le photocopier.
**photograph** NOUN
la **photo** _fem_
**phrase book** NOUN
le **guide de conversation** _masc_
**physics** NOUN
la **physique** _fem_
**She teaches physics.**
Elle enseigne la physique.
**pianist** NOUN
le/la **pianiste** _masc/fem_
**piano** NOUN
le **piano** _masc_
**I play the piano.**
Je joue du piano.
**I have piano lessons.**
Je prends des leçons de piano.
**pick**
**pick** _can be a noun or a verb._
**A** NOUN
**Take your pick!**
Faites votre choix!
**B** VERB
**1** **choisir** _(choose)_
**Pick a card, Jean!**
Choisis une carte, Jean.
**Pick three girls and three boys.**
Choisis trois filles et trois garçons.
**2** **cueillir** _(fruit, flowers)_
**I like picking strawberries.**
J'aime bien cueillir des fraises.
**pick up** VERB
**1** **venir chercher** _(collect)_
**We can come to the airport to pick you up.**
Nous pouvons venir vous chercher à l'aéroport.
**2** **tirer**
**Pick up another card, Susie!**
Tire une autre carte, Susie!
**3** **apprendre** _(learn)_
**I hope I'll pick up some French.**
J'espère apprendre quelques mots de français.
**picnic** NOUN
le **pique-nique** _masc_
**I like picnics.**
J'aime les pique-niques.
**to have a picnic**
pique-niquer
**We had a picnic on the beach.**
Nous avons pique-niqué sur la plage.
**picture** NOUN
**1** l' **image** _fem_
**Look at the picture.**
Regarde l'image.
**There are pictures in this dictionary.**
Il a des images dans ce dictionnaire.
**2** la **photo** _fem_
**This is a picture of my family.**
Voici une photo de ma famille.
**3** le **tableau** _masc_ (PL les
**tableaux** ) _(painting)_
**a famous picture**
un tableau célèbre
**4** le **dessin** _masc (drawing)_
**I'll draw a picture.**
Je vais faire un dessin.
**Draw a picture of your pet, Lisa.**
Dessine ton animal, Lisa.
**pie** NOUN
la **tourte** _fem_
**an apple pie**
une tourte aux pommes
**piece** NOUN
le **morceau** _masc_ (PL les
**morceaux** )
**A small piece, please.**
Un petit morceau, s'il vous plaît.
**pierced** ADJECTIVE
**percé** _masc_
**percée** _fem_
**I've got pierced ears.**
J'ai les oreilles percées.
**pig** NOUN
le **cochon** _masc_
**pigeon** NOUN
le **pigeon** _masc_
**piggy bank** NOUN
la **tirelire** _fem_
**pigtail** NOUN
la **natte** _fem_
**She's got pigtails.**
Elle a des nattes.
**pile** NOUN
la **pile** _fem_
**pill** NOUN
la **pilule** _fem_
**pillow** NOUN
l' **oreiller** _masc_
**a pillow**
un oreiller
**pilot** NOUN
le **pilote** _masc_
**pinball** NOUN
le **flipper** _masc_
**Do you want to play pinball?**
Tu veux jouer au flipper?
**pineapple** NOUN
l' **ananas** _masc_
**pink**
**pink** _can be an adjective or a noun._
**A** ADJECTIVE
**rose**
**a pink blouse**
un chemisier rose
**_Language tip_**
_Colour adjectives come after the noun in French._
**B** NOUN
le **rose** _masc_
**Pink is my favourite colour.**
Ma couleur préférée, c'est le rose.
**pint** NOUN
**a pint of milk**
un demi-litre de lait
_**Did you know...?**_
_In France, measurements are always in litres and centilitres. A pint is about 0.6 litres._
**pipe** NOUN
la **pipe** _fem_
**He smokes a pipe.**
Il fume la pipe.
**pirate** NOUN
le **pirate** _masc_
**pitch** NOUN
le **terrain** _masc_
**a football pitch**
un terrain de football
**pity** NOUN
**What a pity she can't come!**
Quel dommage! Elle ne peut pas venir.
**What a pity!**
Quel dommage!
**pizza** NOUN
la **pizza** _fem_
**place** NOUN
**1** l' **endroit** _masc (location)_
**It's a quiet place.**
C'est un endroit tranquille.
**There are a lot of interesting places to visit.**
Il y a beaucoup d'endroits intéressants à visiter.
**2** la **place** _fem (position)_
**Can I change places?**
Je peux changer de place?
**Léon, change places with Nina!**
Léon, change de place avec Nina!
**plain** ADJECTIVE
**simple**
**a plain white blouse**
un chemisier blanc simple
**plain chocolate** NOUN
le **chocolat à croquer** _masc_
**plait** NOUN
la **natte** _fem_
**She wears her hair in a plait.**
Elle a une natte.
**plan**
**plan** _can be a noun or a verb._
**A** NOUN
**1** le **projet** _masc_
**Have you got plans for the holidays?**
Tu as des projets pour les vacances?
**2** le **plan** _masc (map)_
**a plan of the school**
un plan de l'école
**B** VERB
**préparer**
**We're planning a trip to France.**
Nous préparons un voyage en France.
**plane** NOUN
l' **avion** _masc_
**by plane**
en avion
**plant** NOUN
la **plante** _fem_
**plastic** ADJECTIVE
**en plastique**
**a plastic bag**
un sac en plastique
**plate** NOUN
l' **assiette** _fem_
**platform** NOUN
le **quai** _masc_
**on platform 7**
sur le quai numéro sept
**play**
**play** _can be a noun or a verb._
**A** NOUN
la **pièce** _fem_
**a play by Shakespeare**
une pièce de Shakespeare
**B** VERB
**1** **jouer**
**He's playing with his friends.**
Il joue avec ses amis.
**What sort of music do they play?**
Quel genre de musique jouent-ils?
**2** **jouer à** _(sport, game)_
**I play hockey.**
Je joue au hockey.
**Can you play chess?**
Tu sais jouer aux échecs?
**3** **jouer de** _(instrument)_
**I play the guitar.**
Je joue de la guitare.
**player** NOUN
le **joueur** _masc_
la **joueuse** _fem_
**a football player**
un joueur de football
**playground** NOUN
**1** la **cour de récréation** _fem (at school)_
**2** l' **aire de jeux** _fem (in park)_
**playgroup** NOUN
la **garderie** _fem_
**playing card** NOUN
la **carte à jouer** _fem_ (PL les
**cartes à jouer** )
**playing field** NOUN
le **terrain de sport** _masc_
**playtime** NOUN
la **récréation** _fem_
**at playtime**
à la récréation
**please** EXCLAMATION
**1** **s'il vous plaît** _(polite form)_
**Two coffees, please.**
Deux cafés, s'il vous plaît.
**2** **s'il te plaît** _(familiar form)_
**Please write back soon.**
Réponds vite, s'il te plaît.
**Yes please!**
Oui, merci.
**pleased** ADJECTIVE
**content** _masc_
**contente** _fem_
**My mother's not pleased.**
Ma mère n'est pas contente.
**pleasure** NOUN
le **plaisir** _masc_
**with pleasure**
avec plaisir
**plenty** NOUN
**largement assez**
**I've got plenty.**
J'en ai largement assez.
**You've got plenty of time.**
Vous avez largement le temps.
**That's plenty, thanks.**
Ça suffit largement, merci.
**plug in** VERB
**brancher**
**Is it plugged in?**
Est-ce que c'est branché?
**It's not plugged in.**
Ce n'est pas branché.
**plum** NOUN
la **prune** _fem_
**plum jam**
la confiture de prunes
**plump** ADJECTIVE
**dodu** _masc_
**dodue** _fem_
**plural** NOUN
le **pluriel** _masc_
**plus** PREPOSITION
**plus**
**Four plus three equals seven.**
Quatre plus trois égalent sept.
**p.m.** ABBREVIATION
**at 8 p.m.**
à huit heures du soir
**at 2 p.m.**
à quatorze heures
_**Did you know...?**_
_In France, times are often given using the 24-hour clock._
**poached egg** NOUN
l' **œuf poché** _masc_
**a poached egg**
un œuf poché
**pocket** NOUN
la **poche** _fem_
**pocket calculator** NOUN
la **calculette** _fem_
**pocket money** NOUN
l' **argent de poche** _masc_
**I get £2 a week pocket money.**
Je reçois deux livres d'argent de poche par semaine.
**poem** NOUN
le **poème** _masc_
**point**
**point** _can be a noun or a verb._
**A** NOUN
**1** le **point** _masc (in game)_
**You've got five points.**
Vous avez cinq points.
**What's the point?**
À quoi bon?
**What's the point of leaving so early?**
À quoi bon partir si tôt?
**2** la **virgule** _fem (in decimal numbers)_
**two point five (2.5)**
deux virgule cinq (2,5)
_**Did you know...?**_
_In decimal numbers, the French use a comma instead of a point._
**B** VERB
**Which cake? You can point to it.**
Quel gâteau? Vous pouvez le montrer du doigt.
**The guide pointed out Notre-Dame to us.**
Le guide nous a montré Notre-Dame.
**poison** NOUN
le **poison** _masc_
**poisonous** ADJECTIVE
**1** **venimeux** _masc_
**venimeuse** _fem (snake)_ **a poisonous snake**
un serpent venimeux
**2** **vénéneux** _masc_
**vénéneuse** _fem (mushroom, berry)_
**Don't eat it, it's poisonous!**
Ne mange pas ça, c'est vénéneux!
**police** PL NOUN
la **police** _fem_
**_Language tip_**
**police** _is a singular word in French._
**police car** NOUN
la **voiture de police** _fem_
**policeman** NOUN
le **policier** _masc_
**policewoman** NOUN
la **femme policier** _fem_
**polite** ADJECTIVE
**poli** _masc_
**polie** _fem_
**He's a very polite boy.**
C'est un garçon très poli.
**politely** ADVERB
**poliment**
**polluted** ADJECTIVE
**pollué** _masc_
**polluée** _fem_
**pollution** NOUN
la **pollution** _fem_
**polo shirt** NOUN
le **polo** _masc_
**pond** NOUN
le **bassin** _masc_
**There's a pond in our garden.**
Il y a un bassin dans notre jardin.
**pony** NOUN
le **poney**
_masc_
**_Language tip_**
_The French word has one more letter than the English word. What is it?_
**ponytail** NOUN
la **queue de cheval** _fem_
**I've got a ponytail.**
J'ai une queue de cheval.
**pony trekking** NOUN
**I go pony trekking.**
Je fais des randonnées à dos de poney.
**poodle** NOUN
le **caniche** _masc_
**pool** NOUN
**1** la **piscine** _fem (swimming pool)_
**There's a pool.**
Il y a une piscine.
**2** le **billard américain** _masc (game)_
**Can you play pool?**
Tu sais jouer au billard américain?
**poor** ADJECTIVE
**pauvre**
**Poor David, he's very unlucky!**
Le pauvre David, il n'a vraiment pas de chance!
**pop** NOUN
la **boisson gazeuse** _fem (drink)_
**popcorn** NOUN
le **pop-corn** _masc_
**pope** NOUN
le **pape** _masc_
**pop group** NOUN
le **groupe pop** _masc_
**What's your favourite pop group?**
Quel est ton groupe pop préféré?
**pop music** NOUN
la **musique pop** _fem_
**poppy** NOUN
le **coquelicot** _masc_
**pop song** NOUN
la **chanson pop** _fem_
**popular** ADJECTIVE
**populaire**
**She's a very popular girl.**
C'est une fille très populaire.
**porch** NOUN
le **porche** _masc_
**pork** NOUN
le **porc** _masc_
**a pork chop**
une côtelette de porc
**I don't eat pork.**
Je ne mange pas de porc.
**port** NOUN
le **port** _masc_
**portable** ADJECTIVE
**portable**
**a portable TV**
un téléviseur portable
**_Language tip_**
_If something is_ **portable** , _you can carry it. The French for 'to carry' is_ **porter**.
**portion** NOUN
la **portion** _fem_
**a large portion of chips**
une grosse portion de frites
**Portugal** NOUN
le **Portugal** _masc_
**posh** ADJECTIVE
**chic** _masc, fem, pl_
**a posh hotel**
un hôtel chic
**positive** ADJECTIVE
**certain** _masc_
**certaine** _fem_
**Are you positive, Joëlle?**
Tu en es certaine, Joëlle?
**possibility** NOUN
**It's a possibility.**
C'est possible.
**possible** ADJECTIVE
**possible**
**as soon as possible**
aussitôt que possible
**post**
**post** _can be a noun or a verb._
**A** NOUN
le **courrier** _masc (letters)_
**Is there any post for me?**
Est-ce qu'il y a du courrier pour moi?
**B** VERB
**poster**
**I've got some cards to post.**
J'ai quelques cartes à poster.
**postbox** NOUN
la **boîte aux lettres** _fem_
_**Did you know...?**_
_French postboxes are yellow._
**postcard** NOUN
la **carte postale** _fem_
**Thank you for the postcard, Charlotte.**
Merci pour la carte postale, Charlotte.
**postcode** NOUN
le **code postal** _masc_
**What is your postcode?**
Quel est ton code postal?
**poster** NOUN
le **poster** _masc_
**I've got posters on my bedroom walls.**
J'ai des posters sur les murs de ma chambre.
**_Language tip_**
_In French, you pronounce_ **poster** _as 'post-air'._
**postman** NOUN
le **facteur** _masc_
**He's a postman.**
Il est facteur.
**_Language tip_**
_You do not translate_ **'a'** _when you say what someone's job is in French._
**post office** NOUN
la **poste** _fem_
**Where's the post office, please?**
Où est la poste, s'il vous plaît?
**potato** NOUN
la **pomme de terre** _fem_
**Rice or potatoes?**
Du riz ou des pommes de terre?
**mashed potatoes**
la puré
**boiled potatoes**
les pommes vapeur
**a baked potato**
une pomme de terre cuite au four
**potato salad** NOUN
la **salade de pommes de terre** _fem_
**pottery** NOUN
la **poterie** _fem_
**pound** NOUN
la **livre** _fem_
**How many euros do you get for a pound?**
Combien d'euros a-t-on pour une livre?
**a pound of potatoes**
une livre de pommes de terre
**pour** VERB
**pleuvoir à verse**
**It's pouring.**
Il pleut à verse.
**powerful** ADJECTIVE
**puissant** _masc_
**puissante** _fem_
**practically** ADVERB
**pratiquement**
**It's practically impossible.**
C'est pratiquement impossible.
**practice** NOUN
l' **entraînement** _masc (for sport)_
**football practice**
l'entraînement de foot
**I've got to do my piano practice.**
Je dois travailler mon piano.
**practise** VERB
**1** **travailler** _(instrument)_
**I practise my flute every evening.**
Je travaille ma flûte tous les soirs.
**2** **pratiquer** _(language)_
**I like practising my French.**
J'aime pratiquer mon français.
**3** **s'entraîner** _(sport)_
**The team practises on Thursdays.**
L'équipe s'entraîne le jeudi.
**prawn** NOUN
la **crevette** _fem_
**pray** VERB
**prier**
**Let us pray.**
Prions.
**prayer** NOUN
la **prière** _fem_
**precisely** ADVERB
**at 10 a.m. precisely**
à dix heures précises
**prefer** VERB
**préférer**
**Which would you prefer?**
Lequel préfères-tu?
**Which do you prefer, tennis or football?**
Tu préfères le tennis ou le football?
**I prefer French to geography.**
Je préfère le français à la géographie.
**pregnant** ADJECTIVE
**enceinte**
**She's six months pregnant.**
Elle est enceinte de six mois.
**prep** NOUN
les **devoirs** _masc pl_
**history prep**
les devoirs d'histoire
**prepare** VERB
**préparer**
**She has to prepare lessons in the evening.**
Elle doit préparer ses cours le soir.
**prep school** NOUN
l' **école primaire privée** _fem_
**present**
**present** _can be an adjective or a noun._
**A** ADJECTIVE
**présent** _masc_
**présente** _fem_
**Ten present, two absent.**
Dix présents, deux absents.
**the present tense**
le présent
**B** NOUN
**1** le **cadeau** _masc_
(PL les **cadeaux** ) _(gift)_
**I'm going to give Julie a present.**
Je vais offrir un cadeau à Julie.
**I got lots of presents.**
J'ai eu beaucoup de cadeaux.
**2** le **présent** _masc (time)_
**the present and the future**
le présent et le futur
**president** NOUN
le **président** _masc_
la **présidente** _fem_
**pretend** VERB
**Pretend you are in a café.**
Imagine que tu es dans un café.
**pretty**
**pretty** _can be an adjective or an adverb._
**A** ADJECTIVE
**joli** _masc_ **jolie** _fem_
**She's very pretty.**
Elle est très jolie.
**B** ADVERB
**plutôt**
**It's pretty old.**
C'est plutôt vieux.
**The weather was pretty awful.**
Il faisait un temps minable.
**previous** ADJECTIVE
**précédent** _masc_
**précédente** _fem_
**the previous day**
le jour précédent
**price** NOUN
le **prix** _masc_
**priest** NOUN
le **prêtre** _masc_
**He's a priest.**
Il est prêtre.
**_Language tip_**
_You do not translate_ **'a'** _when you say what someone's job is in
French._
**primary** NOUN
**I am in primary seven.**
Je suis au CM2.
**primary school** NOUN
l' **école primaire** _fem_
**I am at primary school.**
Je suis à l'école primaire.
_**Did you know...?**_
_In France, children start primary school at the age of six. The first year is_ **CP** , _followed by_ **CE1** and **CE2**. _The last two years are_ **CM1** _and_ **CM2**.
**prince** NOUN
le **prince** _masc_
**the Prince of Wales**
le prince de Galles
_**Did you know...?**_
_There are no princes in France, because France is a republic, not a monarchy like Britain._
**princess** NOUN
la **princesse** _fem_
**Princess Anne**
la princesse Anne
**print** VERB
**écrire en majuscules**
**Print your name.**
Écris ton nom en majuscules.
**prison** NOUN
la **prison** _fem_
**in prison**
en prison
**private** ADJECTIVE
**privé** _masc_
**privée** _fem_
**a private school**
une école privée
**I have private lessons.**
Je prends des cours particuliers.
**private school** NOUN
l' **école privée** _fem_
**prize** NOUN
le **prix** _masc_
**The prize is one hundred euros.**
C'est un prix de cent euros.
**You can win a prize.**
Tu peux gagner un prix.
**prize-giving** NOUN
la **distribution des prix** _fem_
**prizewinner** NOUN
le **gagnant**
_masc_
la **gagnante**
_fem_
**probably** ADVERB
**probablement**
**probably not**
probablement pas
**problem** NOUN
le **problème** _masc_
**Is there a problem?**
Il y a un problème?
**What's the problem?**
Qu'est-ce qui ne va pas?
**No problem!**
Pas de problème!
**procession** NOUN
la **procession** _fem_
**profession** NOUN
la **profession** _fem_
**professor** NOUN
le **professeur d'université** _masc_
**profit** NOUN
le **bénéfice** _masc_
**program** NOUN
le **programme** _masc_
**a computer program**
un programme informatique
**programme** NOUN
**1** l' **émission** _fem (on TV, radio)_
**my favourite programme**
mon émission préférée
**2** le **programme** _masc (booklet)_
**Would you like a programme?**
Tu veux un programme?
**progress** NOUN
le **progrès** _masc_
**You're making progress, Éric!**
Tu fais des progrès, Éric!
**projector** NOUN
le **projecteur** _masc_
**promise**
**promise** _can be a noun or a verb._
**A** NOUN
la **promesse** _fem_
**I'll make you a promise.**
Je te fais une promesse.
**That's a promise!**
C'est promis!
**B** VERB
**promettre**
**I promise!**
Je te le promets!
**I'll write, I promise!**
J'écrirai, c'est promis!
**prompt**
**prompt** _can be an adjective or an adverb._
**A** ADJECTIVE
**rapide**
**a prompt reply**
une réponse rapide
**B** ADVERB
**at one o'clock prompt**
à une heure précise
**pronoun** NOUN
le **pronom** _masc_
**pronounce** VERB
**prononcer**
**How do you pronounce that word?**
Comment on prononce ce mot?
**pronunciation** NOUN
la **prononciation** _fem_
**Your pronunciation is good!**
Tu as une bonne prononciation!
**_Language tip_**
_Which vowel is different in the French word?_
**proper** ADJECTIVE
**vrai** _masc_
**vraie** _fem_
**proper French bread**
du vrai pain français
**properly** ADVERB
**comme il faut**
**I can't pronounce it properly.**
Je n'arrive pas à le prononcer comme il faut.
**Protestant**
**Protestant** _can be an adjective or a noun._
**A** ADJECTIVE
**protestant** _masc_
**protestante** _fem_
**B** NOUN
le **protestant** _masc_
la **protestante** _fem_
**I'm a Protestant.**
Je suis protestant.
**_Language tip_**
_In French_ , **protestant** _is not spelled with a capital letter._
**proud** ADJECTIVE
**fier** _masc_
**fière** _fem_
**Her parents are proud of her.**
Ses parents sont fiers d'elle.
**prune** NOUN
le **pruneau** _masc_ (PL les **pruneaux** )
**_Language tip_**
_Be careful! There is a word_ **prune** _in French, but it means 'plum'. A_ **prune** _in English is a dried plum._
**PTO** ABBREVIATION
**T.S.V.P.**
**_Language tip_**
**T.S.V.P.** _stands for_ **'tournez, s'il vous plaît'**. _What does PTO stand for?_
**pub** NOUN
le **pub** _masc_
**public**
**public** _can be a noun or an adjective._
**A** NOUN
le **public** _masc_
**The castle is open to the public.**
Le château est ouvert au public.
**B** ADJECTIVE
**public** _masc_
**publique** _fem_
**a public swimming pool**
une piscine publique
**publicity** NOUN
la **publicité** _fem_
**public school** NOUN
l' **école privée** _fem_
**public transport** NOUN
les **transports en commun**
_masc pl_
**by public transport**
en transports en commun
**pudding** NOUN
le **dessert** _masc_
**Would you like a pudding?**
Tu veux un dessert?
**What's for pudding?**
Qu'est-ce qu'il y a comme dessert?
**pull** VERB
**tirer**
**Pull!**
Tirez!
**pullover** NOUN
le **pull** _masc_
**What colour is your pullover?**
De quelle couleur est ton pull?
**pump** NOUN
**1** la **pompe** _fem (for bike)_
**a bicycle pump**
une pompe à vélo
**2** le **chausson de danse** _masc (shoe)_
**Have you got your pumps?**
Tu as tes chaussons de danse?
**pump up** VERB
**gonfler**
**Pump up your tyres!**
Gonfle tes pneus!
**punch** VERB
**1** **donner un coup de poing à** _(hit)_
**He punched me!**
Il m'a donné un coup de poing!
**2** **composter** _(in ticket machine)_
**Punch your ticket before you get on the train.**
Compostez votre billet avant de monter dans le train.
_**Did you know...?**_
_In France, you have to punch your ticket before you get on the train. If you don't, you can be fined._
**punctual** ADJECTIVE
**Be punctual!**
Soyez à l'heure!
**punctuation** NOUN
la **ponctuation** _fem_
**_Language tip_**
_There is a different vowel in the French word. What is it?_
**punishment** NOUN
la **punition** _fem_
**pupil** NOUN
l' **élève** _masc/fem_
**There are 22 pupils in my class.**
Il y a vingt-deux élèves dans ma classe.
**puppet** NOUN
la **marionnette** _fem_
**puppy** NOUN
le **chiot** _masc_
**pure** ADJECTIVE
**pur** _masc_
**pure** _fem_
**It's pure orange juice.**
C'est du jus d'orange pur.
**purple**
**purple** _can be an adjective or a noun._
**A** ADJECTIVE
**violet** _masc_
**violette** _fem_
**a purple skirt**
une jupe violette
**_Language tip_**
_Colour adjectives come after the noun in French._
**B** NOUN
le **violet** _masc_
**Purple is my favourite colour.**
Ma couleur préférée, c'est le violet.
**purpose** NOUN
**on purpose**
exprès
**You're doing it on purpose.**
Tu le fais exprès.
**purr** VERB
**ronronner**
**The cat is purring.**
Le chat ronronne.
**purse** NOUN
le **porte-monnaie** _masc_
**I've lost my purse.**
J'ai perdu mon porte-monnaie.
**pursuit** NOUN
l' **activité** _fem_
**outdoor pursuits**
les activités de plein air
**push** VERB
**pousser**
**Don't push, boys!**
Arrêtez de pousser, les garçons!
**Push!**
Poussez!
**pushchair** NOUN
la **poussette** _fem_
**put** VERB
**1** **mettre** _(place)_
**Put your chewing gum in the bin.**
Mets ton chewing-gum à la poubelle.
**Where shall I put my things?**
Où est-ce que je peux mettre mes affaires?
**She's putting the baby to bed.**
Elle met le bébé au lit.
**2** **écrire** _(write)_
**Don't forget to put your name on the paper.**
N'oubliez pas d'écrire votre nom sur la feuille.
**put away** VERB
**ranger**
**Put your things away, children.**
Rangez vos affaires, les enfants.
**put back** VERB
**remettre en place**
**Don't forget to put it back.**
N'oublie pas de le remettre en place.
**put down** VERB
**poser**
**Put down a card.**
Pose une carte.
**Put down your hands.**
Baissez la main.
**put off** VERB
**1** **éteindre** _(switch off)_
**Shall I put the light off?**
Est-ce que j'éteins la lumière?
**2** **déranger** _(distract)_
**Stop putting me off!**
Arrête de me déranger!
**put on** VERB
**1** **mettre** _(clothes)_
**I'll put my coat on.**
Je vais mettre mon manteau.
**2** **allumer** _(switch on)_
**Shall I put the light on?**
J'allume la lumière?
**put up** VERB
**1** **mettre** _(pin up)_
**I'll put the poster up on the wall.**
Je vais mettre le poster au mur.
**2** **lever** _(raise)_
**Put up your hands.**
Levez la main.
**3** **augmenter** _(increase)_
**They've put up the price.**
Ils ont augmenté le prix.
**puzzle**
NOUN
le **puzzle**
_masc_
**puzzled** ADJECTIVE
**perplexe**
**You look puzzled!**
Tu as l'air perplexe!
**pyjamas** PL NOUN
le **pyjama** _masc_
**my pyjamas**
mon pyjama
**I've got new pyjamas.**
J'ai un nouveau pyjama.
**a pair of pyjamas**
un pyjama
**_Language tip_**
_In French_ , **pyjama** _is a singular word._
**Pyrenees** PL NOUN
les **Pyrénées** _fem pl_
**in the Pyrenees**
dans les Pyrénées
**We went to the Pyrenees.**
Nous sommes allés dans les Pyrénées.
# **Q q**
**quad bike** NOUN
le **quad** _masc_
**quality** NOUN
la **qualité** _fem_
**quantity** NOUN
la **quantité** _fem_
**quarrel** VERB
**se disputer**
**Don't quarrel!**
Ne vous disputez pas!
**quarter** NOUN
le **quart** _masc_
**a quarter of the class**
un quart de la classe
**It's quarter past six.**
Il est six heures et quart.
**at quarter to eight**
à huit heures moins le quart
**three quarters**
trois quarts
**a quarter of an hour**
un quart d'heure
**three quarters of an hour**
trois quarts d'heure
**a quarter past ten**
dix heures et quart
**a quarter to eleven**
onze heures moins le quart
**quarter final**
NOUN
le **quart de**
finale _masc_
**queen**
NOUN
**1** la **reine**
_fem_
**Queen Elizabeth**
la reine Élisabeth
**2** la **dame** _fem (card)_
**the queen of hearts**
la dame de cœur
**question** NOUN
la **question** _fem_
**Can I ask a question?**
Est-ce que je peux poser une question?
**Are there any questions?**
Vous avez des questions?
**That's a difficult question.**
C'est une question difficile.
**questionnaire** NOUN
le **questionnaire** _masc_
**queue**
**queue** _can be a noun or a verb._
**A** NOUN
la **queue** _fem_
**There's a long queue.**
Il y a une longue queue.
**B** VERB
**faire la queue**
**You have to queue.**
Il faut faire la queue.
**quick** ADJECTIVE
**rapide**
**a quick lunch**
un déjeuner rapide
**It's quicker by train.**
C'est plus rapide en train.
**Be quick, Laurent!**
Dépêche-toi, Laurent!
**Be quick, girls!**
Dépêchez-vous les filles!
**quickly** ADVERB
**vite**
**Am I speaking too quickly?**
Je parle trop vite?
**quiet** ADJECTIVE
**1** **silencieux** _masc_
**silencieuse** _fem (not chatty)_
**You're very quiet, Daphne.**
Tu es bien silencieuse, Daphne.
**2** **tranquille** _(peaceful)_
**a quiet little town**
une petite ville tranquille
**a quiet weekend**
un week-end tranquille
**Be quiet, I'm thinking!**
Tais-toi, je réfléchis!
**Quiet!**
Silence!
**quietly** ADVERB
**doucement**
**Talk quietly.**
Parlez doucement.
**Shut the door quietly.**
Fermez doucement la porte.
**quilt** NOUN
la **couette** _fem_
**quite** ADVERB
**1** **assez** _(rather)_
**It's quite warm today.**
Il fait assez chaud aujourd'hui.
**It's quite a long way.**
C'est assez loin.
**It's quite expensive.**
C'est assez cher.
**quite a lot of money**
pas mal d'argent
**2** **tout à fait** _(completely)_
**I'm quite sure he's coming.**
Je suis tout à fait sûr qu'il va venir.
**Are you ready, Lola? — Not quite.**
Tu es prête, Lola? — Pas tout à fait.
**quite good**
pas mal
**quiz** NOUN
le **jeu-concours** _masc_
# **R r**
**rabbi** NOUN
le **rabbin** _masc_
**rabbit** NOUN
le **lapin** _masc_
**race** NOUN
la **course** _fem_
**a cycle race**
une course cycliste
**Let's have a race!**
On fait la course?
**racer** NOUN
le **vélo de course** _masc_
**I've got a new racer.**
J'ai un nouveau vélo de course.
**racing car** NOUN
la **voiture de course** _fem_
**two racing cars**
deux voitures de course
**racket** NOUN
la **raquette** _fem_
**my tennis racket**
ma raquette de tennis
**radiator** NOUN
le **radiateur** _masc_
**My coat's on the radiator.**
Mon manteau est sur le radiateur.
**radio** NOUN
la **radio** _fem_
**on the radio**
à la radio
**radio cassette** NOUN
le **radiocassette** _masc_
**radio-controlled** ADJECTIVE
**téléguidé** _masc_
**téléguidée** _fem_
**raffle** NOUN
la **tombola** _fem_
**raffle ticket** NOUN
le **billet de tombola** _masc_
**Do you want to buy a raffle ticket?**
Tu veux acheter un billet de tombola?
**rage** NOUN
**to be in a rage**
être furieux
**She's in a rage.**
Elle est furieuse.
**rail** NOUN
**by rail**
en train
**railway** NOUN
le **chemin de fer** _masc_
**railway line** NOUN
le **chemin de fer** _masc_
**railway station** NOUN
la **gare** _fem_
**rain**
**rain** _can be a noun or a verb._
**A** NOUN
la **pluie** _fem_
**in the rain**
sous la pluie
**B** VERB
**pleuvoir**
**It's going to rain.**
Il va pleuvoir.
**It rains a lot here.**
Il pleut beaucoup par ici.
**It's raining.**
Il pleut.
**rainbow** NOUN
l' **arc-en-ciel** _masc_
**raincoat** NOUN
l' **imperméable** _masc_
**rainy** ADJECTIVE
**pluvieux** _masc_
**pluvieuse** _fem_
**a rainy day**
une journée pluvieuse
**raise** VERB
**lever**
**Raise your right arm, everyone.**
Levez le bras droit, tout le monde.
**to raise money**
collecter des fonds
**We're raising money for a new gym.**
Nous collectons des fonds pour un nouveau gymnase.
**raisin** NOUN
le **raisin sec** _masc_
**_Language tip_**
**raisin** _in French means 'grape'. An English_ **raisin** _is a dried grape, which is what_ **raisin sec** _means._
**Ramadan** NOUN
le **ramadan** _masc_
**ramp** NOUN
la **rampe d'accès** _fem_
**ran** VERB _see_ **run**
**random** ADJECTIVE
**at random**
au hasard
**Pick a card at random.**
Choisis une carte au hasard.
**rang** VERB _see_ **ring**
**range** NOUN
le **choix** _masc_
**There's a wide range of colours.**
Il y a un grand choix de coloris.
**rap** NOUN
le **rap** _masc_
**rare** ADJECTIVE
**rare**
**rasher** NOUN
la **tranche** _fem_
**an egg and two rashers of bacon**
un œuf et deux tranches de bacon
**raspberry** NOUN
la **framboise** _fem_
**raspberry jam**
la confiture de framboises
**rat** NOUN
le **rat** _masc_
**rather** ADVERB
**plutôt**
**£20! That's rather expensive!**
Vingt livres! C'est plutôt cher!
**I'd rather...**
J'aimerais mieux...
**I'd rather stay in tonight.**
J'aimerais mieux rester à la maison ce soir.
**Would you like a sweet? — I'd rather have an apple.**
Tu veux un bonbon? — J'aimerais mieux une pomme.
**Which would you rather have?**
Qu'est-ce que tu préfères?
**Would you rather have water or coke?**
Tu préfères boire de l'eau ou du coca?
**ravenous** ADJECTIVE
**I'm ravenous!**
J'ai une faim de loup!
**_Language tip_**
**un loup** _is a wolf, so literally this means 'I'm as hungry as a wolf'._
**raw** ADJECTIVE
**cru** _masc_
**crue** _fem_
**razor** NOUN
le **rasoir** _masc_
**RE** NOUN
l' **éducation religieuse** _fem_
**reach**
**reach** _can be a noun or a verb._
**A** NOUN
**Mum keeps the biscuits out of reach.**
Maman garde les biscuits hors de portée.
**The hotel is within easy reach of the town centre.**
L'hôtel se trouve à proximité du centre-ville.
**B** VERB
**arriver à** _(get to)_
**We hope to reach Paris tomorrow evening.**
Nous espérons arriver à Paris demain soir.
**I can't reach the top shelf.**
Je n'arrive pas à atteindre l'étagère du haut.
**read** VERB
**lire**
**I don't read much.**
Je ne lis pas beaucoup.
**Have you read 'The Prisoner of Azkaban'?**
Est-ce que tu as lu 'le Prisonnier d'Azkaban'?
**read out** VERB
**lire**
**I'll read out the names.**
Je vais lire les noms.
**reading** NOUN
la **lecture** _fem_
**Reading is one of my hobbies.**
La lecture est l'un de mes passe-temps.
**ready** ADJECTIVE
**prêt** _masc_
**prête** _fem_
**Lunch is ready.**
Le déjeuner est prêt.
**She's nearly ready.**
Elle est presque prête.
**Are you ready, children?**
Vous êtes prêts, les enfants?
**Ready, steady, go!**
À vos marques, prêts, partez!
**real** ADJECTIVE
**1** **vrai** _masc_
**vraie** _fem (true)_
**Her real name is Cordelia.**
Son vrai nom, c'est Cordelia.
**2** **véritable**
**It's real leather.**
C'est du cuir véritable.
**really** ADVERB
**vraiment**
**She's really nice.**
Elle est vraiment sympa.
**Do you want to go? — Not really.**
Tu veux y aller? — Pas vraiment.
**reason** NOUN
la **raison** _fem_
**reasonable** ADJECTIVE
**raisonnable**
**Be reasonable, Marie!**
Sois raisonnable, Marie!
**receipt** NOUN
le **ticket de caisse** _masc_
**Take your receipt.**
Prenez votre ticket de caisse.
**receive** VERB
**recevoir**
**I received your letter yesterday.**
J'ai reçu ta lettre hier.
**recent** ADJECTIVE
**récent** _masc_
**récente** _fem_
**recently** ADVERB
**ces derniers temps**
**He's been ill a lot recently.**
Il est souvent malade ces derniers temps.
**reception** NOUN
la **réception** _fem_
**Please leave your key at reception.**
Merci de laisser votre clé à la réception.
**The reception will be at a big hotel.**
La réception aura lieu dans un grand hôtel.
**receptionist** NOUN
le/la **réceptionniste** _masc/fem_
**_Language tip_**
_In French_ , **réceptionniste** _has double_ **n**.
**recipe** NOUN
la **recette** _fem_
**reckon** VERB
**penser**
**What do you reckon?**
Qu'est-ce que tu en penses?
**recognize** VERB
**reconnaître**
**Do you recognize this boy?**
Tu reconnais ce garçon?
**recommend** VERB
**conseiller**
**What do you recommend?**
Qu'est-ce que vous me conseillez?
**I recommend the soup.**
Je vous conseille la soupe.
**record**
**record** _can be a noun or a verb._
**A** NOUN
le **record** _masc (sport)_
**the world record**
le record du monde
**B** VERB
**enregistrer**
**We'll record the song.**
On va enregistrer la chanson.
**recorder** NOUN
la **flûte à bec** _fem_
**I play the recorder.**
Je joue de la flûte à bec.
**rectangle** NOUN
le **rectangle** _masc_
**red**
**red** _can be an adjective or a noun._
**A** ADJECTIVE
**1** **rouge**
**a red rose**
une rose rouge
**The lights are red.**
Le feu est au rouge.
**2** **roux** _masc_
**rousse** _fem (hair)_
**Tamsin's got red hair.**
Tamsin a les cheveux roux.
**_Language tip_**
_Colour adjectives come after the noun in French._
**B** NOUN
le **rouge** _masc_
**Red is my favourite colour.**
Ma couleur préférée, c'est le rouge.
**redecorate** VERB
**1** **retapisser** _(with wallpaper)_
**Mum is helping me redecorate my room.**
Maman m'aide à retapisser ma chambre.
**2** **refaire les peintures** _(with paint)_
**Mum is helping me redecorate my room.**
Maman m'aide à refaire les peintures de ma chambre.
**red-haired** ADJECTIVE
**roux** _masc_
**rousse** _fem_
**redhead** NOUN
le **roux** _masc_
la **rousse** _fem_
**redo** VERB
**refaire**
**I need to redo my homework.**
Je dois refaire mes devoirs.
**reduced** ADJECTIVE
**at a reduced price**
à prix réduit
**reduction** NOUN
la **réduction** _fem_
**a 5% reduction**
une réduction de cinq pour cent
**referee** NOUN
l' **arbitre** _masc_
**reflexive** ADJECTIVE
**a reflexive verb**
un verbe réfléchi
**refreshments** PL NOUN
les **rafraîchissements** _masc pl_
**refrigerator** NOUN
le **réfrigérateur** _masc_
**refugee** NOUN
le **réfugié** _masc_
la **réfugiée** _fem_
**refuse** VERB
**refuser**
**He refuses to help.**
Il refuse d'aider.
**regards** PL NOUN
**Give my regards to Luc.**
Transmets mon bon souvenir à Luc.
**Jean-Louis sends his regards.**
Vous avez le bonjour de Jean-Louis.
**region** NOUN
la **région** _fem_
**in this region**
dans cette région
**register** NOUN
**I'm going to call the register.**
Je vais faire l'appel.
**registration** NOUN
l' **appel** _masc_
**after registration**
après l'appel
**regular** ADJECTIVE
**1** **régulier** _masc_
**régulière** _fem_
**at regular intervals**
à intervalles réguliers
**a regular verb**
un verbe régulier
**You should take regular exercise.**
Il faut faire régulièrement de l'exercice.
**2** **normal** _masc_
**normale** _fem (medium)_
**a regular portion of fries**
une portion de frites normale
**rehearsal** NOUN
la **répétition** _fem_
**reindeer** NOUN
le **renne** _masc_
**relation** NOUN
**my relations**
ma famille
**I've got relations in London.**
J'ai de la famille à Londres.
**relative** NOUN
**all her relatives**
toute sa famille
**I've got relatives in Manchester.**
J'ai de la famille à Manchester.
**relax** VERB
**Relax! Everything's fine.**
Ne t'en fais pas! Tout va bien.
**relaxed** ADJECTIVE
**détendu** _masc_
**détendue** _fem_
**relaxing** ADJECTIVE
**reposant** _masc_
**reposante** _fem_
**I find cooking relaxing.**
Cela me détend de faire la cuisine.
**relay race** NOUN
la **course de relais** _fem_
**We won the relay race.**
Nous avons gagné la course de relais.
**reliable** ADJECTIVE
**fiable**
**a reliable car**
une voiture fiable
**He's not very reliable.**
Il n'est pas très fiable.
**religion** NOUN
la **religion** _fem_
**What religion are you?**
Quelle est votre religion?
**religious** ADJECTIVE
**religieux** _masc_
**religieuse** _fem_
**a religious school**
une école religieuse
**My parents are very religious.**
Mes parents sont très croyants.
**remark** NOUN
la **remarque** _fem_
**remember** VERB
**se souvenir de**
**Who remembers this word?**
Qui se souvient de ce mot?
**Do you remember the rules of the game?**
Tu te souviens des règles du jeu?
**I can't remember his name.**
Je ne me souviens pas de son nom.
**_Language tip_**
_In French, you often say 'don't forget' instead of_ **remember**.
**Remember your passport!**
N'oublie pas ton passeport!
**Remember this word is feminine.**
N'oublie pas que ce mot est féminin.
**Remember to write your name on the form, children.**
N'oubliez pas d'écrire votre nom sur le formulaire, les enfants.
**Sorry, I can't remember.**
Désolé, je ne m'en souviens pas.
**Remembrance Day** NOUN
le **jour de l'Armistice** _masc_
**on Remembrance Day**
le jour de l'Armistice
**remind** VERB
**rappeler**
**Remind me to speak to Daniel.**
Rappelle-moi de parler à Daniel.
**remote** ADJECTIVE
**isolé** _masc_
**isolée** _fem_
**a remote village**
un village isolé
**remote control** NOUN
la **télécommande** _fem_
**remove** VERB
**enlever**
**Please remove your bag from my seat.**
Est-ce que vous pouvez enlever votre sac de mon siège?
**rent**
**rent** _can be a noun or a verb._
**A** NOUN
le **loyer** _masc_
**She has to pay the rent.**
Elle doit payer le loyer.
**B** VERB
**louer**
**We are going to rent a car.**
Nous allons louer une voiture.
**repair** VERB
**réparer**
**Can you repair them?**
Vous pouvez les réparer?
**repeat** VERB
**répéter**
**Repeat after me, everyone.**
Répétez après moi, tout le monde.
**reply**
**reply** _can be a noun or a verb._
**A** NOUN
la **réponse** _fem_
**I got no reply to my letter.**
Je n'ai pas eu de réponse à ma lettre.
**B** VERB
**répondre**
**I hope you will reply soon.**
J'espère que tu vas vite répondre.
**report** NOUN
le **bulletin scolaire** _masc_
**I usually get a good report.**
D'habitude, j'ai un bon bulletin scolaire.
**republic** NOUN
la **république** _fem_
**France is a republic.**
La France est une république.
**request** NOUN
la **demande** _fem_
**another request**
une autre demande
**reservation** NOUN
la **réservation** _fem_
**I've got a reservation.**
J'ai une réservation.
**I'd like to make a reservation for this evening.**
J'aimerais faire une réservation pour ce soir.
**reserve**
**reserve** _can be a noun or a verb._
**A** NOUN
le **remplaçant** _masc_
la **remplaçante** _fem_
**I was reserve in the game last Saturday.**
J'étais remplaçant dans le match de samedi dernier.
**B** VERB
**réserver**
**I'd like to reserve a table for tomorrow evening.**
J'aimerais réserver une table pour demain soir.
**reserved** ADJECTIVE
**réservé** _masc_
**réservée** _fem_
**a reserved seat**
une place réservée
**resolution** NOUN
la **résolution** _fem_
**Have you made any new year's resolutions?**
Tu as pris de bonnes résolutions pour l'année nouvelle?
**resort** NOUN
la **station balnéaire** _fem_
**It's a resort on the Costa del Sol.**
C'est une station balnéaire sur la Costa del Sol.
**a ski resort**
une station de ski
**responsibility** NOUN
la **responsabilité** _fem_
**It's your responsibility.**
C'est ta responsabilité.
**_Language tip_**
_What are the differences in spelling between the French and the English word?_
**responsible** ADJECTIVE
**responsable**
**He's responsible for booking the tickets.**
Il est responsable de la réservation des billets.
**It's a responsible job.**
C'est un poste à responsabilités.
**_Language tip_**
_The_ **i** _in_ **responsible** _becomes an_ **a** _in the French word_ **responsable**.
**rest**
**rest** _can be a noun or a verb._
**A** NOUN
**1** le **repos** _masc_
**five minutes' rest**
cinq minutes de repos
**Can we have a rest?**
On peut se reposer?
**I need a rest.**
J'ai besoin de me reposer.
**2** _(remainder)_
**the rest**
le reste
**I'll do the rest.**
Je ferai le reste.
**the rest of the money**
le reste de l'argent
**B** VERB
**se reposer**
**She's resting in her room.**
Elle se repose dans sa chambre.
**restaurant** NOUN
le **restaurant** _masc_
**We don't often go to restaurants.**
Nous n'allons pas souvent au restaurant.
**restaurant car** NOUN
le **wagon-restaurant** _masc_
**result** NOUN
le **résultat** _masc_
**my exam results**
mes résultats d'examen
**What was the result? — One-nil.**
Quel a été le résultat? — Un à zéro.
**retire** VERB
**prendre sa retraite**
**He's going to retire.**
Il va prendre sa retraite.
**retired** ADJECTIVE
**retraité** _masc_
**retraitée** _fem_
**She's retired.**
Elle est retraitée.
**retirement** NOUN
la **retraite** _fem_
**return**
**return** _can be a noun or a verb._
**A** NOUN
**1** le **retour** _masc_
**after our return**
à notre retour
**the return journey**
le voyage de retour
**2** l' **aller retour** _masc (ticket)_
**A return to Avignon, please.**
Un aller retour pour Avignon, s'il vous plaît.
**Many happy returns!**
Bon anniversaire!
**B** VERB
**1** **revenir** _(come back)_
**I've just returned from holiday.**
Je viens de revenir de vacances.
**2** **rendre** _(give back)_
**I've got to return this book to the library.**
Je dois rendre ce livre à la bibliothèque.
**reverse** ADJECTIVE
**inverse**
**in reverse order**
dans l'ordre inverse
**revise** VERB
**réviser**
**I haven't started revising yet.**
Je n'ai pas encore commencé à réviser.
**revision** NOUN
les **révisions** _fem pl_
**Have you done a lot of revision?**
Est-ce que tu as fait beaucoup de révisions?
**revolution** NOUN
la **révolution** _fem_
**the French Revolution**
la Révolution française
**reward** NOUN
la **récompense** _fem_
**There's a €1000 reward.**
Il y a une récompense de 1000€.
**rewind** VERB
**rembobiner**
**Can you rewind the tape?**
Tu peux rembobiner la cassette?
**rhubarb** NOUN
la **rhubarbe** _fem_
**a rhubarb tart**
une tarte à la rhubarbe
**rhythm** NOUN
le **rythme** _masc_
**_Language tip_**
_Which consonant is missing in the French word?_
**rib** NOUN
la **côte** _fem_
**ribbon** NOUN
le **ruban** _masc_
**rice** NOUN
le **riz** _masc_
**Would you like some rice?**
Vous voulez du riz?
**rich** ADJECTIVE
**riche**
**rid** VERB
**to get rid of**
se débarrasser de
**I need to get rid of my chewing gum.**
Je dois me débarrasser de mon chewing gum.
**ride**
**ride** _can be a noun or a verb._
**A** NOUN
la **promenade à cheval** _fem (on horse)_
**Would you like to go for a ride?**
Tu veux faire une promenade à cheval?
**a bike ride**
un tour en vélo
**I'm going to go for a bike ride.**
Je vais faire un tour en vélo.
**B** VERB
**monter à cheval** _(on horse)_
**I'm learning to ride.**
J'apprends à monter à cheval.
**to ride a bike**
faire du vélo
**Can you ride a bike?**
Tu sais faire du vélo?
**rider** NOUN
le **cavalier** _masc_
la **cavalière** _fem_
**She's a good rider.**
C'est une bonne cavalière.
**ridiculous** ADJECTIVE
**ridicule**
**Don't be ridiculous, Fiona!**
Ne sois pas ridicule, Fiona!
**riding** NOUN
l' **équitation** _fem_
**I like riding.**
J'aime l'équitation.
**to go riding**
faire de l'équitation
**I'd like to go riding.**
Je voudrais faire de l'équitation.
**riding school** NOUN
l' **école d'équitation** _fem_
**right**
**right** _can be an adjective, an adverb or a noun._
**A** ADJECTIVE
**1** **bon** _masc_
**bonne** _fem (correct)_
**That's the right answer!**
C'est la bonne réponse!
**It isn't the right size.**
Ce n'est pas la bonne taille.
**We're on the right train.**
Nous sommes dans le bon train.
**2** **vrai** _masc_
**vraie** _fem (true)_
**That's right!**
C'est vrai!
**3** **droit** _masc_
**droite** _fem (not left)_
**my right hand**
ma main droite
**B** ADVERB
**1** **correctement** _(correctly)_
**Am I pronouncing it right?**
Est-ce que je prononce ça correctement?
**2** **à droite** _(to the right)_
**Turn right at the traffic lights.**
Tournez à droite aux prochains feux.
**C** NOUN _(not left)_
**on the right**
à droite
**a step to the right**
un pas à droite
**You're right, Léa.**
Tu as raison, Léa.
**You're right, sir.**
Vous avez raison, monsieur.
**Right! Let's get started.**
Bon! On commence.
**Go right.**
Allez à droite.
**right-hand** ADJECTIVE
**the right-hand side**
la droite
**It's on the right-hand side.**
C'est à droite.
**right-handed** ADJECTIVE
**droitier** _masc_
**droitière** _fem_
**ring**
**ring** _can be a noun or a verb._
**A** NOUN
**1** la **bague** _fem (jewellery)_
**a gold ring**
une bague en or
**a diamond ring**
une bague de diamants
**a wedding ring**
une alliance
**2** le **cercle** _masc (circle)_
**Stand in a ring.**
Mettez-vous en cercle.
**B** VERB
**1** **appeler** _(phone)_
**You can ring me at home.**
Tu peux m'appeler à la maison.
**2** **sonner** _(make sound)_
**The phone's ringing.**
Le téléphone sonne.
**ring tone** NOUN
la **sonnerie** _fem_
**rink** NOUN
**1** la **patinoire** _fem (for ice-skating)_
**2** la **piste** _fem (for roller-skating)_
**ripe** ADJECTIVE
**mûr** _masc_
**mûre** _fem_
**a ripe peach**
une pêche mûre
**risk** NOUN
le **risque** _masc_
**It's a big risk.**
C'est un gros risque.
**rival**
**rival** _can be a noun or an adjective._
**A** NOUN
le **rival** _masc_
la **rivale** _fem_
**our rivals**
nos rivaux
**B** ADJECTIVE
**rival** _masc_
**rivale** _fem_
**a rival gang**
une bande rivale
**river** NOUN
la **rivière** _fem_
**across the river**
de l'autre côté de la rivière
**_Language tip_**
**fleuve** _is the French word for major rivers that flow into the sea. The five_ **fleuves** _in France are the Seine, the Rhine, the Rhône, the Loire, and the Garonne._
**the river Amazon**
le fleuve Amazone
**Riviera** NOUN
**the French Riviera**
la Côte d'Azur
**road** NOUN
**1** la **route** _fem_
**There's traffic on the roads.**
Il y a de la circulation sur les routes.
**the main road**
la grande route
**2** la **rue** _fem (street)_
**They live across the road.**
Ils habitent de l'autre côté de la rue.
**road sign** NOUN
le **panneau** _masc_
(PL les **panneaux** )
**roadworks** PL NOUN
les **travaux** _masc pl_
**roast** ADJECTIVE
**rôti** _masc_
**rôtie** _fem_
**roast chicken**
le poulet rôti
**roast potatoes**
les pommes de terre rôties
**roast pork**
le rôti de porc
**roast beef**
le rôti de bœuf
**robber** NOUN
le **voleur** _masc_
**a bank robber**
un cambrioleur de banques
**robbery** NOUN
le **vol** _masc_
**a bank robbery**
un hold-up
**robot** NOUN
le **robot** _masc_
**rock** NOUN
**1** le **rocher** _masc (boulder)_
**Shall we sit on this rock?**
On s'asseoit sur ce rocher?
**2** le **rock** _masc (music)_
**a rock concert**
un concert de rock
**He's a rock star.**
C'est une rock star.
**3** le **sucre d'orge** _masc (sweet)_
**a stick of rock**
un bâton de sucre d'orge
**rocket** NOUN
la **fusée** _fem_
**rod** NOUN
la **canne à pêche** _fem_
**role play** NOUN
le **jeu de rôle** _masc_
**We're going to do a role play.**
Nous allons faire un jeu de rôle.
**roll**
**roll** _can be a noun or a verb._
**A** NOUN
le **petit pain** _masc (bread)_
**B** VERB
**rouler**
**Roll the truffles in cocoa powder.**
Roulez les truffes dans la poudre de cacao.
**Roll the dice.**
Lance le dé.
**roll call** NOUN
l' **appel** _masc_
**Rollerblade** ® NOUN
le **roller** _masc_
**a pair of Rollerblades**
une paire de rollers
**rollercoaster** NOUN
les **montagnes russes** _fem pl_
**roller skates** PL NOUN
les **patins à roulettes** _masc pl_
**roller-skating** NOUN
le **patin à roulettes** _masc_
**Do you want to go roller-skating?**
Tu veux faire du patin à roulettes?
**Roman** NOUN
**the Romans**
les Romains
**Roman Catholic** NOUN
le/la **catholique** _masc/fem_
**He's a Roman Catholic.**
Il est catholique.
**_Language tip_**
**catholique** _is not spelled with a capital letter._
**romantic** ADJECTIVE
**romantique**
**roof** NOUN
le **toit** _masc_
**room** NOUN
**1** la **pièce** _fem_
**the biggest room in the house**
la plus grande pièce de la maison
**2** la **chambre** _fem (bedroom)_
**My room is the smallest.**
Ma chambre est la plus petite.
**a single room**
une chambre pour une personne
**a double room**
une chambre pour deux personnes
**3** la **salle** _fem (in school)_
**the music room**
la salle de musique
**4** la **place** _fem (space)_
**Is there room for me?**
Est-ce qu'il y a de la place pour moi?
**rope** NOUN
la **corde** _fem_
**rose** NOUN
la **rose** _fem_
**a bunch of roses**
un bouquet de roses
**rotten** ADJECTIVE
**rotten weather**
un temps pourri
**rough** ADJECTIVE
**violent** _masc_
**violente** _fem_
**roughly** ADVERB
**à peu près**
**It weighs roughly 20 kilos.**
Ça pèse à peu près vingt kilos.
**round**
**round** _can be an adjective, a preposition or a noun._
**A** ADJECTIVE
**rond** _masc_
**ronde** _fem_
**a round table**
une table ronde
**B** PREPOSITION
**autour de**
**Sit round the table.**
Asseyez-vous autour de la table.
**It's just round the corner.**
C'est tout près.
**round here**
près d'ici
**Is there a chemist's round here?**
Il y a une pharmacie près d'ici?
**C** NOUN
la **manche** _fem (of tournament)_
**the next round**
la prochaine manche
**a round of golf**
une partie de golf
**roundabout** NOUN
le **manège** _masc_
**rounders** NOUN
**Rounders is a bit like baseball.**
Le 'rounders' ressemble un peu au base-ball.
_**Did you know...?**_
_Rounders is not played in France._
**row**
**row** _can be a noun or a verb._
**A** NOUN
la **rangée** _fem_
**a row of houses**
une rangée de maisons
**2** le **rang**
_masc (of seats)_
**Our seats are in the front row.**
Nos places se trouvent au premier rang.
**3** le **vacarme** _masc (noise)_
**What a row!**
Quel vacarme!
**B** VERB
**ramer**
**I can row.**
Je sais ramer.
**_Language tip_**
**row** _can be pronounced in two different ways. Be careful to pick the right translation!_
**rowing boat** NOUN
le **bateau à rames** _masc_
**royal** ADJECTIVE
**royal** _masc_
**royale** _fem_
**the royal family**
la famille royale
**rubber** NOUN
la **gomme** _fem_
**Can I borrow your rubber?**
Je peux emprunter ta gomme?
**rubber band** NOUN
l' **élastique** _masc_
**rubbish**
**rubbish** _can be a noun or an adjective._
**A** NOUN
**1** les **ordures** _fem pl (garbage)_
**Where shall I put the rubbish?**
Où est-ce que je mets les ordures?
**2** les **bêtises** _fem pl (nonsense)_
**Don't talk rubbish!**
Ne dis pas de bêtises!
**B** ADJECTIVE
**nul** _masc_
**nulle** _fem (useless)_
**They're a rubbish team!**
Cette équipe est nulle!
**The film was rubbish.**
Le film était nul.
**rubbish bin** NOUN
la **poubelle** _fem_
**rucksack** NOUN
le **sac à dos** _masc_
**rude** ADJECTIVE
**impoli** _masc_
**impolie** _fem_
**Don't be rude!**
Ne sois pas impoli!
**a rude word**
un gros mot
**rug** NOUN
**1** le **tapis** _masc (carpet)_
**a Persian rug**
un tapis persan
**2** la **couverture** _fem (blanket)_
**a travel rug**
une couverture de voyage
**a tartan rug**
un plaid écossais
**rugby** NOUN
le **rugby** _masc_
**I play rugby.**
Je joue au rugby.
**ruin**
**ruin** _can be a noun or a verb._
**A** NOUN
la **ruine** _fem_
**the ruins of the castle**
les ruines du château
**B** VERB
**abîmer**
**You'll ruin your shoes.**
Tu vas abîmer tes chaussures.
**rule** NOUN
**1** la **règle** _fem (of game)_
**the rules of the game**
les règles du jeu
**2** _(regulations)_
**the rules**
le règlement
**It's against the rules.**
C'est contre le règlement.
**ruler** NOUN
la **règle** _fem_
**Can I borrow your ruler?**
Je peux emprunter ta règle?
**run**
**run** _can be a noun or a verb._
**A** NOUN
**Do you want to go for a run?**
Tu veux courir?
**I go for a run every morning.**
Je cours tous les matins.
**I did a ten-kilometre run.**
J'ai couru dix kilomètres.
**B** VERB
**1** **courir**
**Run!**
Cours!
**I ran two kilometres.**
J'ai couru deux kilomètres.
**2** **organiser** _(organize)_
**They run French courses.**
Ils organisent des cours de français.
**runner** NOUN
le **coureur** _masc_
la **coureuse** _fem_
**runner-up** NOUN
le **second** _masc_
la **seconde** _fem_
**running** NOUN
la **course** _fem_
**Running is my favourite sport.**
Mon sport préféré, c'est la course.
**rush**
**rush** _can be a noun or a verb._
**A** NOUN
la **hâte** _fem_
**in a rush.**
à la hâte
**B** VERB
**se dépêcher**
**There's no need to rush.**
Ce n'est pas la peine de se dépêcher.
**rush hour** NOUN
les **heures de pointe** _fem pl_
**in the rush hour**
aux heures de pointe
# **S s**
**Sabbath** NOUN
**1** le **dimanche** _masc (Christian)_
**2** le **sabbat** _masc (Jewish)_
**sack** NOUN
le **sac** _masc_
**sad** ADJECTIVE
**triste**
**saddle** NOUN
la **selle** _fem_
**sadly** ADVERB
**tristement**
**safe** ADJECTIVE
**1** **sans danger** _masc, fem, pl_
_(not dangerous)_
**Don't worry, it's perfectly safe.**
Ne vous inquiétez pas, c'est absolument sans danger.
**2** **sûr** _masc_
**sûre** _fem (secure)_
**Put it in a safe place.**
Mets-le en lieu sûr.
**safely** ADVERB
**The parcel arrived safely.**
Le paquet est bien arrivé.
**safety** NOUN
la **sécurité** _fem_
**said** VERB _see_ **say**
**sailing** NOUN
la **voile** _fem_
**His hobby is sailing.**
Son passe-temps, c'est la voile.
**to go sailing**
faire de la voile
**I'd like to go sailing.**
J'aimerais faire de la voile.
**sailing boat** NOUN
le **voilier** _masc_
**saint** NOUN
le **saint** _masc_
la **sainte** _fem_
**salad** NOUN
la **salade** _fem_
**Would you like some salad?**
Tu veux de la salade?
**salad cream** NOUN
la **mayonnaise** _fem_
**salad dressing** NOUN
la **vinaigrette** _fem_
**salary** NOUN
le **salaire** _masc_
**sale** NOUN
**'for sale'**
'à vendre'
**salmon** NOUN
le **saumon** _masc_
**salt** NOUN
le **sel** _masc_
**same**
**same** _can be an adjective or a pronoun._
**A** ADJECTIVE
**même**
**the same class**
la même classe
**at the same time**
en même temps
**We've got the same colour T-shirts.**
Noun avons des T-shirts de la même couleur.
**B** PRONOUN
**the same**
pareil
**They're exactly the same.**
Ils sont exactement pareils.
**It's not the same.**
Ça n'est pas pareil.
**_Language tip_**
_Use_ **pareille** _for something feminine._
**Our trainers are the same.**
Nos baskets sont pareilles.
**sand** NOUN
le **sable** _masc_
**sandal** NOUN
la **sandale** _fem_
**a pair of sandals**
une paire de sandales
**sand castle** NOUN
le **château de sable** _masc_
**sandwich** NOUN
le **sandwich** _masc_
**a cheese sandwich**
un sandwich au fromage
**sang** VERB _see_ **sing**
**Santa Claus** NOUN
le **père Noël** _masc_
_**Did you know...?**_
_In France, children don't leave anything for Santa to eat!_
**satchel** NOUN
le **cartable** _masc_
**My satchel is black.**
Mon cartable est noir.
**satisfied** ADJECTIVE
**satisfait** _masc_
**satisfaite** _fem_
**sat nav** NOUN
la **navigation par satellite** _fem_
**Saturday** NOUN
le **samedi** _masc_
**It's Saturday today.**
Aujourd'hui c'est samedi.
**I've got a Saturday job.**
Je travaille le samedi.
**on Saturday**
samedi
**on Saturdays**
le samedi
**every Saturday**
tous les samedis
**last Saturday**
samedi dernier
**next Saturday**
samedi prochain
**_Language tip_**
_Days of the week are not written with a capital letter in French._
**sauce** NOUN
la **sauce** _fem_
**saucepan** NOUN
la **casserole** _fem_
**saucer** NOUN
la **soucoupe** _fem_
**sausage** NOUN
la **saucisse** _fem_
**sausage and chips**
une saucisse-frites
**a sausage roll**
un friand à la saucisse
**save** VERB
**1** **mettre de l'argent de côté** _(save up)_
**I'm saving for a new bike.**
Je mets de l'argent de côté pour un nouveau vélo.
**2** **sauver** _(rescue)_
**He saved my life.**
Il m'a sauvé la vie.
**3** **sauvegarder** _(on computer)_
**I saved the file.**
J'ai sauvegardé le fichier.
**to save time**
gagner du temps
**It'll save time.**
Ça nous fera gagner du temps.
**save up** VERB
**mettre de l'argent de côté**
**I'm saving up for a new bike.**
Je mets de l'argent de côté pour un nouveau vélo.
**savoury** ADJECTIVE
**salé** _masc_
**salée** _fem_
**Is it sweet or savoury?**
C'est sucré ou salé?
**saw** VERB _see_ **see**
**say** VERB
**dire**
**I don't know how to say it in French.**
Je ne sais pas comment ça se dit en français.
**Say hello, Donald.**
Dis bonjour, Donald.
**Say hello, children.**
Dites bonjour, les enfants.
**What did you say?**
Qu'est-ce que tu as dit?
**I said no.**
J'ai dit non.
**How do you say 'Sorry' in French?**
Comment est-ce qu'on dit 'Sorry' en français?
**Say the words again, children.**
Répétez ces mots, les enfants.
**Say it after me, Aurélie.**
Répète après moi, Aurélie.
**Could you say that again, please?**
Pourriez-vous répéter s'il vous plaît?
**scampi** PL NOUN
les **scampi** _masc pl_
**scared** ADJECTIVE
**to be scared**
avoir peur
**I'm scared of dogs.**
J'ai peur des chiens.
**I'm scared!**
J'ai peur!
**scarf** NOUN
l' **écharpe** _fem_
**a hat and scarf**
un bonnet et une écharpe
**scary** ADJECTIVE
**effrayant** _masc_
**effrayante** _fem_
**It was really scary.**
C'était vraiment effrayant.
**scenery** NOUN
le **paysage** _masc_
**school** NOUN
l' **école** _fem_
**I love school.**
J'adore l'école.
**the school library**
la bibliothèque de l'école
**I go to school with Marc.**
Je vais à l'école avec Marc.
**at school**
à l'école
**schoolbag** NOUN
le **cartable** _masc_
**schoolboy** NOUN
l' **écolier** _masc_
**schoolchildren** NOUN
les **écoliers** _masc pl_
**schoolgirl** NOUN
l' **écolière** _fem_
**school holidays** PL NOUN
les **vacances scolaires** _fem pl_
**school uniform** NOUN
l' **uniforme scolaire** _masc_
_**Did you know...?**_
_French children don't wear school uniform._
**science** NOUN
la **science** _fem_
**scientist** NOUN
le **chercheur** _masc_
la **chercheuse** _fem_
**scissors** PL NOUN
les **ciseaux** _masc pl_
**a pair of scissors**
une paire de ciseaux
**scooter** NOUN
**1** la **trottinette** _fem (for children)_
**2** le **scooter** _masc (motorbike)_
**score**
**score** _can be a noun or a verb._
**A** NOUN
le **score** _masc_
**What's the score?**
Quel est le score?
**The score is three–nil.**
Le score est de trois à zéro.
**B** VERB
**1** **marquer** _(goal, point)_
**He scores lots of goals.**
Il marque beaucoup de buts.
**I scored a goal.**
J'ai marqué un but.
**2** **compter les points** _(keep score)_
**Who's going to score?**
Qui va compter les points?
**Scot** NOUN
l' **Écossais** _masc_
l' **Écossaise** _fem_
**Scotland** NOUN
l' **Écosse** _fem_
**Stirling is in Scotland.**
Stirling est en Écosse.
**When are you coming to Scotland?**
Quand est-ce que tu viens en Écosse?
**Tommy is from Scotland.**
Tommy est écossais.
**Elspeth is from Scotland.**
Elspeth est écossaise.
**in Scotland**
en Écosse
**to Scotland**
en Écosse
**I'm from Scotland.**
Je suis écossais.
**Scotsman** NOUN
l' **Écossais** _masc_
**Scotswoman** NOUN
l' **Écossaise** _fem_
**Scottish** ADJECTIVE
**écossais** _masc_
**écossaise** _fem_
**a Scottish accent**
un accent écossais
**_Language tip_**
**Scottish** _always has a capital letter, but_ **écossais** _doesn't._
**Scout** NOUN
le **scout** _masc_
**I'm in the Scouts.**
Je suis scout.
_**Did you know...?**_
_Guides and scouts are not as common in France as they are in Britain._
**scrambled eggs** PL NOUN
les **œufs brouillés** _masc pl_
**scrapbook** NOUN
l' **album** _masc_
**scream** VERB
**hurler**
**Simon says 'Scream!'**
Jacques a dit 'Hurlez!'
**screen** NOUN
l' **écran** _masc_
**sea** NOUN
la **mer** _fem_
**I live by the sea.**
J'habite au bord de la mer.
**seafood** NOUN
les **fruits de mer** _masc pl_
**seagull** NOUN
la **mouette** _fem_
**seashore** NOUN
le **bord de la mer** _masc_
**on the seashore**
au bord de la mer
**seasick** ADJECTIVE
**I get seasick.**
J'ai le mal de mer.
**seaside** NOUN
le **bord de la mer** _masc_
**at the seaside**
au bord de la mer
**season** NOUN
la **saison** _fem_
**What's your favourite season?**
Quelle est ta saison préférée?
**season ticket** NOUN
la **carte d'abonnement** _fem_
**seat** NOUN
le **siège** _masc_
**I'd like a seat by the window.**
Je voudrais un siège côté fenêtre.
**Go back to your seat, Michel!**
Retourne à ta place, Michel!
**second**
**second** _can be an adjective or a noun._
**A** ADJECTIVE
**deuxième**
**on the second page**
à la deuxième page
**I came second.**
Je suis arrivé deuxième.
**B** NOUN
la **seconde** _fem_
**It'll only take a second.**
Ça va prendre juste une seconde.
**the second of March**
le deux mars
**secondary school** NOUN
**1** le **collège** _masc (for pupils 11–15)_
**2** le **lycée** _masc (for pupils 15–18)_
_**Did you know...?**_
_In France, pupils go to a_ **collège** _between the ages of 11 and 15, and then to a_ **lycée** _until the age of 18._
**secret**
**secret** _can be a noun or an adjective._
**A** NOUN
le **secret** _masc_
**It's a secret.**
C'est un secret.
**Can you keep a secret?**
Tu sais garder un secret?
**in secret**
en secret
**B** ADJECTIVE
**secret** _masc_ **secrète** _fem_
**a secret passage**
un passage secret
**secretary** NOUN
le/la **secrétaire** _masc/fem_
**She's a secretary.**
Elle est secrétaire.
**_Language tip_**
_When you say what someone's job is in French, you do not translate_ **a**.
**secretly** NOUN
**secrètement**
**see** VERB
**voir**
**I can see her car.**
Je vois sa voiture.
**Can you see the difference?**
Est-ce que tu vois la différence?
**We're going to see Granny and Grandpa.**
On va voir Papi et Mamie.
**I saw Denis yesterday.**
J'ai vu Denis hier.
**Have you seen Pascal?**
Est-ce que tu as vu Pascal?
**See you!**
Salut!
**See you tomorrow!**
À demain!
**See you soon!**
À bientôt!
**seed** NOUN
la **graine** _fem_
**sunflower seeds**
des graines de tournesol
**seem** VERB
**There seems to be a problem.**
Il semble y avoir un problème.
**seen** VERB _see_ **see**
**seesaw** NOUN
le **tapecul** _masc_
**_Language tip_**
**tapecul** _is made up of the words_ **tape** _(meaning 'bang') and **cul** (meaning 'bottom'). This is what a seesaw sometimes does to you._
**selfish** ADJECTIVE
**égoïste**
**Don't be so selfish, Charles.**
Ne sois pas si égoïste, Charles.
**self-service** ADJECTIVE
**The café is self-service.**
Le café est un self-service.
**a self-service restaurant**
un self
**sell** VERB
**vendre**
**He's selling his car.**
Il vend sa voiture.
**The tickets are all sold out.**
Il ne reste plus de billets.
**_Language tip_**
_The English word 'vendor' is related to the French word_ **vendre**. _A vendor is someone who is selling something._
**Sellotape** ® NOUN
le **scotch** ® _masc_
**semicircle** NOUN
le **demi-cercle** _masc_
**Get into a semicircle.**
Mettez-vous en demi-cercle.
**semi-final** NOUN
la **demi-finale** _fem_
**send** VERB
**envoyer**
**I'm going to send Magali a postcard.**
Je vais envoyer une carte postale à Magali.
**Send me an email.**
Envoie-moi un e-mail.
**My penfriend has sent me some photos.**
Ma correspondante m'a envoyé des photos.
**senior** ADJECTIVE
**senior school**
le lycée
**sense** NOUN
**sense of humour**
le sens de l'humour
**Our teacher has a sense of humour.**
Notre prof a le sens de l'humour.
**He's got no sense of humour.**
Il n'a aucun sens de l'humour.
**sensible** ADJECTIVE
**raisonnable**
**Be sensible, Brigitte!**
Sois raisonnable, Brigitte!
**Be sensible, children!**
Soyez raisonnables, les enfants!
**_Language tip_**
**raisonnable** _is similar to the English word 'reasonable', but it has two **n** s. Can you see another difference?_
**sent** VERB _see_ **send**
**sentence** NOUN
la **phrase** _fem_
**What does this sentence mean?**
Que veut dire cette phrase?
**separate** ADJECTIVE
**a separate piece of paper**
une feuille différente
**Put the green cards in a separate pile.**
Fais une pile à part avec les cartes vertes.
**September** NOUN
**septembre** _masc_
**September or October?**
Septembre ou octobre?
**My birthday's in September.**
Mon anniversaire est en septembre.
**in September**
en septembre
**the fifth of September**
le cinq septembre
**_Language tip_**
_The months in French are not spelled with a capital letter._
**sequence** NOUN
l' **ordre** _masc_
**Put the pictures in sequence, Paul.**
Mets les images dans l'ordre, Paul.
**series** NOUN
la **série** _fem_
**a TV series**
une série télévisée
**serious** ADJECTIVE
**sérieux** _masc_
**sérieuse** _fem_
**You look very serious.**
Tu as l'air sérieux.
**Are you serious?**
Sérieusement?
**serve** VERB
**servir**
**They're serving lunch now.**
On sert le déjeuner en ce moment.
**It serves you right.**
C'est bien fait pour toi.
**service** NOUN
**1** le **service** _masc (in restaurant)_
**Service is included.**
Le service est compris.
**2** l' **office** _masc (in church)_
**service charge** NOUN
le **service** _masc_
**There's no service charge.**
Le service est compris.
**service station** NOUN
la **station-service** _fem_
**serviette** NOUN
la **serviette** _fem_
**set** VERB
**se coucher**
**The sun is setting.**
Le soleil se couche.
**to set the table**
mettre la table
**Could you set the table?**
Tu peux mettre la table?
**set off** VERB
**partir**
**What time are you setting off?**
À quelle heure tu pars?
**settee** NOUN
le **canapé** _masc_
**settle down** VERB
**Settle down, children!**
Du calme, les enfants!
**seven** NUMBER
**sept**
**seven euros**
sept euros
**She's seven.**
Elle a sept ans.
**_Language tip_**
_In English, you can say_ **seven** _or_ **seven years old**. _In French, you can only say_ **sept ans**.
**seventeen** NUMBER
**dix-sept**
**seventeen euros**
dix-sept euros
**He's seventeen.**
Il a dix-sept ans.
**_Language tip_**
_In English, you can say_ **seventeen** _or_ **seventeen years old**. _In French, you can only say_ **dix-sept ans**.
**seventeenth** ADJECTIVE
**dix-septième**
**on the seventeenth floor**
au dix-septième étage
**the seventeenth of August**
le dix-sept août
**seventh** ADJECTIVE
**septième**
**on the seventh floor**
au septième étage
**the seventh of August**
le sept août
**seventy** NUMBER
**soixante-dix**
**_Language tip_**
_The French word consists of two numbers, what are they?_
**several** PRONOUN
**plusieurs**
**Several children are absent.**
Plusieurs enfants sont absents.
**sewing** NOUN
la **couture** _fem_
**I like sewing.**
J'aime faire de la couture.
**shade** NOUN
l' **ombre** _fem_
**It was 35 degrees in the shade.**
Il faisait trente-cinq à l'ombre.
**shadow** NOUN
l' **ombre** _fem_
**shake** VERB
**to shake hands with somebody**
serrer la main à quelqu'un
**Simon says 'Shake hands with your best friend!'**
Jacques a dit 'Serrez la main à votre meilleur ami!'
**French people shake hands a lot.**
Les Français se serrent beaucoup la main.
_**Did you know...?**_
_French boys shake hands with their friends when they arrive at school in the morning._
**shall** VERB
**Shall I shut the window?**
Je ferme la fenêtre?
**Shall I go first?**
Je commence?
**Shall I put the light on?**
J'allume?
**_Language tip_**
_To ask if you should do something, you can make a question by changing your tone of voice. Try it!_
**shame** NOUN
**What a shame! She can't come!**
Quel dommage! Elle ne peut pas venir!
**What a shame!**
Quel dommage!
**shampoo** NOUN
le **shampooing** _masc_
**a bottle of shampoo**
une bouteille de shampooing
**shape** NOUN
la **forme** _fem_
**share** VERB
**partager**
**I share a room with Léa.**
Je partage ma chambre avec Léa.
**sharp** ADJECTIVE
**coupant** _masc_
**coupante** _fem_
**Be careful, it's sharp.**
Attention, c'est coupant.
**she** PRONOUN
**elle**
**She's very nice.**
Elle est très gentille.
**sheep** NOUN
le **mouton** _masc_
**sheet** NOUN
le **drap** _masc_
**clean sheets**
des draps propres
**a sheet of paper**
une feuille de papier
**shelf** NOUN
l' **étagère** _fem_
**shell** NOUN
le **coquillage** _masc_
**shelves** PL NOUN
les **étagères** _fem pl_
**she's** = **she is, she has**
**Shetland Islands**
PL NOUN
les **îles Shetland** _fem pl_
**shine** VERB
**briller**
**The sun is shining.**
Le soleil brille.
**_Language tip_**
_The French word **briller** is related to the English word 'brilliant', which can describe something that shines brightly._
**ship** NOUN
le **bateau** _masc_ (PL les **bateaux** )
**shirt** NOUN
**1** la **chemise** _fem (man's)_
**a white shirt**
une chemise blanche
**2** le **maillot** _masc (footballer's)_
**shocking** ADJECTIVE
**choquant** _masc_
**choquante** _fem_
**It's shocking!**
C'est choquant!
**shoe** NOUN
la **chaussure** _fem_
**I've got new shoes.**
J'ai de nouvelles chaussures.
**shoe shop** NOUN
le **magasin de chaussures** _masc_
**shooting** NOUN
la **chasse** _fem_
**He goes shooting.**
Il va à la chasse.
**shop** NOUN
le **magasin** _masc_
**The shop is shut.**
Le magasin est fermé.
**a sports shop**
un magasin de sports
**shop assistant** NOUN
le **vendeur** _masc_
la **vendeuse** _fem_
**She's a shop assistant.**
Elle est vendeuse.
**_Language tip_**
_You do not translate_ **'a'** _when you say what someone's job is in French._
**shopkeeper** NOUN
le **commerçant** _masc_
la **commerçante** _fem_
**shopping** NOUN
les **courses** _fem pl_
**Can you get the shopping from the car?**
Tu peux aller chercher les courses dans la voiture?
**_Language tip_**
_If you're shopping for food, you say_ **Je fais les courses**. _If you're looking round the shops, you say_ **Je fais les magasins**.
_**Did you know...?**_
_In Quebec, you can say_ **Je magasine** _whether you are shopping for food or looking round the shops._
**I do the shopping for my granny.**
Je fais les courses pour ma grand-mère.
**I go shopping with my friends.**
Je fais les magasins avec mes amies.
**shopping bag** NOUN
le **sac à provisions** _masc_
**shopping centre** NOUN
le **centre commercial** _masc_
**short** ADJECTIVE
**1** **court** _masc_
**courte** _fem (in length)_
**a short skirt**
une jupe courte
**short hair**
les cheveux courts
**2** **petit** _masc_
**petite** _fem (in time)_
**a short walk**
une petite promenade
**shorts** PL NOUN
le **short** _masc_
**My shorts are green.**
Mon short est vert.
**a pair of shorts**
un short
**_Language tip_**
**short** _is a singular word in French._
**short-sighted** ADJECTIVE
**myope**
**shoulder** NOUN
l' **épaule** _fem_
**should** VERB
**You should try it.**
Tu devrais essayer.
**You shouldn't do that.**
Tu ne devrais pas faire ça.
**shout** VERB
**crier**
**Don't shout, children!**
Ne criez pas, les enfants!
**show** VERB
**montrer**
**Show me!**
Montrez-moi!
**Shall I show you the photos?**
Je te montre les photos?
**shower** NOUN
la **douche** _fem_
**I'm going to have a shower.**
Je vais prendre une douche.
**Shrove Tuesday** NOUN
le **mardi gras** _masc_
_**Did you know...?**_
**Shrove Tuesday** _is the same as_ **Pancake Day** _and is celebrated in France as well. French children dress up and eat pancakes_ ( **crêpes** ).
**shrug** VERB
**Simon says 'Shrug your shoulders!'**
Jacques a dit 'Haussez les épaules!'
**shuffle** VERB
**You have to shuffle the cards.**
Il faut battre les cartes.
**shut**
**shut** _can be a verb or an adjective._
**A** VERB
**fermer**
**Shut your books, children.**
Fermez vos livres, les enfants.
**Open your mouth and shut your eyes.**
Ouvre la bouche et ferme les yeux.
**What time do the shops shut?**
Les magasins ferment à quelle heure?
**Shut up!**
Tais-toi!
**B** ADJECTIVE
**fermé** _masc_
**fermée** _fem_
**The door is shut.**
La porte est fermée.
**The shop is shut.**
Le magasin est fermé.
**shutters** PL NOUN
les **volets** _masc pl_
**shy** ADJECTIVE
**timide**
**sick** ADJECTIVE
**malade**
**He is sick.**
Il est malade.
**to be sick**
vomir
**I'm going to be sick.**
Je vais vomir.
**I feel sick.**
J'ai envie de vomir.
**side** NOUN
**1** le **côté** _masc (of object, building, car)_
**on this side**
de ce côté
**It's on this side of the street.**
C'est de ce côté de la rue.
**It's on the other side.**
C'est de l'autre côté.
**2** l' **équipe** _fem (team)_
**He's on my side.**
Il est dans mon équipe.
**sightseeing** NOUN
le **tourisme**
_masc_
**We're going to go sightseeing.**
Nous allons faire du tourisme.
**sign**
**sign** _can be a noun or a verb._
**A** NOUN
**a road sign**
un panneau
**B** VERB
**signer**
**Sign here, please.**
Signez ici, s'il vous plaît.
**signal** NOUN
le **signal** _masc_ (PL les **signaux** )
**signature** NOUN
la **signature** _fem_
**sign language** NOUN
le **langage des signes** _masc_
**silence** NOUN
le **silence** _masc_
**silent** ADJECTIVE
**silencieux** _masc_
**silencieuse** _fem_
**silk** ADJECTIVE
**en soie**
**a silk scarf**
un foulard en soie
**silly** ADJECTIVE
**bête**
**Don't be silly, Nadège!**
Ne sois pas bête, Nadège!
**silver**
**silver** _can be a noun or an adjective._
**A** NOUN
l' **argent** _masc_
**gold and silver**
l'or et l'argent
**B** ADJECTIVE
**en argent**
**a silver chain**
une chaîne en argent
**a silver medal**
une médaille d'argent
**Simon says** NOUN
**Jacques a dit**
**simple** ADJECTIVE
**simple**
**It's very simple.**
C'est très simple.
**since** PREPOSITION
**depuis**
**since Christmas**
depuis Noël
**since then**
depuis ce moment-là
**sincerely**
**Yours sincerely...**
Cordialement...
**sing** VERB
**chanter**
**I sing in the choir.**
Je chante dans la chorale.
**Sing everyone!**
Allez, chantez!
**singer** NOUN
le **chanteur** _masc_
la **chanteuse** _fem_
**single**
**single** _can be an adjective or a noun._
**A** ADJECTIVE
**a single room**
une chambre pour une personne
**B** NOUN
l' **aller simple** _masc (ticket)_
**A single to Toulouse, please.**
Un aller simple pour Toulouse, s'il vous plaît.
**singular** NOUN
le **singulier** _masc_
**in the singular**
au singulier
**sink** NOUN
l' **évier** _masc_
**sir** NOUN
**monsieur** _masc_
**Yes sir.**
Oui, monsieur.
**sister** NOUN
la **sœur** _fem_
**my little sister**
ma petite sœur
**I've got one sister.**
J'ai une sœur.
**I haven't got a sister.**
Je n'ai pas de sœur.
**Have you got any brothers or sisters?**
Tu as des frères et sœurs?
**sit** VERB
**s'asseoir**
**I want to sit beside my friend.**
Je veux m'asseoir à côté de mon amie.
**Can I sit here?**
Je peux m'asseoir ici?
**Jean-Pierre sits next to Christelle.**
Jean-Pierre s'assoit à côté de Christelle.
**sit down** VERB
**s'asseoir**
**Sit down, Mathilde.**
Assieds-toi, Mathilde.
**You can sit down now, Mathieu.**
Tu peux t'asseoir maintenant, Mathieu.
**Sit down, children.**
Asseyez-vous, les enfants.
**site** NOUN
**1** le **camping** _masc (campsite)_
**2** le **site web** _masc (website)_
**sitting room** NOUN
le **salon** _masc_
**situation** NOUN
la **situation** _fem_
**six** NUMBER
**six**
**six euros**
six euros
**She's six.**
Elle a six ans.
**_Language tip_**
_In English, you can say_ **six** _or_ **six years old**. _In French, you can only say_ **six ans**.
**sixteen** NUMBER
**seize**
**sixteen euros**
seize euros
**He's sixteen.**
Il a seize ans.
**_Language tip_**
_In English, you can say_ **sixteen** _or_ **sixteen years old**. _In French, you can only say_ **seize ans**.
**sixteenth** ADJECTIVE
**seizième**
**on the sixteenth floor**
au seizième étage
**the sixteenth of August**
le seize août
**sixth** ADJECTIVE
**sixième**
**on the sixth floor**
au sixième étage
**the sixth of August**
le six août
**sixth form** NOUN
le **lycée** _masc_
**sixty** NUMBER
**soixante**
**My aunt is sixty.**
Ma tante a soixante ans.
**_Language tip_**
_In English, you can say_ **sixty** _or_ **sixty years old**. _In French, you can only say_ **soixante ans**.
**size** NOUN
la **taille** _fem_
**It's the right size.**
C'est la bonne taille.
**skate** VERB
**faire du patin à glace**
**I like to skate.**
J'aime faire du patin à glace.
**skateboard** NOUN
le **skateboard** _masc_
**skateboarding** NOUN
le **skateboard** _masc_
**I like skateboarding.**
J'aime le skateboard.
**I go skateboarding with Kieran.**
Je fais du skateboard avec Kieran.
**skating** NOUN
le **patin à glace** _masc_
**I like skating.**
J'aime le patin à glace.
**I go skating.**
Je fais du patin à glace.
**skeleton** NOUN
le **squelette** _masc_
**ski**
**ski** _can be a verb or a noun._
**A** VERB
**skier**
**Can you ski?**
Tu sais skier?
**B** NOUN
le **ski** _masc_
**ski boots** PL NOUN
les **chaussures de ski** _fem pl_
**ski lift** NOUN
le **remonte-pente** _masc_
**ski slope** NOUN
la **piste de ski** _fem_
**skiing** NOUN
le **ski** _masc_
**Do you like skiing?**
Tu aimes le ski?
**I'd like to go skiing.**
J'aimerais faire du ski.
**I'm going on a skiing holiday.**
Je vais aux sports d'hiver.
**skin** NOUN
la **peau** _fem_
**skinny** ADJECTIVE
**maigre**
**skipping rope** NOUN
la **corde à sauter** _fem_
**skirt** NOUN
la **jupe** _fem_
**a black skirt**
une jupe noire
**sky** NOUN
le **ciel** _masc_
**The sky is blue.**
Le ciel est bleu.
**slam** VERB
**claquer**
**Don't slam the door.**
Ne claque pas la porte.
**sledge** NOUN
la **luge** _fem_
**sledging** NOUN
**Let's go sledging!**
Allons faire de la luge!
**sleep** VERB
**dormir**
**My cat sleeps in a box.**
Mon chat dort dans une boîte.
**Did you sleep well, Cyril?**
Tu as bien dormi, Cyril?
**sleeping bag** NOUN
le **sac de couchage** _masc_
**sleepover** NOUN
**My friend is coming for a sleepover tonight.**
Mon amie vient dormir chez moi ce soir.
**We're going to Jasmine's for a sleepover.**
On va dormir chez Jasmine.
**sleepy** ADJECTIVE
**I'm sleepy.**
J'ai sommeil.
**sleeve** NOUN
la **manche** _fem_
**a shirt with long sleeves**
une chemise à manches longues
**a shirt with short sleeves**
une chemise à manches courtes
**slice** NOUN
la **tranche** _fem_
**slide** NOUN
**1** le **toboggan** _masc (in playground)_
**2** la **barrette** _fem (hair slide)_
**3** la **diapositive** _fem (photo)_
**slight** ADJECTIVE
**léger** _masc_
**légère** _fem_
**a slight problem**
un léger problème
**slightly** ADVERB
**légèrement**
**slim**
**slim** _can be an adjective or a verb._
**A** ADJECTIVE
**mince**
**You're slim!**
Tu es mince!
**B** VERB
**faire un régime** _(be on a diet)_
**I'm slimming.**
Je fais un régime.
**slipper** NOUN
le **chausson** _masc_
**a pair of slippers**
des chaussons
**slow** ADJECTIVE
**lent** _masc_
**lente** _fem_
**The music is too slow.**
La musique est trop lente.
**slowly** ADVERB
**lentement**
**Could you speak more slowly?**
Vous pouvez parler plus lentement?
**smack** NOUN
la **tape** _fem_
**small** ADJECTIVE
**petit** _masc_
**petite** _fem_
**smart** ADJECTIVE
**1** **chic** _masc, fem, pl_
**smart clothes**
des vêtements chic
**2** **intelligent** _masc_
**intelligente** _fem (clever)_
**She's very smart.**
Elle est très intelligente.
**smart phone** NOUN
le **smartphone** _masc_
**smell**
**smell** _can be a noun or a verb._
**A** NOUN
l' **odeur** _fem_
**a nice smell**
une bonne odeur
**B** VERB
**sentir**
**Mmm, that smells nice!**
Mmm, ça sent bon!
**smile**
**smile** _can be a noun or a verb._
**A** NOUN
le **sourire** _masc_
**a beautiful smile**
un beau sourire
**B** VERB
**sourire**
**Why are you smiling?**
Pourquoi tu souris?
**smiley** NOUN
le **smiley** _masc_
**smoke** VERB
**fumer**
**I don't smoke.**
Je ne fume pas.
**smoking** NOUN
**Smoking is bad for you.**
Le tabac est mauvais pour la santé.
**'no smoking'**
'défense de fumer'
**smoothie** NOUN
la **boisson frappée aux fruits** _fem_
**snack** NOUN
le **casse-croûte** _masc_
**You can get a snack in the canteen.**
On peut s'acheter un casse-croûte à la cantine.
**snack bar** NOUN
le **snack-bar** _masc_
**snail** NOUN
l' **escargot** _masc_
**snake** NOUN
le **serpent** _masc_
**snooker** NOUN
le **billard** _masc_
**I play snooker.**
Je joue au billard.
**snow**
**snow** _can be a noun or a verb._
**A** NOUN
la **neige** _fem_
**B** VERB
**neiger**
**It's going to snow.**
Il va neiger.
**It snows a lot in the mountains.**
Il neige beaucoup à la montagne.
**It's snowing.**
Il neige.
**snowball** NOUN
la **boule de neige** _fem_
**lots of snowballs**
beaucoup de boules de neige
**snowboarding** NOUN
le **snowboard** _masc_
**I like snowboarding.**
J'aime faire du snowboard.
**snowflake** NOUN
le **flocon de neige** _masc_
**snowman** NOUN
le **bonhomme de neige** _masc_
**I'm going to make a snowman.**
Je vais faire un bonhomme de neige.
**so**
**so** _can be an adverb or a conjunction._
**A** ADVERB
**1** **si**
**Don't eat so fast!**
Ne mange pas si vite!
**2** **tellement** _(too)_
**You talk so fast.**
Tu parles tellement vite.
**It's so difficult.**
C'est tellement difficile.
**I love you so much.**
Je t'aime tellement.
**B** CONJUNCTION
**alors**
**It's Luc's birthday, so I've got him a present.**
C'est l'anniversaire de Luc, alors je lui ai acheté un cadeau.
**so do I**
moi aussi
**so have I**
moi aussi
**so am I**
moi aussi
**I think so.**
Je crois.
**I hope so.**
J'espère bien.
**soap** NOUN
le **savon** _masc_
**soccer** NOUN
le **football** _masc_
**sock** NOUN
la **chaussette** _fem_
**I'm wearing white socks.**
Je porte des chaussettes blanches.
**sofa** NOUN
le **canapé** _masc_
**soft** ADJECTIVE
**1** **doux** _masc_
**douce** _fem (voice, texture)_
**2** **mou** _masc_
**molle** _fem (pillow, bed, ball)_
**soft drink** NOUN
la **boisson non alcoolisée** _fem_
**soil** NOUN
la **terre** _fem_
**sold** ADJECTIVE
**vendu** _masc_
**vendue** _fem_
**soldier** NOUN
le **soldat** _masc_
**He's a soldier.**
Il est soldat.
**_Language tip_**
_You do not translate_ **'a'** _when you say what someone's job is in French._
**some**
**some** _can be an adjective or a pronoun._
**A** ADJECTIVE
**1** _(a certain amount of)_
**_Language tip_**
**Some** _can be_ **du** , **de la** , **de l'** _and_ **des** _in the same way that_ **the** _can be_ **le** , **la** , **l'** _or_ **les**.
**du**
**Would you like some bread?**
Voulez-vous du pain?
**de la**
**Would you like some soup?**
Voulez-vous de la soupe?
**de l'**
**Have you got some mineral water?**
Avez-vous de l'eau minérale?
**des**
**I've got some sweets.**
J'ai des bonbons.
**2** **des** _(certain)_
**Some children are absent.**
Il y a des enfants absents.
**B** PRONOUN
**1** **certains** _masc pl_
**certaines** _fem pl (certain ones)_
**some of my friends**
certains de mes amis
**Have you got all her books? — I've got some.**
Tu as tous ses livres? — J'en ai certains.
**2** **quelques-uns** _masc pl_
**quelques-unes**
_fem pl (some, not all)_
**I've got some, but not many.**
J'en ai quelques-uns, mais pas beaucoup.
**3** **en**
**_Language tip_**
_The word_ **en** _can mean 'some of them', or 'some of it'. Notice its position in sentences._
**Chips? — No thanks, I've got some.**
Des frites? — Non merci, j'en ai déjà.
**I've got a bar of chocolate.
Do you want some?**
J'ai une barre de chocolat. Tu en veux?
**I've got some.**
J'en ai.
**Would you like some?**
Tu en veux?
**somebody** PRONOUN
**quelqu'un**
**Somebody is going to win £100!**
Quelqu'un va gagner cent livres!
**someone** PRONOUN
**quelqu'un**
**Someone is going to win £100!**
Quelqu'un va gagner cent livres!
**something** PRONOUN
**quelque chose**
**Are you looking for something?**
Tu cherches quelque chose?
**something special**
quelque chose de spécial
**something hot**
quelque chose de chaud
**I can see something green.**
Je vois quelque chose de vert.
**sometimes** ADVERB
**quelquefois**
**sometimes, but not very often**
quelquefois, mais pas très souvent
**somewhere** ADVERB
**quelque part**
**It's somewhere in the classroom.**
C'est quelque part dans la classe.
**son** NOUN
le **fils** _masc_
**her son**
son fils
**song** NOUN
la **chanson** _fem_
**We're going to sing a song.**
Nous allons chanter une chanson.
**I know some French songs.**
Je connais des chansons françaises.
**soon** ADVERB
**bientôt**
**It'll soon be lunchtime.**
C'est bientôt l'heure du déjeuner.
**very soon**
très bientôt
**as soon as possible**
aussitôt que possible
**Write soon!**
Écris-moi vite!
**sorcerer** NOUN
le **sorcier** _masc_
**sore** ADJECTIVE
**It's sore.**
Ça fait mal.
**My head is sore.**
J'ai mal à la tête.
**sorry** ADJECTIVE
**désolé** _masc_
**désolée** _fem_
**I'm really sorry.**
Je suis vraiment désolé.
**I'm sorry I'm late.**
Je suis désolé d'être en retard.
**I'm sorry, I can't.**
Je suis désolé, je ne peux pas.
**sorry!**
pardon!
**sort** NOUN
la **sorte** _fem_
**What sort of bike have you got?**
Quelle sorte de vélo as-tu?
**sound**
**sound** _can be a noun or a verb._
**A** NOUN
**1** le **bruit** _masc (noise)_
**Don't make a sound!**
Pas un bruit!
**2** le **son** _masc (volume)_
**Can I turn the sound down?**
Je peux baisser le son?
**B** VERB
**That sounds interesting.**
Ça a l'air intéressant.
**That sounds like a good idea.**
C'est une bonne idée.
**soup** NOUN
la **soupe** _fem_
**vegetable soup**
la soupe aux légumes
**sour** ADJECTIVE
**aigre**
**south**
**south** _can be an adjective or a noun._
**A** ADJECTIVE
**sud** _masc, fem, pl_
**the south coast**
la côte sud
**B** NOUN
le **sud** _masc_
**in the south**
dans le sud
**the South of France**
le sud de la France
**Arles is in the South of France.**
Arles est dans le sud de la France.
**southern** ADJECTIVE
**Southern England**
le sud de l'Angleterre
**South Pole** NOUN
le **pôle Sud** _masc_
**South Wales** NOUN
le **sud du Pays de Galles** _masc_
**souvenir** NOUN
le **souvenir** _masc_
**a souvenir shop**
une boutique de souvenirs
**space** NOUN
**1** la **place** _fem (room)_
**There's lots of space.**
Il y a beaucoup de place.
**2** l' **espace** _masc (gap)_
**Leave a space for a picture.**
Laissez un espace pour le dessin.
**3** la **case** _fem (in game)_
**Go back three spaces.**
Recule de trois cases.
**4** l' **espace** _masc (outer space)_
**spaceship** NOUN
le **vaisseau spatial** _masc_
**spade** NOUN
**1** la **pelle** _fem (shovel)_
**a bucket and spade**
un seau et une pelle
**2** _(in cards)_
**spades**
le pique
**the ace of spades**
l'as de pique
**Spain** NOUN
l' **Espagne** _fem_
**Spanish**
**Spanish** _can be an adjective or a noun._
**A** ADJECTIVE
**espagnol** _masc_ **espagnole** _fem_
**He's Spanish.**
Il est espagnol.
**She's Spanish.**
Elle est espagnole.
**B** NOUN
l' **espagnol** _masc (language)_
**_Language tip_**
**Spanish** _always has a capital letter, but_ **espagnol** _doesn't._
**spare room** NOUN
la **chambre d'amis** _fem_
**spare time** NOUN
le **temps libre** _masc_
**What do you do in your spare time?**
Qu'est-ce que tu fais pendant ton temps libre?
**sparkling** ADJECTIVE
**pétillant** _masc_
**pétillante** _fem_
**a bottle of sparkling water**
une bouteille d'eau pétillante
**sparkling wine**
le mousseux
**speak** VERB
**parler**
**Please could you speak more slowly.**
Vous pouvez parler plus lentement, s'il vous plaît?
**I speak French.**
Je parle français.
**Do you speak English?**
Est-ce que vous parlez anglais?
**special** ADJECTIVE
**spécial** _masc_
**spéciale** _fem_
**speciality** NOUN
la **spécialité** _fem_
**specially** ADVERB
**surtout**
**It rains a lot, specially in winter.**
Il pleut beaucoup, surtout en hiver.
**spectator** NOUN
le **spectateur** _masc_
la **spectatrice** _fem_
**speech** NOUN
le **discours** _masc_
**speed** NOUN
la **vitesse** _fem_
**a ten-speed bike**
un vélo à dix vitesses
**speedboat** NOUN
la **vedette** _fem_
**spell** VERB
**1** **écrire** _(in writing)_
**How do you spell that?**
Comment ça s'écrit?
**_Language tip_**
_You can also say_ **Ça s'écrit comment?** _or_ **Comment est-ce que ça s'écrit?**
**2** **épeler** _(out loud)_
**Can you spell that please?**
Est-ce que vous pouvez l'épeler, s'il vous plaît?
**spelling** NOUN
l' **orthographe** _fem_
**a spelling mistake**
une faute d'orthographe
**spend** VERB
**1** **dépenser** _(money)_
**I spent £20 on presents.**
J'ai dépensé vingt livres en cadeaux.
**2** **passer** _(time)_
**We are going to spend two weeks in France.**
Nous allons passer deux semaines en France.
**spicy** ADJECTIVE
**épicé** _masc_
**épicée** _fem_
**spider** NOUN
l' **araignée** _fem_
**spinach** NOUN
les **épinards** _masc pl_
**spite** NOUN
**in spite of**
malgré
**in spite of the weather**
malgré le temps
**split** VERB
**1** **se séparer** _(divide)_
**Split into two groups.**
Séparez-vous en deux groupes.
**2** **partager** _(share)_
**Let's split the money between us.**
Partageons l'argent entre nous.
**spoiled** ADJECTIVE
**gâté** _masc_
**gâtée** _fem_
**a spoiled child**
un enfant gâté
**spoilsport** NOUN
le/la **trouble-fête** _masc, fem, pl_
**Don't be a spoilsport!**
Ne joue pas les trouble-fête!
**spoilt** ADJECTIVE
**gâté** _masc_
**gâtée** _fem_
**a spoilt child**
un enfant gâté
**sponge** NOUN
l' **éponge** _fem_
**sponge bag** NOUN
la **trousse de toilette** _fem_
**sponge cake** NOUN
le **biscuit de Savoie** _masc_
**sponsor** VERB
**parrainer**
**Twenty people are sponsoring me.**
Vingt personnes me parrainent.
_**Did you know...?**_
_Getting sponsored for charity is not very common in France._
**spoon** NOUN
la **cuillère** _fem_
**I haven't got a spoon.**
Je n'ai pas de cuillère.
**sport** NOUN
le **sport** _masc_
**What's your favourite sport?**
Quel est ton sport préféré?
**It's my favourite sport.**
C'est mon sport préféré.
**What sports do you play?**
Qu'est-ce que tu fais comme sport?
**sports bag** NOUN
le **sac de sport** _masc_
**sports car** NOUN
la **voiture de sport** _fem_
**spot**
**spot** _can be a noun or a verb._
**A** NOUN
**1** le **pois** _masc (dot)_
**a red dress with white spots**
une robe rouge à pois blancs
**2** le **bouton** _masc (pimple)_
**He's covered in spots.**
Il est couvert de boutons.
**B** VERB
**trouver**
**Can you spot the odd one out?**
Trouvez-vous l'intrus?
**spring** NOUN
le **printemps** _masc_
**It's the first day of spring.**
C'est le premier jour du printemps.
**in spring**
au printemps
**springtime** NOUN
le **printemps** _masc_
**in springtime**
au printemps
**sprouts** PL NOUN
les **choux de Bruxelles** _masc pl_
**square** NOUN
**1** le **carré** _masc (shape)_
**a square and a triangle**
un carré et un triangle
**2** la **place** _fem (in town)_
**There's a statue in the middle of the square.**
Il y a une statue au centre de la place.
**squash** NOUN
**1** _(drink)_ **orange squash**
l'orangeade _fem_
**2** le **squash** _masc (sport)_
**I play squash.**
Je joue au squash.
**squirrel** NOUN
l' **écureuil** _masc_
**stable** NOUN
l' **écurie** _fem_
**stack** NOUN
la **pile** _fem_
**a stack of books**
une pile de livres
**stadium** NOUN
le **stade** _masc_
**staff** NOUN
**1** les **profs** _masc pl (in school)_
**staffroom** NOUN
la **salle des profs** _fem_
**staircase** NOUN
l' **escalier** _masc_
**stairs** PL NOUN
l' **escalier** _masc_
**Go down the stairs.**
Descends l'escalier.
**_Language tip_**
**escalier** _is a singular word._
**stamp**
**stamp** _can be a noun or a verb._
**A** NOUN
le **timbre** _masc_
**a French stamp**
un timbre français
**My hobby is stamp collecting.**
Je collectionne les timbres.
**B** VERB
**taper du pied**
**Stamp your feet, everybody!**
Tapez des pieds, tout le monde!
**stamp album** NOUN
l' **album de timbres** _masc_
**stamp collection** NOUN
la **collection de timbres** _fem_
**stand** VERB
**Stand in a line.**
Mettez-vous en rang.
**Stand over there, Alain.**
Mets-toi là, Alain.
**stand for** VERB
**être l'abréviation de**
**'SVP' stands for 's'il vous plaît'.**
'SVP' est l'abréviation de 's'il vous plaît'.
**_Language tip_**
_What are the two differences in the spelling of the French word_ **abréviation** _and the English word_ **abbreviation**?
**stand up** VERB
**se lever**
**Stand up, Élodie!**
Lève-toi, Élodie!
**Stand up, children!**
Levez-vous, les enfants!
**star** NOUN
**1** l' **étoile** _fem (in sky)_
**the moon and the stars**
la lune et les étoiles
**2** la **vedette** _fem (person)_
**He's a TV star.**
C'est une vedette de la télé.
**start**
**start** _can be a verb or a noun._
**A** VERB
**1** **commencer** _(begin)_
**What time does it start?**
Ça commence à quelle heure?
**It starts with a P.**
Ça commence par un P.
**I'll start again.**
Je recommence.
**_Language tip_**
_When_ **start** _is followed by another verb it is translated by_ **commencer à**.
**Let's start playing.**
On commence à jouer.
**You can start writing now.**
Vous pouvez commencer à écrire maintenant.
**Don't start being silly, Anne.**
Ne commence pas à faire l'imbécile, Anne.
**Let's start.**
On commence.
**Start now, children.**
Commencez maintenant, les enfants.
**Fleur, you start.**
Commence, Fleur.
**2** **créer** _(set up)_
**We want to start a French club.**
On veut créer un club de français.
**B** NOUN
**1** le **début** _masc_
**at the start of December**
début décembre
**Shall we make a start?**
On commence?
**2** le **départ** _masc (of race)_
**starter** NOUN
l' **entrée** _fem_
**starve** VERB
**I'm starving!**
Je meurs de faim!
**station** NOUN
la **gare** _fem_
**Where is the station?**
Où est la gare?
**statue** NOUN
la **statue** _fem_
**stay**
**stay** _can be a verb or a noun._
**A** VERB
**1** **rester** _(remain)_
**Stay here, Michelle!**
Reste ici, Michelle!
**Stay in the garden, children.**
Restez dans le jardin, les enfants.
**2** **loger** _(spend the night)_
**We're going to stay with friends.**
Nous allons loger chez des amis.
**Where are you staying?**
Où est-ce que vous logez?
**We stayed in Paris for three days.**
Nous avons passé trois jours à Paris.
**B** NOUN
le **séjour** _masc_
**my stay in France**
mon séjour en France
**stay in** VERB
**rester à la maison**
**I'm staying in tonight.**
Ce soir je reste à la maison.
**steak** NOUN
le **steak** _masc_
**I'd like steak and chips.**
Je voudrais un steak frites.
**steal** VERB
**voler**
**Who's stolen my pencil case?**
Qui a volé ma trousse?
**step** NOUN
**1** le **pas** _masc (pace)_
**a step backwards**
un pas en arrière
**Take a step forward, boys.**
Faites un pas en avant, les garçons.
**2** la **marche** _fem (stair)_
**Mind the step.**
Attention à la marche.
**stepbrother** NOUN
le **demi-frère** _masc_
**his stepbrother**
son demi-frère
**stepfather** NOUN
le **beau-père** _masc_
**my stepfather**
mon beau-père
**stepmother** NOUN
la **belle-mère** _fem_
**my stepmother**
ma belle-mère
**stepsister** NOUN
la **demi-sœur** _fem_
**her stepsister**
sa demi-sœur
**stew** NOUN
le **ragoût** _masc_
**stewardess** NOUN
l' **hôtesse de l'air** _fem_
**stick** VERB
**coller**
**Stick the stamps on the envelope.**
Collez les timbres sur l'enveloppe.
**stick out** VERB
**Don't stick out your tongue!**
Ne tire pas la langue!
**sticker** NOUN
l' **autocollant** _masc_
**still**
**still** _can be an adverb or an adjective._
**A** ADVERB
**encore**
**You've still got two cards.**
Tu as encore deux cartes.
**I'm still hungry.**
J'ai encore faim.
**B** ADJECTIVE
**Keep still, Charlotte!**
Ne bouge pas, Charlotte!
**Sit still, David!**
Reste tranquille, David!
**stitch** NOUN
le **point de suture** _masc_
**I've got five stitches.**
J'ai cinq points de suture.
**stomach** NOUN
l' **estomac** _masc_
**stomachache** NOUN
**I've got stomachache.**
J'ai mal au ventre.
**stone** NOUN
**1** la **pierre** _fem (rock)_
**a stone wall**
un mur en pierre
**2** _(in weight)_
**I weigh five stone.**
Je pèse trente kilos.
_**Did you know...?**_
_In France, weight is always given in kilos. A stone is about 6.3 kg._
**stool** NOUN
le **tabouret** _masc_
**stop**
**stop** _can be a verb or a noun._
**A** VERB
**arrêter**
**Stop, that's enough!**
Arrête, ça suffit!
**Stop talking, children.**
Arrêtez de parler, les enfants.
**Stop it!**
Arrête!
**B** NOUN
l' **arrêt** _masc_
**a bus stop**
un arrêt de bus
**storey** NOUN
l' **étage** _masc_
**a three-storey building**
un immeuble à trois étages
**storm** NOUN
**1** la **tempête** _fem (with strong winds)_
**2** l' **orage** _masc (thunderstorm)_
**stormy** ADJECTIVE
**stormy weather**
un temps orageux
**story** NOUN
l' **histoire** _fem_
**I'm going to tell you a story.**
Je vais vous raconter une histoire.
**stove** NOUN
la **cuisinière** _fem_
**straight**
**straight** _can be an adjective or an adverb._
**A** ADJECTIVE
**droit** _masc_
**droite** _fem_
**a straight line**
une ligne droite
**2** **raide** _(hair)_
**I've got straight hair.**
J'ai les cheveux raides.
**B** ADVERB
**straight away**
tout de suite
**straight on**
tout droit
**Go straight on.**
Allez tout droit.
**strange** ADJECTIVE
**bizarre**
**That's strange!**
C'est bizarre!
**stranger** NOUN
l' **inconnu** _masc_
l' **inconnue** _fem_
**Don't talk to strangers.**
Ne parle pas aux inconnus.
**I'm a stranger here.**
Je ne suis pas d'ici.
**strap** NOUN
le **bracelet** _masc_
**I need a new strap for my watch.**
J'ai besoin d'un nouveau bracelet pour ma montre.
**straw** NOUN
la **paille** _fem_
**strawberry** NOUN
la **fraise** _fem_
**strawberry jam**
la confiture de fraises
**a strawberry ice cream**
une glace à la fraise
**stream** NOUN
le **ruisseau** _masc_ (PL les **ruisseaux** )
**street** NOUN
la **rue** _fem_
**in the street**
dans la rue
**stretch** VERB
**Stretch up high!**
Étirez-vous!
**Stretch out your arms!**
Tendez les bras!
**strict** ADJECTIVE
**strict** _masc_
**stricte** _fem_
**strike** NOUN
la **grève** _fem_
**They are on strike.**
Ils sont en grève.
**striker** NOUN
le **buteur** _masc (footballer)_
**string** NOUN
**1** la **ficelle** _fem_
**a piece of string**
un bout de ficelle
**2** la **corde** _fem (of violin, guitar)_
**stripe** NOUN
la **rayure** _fem_
**stripy** ADJECTIVE
**rayé** _masc_
**rayée** _fem_
**a stripy shirt**
une chemise rayée
**strong** ADJECTIVE
**fort** _masc_
**forte** _fem_
**She's very strong.**
Elle est très forte.
**student** NOUN
l' **étudiant** _masc_
l' **étudiante** _fem_
**study** VERB
**My sister's studying for her exams.**
Ma sœur révise pour ses examens.
**stuff** NOUN
les **affaires** _fem pl_
**Have you got all your stuff?**
Est-ce que tu as toutes tes affaires?
**stuffy** ADJECTIVE
**It's stuffy in here.**
On étouffe ici.
**stupid** ADJECTIVE
**stupide**
**a stupid joke**
une plaisanterie stupide
**subject** NOUN
la **matière** _fem_
**What's your favourite subject?**
Quelle est ta matière préférée?
**subtitles** PL NOUN
les **sous-titres** _masc pl_
**a French film with English subtitles**
un film français avec des sous-titres en anglais
**subtract** VERB
**retrancher**
**Subtract three from five.**
Retranchez trois à cinq.
**suburb** NOUN
la **banlieue** _fem_
**a suburb of Paris**
une banlieue de Paris
**They live in the suburbs.**
Ils habitent en banlieue.
**success** NOUN
le **succès** _masc_
**another wonderful success**
encore un formidable succès
**The party was a great success.**
La soirée était très réussie.
**such** ADVERB
**si**
**such nice people**
des gens si gentils
**such a long journey**
un voyage si long
**such as**
comme
**towns such as Avignon and Arles**
des villes comme Avignon et Arles
**sudden** ADJECTIVE
**soudain** _masc_
**soudaine** _fem_
**a sudden change**
un changement soudain
**suede** NOUN
le **daim** _masc_
**a suede jacket**
une veste en daim
**sugar** NOUN
le **sucre** _masc_
**Do you take sugar?**
Est-ce que vous prenez du sucre?
**More sugar?**
Encore un peu de sucre?
**suggestion** NOUN
la **suggestion** _fem_
**Have you got any suggestions?**
Vous avez des suggestions?
**suit**
**suit** _can be a noun or a verb._
**A** NOUN
**1** le **costume** _masc (man's)_
**2** le **tailleur** _masc (woman's)_
**B** VERB
**That dress suits you.**
Cette robe te va bien.
**suitcase** NOUN
la **valise** _fem_
**summer** NOUN
l' **été** _masc_
**We're going to France this summer.**
Nous allons en France cet été.
**in summer**
en été
**this summer**
cet été
**last summer**
l'été dernier
**summer holidays** PL NOUN
les **vacances d'été** _fem pl_
**in the summer holidays**
pendant les vacances d'été
**summertime** NOUN
l' **été** _masc_
**in summertime**
en été
**summit** NOUN
le **sommet** _masc_
**sums** PL NOUN
le **calcul** _masc_
**She's good at sums.**
Elle est bonne en calcul.
**_Language tip_**
**calcul** _is a singular word._
**sun** NOUN
le **soleil** _masc_
**in the sun**
au soleil
**sunbathe** VERB
**se faire bronzer**
**I like sunbathing.**
J'aime me faire bronzer.
**sunburnt** ADJECTIVE
**I got sunburnt.**
J'ai attrapé un coup de soleil.
**sun cream** NOUN
la **crème solaire** _fem_
**Sunday** NOUN
le **dimanche** _masc_
**It's Sunday today.**
Aujourd'hui, c'est dimanche
**on Sunday**
dimanche
**on Sundays**
le dimanche
**every Sunday**
tous les dimanches
**last Sunday**
dimanche dernier
**next Sunday**
dimanche prochain
**_Language tip_**
_Days of the week are not written with a capital letter in French._
**Sunday school** NOUN
le **catéchisme** _masc_
_**Did you know...?**_
_In France,_ **le catéchisme** _is on Wednesday mornings, when most children don't have ordinary school._
**sunflower** NOUN
le **tournesol** _masc_
**sunglasses** PL NOUN
les **lunettes de soleil** _fem pl_
**a pair of sunglasses**
une paire de lunettes de soleil
**sunny** ADJECTIVE
**It's a sunny day.**
C'est une belle journée.
**It's sunny.**
Il fait du soleil.
**sunset** NOUN
le **coucher du soleil** _masc_
**at sunset**
au coucher du soleil
**sunshine** NOUN
le **soleil** _masc_
**lots of sunshine**
beaucoup de soleil
**super** ADJECTIVE
**formidable**
**supermarket** NOUN
le **supermarché** _masc_
**supper** NOUN
le **dîner** _masc_
**supply teacher** NOUN
le **suppléant** _masc_
la **suppléante** _fem_
**She's a supply teacher.**
Elle est suppléante.
**_Language tip_**
_You do not translate_ **'a'** _when you say what someone's job is in French._
**support** VERB
**être supporter de**
**I support Manchester United.**
Je suis supporter de Manchester United.
**What team do you support?**
Tu es supporter de quelle équipe?
**supporter** NOUN
le **supporter** _masc_
**a Liverpool supporter**
un supporter de Liverpool
**suppose** VERB
**imaginer**
**I suppose he's late.**
J'imagine qu'il est en retard.
**You're not supposed to do that, Thérèse.**
Tu n'es pas censée faire ça, Thérèse.
**sure** ADJECTIVE
**sûr** _masc_
**sûre** _fem_
**Are you sure, Inès?**
Tu es sûre, Inès?
**I'm not sure.**
Je ne suis pas sûr.
**surface** NOUN
la **surface** _fem_
**surfboard** NOUN
la **planche de surf** _fem_
**surfing** NOUN
le **surf** _masc_
**I go surfing.**
Je fais du surf.
**surname** NOUN
le **nom de famille** _masc_
**What's your surname?**
Quel est votre nom de famille?
**surprise** NOUN
la **surprise** _fem_
**What a surprise!**
Quelle surprise!
**survey** NOUN
le **sondage** _masc_
**We're doing a survey on pets.**
On fait un sondage sur les animaux domestiques.
**suspend** VERB
**He's been suspended.**
Il s'est fait exclure.
**swam** VERB _see_ **swim**
**swan** NOUN
le **cygne** _masc_
**swap** VERB
**échanger**
**Do you want to swap?**
Tu veux échanger?
**Let's swap places.**
Changeons de place.
**sweater** NOUN
le **pull** _masc_
**a white sweater**
un pull blanc
**sweatshirt** NOUN
le **sweat** _masc_
**a dark green sweatshirt**
un sweat vert foncé
**sweet**
**sweet** _can be a noun or an adjective._
**A** NOUN
**1** le **bonbon** _masc (candy)_
**a bag of sweets**
un paquet de bonbons
**2** le **dessert** _masc (pudding)_
**Sweets: ice cream or chocolate mousse**
Desserts: glace ou mousse au chocolat
**B** ADJECTIVE
**1** **sucré** _masc_
**sucrée** _fem (sugary)_
**It's too sweet.**
C'est trop sucré.
**2** **gentil** _masc_
**gentille** _fem (kind)_
**She's a sweet person.**
Elle est gentille.
**3** **mignon** _masc_
**mignonne** _fem (cute)_
**Isn't she sweet?**
Comme elle est mignonne!
**sweetcorn** NOUN
le **maïs doux** _masc_
**sweetie** NOUN
le **bonbon** _masc_
**swim**
**swim** _can be a verb or a noun._
**A** VERB
**nager**
**Can you swim?**
Tu sais nager?
**I can swim.**
Je sais nager.
**I can't swim.**
Je ne sais pas nager.
**B** NOUN
**I want to go for a swim.**
Je veux aller me baigner.
**swimmer** NOUN
le **nageur** _masc_
la **nageuse** _fem_
**She's a good swimmer.**
C'est une bonne nageuse.
**swimming** NOUN
la **natation** _fem_
**Do you like swimming?**
Tu aimes la natation?
**I go swimming on Wednesdays.**
Je vais à la piscine le mercredi.
**swimming costume** NOUN
le **maillot de bain** _masc_
**swimming pool** NOUN
la **piscine** _fem_
**swimming trunks** PL NOUN
le **maillot de bain** _masc_
**I've got new swimming trunks.**
J'ai un nouveau maillot de bain.
**_Language tip_**
**maillot de bain** _is a singular word._
**swimsuit** NOUN
le **maillot de bain** _masc_
**swing** NOUN
la **balançoire** _fem_
**Swiss** ADJECTIVE
**suisse**
**Sabine is Swiss.**
Sabine est suisse.
**_Language tip_**
**Swiss** _is always written with a capital letter,_ **suisse** _is not._
**switch**
**switch** _can be a noun or a verb._
**A** NOUN
le **bouton** _masc_
**Where's the switch?**
Où est le bouton?
**B** VERB
**changer de**
**Switch partners!**
Changez de partenaire!
**switch off** VERB
**éteindre**
**Switch off the computer, Nina.**
Éteins l'ordinateur, Nina.
**switch on** VERB
**allumer**
**Switch on the light, Pierre.**
Allume la lumière, Pierre.
**Switzerland** NOUN
la **Suisse** _fem_
**swop** VERB
**échanger**
**Do you want to swop?**
Tu veux échanger?
**Let's swop places.**
Changeons de place.
**symbol** NOUN
le **symbole** _masc_
**sympathetic** ADJECTIVE
**compréhensif** _masc_
**compréhensive** _fem_
# **T t**
**table** NOUN
la **table** _fem_
**It's on the table.**
C'est sur la table.
**the three times table**
la table de trois
**tablecloth** NOUN
la **nappe** _fem_
**tablespoon** NOUN
la **grande cuillère** _fem_
**table tennis** NOUN
le **ping-pong** _masc_
**tail** NOUN
la **queue** _fem_
**Pin the tail on the donkey.**
Accroche la queue à l'âne.
**_Language tip_**
**la queue** _also has the same meaning as 'queue' in English. Queues are often long and thin, like a tail._
**Heads or tails?**
Pile ou face?
**take**
**1** **prendre** _(thing)_
**Take a card, Luc.**
Prends une carte, Luc.
**Take one card each.**
Prenez une carte chacun.
**I don't take sugar.**
Je ne prends pas de sucre.
**It takes about an hour.**
Ça prend environ une heure.
**Who's taken my ruler?**
Qui a pris ma règle?
**2** **emmener** _(person)_
**Mum's going to take me to the fair.**
Maman va m'emmener à la fête foraine.
**take away** VERB
**30 take away 9 is 21.**
Trente moins neuf égale vingt et un.
**take back** VERB
**rapporter**
**I'm going to take this book back to the library.**
Je vais rapporter ce livre à la bibliothèque.
**take down** VERB
**enlever**
**Take the posters down.**
Enlève les posters.
**taken** VERB _see_ **take**
**take off** VERB
**enlever**
**Take your coats off.**
Enlevez vos manteaux.
**takeoff** NOUN
le **décollage** _masc_
**take out** VERB
**sortir**
**I take the dog out at about six o'clock.**
Je sors le chien vers six heures.
**talk**
**talk** _can be a verb or a noun._
**A** VERB
**parler**
**You talk too much.**
Tu parles trop.
**Today we're going to talk about Paris.**
Aujourd'hui nous allons parler de Paris.
**B** NOUN
**Let's have a talk about it.**
Parlons-en.
**talkative** ADJECTIVE
**bavard** _masc_
**bavarde** _fem_
**tall** ADJECTIVE
**1** **grand** _masc_
**grande** _fem (person, tree)_
**Clément is tall.**
Clément est grand.
**Yvette is tall.**
Yvette est grande.
**2** **haut** _masc_
**haute** _fem (building)_
**a very tall building**
un très haut immeuble
**How tall are you?**
Tu mesures combien?
**I'm one metre thirty tall.**
Je mesure un mètre trente.
**tan** NOUN
le **bronzage** _masc_
**She's got an amazing tan.**
Elle a un bronzage superbe.
**tangerine** NOUN
la **mandarine** _fem_
**tap** NOUN
le **robinet** _masc_
**Turn on the tap.**
Ouvre le robinet.
**tap-dancing** NOUN
les **claquettes** _fem pl_
**I do tap-dancing.**
Je fais des claquettes.
**tape**
**tape** _can be a verb or a noun._
**A** VERB
**enregistrer**
**I'm going to tape the song.**
Je vais enregistrer la chanson.
**B** NOUN
la **cassette** _fem_
**a tape of Kylie Minogue**
une cassette de Kylie Minogue
**tape recorder** NOUN
le **magnétophone** _masc_
**target** NOUN
la **cible** _fem_
**tart** NOUN
la **tarte** _fem_
**an apple tart**
une tarte aux pommes
**tartan** ADJECTIVE
**écossais** _masc_
**écossaise** _fem_
**a tartan scarf**
une écharpe écossaise
**_Language tip_**
**écossais** _can also mean Scottish._
**taste**
**taste** _can be a noun or a verb._
**A** NOUN
le **goût** _masc_
**It's got a strange taste.**
Ça a un goût bizarre.
**Would you like a taste?**
Tu veux goûter?
**B** VERB
**goûter**
**Would you like to taste it?**
Vous voulez y goûter?
**tasty** ADJECTIVE
**savoureux** _masc_
**savoureuse** _fem_
**tattoo** NOUN
le **tatouage** _masc_
**taxi** NOUN
le **taxi** _masc_
**by taxi**
en taxi
**taxi driver** NOUN
le **chauffeur de taxi** _masc_
**tea**
**1** NOUN
le **thé** _masc (drink)_
**a cup of tea**
une tasse de thé
**tea with milk**
du thé au lait
_**Did you know...?**_
_In France, it is more common to have lemon with your tea._
**2** le **dîner** _masc (evening meal)_
**We were having tea.**
Nous étions en train de dîner.
**tea bag** NOUN
le **sachet de thé** _masc_
**teach** VERB
**1** **enseigner** _(in school)_
**Mrs Morrison teaches us French.**
Madame Morrison nous enseigne le français.
**2** **apprendre**
**My cousin is teaching me the guitar.**
Ma cousine m'apprend la guitare.
**teacher** NOUN
**1** le **professeur des écoles** _masc (in primary school)_
**Mr Price is our teacher.**
Mr Price est notre professeur.
**2** le **professeur** _masc (in secondary school)_
**a maths teacher**
un professeur de maths
**She's a teacher.**
Elle est professeur.
**_Language tip_**
_When you say what someone's job is in French, you do not translate_ **a**.
**team** NOUN
l' **équipe** _fem_
**a football team**
une équipe de football
**She's in my team.**
Elle est dans mon équipe.
**We're going to divide the class into two teams.**
On va diviser la classe en deux équipes.
**teaspoon** NOUN
la **petite cuillère** _fem_
**teatime** NOUN
l' **heure du dîner** _fem_
**at teatime**
à l'heure du dîner
**tea towel** NOUN
le **torchon** _masc_
**technology** NOUN
la **technologie** _fem_
**teddy bear** NOUN
le **nounours** _masc_
**teenager** NOUN
l' **adolescent** _masc_
l' **adolescente** _fem_
**teens** PL NOUN
**She's in her teens.**
C'est une adolescente.
**He's in his teens.**
C'est un adolescent.
**tee-shirt** NOUN
le **tee-shirt** _masc_
**teeth** PL NOUN
les **dents** _fem pl_
**I clean my teeth three times a day.**
Je me brosse les dents trois fois par jour.
**telephone** NOUN
le **téléphone** _masc_
**on the telephone**
au téléphone
**telephone call** NOUN
le **coup de téléphone** _masc_
**telephone number** NOUN
le **numéro de téléphone** _masc_
**television** NOUN
la **télévision** _fem_
**on television**
à la télévision
**television programme** NOUN
l' **émission de télévision** _fem_
**tell** VERB
**1** **dire**
**Tell me why, Marc.**
Dis-moi pourquoi, Marc.
**Tell me your names.**
Dites-moi vos noms.
**I'm going to tell my mum.**
Je vais le dire à ma maman.
**I told you to wait.**
Je t'ai dit d'attendre.
**2** **parler** _(talk about)_
**I'll tell you about myself.**
Je vais te parler de moi.
**Tell your penfriends about yourselves.**
Parlez de vous à vos correspondants.
**3** **raconter** _(story)_
**I'm going to tell you a story.**
Je vais vous raconter une histoire.
**tell off** VERB
**gronder**
**She tells me off if I'm late.**
Elle me gronde si je suis en retard.
**telly** NOUN
la **télé** _fem_
**I watch telly a lot.**
Je regarde beaucoup la télé.
**on telly**
à la télé
**temperature** NOUN
**I've got a temperature.**
J'ai de la fièvre.
**ten** NUMBER
**dix**
**ten euros**
dix euros
**It's ten to three.**
Il est trois heures moins dix.
**It's ten past two.**
Il est deux heures dix.
**I'm ten.**
J'ai dix ans.
**_Language tip_**
_In English, you can say_ **ten** _or_ **ten years old**. _In French, you can only say_ **dix ans**.
**tennis** NOUN
le **tennis** _masc_
**I play tennis.**
Je joue au tennis.
**tennis ball** NOUN
la **balle de tennis** _fem_
**tennis court** NOUN
le **court de tennis** _masc_
**tennis racket** NOUN
la **raquette de tennis** _fem_
**tennis player** NOUN
le **joueur de tennis** _masc_
la **joueuse de tennis** _fem_
**tenpin bowling** NOUN
le **bowling** _masc_
**Do you want to go tenpin bowling?**
Tu veux jouer au bowling?
**tent** NOUN
la **tente** _fem_
**_Language tip_**
_What extra vowel does the French word have that the English word doesn't?_
**tenth** ADJECTIVE
**dixième**
**on the tenth floor**
au dixième étage
**the tenth of August**
le dix août
**term** NOUN
le **trimestre** _masc_
**It'll soon be the end of term.**
C'est bientôt la fin du trimestre.
**terrible** ADJECTIVE
**épouvantable**
**My French is terrible.**
Mon français est épouvantable.
**terrified** ADJECTIVE
**terrifié** _masc_
**terrifiée** _fem_
**I was terrified!**
J'étais terrifié!
**test** NOUN
l' **interrogation** _fem_
**I've got a test tomorrow.**
J'ai une interrogation demain.
**text**
**text** _can be a noun or a verb._
**A** NOUN
le **SMS** _masc_
**Send me a text.**
Envoie-moi un SMS.
**B** VERB
**envoyer un SMS à** **J'ai envoyé un SMS à Lara.**
I texted Lara.
**textbook** NOUN
le **manuel** _masc_
**a French textbook**
un manuel de français
**text message** NOUN
le **SMS** _masc_
**than** CONJUNCTION
**que**
**She's taller than me.**
Elle est plus grande que moi.
**Are you older than him?**
Tu es plus vieux que lui?
**thank you** EXCLAMATION
**merci!**
**Thank you very much.**
Merci beaucoup.
**thanks** EXCLAMATION
**merci!**
**No thanks.**
Non merci.
**that**
**that** _can be a pronoun, an adjective or a conjunction._
**A** PRONOUN
**ça**
**Do you see that?**
Tu vois ça?
**That's my brother.**
C'est mon frère.
**That's my friend Bernadette.**
C'est mon amie Bernadette.
**That's right! Well done.**
C'est ça! Bravo!
**What's that?**
Qu'est-ce que c'est?
**How much is that?**
C'est combien?
**Who's that?**
C'est qui?
**I know that.**
Je le sais.
**Is that him?**
C'est lui?
**Is that her?**
C'est elle?
**B** ADJECTIVE
**ce** _masc_ **cette** _fem_
**that dog**
ce chien
**that woman**
cette femme
**_Language tip_**
**Ce** _changes to_ **cet** _with masculine nouns starting with a vowel sound._
**that man**
cet homme
**that bird**
cet oiseau
**_Language tip_**
_When you say_ **that one** _when you are pointing, use_ **celui-là** _if the French noun is masculine, and_ **celle-là** _if it is feminine._
**This man? — No, that one.**
Cet homme-ci? — Non, celui-là.
**This colour? — No, that one.**
Cette couleur? — Non, celle-là.
**C** CONJUNCTION
**que**
**I think that you're right.**
Je pense que tu as raison.
**I think that it's raining.**
Je crois qu'il pleut.
**I think that Henri is ill.**
Je crois qu'Henri est malade.
**the** ARTICLE
**_Language tip_**
_Use_ **le** _with a masculine noun, and_ **la** _with a feminine noun. Use_ **l'** _before a vowel sound. For plural nouns always use_ **les**.
**le**
**the boy**
le garçon
**l'**
**the man**
l'homme
**the orange**
l'orange
**la**
**the girl**
la fille
**les**
**the children**
les enfants
**theatre** NOUN
le **théâtre** _masc_
**their** ADJECTIVE
**leur** _masc, fem_ (PL
**leurs** )
**their house**
leur maison
**their parents**
leurs parents
**theirs** PRONOUN
**à eux** _masc pl_ (FEM PL
**à elles** )
**This car is theirs.**
Cette voiture est à eux.
**Whose is this? — It's theirs.**
C'est à qui? — À eux.
**them** PRONOUN
**1** **les**
**I can't see them.**
Je ne les vois pas.
**Do you want them?**
Tu les veux?
**2** **leur** _(for them, to them)_
**I'm going to buy them a present.**
Je vais leur acheter un cadeau.
**Can you give them a message?**
Tu peux leur donner un message?
**3** **eux** _masc pl_
**elles** _fem pl (after a preposition)_
**It's not for you, it's for them.**
Ce n'est pas pour toi, c'est pour eux.
**Ann and Sophie are here, and Graham's with them.**
Ann et Sophie sont là, et Graham est avec elles.
**theme park** NOUN
le **parc d'attractions** _masc_
**themselves** PRONOUN
**1** **se**
**They're enjoying themselves.**
Ils s'amusent.
**2** **eux-mêmes** _masc pl_
**elles-mêmes** _fem pl (by themselves)_
**They did it themselves.**
Ils l'ont fait eux-mêmes.
**then** CONJUNCTION
**ensuite**
**I get dressed. Then I have breakfast.**
Je m'habille. Ensuite je prends mon petit déjeuner.
**there** ADVERB
**1** **là**
**Put it there, on the table.**
Mets-le là, sur la table.
**up there**
là-haut
**down there**
là-bas
**2** **y** _(to there)_
**I'm going there on Friday.**
J'y vais vendredi.
**_Language tip_**
_To say either_ **there is** _or_ **there are** _use_ **il y a**.
**There's a new boy in the class.**
Il y a un nouveau dans la classe.
**There are five people in my family.**
Il y a cinq personnes dans ma famille.
**How many biscuits are there?**
Il y a combien de biscuits?
**There are lots.**
Il y en a beaucoup.
**There aren't many.**
Il n'y en a pas beaucoup.
**over there**
là-bas
**There he is!**
Le voilà!
**There they are!**
Les voilà!
**There is...**
Il y a...
**There are...**
Il y a...
**these**
**these** _can be an adjective or a pronoun._
**A** ADJECTIVE
**ces**
**these shoes**
ces chaussures
**B** PRONOUN
**ceux-ci** _masc pl_
**celles-ci** _fem pl_
**Which sweets do you want? — These.**
Quels bonbons veux-tu? — Ceux-ci.
**Which seats are free? — These.**
Quelles places sont libres? — Celles-ci.
**they** PRONOUN
**_Language tip_**
_Check if_ **they** _stands for a masculine or feminine noun;_ **ils** _is used for masculine nouns and_ **elles** _for feminine nouns._
**ils** _masc pl_
**Where are your friends? — They're over there.**
Où sont tes amis? — Ils sont là-bas.
**elles** _fem pl_
**Are your socks white? — No, they're grey.**
Tes chaussettes sont blanches? — Non, elles sont grises.
**thief** NOUN
le **voleur** _masc_
la **voleuse** _fem_
**thin** ADJECTIVE
**1** **mince** _(person, slice)_
**I'm quite thin.**
Je suis assez mince.
**2** **maigre** _(skinny)_
**She's got very thin legs.**
Elle a les jambes très maigres.
**thing** NOUN
**1** la **chose** _fem_
**I've got lots of things to do.**
J'ai beaucoup de choses à faire.
**There are beautiful things in the museum.**
Il y a de belles choses au musée.
**2** _(belongings)_
**my things**
mes affaires
**think**
**1** **penser** _(believe)_
**I think he's here.**
Je pense qu'il est là.
**I think so.**
Oui, je crois.
**I don't think so.**
Je ne crois pas.
**2** **réfléchir** _(spend time thinking)_
**Think carefully, Jason.**
Réfléchis bien, Jason.
**Think carefully, children.**
Réfléchissez bien, les enfants.
**I'll think about it.**
Je vais y réfléchir.
**third** ADJECTIVE
**troisième**
**It's the third time.**
C'est la troisième fois.
**I came third.**
Je suis arrivé troisième.
**the third of March**
le trois mars
**thirsty** ADJECTIVE
**Are you thirsty?**
Tu as soif?
**I'm not thirsty.**
Je n'ai pas soif.
**I'm thirsty.**
J'ai soif.
**thirteen** NUMBER
**treize**
**thirteen euros**
treize euros
**I'm thirteen.**
J'ai treize ans.
**_Language tip_**
_In English, you can say_ **thirteen** _or_ **thirteen years old**. _In French, you can only say_ **treize ans**.
**thirteenth** ADJECTIVE
**treizième**
**on the thirteenth floor**
au treizième étage
**the thirteenth of August**
le treize août
**thirty** NUMBER
**trente**
**My aunt is thirty.**
Ma tante a trente ans.
**_Language tip_**
_In English, you can say_ **thirty** _or_ **thirty years old**. _In French, you can only say_ **trente ans**.
**this**
**this** _can be an adjective or a pronoun._
**A** ADJECTIVE
**ce** _masc_ **cette** _fem_
**this book**
ce livre
**this time**
cette fois
**_Language tip_**
_Use_ **cet** _with masculine nouns starting with a vowel sound._
**this man**
cet homme
**_Language tip_**
_For_ **this one** _use_ **celui-ci** _if the French noun it refers to is masculine, and_ **celle-ci** _if it is feminine._
**Which T-shirt do you want? — This one.**
Quel tee-shirt veux-tu? — Celui-ci.
**That card? — No, this one.**
Cette carte-là? — Non, celle-ci.
**B** PRONOUN
**ça**
**Look at this.**
Regarde ça.
**this morning**
ce matin
**this year**
cette année
**this afternoon**
cet après-midi
**What's this?**
Qu'est-ce que c'est?
**those**
**those** _can be an adjective or a pronoun._
**A** ADJECTIVE
**ces**
**those shoes**
ces chaussures
**B** PRONOUN
**ceux-là** _masc pl_ **celles-là** _fem pl_ **Which sweets do you want? — Those.**
Quels bonbons veux-tu? — Ceux-là.
**Which seats are free? — Those.**
Quelles places sont libres? — Celles-là.
**thousand** NUMBER
**a thousand**
mille
**a thousand euros**
mille euros
**thousands of people**
des milliers de personnes
**three** NUMBER
**trois**
**three euros**
trois euros
**She's three.**
Elle a trois ans.
**_Language tip_**
_In English, you can say_ **three** _or_ **three years old**. _In French, you can only say_ **trois ans**.
**throat** NOUN
la **gorge** _fem_
**I've got a sore throat.**
J'ai mal à la gorge.
**through** PREPOSITION
**par**
**through the window**
par la fenêtre
**throw** VERB
**lancer**
**Throw me the ball.**
Lance-moi la balle.
**throw away** VERB
**jeter**
**Don't throw it away!**
Ne le jette pas!
**thumb** NOUN
le **pouce** _masc_
**thunder** NOUN
le **tonnerre** _masc_
**There was thunder and lightning.**
Il y avait du tonnerre et des éclairs.
**thunderstorm** NOUN
l' **orage** _masc_
**Thursday** NOUN
le **jeudi** _masc_
**It's Thursday today.**
Aujourd'hui c'est jeudi.
**on Thursday**
jeudi
**on Thursdays**
le jeudi
**every Thursday**
tous les jeudis
**last Thursday**
jeudi dernier
**next Thursday**
jeudi prochain
**_Language tip_**
_Days of the week are not written with a capital letter in French._
**tick**
**tick** _can be a noun or a verb._
**A** NOUN
**Put a tick or a cross.**
Cochez ou mettez une croix.
**B** VERB
**cocher**
**Tick the right box.**
Cochez la bonne case.
**ticket** NOUN
**1** le **ticket** _masc (for bus, tube, cinema, museum)_
**a bus ticket**
un ticket de bus
**2** le **billet**
_masc (for plane, train, concert)_
**ticket office** NOUN
le **guichet** _masc_
**tidy**
**tidy** _can be an adjective or a verb._
**A** ADJECTIVE
**bien rangé** _masc_
**bien rangée** _fem (place)_
**My room is tidy.**
Ma chambre est bien rangée.
**B** VERB
**ranger**
**Go and tidy your room.**
Va ranger ta chambre.
**tidy up** VERB
**ranger**
**Don't forget to tidy up afterwards, children.**
N'oubliez pas de ranger après, les enfants.
**tie**
**tie** _can be a noun or a verb._
**A** NOUN
la **cravate** _fem_
**B** VERB
**nouer**
**Tie your laces.**
Noue tes lacets.
**tiger** NOUN
le **tigre** _masc_
**tight** ADJECTIVE
**1** **moulant** _masc_
**moulante** _fem (tight-fitting)_
**a tight skirt**
une jupe moulante
**2** **juste** _(too tight)_
**This dress is a bit tight.**
Cette robe est un peu juste.
**tights** PL NOUN
le **collant** _masc_
**I'm wearing black tights.**
Je porte un collant noir.
**_Language tip_**
**collant** _is a singular word._
**till**
**till** _can be a noun or a preposition._
**A** NOUN
la **caisse** _fem_
**at the till**
à la caisse
**B** PREPOSITION
**1** **jusqu'à**
**He's staying till Monday.**
Il reste jusqu'à lundi.
**2** **avant** _(with 'not')_
**not until tomorrow**
pas avant demain
**3** **à**
**from nine till five**
de neuf heures à cinq heures
**from Monday till Friday**
du lundi au vendredi
**time** NOUN
**1** l' **heure** _fem (on clock)_
**What time is it?**
Quelle heure est-il?
**_Language tip_**
_You can also say:_ **Il est quelle heure?**
**What time?**
À quelle heure?
**What time do you get up?**
À quelle heure tu te lèves?
**What time does the train arrive?**
Le train arrive à quelle heure?
**2** le **temps** _masc (amount of time)_
**I'm sorry, I haven't got time.**
Je suis désolé, je n'ai pas le temps.
**It's time to go.**
Il est temps de partir.
**3** la **fois** _fem (occasion)_
**this time**
cette fois
**next time**
la prochaine fois
**the first time**
la première fois
**two at a time**
deux à la fois
**two times two is four**
deux fois deux égalent quatre
**What time is it?**
Quelle heure est-il?
**It's lunch time.**
C'est l'heure du déjeuner.
**How many times?**
Combien de fois?
**Have a good time, girls!**
Amusez-vous bien, les filles!
**Have a good time, Léa!**
Amuse-toi bien, Léa!
**timetable** NOUN
**1** l' **emploi du temps** _masc (at school)_
**2** l' **horaire** _masc (for train, bus)_
**tin** NOUN
la **boîte** _fem_
**a tin of soup**
une boîte de soupe
**tin opener** NOUN
l' **ouvre-boîte** _masc_
**tinsel** NOUN
les **guirlandes de Noël** _fem pl_
**tiny** ADJECTIVE
**minuscule**
**tip** NOUN
le **pourboire** _masc_
**It's a tip for the waiter.**
C'est un pourboire pour le serveur.
**tiptoe** NOUN
**on tiptoe**
sur la pointe des pieds
**tired** ADJECTIVE
**fatigué** _masc_
**fatiguée** _fem_
**I'm tired.**
Je suis fatigué.
**tiring** ADJECTIVE
**fatigant** _masc_
**fatigante** _fem_
**tissue** NOUN
le **kleenex** ® _masc_
**Have you got a tissue?**
Tu as un kleenex?
**title** NOUN
le **titre** _masc_
**to** PREPOSITION
**_Language tip_**
**à** _+_ **le** _changes to_ **au**.
**à** \+ **les** _changes to_ **aux**.
**1** **à**
**We're going to London.**
Nous allons à Londres.
**I go to school with my friend.**
Je vais à l'école avec mon amie.
**We're ready to start.**
Nous sommes prêts à commencer.
**from nine o'clock to half past three**
de neuf heures à trois heures et demie
**au**
**We're going to a restaurant.**
Nous allons au restaurant.
**aux**
**Can I go to the toilet?**
Je peux aller aux toilettes?
**_Language tip_**
_To talk about going to a country, use_ **au** _if the country is masculine_ , **en** _if the country is feminine, and_ **aux** _if the country is plural._
**We're going to Wales.**
Nous allons au pays de Galles.
**I'm going to Scotland.**
Je vais en Écosse.
**We're going to the United States.**
Nous allons aux États-Unis.
**2** **de**
**the train to London**
le train de Londres **the plane to Paris**
l'avion pour Paris
**3** **chez** _(to someone's house)_
**I'm going to Anne's house.**
Je vais chez Anne.
**Let's go to mine.**
Allons chez moi.
**I'm going to the doctor.**
Je vais chez le docteur.
**4** **jusqu'à** _(up to)_
**Count to ten, everyone.**
Comptez jusqu'à dix, tout le monde.
**to Paris**
à Paris
**to France**
en France
**to Portugal**
au Portugal
**to the swimming pool**
à la piscine
**to the supermarket**
au supermarché
**to my house**
chez moi
**toad** NOUN
le **crapaud** _masc_
**toast** NOUN
le **pain grillé** _masc_
**a piece of toast**
une tranche de pain grillé
**toastie** NOUN
le **sandwich chaud** _masc_
**today** ADVERB
**aujourd'hui**
**What's the date today?**
Quelle est la date aujourd'hui?
**It's Monday today.**
Aujourd'hui c'est lundi.
**toe** NOUN
le **doigt de pied** _masc_
**_Language tip_**
**doigt** _also means 'finger'. The French_ **doigt de pied** _actually means 'foot finger'!_
**toffee** NOUN
le **caramel** _masc_
**together** ADVERB
**ensemble**
**toilet** NOUN
les **toilettes** _fem pl_
**Can I go to the toilet?**
Je peux aller aux toilettes?
**token** NOUN
**a gift token**
un bon-cadeau
**told** VERB _see_ **tell**
**tomato** NOUN
la **tomate** _fem_ **tomato soup**
la soupe à la tomate
**tomorrow** ADVERB
**demain**
**Let's go swimming tomorrow.**
Allons nager demain.
**tomorrow morning**
demain matin
**the day after tomorrow**
après-demain
**tomorrow night**
demain soir
**See you tomorrow.**
À demain.
**tongue** NOUN
la **langue** _fem_
**_Language tip_**
**la langue** _is related to the word 'language'. You use your tongue to speak a language._
**tonight** ADVERB
**ce soir**
**Are you going out tonight?**
Tu sors ce soir?
**tonsillitis** NOUN
l' **angine** _fem_
**too** ADVERB
**1** **aussi** _(as well)_
**My sister is coming too.**
Ma sœur vient aussi.
**2** **trop** _(very)_
**The water's too hot.**
L'eau est trop chaude.
**You're too late.**
Tu arrives trop tard.
**_Language tip_**
_You can use_ **trop** _with a verb to mean_ **too much**.
**Danielle, you talk too much.**
Danielle, tu parles trop.
**It costs too much.**
Ça coûte trop cher.
**_Language tip_**
_You can use_ **trop de** _with a noun, to mean_ **too much** _or_ **too many**.
**too much noise**
trop de bruit
**too many mistakes**
trop d'erreurs
**Me too.**
Moi aussi.
**toonie** NOUN _(Canada)_
le **deux dollars** _masc_
**tooth** NOUN
la **dent** _fem_
**_Language tip_**
**la dent** _is related to the word 'dentist'. A dentist looks after your teeth._
**toothache** NOUN
**I've got toothache.**
J'ai mal aux dents.
**toothbrush** NOUN
la **brosse à dents** _fem_
**toothpaste** NOUN
le **dentifrice** _masc_
**top**
**top** _can be a noun or an adjective._
**A** NOUN
**1** le **haut** _masc_
**a black skirt and a white top**
une jupe noire et un haut blanc
**at the top of the page**
en haut de la page
**2** le **sommet** _masc (of mountain)_
**the top of Snowdon**
le sommet de Snowdon
**on top of**
sur
**on top of the fridge**
sur le frigo
**B** ADJECTIVE
**He always gets top marks in French.**
Il a toujours d'excellentes notes en français.
**the top floor**
le dernier étage
**on the top floor**
au dernier étage
**torch** NOUN
la **lampe de poche** _fem_
**tortoise** NOUN
la **tortue** _fem_
**total** NOUN
le **total** _masc_ (PL les **totaux** )
**touch** VERB
**toucher**
**Don't touch that!**
N'y touche pas!
**tour** NOUN
la **visite** _fem_
**a tour of the museum**
une visite du musée
**tourism** NOUN
le **tourisme** _masc_
**tourist** NOUN
le **touriste** _masc_
la **touriste** _fem_
**There are lots of tourists.**
Il y a beaucoup de touristes.
**tourist information office** NOUN
l' **office du tourisme** _masc_
**towards** PREPOSITION
**vers**
**Come towards me.**
Viens vers moi.
**towel** NOUN
la **serviette** _fem_
**tower** NOUN
la **tour** _fem_
**a tower block**
une tour
**town** NOUN
la **ville** _fem_
**I'm going into town.**
Je vais en ville.
**the town centre**
le centre-ville
**toy** NOUN
le **jouet** _masc_
**_Language tip_**
_The noun_ **le jouet** _is related to the verb_ **jouer** , _which means 'to play'._
**toy shop** NOUN
le **magasin de jouets** _masc_
**tracksuit** NOUN
le **jogging** _masc_
**tractor** NOUN
le **tracteur** _masc_
**tradition** NOUN
la **tradition** _fem_
**traffic** NOUN
la **circulation** _fem_
**There's a lot of traffic.**
Il y a beaucoup de circulation.
**traffic lights** PL NOUN
les **feux** _masc pl_
**train** NOUN
le **train** _masc_
**by train**
en train
**We're going by train.**
Nous y allons en train.
**trainers** PL NOUN
les **baskets** _fem pl_
**a pair of trainers**
une paire de baskets
**tram** NOUN
le **tramway** _masc_
**trampoline** NOUN
le **trampoline** _masc_
**translate** VERB
**traduire**
**I can translate the menu into English.**
Je sais traduire le menu en anglais.
**translation** NOUN
la **traduction** _fem_
**travel agent's** NOUN
l' **agence de voyages** _fem_
**travelling** NOUN
**I love travelling.**
J'adore les voyages.
**treasure** NOUN
le **trésor** _masc_
**tree** NOUN
l' **arbre** _masc_
**triangle** NOUN
le **triangle** _masc_
**trick** NOUN
le **tour** _masc_
**I can do magic tricks.**
Je sais faire des tours de magie.
**trip** NOUN
le **voyage** _masc_
**We're going on a trip to London.**
Nous faisons un voyage à Londres.
**Have a good trip!**
Bon voyage!
**trolley** NOUN
le **chariot** _masc_
**trouble** NOUN
le **problème** _masc_
**The trouble is, it's too expensive.**
Le problème, c'est que c'est trop cher.
**Éric is always getting into trouble.**
Éric fait tout le temps des bêtises.
**trousers** PL NOUN
le **pantalon** _masc_
**I'm wearing black trousers.**
Je porte un pantalon noir.
**_Language tip_**
**pantalon** _is a singular word._
**trout** NOUN
la **truite** _fem_
**truck** NOUN
le **camion** _masc_
**true** ADJECTIVE
**vrai** _masc_
**vraie** _fem_
**That's true.**
C'est vrai.
**That's not true.**
Ce n'est pas vrai.
**True or false?**
Vrai ou faux?
**trumpet** NOUN
la **trompette** _fem_
**She plays the trumpet.**
Elle joue de la trompette.
**trunks** PL NOUN
**le maillot de bain** _masc_
**I've got new trunks.**
J'ai un nouveau maillot de bain.
**_Language tip_**
**maillot de bain** _is a singular word._
**truth** NOUN
la **vérité** _fem_
**Tell me the truth.**
Dis-moi la vérité.
**try**
**try** _can be a verb or a noun._
**A** VERB
**1** **essayer** _(attempt)_
**I'm going to try.**
Je vais essayer.
**Try to remember.**
Essaie de te souvenir.
**Try again, everyone.**
Encore une fois, toute la classe.
**You're not trying, Éric.**
Tu ne fais pas d'effort, Éric.
**2** **goûter** _(taste)_
**Would you like to try some?**
Voulez-vous goûter?
**B** NOUN
l' **essai** _masc_
**his third try**
son troisième essai
**Good try!**
Pas mal!
**Can I have a try?**
Je peux essayer?
**try on** VERB
**essayer**
**Can I try it on?**
Je peux l'essayer?
**T-shirt** NOUN
le **tee-shirt** _masc_
**tube** NOUN
**the Tube**
le métro
**Tuesday** NOUN
le **mardi** _masc_
**It's Tuesday today.**
Aujourd'hui c'est mardi.
**on Tuesday**
mardi
**on Tuesdays**
le mardi
**every Tuesday**
tous les mardis
**last Tuesday**
mardi dernier
**next Tuesday**
mardi prochain
**_Language tip_**
_Days of the week are not written with a capital letter in French._
**tummy** NOUN
le **ventre** _masc_
**tummy ache** NOUN
**I've got tummy ache.**
J'ai mal au ventre.
**tuna** NOUN
le **thon** _masc_
**a tuna salad**
une salade de thon
**tune** NOUN
l' **air** _masc_
**I know the tune.**
Je connais l'air.
**tunnel** NOUN
le **tunnel** _masc_
**the Channel Tunnel**
le tunnel sous la Manche
**tuque** NOUN _(Canada)_
la **tuque** _fem_
**turkey** NOUN
**1** la **dinde** _fem (meat)_
**2** le **dindon** _masc (bird)_
**turn**
**turn** _can be a noun or a verb._
**A** NOUN
le **tour** _masc (go)_
**You miss a turn.**
Passe ton tour.
**Whose turn is it?**
C'est à qui le tour?
**It's my turn!**
C'est mon tour!
**B** VERB
**tourner**
**Turn right at the lights.**
Tournez à droite aux feux.
**turn off** VERB
**éteindre**
**Could you turn off the light?**
Tu peux éteindre?
**turn on** VERB
**allumer**
**Could you turn on the light?**
Tu peux allumer?
**turn over** VERB
**retourner**
**Turn over the cards, everyone.**
Retournez les cartes, tout le monde.
**turn round** VERB
**se retourner**
**Turn round, children!**
Retournez-vous, les enfants!
**turquoise**
**turquoise** _can be an adjective or a noun._
**A** ADJECTIVE
**turquoise** _masc, fem, pl_
**a turquoise top**
un haut turquoise
**_Language tip_**
_Colour adjectives come after the noun in French._
**B** NOUN
le **turquoise** _masc_
**Turquoise is my favourite colour.**
Ma couleur préférée, c'est le turquoise.
**TV** NOUN
la **télé** _fem_
**on TV**
à la télé
**twelfth** ADJECTIVE
**douzième**
**on the twelfth floor**
au douzième étage
**the twelfth of August**
le douze août
**twelve** NUMBER
**douze**
**twelve euros**
douze euros
**I have lunch at twelve o'clock.**
Je déjeune à midi.
**It is twelve thirty.**
Il est midi et demi.
**twelve o'clock**
midi
**twelve o'clock at night**
minuit
**I'm twelve.**
J'ai douze ans.
**_Language tip_**
_In English, you can say_ **twelve** _or_ **twelve years old**. _In French, you can only say_ **douze ans**.
**twentieth** ADJECTIVE
**vingtième**
**the twentieth time**
la vingtième fois
**the twentieth of May**
le vingt mai
**twenty** NUMBER
**vingt**
**twenty euros**
vingt euros
**It's twenty to two.**
Il est deux heures moins vingt.
**It's twenty past eleven.**
Il est onze heures vingt.
**He's twenty.**
Il a vingt ans.
**_Language tip_**
_In English, you can say_ **twenty** _or_ **twenty years old**. _In French, you can only say_ **vingt ans**.
**twice** ADVERB
**deux fois**
**twin** NOUN
le **jumeau** _masc_ (PL les **jumeaux** )
la **jumelle** _fem_ (PL les **jumelles** )
**my twin brother**
mon frère jumeau
**her twin sister**
sa sœur jumelle
**identical twins**
les vrais jumeaux
**twin room** NOUN
la **chambre à deux lits** _fem_
**twinned** ADJECTIVE
**jumelé** _masc_
**jumelée** _fem_
**Stroud is twinned with Châteaubriant.**
Stroud est jumelée avec Châteaubriant.
**two** NUMBER
**deux**
**two euros**
deux euros
**Get into twos.**
Mettez-vous deux par deux.
**She's two.**
Elle a deux ans.
**_Language tip_**
_In English, you can say_ **two** _or_ **two years old**. _In French, you can only say_ **deux ans**.
**type** NOUN
le **type** _masc_
**What type of camera have you got?**
Quel type d'appareil photo as-tu?
**tyre** NOUN
le **pneu** _masc_
# **U u**
**UFO** NOUN
l' **OVNI** _masc_
**ugly** ADJECTIVE
**laid** _masc_
**laide** _fem_
**UK** NOUN
le **Royaume-Uni** _masc_
**in the UK**
au Royaume-Uni
**to the UK**
au Royaume-Uni
**I live in the UK.**
J'habite au Royaume-Uni.
**Ulster** NOUN
l' **Irlande du Nord** _fem_
**in Ulster**
en Irlande du Nord
**umbrella** NOUN
**1** le **parapluie** _masc_
**_Language tip_**
_The French for rain is 'pluie'._
**un parapluie** _is something that keeps the rain off you._
**2** le **parasol** _masc (sunshade)_
**umpire** NOUN
**1** le **juge de chaise** _masc (in tennis)_
**2** l' **arbitre** _masc (in cricket)_
**unbeatable** ADJECTIVE
**imbattable**
**unbelievable** ADJECTIVE
**incroyable**
**That's unbelievable!**
C'est incroyable!
**uncle** NOUN
l' **oncle** _masc_
**my uncle**
mon oncle
**uncomfortable** ADJECTIVE
**pas confortable**
**The seats are rather uncomfortable.**
Les sièges ne sont pas très confortables.
**under** PREPOSITION
**1** **sous** _(beneath)_
**The cat's under the table.**
Le chat est sous la table.
**The tunnel goes under the Channel.**
Le tunnel passe sous la Manche.
**under there**
là-dessous
**What's under there?**
Qu'est-ce qu'il y a là-dessous?
**2** **moins de** _(less than)_
**It costs under £10.**
Ça coûte moins de dix livres.
**children under ten**
les enfants de moins de dix ans
**underground**
**underground** _can be a noun, an adjective or an adverb._
**A** NOUN
le **métro** _masc_
**by underground**
en métro
**B** ADJECTIVE
**souterrain** _masc_
**souterraine** _fem_
**an underground car park**
un parking souterrain
**C** ADVERB
**sous terre**
**Moles live underground.**
Les taupes vivent sous terre.
**underneath**
**underneath** _can be a preposition or an adverb._
**A** PREPOSITION
**sous**
**underneath the carpet**
sous la moquette
**B** ADVERB
**dessous**
**Look underneath, Pierre!**
Regarde dessous, Pierre!
**understand** VERB
**comprendre**
**_Language tip_**
_The English words 'comprehend' and 'comprehension' are related to_ **comprendre**. _Comprehension exercises test your understanding of something._
**Do you all understand?**
Vous comprenez tous?
**Do you understand, Richard?**
Tu comprends, Richard?
**I don't understand this word.**
Je ne comprends pas ce mot.
**I understood almost everything.**
J'ai presque tout compris.
**It's easy to understand.**
C'est facile à comprendre.
**I don't understand.**
Je ne comprends pas.
**Did you understand, Claire?**
Tu as compris, Claire?
**Did you understand, children?**
Vous avez compris, les enfants?
**understood** VERB _see_ **understand**
**underwear** NOUN
les **sous-vêtements** _masc pl_
**undone** ADJECTIVE
**défait** _masc_
**défaite** _fem_
**Your laces are undone.**
Tes lacets sont défaits.
**undressed** ADJECTIVE
**to get undressed**
se déshabiller
**I'm getting undressed.**
Je me déshabille.
**_Language tip_**
**Je m'habille** _means 'I'm getting dressed'. By adding_ **dés** _to the start of the French verb, you make the opposite._
**unemployed** ADJECTIVE
**au chômage**
**He's unemployed.**
Il est au chômage.
**unfair** ADJECTIVE
**injuste**
**That's unfair!**
C'est injuste!
**unfashionable** ADJECTIVE
**démodé** _masc_
**démodée** _fem_
**unfold** VERB
**déplier**
**Unfold the map.**
Déplie la carte.
**_Language tip_**
**plier** _means 'to fold'. By adding_ **dé** _to the start of the French verb, you make the opposite. In English, you add **un** to make the opposite._
**unforgettable** ADJECTIVE
**inoubliable**
**unfortunately** ADVERB
**malheureusement**
**Unfortunately it's too late.**
Malheureusement, c'est trop tard.
**Unfortunately not.**
Malheureusement, non.
**unhappy** ADJECTIVE
**malheureux** _masc_
**malheureuse** _fem_
**He's unhappy at school.**
Il est malheureux à l'école.
**You look unhappy.**
Tu as l'air triste.
**uni** NOUN
la **fac** _fem_
**She's at uni.**
Elle est à la fac.
**uniform** NOUN
l' **uniforme** _masc_
**We wear school uniform.**
Nous portons un uniforme scolaire.
_**Did you know...?**_
_French children don't wear school uniform._
**Union Jack** NOUN
le **drapeau du Royaume-Uni** _masc_
_**Did you know...?**_
**le drapeau tricolore** _is the French flag: its three colours are blue, white and red._
**United Kingdom** NOUN
le **Royaume-Uni** _masc_
**to the United Kingdom**
au Royaume-Uni
**in the United Kingdom**
au Royaume-Uni
**United States** NOUN
les **États-Unis** _masc pl_
**in the United States**
aux États-Unis
**to the United States**
aux États-Unis
**universe** NOUN
l' **univers** _masc_
**university** NOUN
l' **université** _fem_
**She's at university.**
Elle va à l'université.
**Do you want to go to university?**
Tu veux aller à l'université?
**Lancaster University**
l'université de Lancaster
**unless** CONJUNCTION
**Don't do it unless I say 'Simon says'.**
Ne le faites pas si je ne dis pas 'Jacques a dit'.
**I'll have that biscuit, unless you want it.**
Je veux bien ce biscuit si tu n'en veux pas.
**unlikely** ADJECTIVE
**peu probable**
**It's possible, but unlikely.**
C'est possible, mais peu probable.
**unlucky** ADJECTIVE
**1** _(person)_
**If you are unlucky, try again.**
Si tu n'as pas de chance, recommence.
**I'm always unlucky.**
Je n'ai jamais de chance.
**2** _(number, animal)_
**Thirteen is an unlucky number.**
Le nombre treize porte malheur.
**It's unlucky to walk under a ladder.**
Ça porte malheur de passer sous une échelle.
_**Did you know...?**_
_French people think black cats are unlucky._
**unnecessary** ADJECTIVE
**inutile**
**unpack** VERB
**défaire**
**I'm going to unpack my suitcase.**
Je vais défaire ma valise.
**_Language tip_**
**Je fais ma valise** _means 'I'm packing my case'. By adding_ **dé** _to the start of the French verb, you give it the opposite meaning. In English, you add_ **un** _to make the opposite._
**unpleasant** ADJECTIVE
**désagréable**
**unpopular** ADJECTIVE
**impopulaire**
**unpredictable** ADJECTIVE
**imprévisible**
**The weather is unpredictable.**
Le temps est imprévisible.
**unreliable** ADJECTIVE
**pas fiable**
**Our car is unreliable.**
Notre voiture n'est pas fiable.
**unsuitable** ADJECTIVE
**inapproprié** _masc_
**inappropriée** _fem_
**untidy** ADJECTIVE
**en désordre**
**My bedroom's always untidy.**
Ma chambre est toujours en désordre.
**My writing is untidy.**
J'écris mal.
**until** PREPOSITION
**1** **jusqu'à**
**He's here until tomorrow.**
Il est là jusqu'à demain.
**The supermarket is open until ten.**
Le supermarché reste ouvert jusqu'à dix heures du soir.
**2** **avant** _(with 'not')_
**not until tomorrow**
pas avant demain
**When will it be ready? — Not until next week.**
Quand est-ce que ça sera prêt? — Pas avant la semaine prochaine.
**3** **à**
**from nine until five**
de neuf heures à cinq heures
**from Monday until Friday**
du lundi jusqu'au vendredi
**unusual** ADJECTIVE
**peu courant** _masc_
**peu courante** _fem_
**It's an unusual name.**
C'est un nom peu courant.
**up**
**up** _can be an adverb, an adjective or a preposition._
**A** ADVERB
**en haut**
**up on the hill**
en haut de la colline
**up to**
jusqu'à
**Let's count up to fifty.**
Comptons jusqu'à cinquante.
**up to now**
jusqu'à présent
**up here**
ici **up there**
là-haut
**It's up to you.**
C'est à vous de décider.
**B** ADJECTIVE
**levé** _masc_
**levée** _fem (person)_
**I'm always up before eight.**
Je suis toujours levé avant huit heures.
**He's not up yet.**
Il n'est pas encore levé.
**C** PREPOSITION
**The post office is up the road.**
La poste est en haut de la rue.
**The cat is up on the roof.**
Le chat est en haut sur le toit.
**upper** ADJECTIVE
**supérieur** _masc_
**supérieure** _fem_
**on the upper floor**
à l'étage supérieur
**upper sixth** NOUN
**She's in the upper sixth.**
Elle est en terminale.
_**Did you know...?**_
_In French secondary schools, the years are counted from the_ **sixième** _(youngest) to_ **première** _and_ **terminale** _(oldest)._
**upset**
**upset** _can be an adjective or a verb._
**A** ADJECTIVE
**secoué** _masc_
**secouée** _fem_
**She's still a bit upset.**
Elle est encore un peu secouée.
**I had an upset stomach.**
J'avais l'estomac dérangé.
**B** VERB
**faire de la peine**
**I don't want to upset my granny.**
Je ne veux pas faire de peine à ma grand-mère.
**upside down** ADVERB
**à l'envers**
**That painting is upside down.**
Ce tableau est à l'envers.
**upstairs** ADVERB
**en haut**
**Where's your coat? — It's upstairs.**
Où est ton manteau? — Il est en haut.
**up-to-date** ADJECTIVE
**moderne**
**upwards** ADVERB
**vers le haut**
**urgent** ADJECTIVE
**urgent** _masc_
**urgente** _fem_
**Is it urgent?**
C'est urgent?
**US** NOUN
les **USA** _masc pl_
**in the US**
aux USA
**to the US**
aux USA
**from the US**
des USA
**us** PRONOUN
**nous**
**Come with us.**
Viens avec nous.
**Tell us the story.**
Raconte-nous l'histoire.
**USA** NOUN
les **USA** _masc pl_
**in the USA**
aux USA
**to the USA**
aux USA
**from the USA**
des USA
**use**
**use** _can be a verb or a noun._
**A** VERB
**utiliser**
**You can use a spoon or a fork.**
Tu peux utiliser une cuillère ou une fourchette.
**Can we use a dictionary in the exam?**
Est-ce qu'on peut utiliser un dictionnaire à l'examen?
**Can I use your phone?**
Je peux téléphoner?
**Can I use the toilet?**
Je peux aller aux toilettes?
**B** NOUN
**It's no use.**
Ça ne sert à rien.
**use up** VERB
**finir**
**We've used up all the paint.**
Nous avons fini la peinture.
**used** ADJECTIVE
**I'm used to getting up early.**
J'ai l'habitude de me lever tôt.
**I'm used to it.**
J'ai l'habitude.
**I'm not used to it.**
Je n'ai pas l'habitude.
**useful** ADJECTIVE
**utile**
**useless** ADJECTIVE
**nul** _masc_
**nulle** _fem_
**This map is useless.**
Cette carte est nulle.
**You're useless!**
Tu es nul!
**usual** ADJECTIVE
**habituel** _masc_
**habituelle** _fem_
**my usual seat**
ma place habituelle
**as usual**
comme d'habitude
**usually** ADVERB
**en général**
**I usually wear trousers.**
En général, je porte un pantalon.
**utility room** NOUN
la **buanderie** _fem_
# **V v**
**vacancy** NOUN
**'no vacancies'**
'complet'
**vacuum cleaner** NOUN
l' **aspirateur** _masc_
**vague** ADJECTIVE
**vague**
**Valentine card** NOUN
la **carte de la Saint-Valentin** _fem_
**Valentine's Day** NOUN
la **Saint-Valentin** _fem_
**valley** NOUN
la **vallée** _fem_
**valuable** ADJECTIVE
**de valeur**
**a valuable picture**
un tableau de valeur
**van** NOUN
la **camionnette** _fem_
**_Language tip_**
_'Un camion' is a lorry. The ending_ **-ette** _shows that_ **une camionnette** _is smaller than a lorry._
**vandal** NOUN
le/la **vandale** _masc/fem_
**vandalism** NOUN
le **vandalisme** _masc_
**vanilla** NOUN
la **vanille** _fem_
**vanilla ice cream**
la glace à la vanille
**varied** ADJECTIVE
**varié** _masc_
**variée** _fem_
**variety** NOUN
la **variété** _fem_
**There's lots of variety.**
Il y a beaucoup de variété.
**various** ADJECTIVE
**plusieurs**
**There are various possibilities.**
Il y a plusieurs possibilités.
**vase** NOUN
le **vase** _masc_
**VDU** NOUN
la **console** _fem_
**vegan** NOUN
le **végétalien** _masc_
la **végétalienne** _fem_
**I'm a vegan.**
Je suis végétalienne.
**vegetable** NOUN
le **légume** _masc_
**vegetable soup**
la soupe aux légumes
**Would you like some vegetables?**
Vous voulez des légumes?
**vegetarian**
**vegetarian** _can be an adjective or a noun._
**A** ADJECTIVE
**végétarien** _masc_
**végétarienne** _fem_
**vegetarian lasagne**
les lasagnes végétariennes
**B** NOUN
le **végétarien** _masc_
la **végétarienne** _fem_
**I'm a vegetarian.**
Je suis végétarien.
**Susie's a vegetarian.**
Susie est végétarienne.
**verb** NOUN
le **verbe** _masc_
**very** ADVERB
**très**
**very tall**
très grand
**not very interesting**
pas très intéressant
**very much**
beaucoup
**very soon**
très bientôt
**I'm very sorry.**
Je suis vraiment désolé.
**vest** NOUN
le **maillot de corps** _masc_
**vet** NOUN
le/la **vétérinaire** _masc/fem_
**She's a vet.**
Elle est vétérinaire.
**_Language tip_**
_When you say what someone's job is in French, you do not translate_ **a**.
**vicar** NOUN
le **pasteur** _masc_
**My uncle's a vicar.**
Mon oncle est pasteur.
**_Language tip_**
_When you say what someone's job is in French, you do not translate_ **a**.
**video**
**video** _can be a noun or a verb._
**A** NOUN
**1** la **vidéo** _fem (film)_
**We're going to watch a video.**
Nous allons regarder une vidéo.
**2** la **cassette vidéo** _fem (cassette)_
**I've got the video.**
J'ai la cassette vidéo.
**3** le **magnétoscope** _masc (video recorder)_
**Can you switch on the video?**
Tu peux allumer le magnétoscope?
**B** VERB
**filmer**
**We're going to video the concert.**
On va filmer le concert.
**video game** NOUN
le **jeu vidéo** _masc_
**I like playing video games.**
J'aime les jeux vidéo.
**video recorder** NOUN
le **magnétoscope** _masc_
**video shop** NOUN
le **vidéoclub** _masc_
**view** NOUN
la **vue** _fem_
**There's an amazing view.**
Il y a une vue extraordinaire.
**villa** NOUN
la **villa** _fem_
**village** NOUN
le **village** _masc_
**in the village**
dans le village
**vinegar** NOUN
le **vinaigre** _masc_
**vineyard** NOUN
le **vignoble** _masc_
**violent** ADJECTIVE
**violent** _masc_
**violente** _fem_
**violin** NOUN
le **violon** _masc_
**I play the violin.**
Je joue du violon.
**virus** NOUN
le **virus** _masc_
**visit**
**visit** _can be a noun or a verb._
**A** NOUN
**1** la **visite** _fem (to tourist attraction)_
**a visit to Edinburgh castle**
une visite du château d'Édimbourg
**2** le **séjour** _masc (to country)_
**Did you enjoy your visit to France?**
Ton séjour en France s'est bien passé?
**B** VERB
**1** **rendre visite à** _(person)_
**I'm going to visit friends.**
Je vais rendre visite à des amis.
**2** **visiter** _(place)_
**We're going to visit the castle.**
Nous allons visiter le château.
**visitor** NOUN
l' **invité** _masc_
l' **invitée** _fem_
**Today we've got a French visitor.**
Aujourd'hui, nous avons un invité français.
**vitamin** NOUN
la **vitamine** _fem_
**_Language tip_**
_What extra vowel does the French word have?_
**vocabulary** NOUN
le **vocabulaire** _masc_
**voice** NOUN
la **voix** _fem_ (PL les **voix** )
**volleyball** NOUN
le **volley-ball** _masc_
**We sometimes play volleyball.**
Quelquefois nous jouons au volley-ball.
**volunteer** NOUN
le/la **volontaire** _masc/fem_
# **W w**
**waist** NOUN
la **taille** _fem_
**wait** VERB
**attendre**
**Wait Mathieu, it's not your turn.**
Attends Mathieu, ce n'est pas ton tour.
**Wait boys, I'm coming.**
Attendez les garçons, j'arrive.
**Wait for me!**
Attends-moi!
**Wait a minute!**
Attends!
**Wait a minute, children!**
Attendez, les enfants!
**waiter** NOUN
le **serveur** _masc_
**waiting room** NOUN
la **salle d'attente** _fem_
**waitress** NOUN
la **serveuse** _fem_
**wake up** VERB
**se réveiller**
**Wake up, Marie!**
Réveille-toi, Marie!
**Wales** NOUN
le **pays de Galles** _masc_
**Swansea is in Wales.**
Swansea est au pays de Galles.
**When are you coming to Wales?**
Quand est-ce que tu viens au pays de Galles?
**Bronwen is from Wales.**
Bronwen est galloise.
**_Language tip_**
_How can you tell that Bronwen is a girl's name in this example sentence?_
**the Prince of Wales**
le prince de Galles
**walk**
**walk** _can be a verb or a noun._
**A** VERB
**1** **marcher**
**He walks fast.**
Il marche vite.
**Walk faster, Serge.**
Marche plus vite, Serge.
**Walk faster, children.**
Marchez plus vite, les enfants.
**2** **aller à pied** _(go on foot)_
**Are you walking or going by bus?**
Tu y vas à pied ou en bus?
**I walked 10 kilometres.**
J'ai fait dix kilomètres à pied.
**B** NOUN
la **promenade** _fem_
**Would you like to go for a walk?**
Tu veux faire une promenade?
**_Language tip_**
**promenade** _is used in English to mean a road by the sea where you can go for a walk._
**walking** NOUN
la **marche** _fem_
**My parents like walking.**
Mes parents aiment la marche.
**Walkman** ® NOUN
le **walkman** ® _masc_
**wall** NOUN
le **mur** _masc_
**There are posters on the wall.**
Il y a des posters au mur.
**wallet** NOUN
le **portefeuille** _masc_
**want** VERB
**vouloir**
**Do you want some cake?**
Tu veux du gâteau?
**I don't want to play.**
Je ne veux pas jouer.
**What do you want to do tomorrow?**
Qu'est-ce que tu veux faire demain?
**What do you want, Marie?**
Qu'est-ce que tu veux, Marie?
**What do you want, boys?**
Qu'est-ce que vous voulez, les garçons?
**war** NOUN
la **guerre** _fem_
**wardrobe** NOUN
l' **armoire** _fem_
**warm** ADJECTIVE
**chaud** _masc_
**chaude** _fem_
**warm water**
l'eau chaude
**It's warm.**
Il fait chaud.
**I'm warm.**
J'ai chaud.
**was** VERB _see_ **be**
**wash** VERB
**1** **laver** _(thing)_
**I'll wash the grapes.**
Je vais laver le raisin.
**2** **se laver** _(oneself)_
**At seven I get up, wash and get dressed.**
À sept heures je me lève, je me lave et je m'habille.
**_Language tip_**
_Notice how **my** is translated in the next two examples._
**I'm going to wash my hands.**
Je vais me laver les mains.
**I want to wash my hair.**
Je veux me laver les cheveux.
**Wash your hands!**
Lave-toi les mains!
**washbasin** NOUN
le **lavabo** _masc_
**washing machine** NOUN
la **machine à laver** _fem_
**washing-up** NOUN
**Who's going to do the washing-up?**
Qui va faire la vaisselle?
**I often do the washing-up.**
Je fais souvent la vaisselle.
**washroom** NOUN _(Canada)_
les **toilettes** _fem pl_
**wasn't** (= **was not** ) VERB _see_ **be**
**wasp** NOUN
la **guêpe** _fem_
**waste** NOUN
**It's a waste of time.**
C'est une perte de temps.
**wastepaper basket** NOUN
la **corbeille à papier** _fem_
**Put your chewing gum in the wastepaper basket.**
Mets ton chewing gum dans la corbeille à papier.
**watch**
**watch** _can be a noun or a verb._
**A** NOUN
la **montre** _fem_
**I haven't got a watch.**
Je n'ai pas de montre.
**B** VERB
**regarder**
**I watch television on Saturday mornings.**
Je regarde la télévision le samedi matin.
**Watch me, Mum!**
Regarde-moi, maman!
**watch out** VERB
**faire attention**
**You need to watch out.**
Il faut faire attention.
**Watch out!**
Attention!
**water** NOUN
l' **eau** _fem_
**a glass of water**
un verre d'eau
**wave** NOUN
la **vague** _fem_
**There are sometimes big waves.**
Il y a parfois des grosses vagues.
**wavy** ADJECTIVE
**wavy hair**
les cheveux ondulés
**way** NOUN
**1** le **chemin** _masc (to place)_
**I don't know the way.**
Je ne connais pas le chemin.
**Ask the way.**
Demande le chemin.
**Can you tell me the way to the station?**
Vous pouvez me dire comment aller à la gare?
**It's a long way.**
C'est loin.
**Which way is it?**
C'est par où?
**It's this way.**
C'est par ici.
**2** la **façon** _fem (manner)_
**What's the best way to learn French?**
Quelle est la meilleure façon d'apprendre le français?
**Do it this way, Sophie.**
Fais-le comme ça, Sophie.
**way in** NOUN
l' **entrée** _fem_
**way out** NOUN
la **sortie** _fem_
**Where's the way out?**
Où est la sortie?
**we** PRONOUN
**_Language tip_**
_There are two ways of saying 'we'. In spoken French_ , **on** _is used more often than_ **nous**.
**1** **nous**
**We're staying here for a week.**
Nous restons une semaine ici.
**2** **on**
**Shall we start?**
On commence?
**wear** VERB
**porter**
**She's wearing a hat.**
Elle porte un chapeau.
**I wear glasses.**
Je porte des lunettes.
**weather** NOUN
le **temps** _masc_
**because of the weather**
à cause du temps
**What's the weather like today?**
Quel temps fait-il aujourd'hui?
**The weather's not very nice.**
Il ne fait pas très beau.
**What's the weather like?**
Quel temps fait-il?
**The weather's nice.**
Il fait beau temps.
**weather forecast** NOUN
la **météo** _fem_
**webcam** NOUN
la **webcam** _fem_
**website** NOUN
le **site web** _masc_
**wedding** NOUN
le **mariage** _masc_
**It's my cousin's wedding today.**
Aujourd'hui, c'est le mariage de ma cousine.
**wedding anniversary** NOUN
l' **anniversaire de mariage** _masc_
**Wednesday** NOUN
le **mercredi** _masc_
**It's Wednesday today.**
Aujourd'hui c'est mercredi.
**on Wednesday**
mercredi
**on Wednesdays**
le mercredi
**every Wednesday**
tous les mercredis
**last Wednesday**
mercredi dernier
**next Wednesday**
mercredi prochain
**_Language tip_**
_Days of the week are not written with a capital letter in French._
**week** NOUN
la **semaine** _fem_
**two weeks**
deux semaines
**this week**
cette semaine
**last week**
la semaine dernière
**every week**
toutes les semaines
**next week**
la semaine prochaine
**in a week's time**
dans une semaine
**weekday** NOUN
**on weekdays**
en semaine
**weekend** NOUN
le **week-end** _masc_
**What are you doing at the weekend?**
Qu'est-ce que tu fais ce week-end?
**at weekends**
le week-end
**last weekend**
le week-end dernier
**next weekend**
le week-end prochain
_**Did you know...?**_
_In Quebec,_ **la fin de semaine** _is used instead of_ **le week-end**.
**welcome** ADJECTIVE
**Welcome!**
Bienvenue!
**Welcome to Scotland!**
Bienvenue en Écosse!
**Thank you! — You're welcome!**
Merci! — De rien!
**well**
**well** _can be an adverb or an adjective._
**A** ADVERB
**bien**
**The team is playing well.**
L'équipe joue bien.
**as well**
aussi
**We're going to Chartres as well as Paris.**
Nous allons à Paris et aussi à Chartres.
**B** ADJECTIVE _(in good health)_
**He's not well.**
Il ne va pas bien.
**I'm not very well at the moment.**
Je ne vais pas très bien en ce moment.
**Well done!**
Bravo!
**Get well soon!**
Remets-toi vite!
**well-behaved** ADJECTIVE
**sage**
**wellies** PL NOUN
les **bottes en caoutchouc** _fem pl_
**wellingtons** PL NOUN
les **bottes en caoutchouc** _fem pl_
**well-known** ADJECTIVE
**célèbre**
**a well-known film star**
une vedette de cinéma célèbre
**Welsh**
**Welsh** _can be an adjective or a noun._
**A** ADJECTIVE
**gallois** _masc_
**galloise** _fem_
**She's Welsh.**
Elle est galloise.
**Welsh people**
les Gallois
**_Language tip_**
**gallois** _is not spelled with a capital letter except when it means a Welsh person._
**B** NOUN
le **gallois** _masc (language)_
**Welshman** NOUN
le **Gallois** _masc_
**Welshwoman** NOUN
la **Galloise** _fem_
**went** VERB _see_ **go**
**were** VERB _see_ **be**
**weren't** (= **were not** ) VERB _see_ **be**
**west**
**west** _can be an adjective or a noun._
**A** ADJECTIVE
**ouest** _masc, fem, pl_
**the west coast**
la côte ouest
**B** NOUN
l' **ouest** _masc_
**in the west**
dans l'ouest
**West Country** NOUN
le **sud-ouest de
l'Angleterre** _masc_
**western** NOUN
le **western** _masc_
**I like westerns.**
J'aime les westerns.
**West Indian** ADJECTIVE
**antillais** _masc_
**antillaise** _fem_
**She's West Indian.**
Elle est antillaise.
**_Language tip_**
_The adjective_ **West Indian** _is spelled with a capital letter, but_ **antillais** _is not._
**West Indies** PL NOUN
les **Antilles** _fem pl_
**wet** ADJECTIVE
**mouillé** _masc_
**mouillée** _fem_
**wet clothes**
des vêtements mouillés
**I'm wet.**
Je suis mouillé.
**It's wet today.**
Il pleut aujourd'hui.
**whale** NOUN
la **baleine** _fem_
**what**
**what** _can be a pronoun or an adjective._
**A** PRONOUN
**1** **qu'est-ce que**
**What are you doing, children?**
Qu'est-ce que vous faites, les enfants?
**What's happening?**
Qu'est-ce qu'il se passe?
**What's the matter?**
Qu'est-ce qu'il y a?
**Take a card and tell your partner what it is.**
Prends une carte, et dis à ton partenaire ce que c'est.
**2** **quel** _masc_
**quelle** _fem_
**What's your phone number?**
Quel est ton numéro de téléphone?
**What's the capital of Belgium?**
Quelle est la capitale de la Belgique?
**B** ADJECTIVE
**quel** _masc_
**quelle** _fem (which)_
**What letter does it start with?**
Ça commence par quelle lettre?
**What colour is it?**
C'est de quelle couleur?
**What?**
Comment?
**What is it?**
Qu'est-ce que c'est?
**What do you want?**
Qu'est-ce que tu veux?
**What's the weather like?**
Quel temps fait-il?
**What's your name?**
Comment tu t'appelles?
**What time is it?**
Quelle heure est-il?
**What day is it today?**
Quel jour sommes-nous?
**wheel** NOUN
la **roue** _fem_
**wheelchair** NOUN
le **fauteuil roulant** _masc_
**when** ADVERB
**quand**
**When it rains we stay in the classroom.**
Quand it pleut nous restons dans la classe.
**When's your birthday?**
C'est quand, ton anniversaire?
**_Language tip_**
_You can also say:_ **Ton anniversaire, c'est quand?**
**where** ADVERB, CONJUNCTION
**où**
**_Language tip_**
**où** _can come first or last in a sentence._
**Where's Emma today?**
Où est Emma aujourd'hui?
**Where are you going?**
Tu vas où?
**Where do you live?**
Où habites-tu?
**which**
**which** _can be an adjective or a pronoun._
**A** ADJECTIVE
**quel** _masc_
**quelle** _fem_
**Which flavour do you want?**
Quel parfum est-ce que tu veux?
**Which number is it?**
C'est quel numéro?
**B** PRONOUN
**lequel** _masc_ **laquelle** _fem_
**Which would you like?**
Vous voulez lequel?
**Which is your car?**
C'est laquelle, ta voiture?
**Which do you prefer, cricket or football?**
Qu'est-ce que tu préfères, le cricket ou le football?
**while** CONJUNCTION
**pendant que**
**While you're here we can do some sightseeing.**
On peut faire du tourisme pendant que tu es là.
**whipped cream** NOUN
la **crème fouettée** _fem_
**whiskers** PL NOUN
les **moustaches** _fem pl_
**white**
**white** _can be an adjective or a noun._
**A** ADJECTIVE
**blanc** _masc_
**blanche** _fem_
**He's wearing white trousers.**
Il porte un pantalon blanc.
**My shirt is white.**
Ma chemise est blanche.
**_Language tip_**
_Colour adjectives come after the noun in French._
**B** NOUN
le **blanc** _masc_
**The bride is wearing white.**
La mariée est vêtue de blanc.
**whiteboard** NOUN
le **tableau blanc** _masc_ (PL les **tableaux blancs** )
**an interactive whiteboard**
un tableau interactif
**white coffee** NOUN
le **café au lait** _masc_
**Whitsun** NOUN
la **Pentecôte** _fem_
**who** PRONOUN
**qui**
**Who wants to start?**
Qui veut commencer?
**Who's that?**
C'est qui?
**_Language tip_**
_You can also say:_ **Qui est-ce?**
**whole** ADJECTIVE
**tout** _masc_
**toute** _fem_
**the whole class**
toute la classe
**the whole afternoon**
tout l'après-midi
**the whole world**
le monde entier
**whose** PRONOUN, ADJECTIVE
**à qui**
**Whose pencil case is this?**
À qui est cette trousse?
**Whose turn is it?**
C'est à qui le tour?
**Whose is this?**
C'est à qui?
**why** ADVERB
**pourquoi**
**Why are you crying?**
Pourquoi tu pleures?
**That's why I can't come.**
Voilà pourquoi je ne peux pas venir.
**Why not?**
Pourquoi pas?
**wide** ADJECTIVE
**large**
**a wide road**
une route large
**widow** NOUN
la **veuve** _fem_
**widower** NOUN
le **veuf** _masc_
**wife** NOUN
la **femme** _fem_
**She's his wife.**
C'est sa femme.
**wifi** NOUN
le **wifi** _masc_
**wild** ADJECTIVE
**sauvage**
**a wild animal**
un animal sauvage
**will** VERB
**It will soon be my birthday.**
C'est bientôt mon anniversaire.
**It'll soon be the holidays.**
C'est bientôt les vacances.
**I'll come with you.**
Je vais venir avec toi.
**Do you think he will come?**
Tu crois qu'il va venir?
**Colette won't come.**
Colette ne viendra pas.
**Will you help me?**
Est-ce que tu peux m'aider?
**win** VERB
**gagner**
**I've won!**
J'ai gagné!
**wind** NOUN
le **vent** _masc_
**There is a lot of wind.**
Il y a beaucoup de vent.
**window** NOUN
la **fenêtre** _fem_
**Look out of the window, boys.**
Regardez par la fenêtre, les garçons.
**a shop window**
une vitrine
**windy** ADJECTIVE
**a windy day**
un jour de grand vent
**It's windy.**
Il y a du vent.
**wine** NOUN
le **vin** _masc_
**a bottle of wine**
une bouteille de vin
**a glass of wine**
un verre de vin
**white wine**
le vin blanc
**red wine**
le vin rouge
**winner** NOUN
le **gagnant** _masc_
la **gagnante** _fem_
**winning** ADJECTIVE
**the winning team**
l'équipe gagnante
**winter** NOUN
l' **hiver** _masc_
**last winter**
l'hiver dernier
**in winter**
en hiver
**winter sports** PL NOUN
les **sports d'hiver** _masc pl_
**winter time** NOUN
l' **hiver** _masc_
**in wintertime**
en hiver
**wish**
**wish** _can be a noun or a verb._
**A** NOUN
le **vœu** _masc_ (PL les **vœux** )
**Make a wish!**
Fais un vœu!
**with best wishes, Kathy**
bien amicalement, Kathy
**'best wishes'**
'meilleurs vœux'
**B** VERB
**I wish I could!**
Si je pouvais!
**witch** NOUN
la **sorcière** _fem_
**with** PREPOSITION
**1** **avec**
**Come with me.**
Venez avec moi.
**Tea with milk?**
Du thé avec du lait?
**It begins with 'b'.**
Ça commence par un 'b'.
**2** **chez** _(at the home of)_
**We're going to stay with friends.**
Nous allons loger chez des amis.
**I live with my dad.**
J'habite chez mon père.
**without** PREPOSITION
**sans**
**I drink coffee without sugar.**
Je bois mon café sans sucre.
**without a coat**
sans manteau
**without speaking**
sans parler
**wives** PL NOUN
les **femmes** _fem pl_
**wolf** NOUN
le **loup** _masc_
**woman** NOUN
la **femme** _fem_
**three women and two men**
trois femmes et deux hommes
**won** VERB _see_ **win**
**wonder** VERB
**se demander**
**I wonder where Caroline is.**
Je me demande où est Caroline.
**won't** (= **will not** ) VERB _see_ **will**
**wonderful** ADJECTIVE
**formidable**
**wood** NOUN
le **bois** _masc_
**wool** NOUN
la **laine** _fem_
**It's made of wool.**
C'est en laine.
**word** NOUN
le **mot** _masc_
**Repeat the words, everyone.**
Répétez les mots, tout le monde.
**I've forgotten the word.**
J'ai oublié le mot.
**What's the word for 'shop' in French?**
Comment dit-on 'shop' en français?
**I don't know the word.**
Je ne connais pas le mot.
**the words** _(lyrics)_
les paroles
**We're going to learn the words of a song.**
Nous allons apprendre les paroles d'une chanson.
**work**
**work** _can be a verb or a noun._
**A** VERB
**1** **travailler** _(person)_
**She works in a shop.**
Elle travaille dans un magasin.
**2** **marcher** _(machine, plan)_
**The heating isn't working.**
Le chauffage ne marche pas.
**B** NOUN
le **travail** _masc_
**He's at work at the moment.**
Il est au travail en ce moment.
**I've got a lot of work to do.**
J'ai beaucoup de travail à faire.
**at work**
au travail
**worker** NOUN
**She's a good worker.**
Elle travaille bien.
**worksheet** NOUN
la **feuille d'exercices** _fem_
**Have you got a worksheet Max?**
Max, tu as une feuille d'exercices?
**world** NOUN
le **monde**
_masc_
**the whole world**
le monde entier
**He's the world champion.**
Il est champion du monde.
**worried** ADJECTIVE
**inquiet** _masc_
**inquiète** _fem_
**She's very worried.**
Elle est très inquiète.
**worry** VERB
**s'inquiéter**
**Don't worry, Mum!**
Ne t'inquiète pas, Maman!
**worse**
**worse** _can be an adjective or an adverb._
**A** ADJECTIVE
**pire**
**The weather is worse in Scotland.**
Le temps est pire en Écosse.
**B** ADVERB
**plus mal**
**I'm feeling worse.**
Je me sens plus mal.
**worst** ADJECTIVE
**the worst**
le plus mauvais
**_Language tip_**
_Use_ **la plus mauvaise** _if the noun is feminine._
**I always get the worst mark.**
J'ai toujours la plus mauvaise note.
**Ten! My worst score.**
Dix! Mon plus mauvais score.
**Maths is my worst subject.**
Je suis vraiment nul en maths.
**would** VERB
**1** _(in offers)_
**Would you like to play with me?**
Tu veux jouer avec moi?
**Would you like coffee, sir?**
Vous voulez du café, monsieur?
**2** _(in requests)_
**I'd like a hot chocolate, please.**
Je voudrais un chocolat chaud, s'il vous plaît.
**My friend would like a coke.**
Mon ami voudrait un coca.
**What would you like, sir?**
Vous désirez, monsieur?
**What would you like, dear?**
Qu'est-ce que tu veux, ma chérie?
**_Language tip_**
_You can also say:_ **Que veux-tu, ma chérie?**
**3** _(in polite orders)_
**Would you give out the books, Hugues?**
Tu peux distribuer les cahiers, Hugues?
**Would you close the door please?**
Vous pouvez fermer la porte, s'il vous plaît?
**wrapping paper** NOUN
le **papier cadeau** _masc_
**write** VERB
**écrire**
**Write your names.**
Écrivez vos noms.
**Write to me soon, Roxanne.**
Écris-moi vite, Roxanne.
**I'm going to write to my penfriend.**
Je vais écrire à ma correspondante.
**Write soon!**
Écris-moi vite!
**write down**
**noter**
**I'll write down the address.**
Je vais noter l'adresse.
**Can you write it down for me, please?**
Vous pouvez me l'écrire, s'il vous plaît?
**writing** NOUN
l' **écriture** _fem_
**I can't read your writing.**
Je n'arrive pas à lire ton écriture.
**wrong**
**wrong** _can be an adjective or an adverb._
**A** ADJECTIVE
**Number two is right, but number three is wrong.**
Le numéro deux est juste, mais le numéro trois est faux.
**I got three questions wrong.**
J'ai eu trois questions fausses.
**You're looking at the wrong page.**
Tu n'es pas à la bonne page.
**That's the wrong answer.**
Ce n'est pas la bonne réponse.
**B** ADVERB
**mal**
**You're saying it wrong.**
Tu le dis mal.
**Have I spelled it wrong?**
Je l'ai mal écrit?
**What's wrong?**
Qu'est-ce qui ne va pas?
**What's wrong with you?**
Qu'est-ce que tu as?
# **X x**
**Xmas** NOUN
**Noël** _masc_
**X-ray**
**X-ray** _can be a verb or a noun._
**A** VERB
**faire une radio de**
**They're going to X-ray my leg.**
Ils vont faire une radio de ma jambe.
**They X-rayed my arm.**
Ils ont fait une radio de mon bras.
**B** NOUN
la **radio** _fem_
**I'm going to have an X-ray.**
Je vais passer une radio.
# **Y y**
**yacht** NOUN
**1** le **voilier** _masc (sailing boat)_
**2** le **yacht** _masc (luxury motorboat)_
**yard** NOUN
la **cour** _fem_
**in the yard**
dans la cour
**year** NOUN
l' **année** _fem_
**next year**
l'année prochaine
**_Language tip_**
_There are two words for_ **year** : **année** _and_ **an**. _Use_ **an** _with numbers._
**a hundred years**
cent ans
**an eight-year-old child**
un enfant de huit ans
**this year**
cette année
**I'm ten years old.**
J'ai dix ans.
**I'm in Year 6.**
Je suis au CM2.
**She's in Year 5.**
Elle est au CM1.
_**Did you know...?**_
_In France, children start primary school at the age of six. The first year is_ **CP** , _followed by_ **CE1** _and_ **CE2**. _The last two years are_ **CM1** _and_ **CM2**.
**yellow**
**yellow** _can be an adjective or a noun._
**A** ADJECTIVE
**jaune**
**I'm wearing yellow shorts.**
Je porte un short jaune.
**_Language tip_**
_Colour adjectives come after the noun in French._
**B** NOUN
le **jaune** _masc_
**Yellow is my favourite colour.**
Ma couleur préférée, c'est le jaune.
**yes** ADVERB
**oui**
**Do you like it? — Yes.**
Tu aimes ça? — Oui.
**Answer yes or no.**
Réponds par oui ou par non.
**yesterday** ADVERB
**hier**
**When? — Yesterday.**
Quand? — Hier.
**I was absent yesterday.**
Hier, j'étais absente.
**yesterday morning**
hier matin
**yesterday afternoon**
hier après-midi
**yesterday evening**
hier soir
**yet** ADVERB
**encore**
**I haven't finished yet.**
Je n'ai pas encore fini.
**Have you finished yet, children?**
Vous avez fini, les enfants?
**Not yet.**
Pas encore.
**yoghurt** NOUN
le **yaourt** _masc_
**you** PRONOUN
**_Language tip_**
_Only use_ **tu** _when you're talking to your family or to someone of your own age, or younger. Use_ **vous** _when you're talking to several people, or to an adult you don't know very well. The teacher calls you_ **'tu'** , _but you call the teacher_ **'vous'**.
**1** **tu** _(singular and subject of verb)_
**Do you like football, Nina?**
Tu aimes le football, Nina?
**Do you understand, Michelle?**
Tu comprends, Michelle?
**2** **te** _(singular and object of verb)_
**I know you.**
Je te connais.
**_Language tip_**
**te** _changes to_ **t'** _before a vowel sound._
**I love you.**
Je t'aime.
**3** **toi** _(singular and after a preposition)_
**I'll come with you.**
Je viens avec toi.
**It's for you, Xavier.**
C'est pour toi, Xavier.
**She's younger than you.**
Elle est plus jeune que toi.
**4** **vous** _(polite form or plural)_
**Do you understand, children?**
Vous comprenez, les enfants?
**Are you listening, Gaëlle and Richard?**
Vous écoutez, Gaëlle et Richard?
**Could you move out of the way please, miss?**
Vous pouvez vous pousser s'il vous plaît, madame?
**Can I help you?**
Est-ce que je peux vous aider?
**It's for you, children.**
C'est pour vous, les enfants.
**young** ADJECTIVE
**jeune**
**You're too young.**
Tu es trop jeune.
**younger** ADJECTIVE
**plus jeune**
**He's younger than me.**
Il est plus jeune que moi.
**youngest** ADJECTIVE
**plus jeune**
**my youngest brother**
mon plus jeune frère
**_Language tip_**
_To say that someone is_ **the youngest** , _use_ **le plus jeune** _for a boy and_ **la plus jeune** _for a girl._
**Hugo's the youngest.**
Hugo est le plus jeune.
**She's the youngest in the class.**
C'est la plus jeune de la classe.
**your** ADJECTIVE
**_Language tip_**
_When you want to say something like 'your name', 'your house', or 'your hair' in French, you need to know if 'name', 'house', 'hair' are masculine, feminine, or plural, because there are three possible words for_ **your**.
**1** **ton** _masc (to someone you call 'tu')_
**Is that your brother?**
C'est ton frère?
**ta** _fem_
**Is that your sister?**
C'est ta sœur?
**tes** _pl_
**your parents**
tes parents
**_Language tip_**
**ta** _changes to_ **ton** _before a vowel sound._
**your friend Éléonore**
ton amie Éléonore
**2** **votre** _(to people you call 'vous')_
**your house**
votre maison
**When's your birthday, miss?**
Quelle est la date de votre anniversaire, madame?
**vos** _pl_
**Take your things out.**
Sortez vos affaires.
**_Language tip_**
_Notice how_ **your** _is translated in the next two examples._
**Wash your hands, Laura.**
Lave-toi les mains, Laura.
**Wash your hands, children.**
Lavez-vous les mains, les enfants.
**yours** PRONOUN
**1** **à toi** _(to someone you call 'tu')_
**Is this yours, Frank?**
C'est à toi, Frank?
**Whose is this? — It's yours, dear.**
C'est à qui? — À toi, chéri.
**2** **à vous** _(to people you call 'vous')_
**Is this yours, sir?**
C'est à vous, monsieur?
**These tickets are yours.**
Ces billets sont à vous.
**Whose is this? — It's yours.**
C'est à qui? — À vous.
**yourself** PRONOUN
**1** **te** _(to someone you call 'tu')_
**You'll make yourself sick!**
Tu vas te rendre malade!
**_Language tip_**
**te** _changes to_ **t'** _before a vowel sound._
**Are you enjoying yourself?**
Tu t'amuses bien?
**2** **toi**
**_Language tip_**
_After a preposition, use_ **toi** _instead of_ **te**.
**Tell me about yourself!**
Parle-moi de toi!
**3** **vous** _(to someone you call 'vous')_
**Help yourself, Mrs Day!**
Servez-vous, Madame Day!
**Tell me about yourself!**
Parlez-moi de vous!
**yourselves** PRONOUN
**1** **vous**
**Did you enjoy yourselves?**
Vous vous êtes bien amusés?
**2** **vous-mêmes**
**Do it yourselves!**
Faites-le vous-mêmes!
**youth club** NOUN
le **centre de jeunes** _masc_
**at the youth club**
au centre de jeunes
**youth hostel** NOUN
l' **auberge de jeunesse** _fem_
**We're going to stay at a youth hostel.**
Nous allons loger dans une auberge de jeunesse.
# **Z z**
**zebra** NOUN
le **zèbre** _masc_
**zero** NOUN
le **zéro** _masc_
**zoo** NOUN
le **zoo** _masc_
**We went to the zoo on Saturday.**
Samedi, nous sommes allésau zoo.
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First Edition 2014
Previously published as Collins First Time French Dictionary 2003, 2006, 2012
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BRUSSELS - NATO Secretary-General Anders Fogh Rasmussen announced Tuesday the alliance will send an expert mission to Libya at short notice to assess needs as the country faces a flow of insurgents from Mali.
Security experts worry that the al-Qaida-linked militants - pushed out of Mali after French military intervention - may be trying to establish a safe haven in southern Libya.
The mission "will go as soon as possible and, together with the Libyans, identify the areas in which the Libyans think they need advice and areas where we do believe we can add value," Rasmussen said ahead of the opening session of a meeting of NATO defense ministers.
He insisted it will not mean putting boots on the ground in the North African nation.
`'This is not about deploying troops to Libya. If we are to engage in training activities, such activities could take place outside Libya," he said.
U.S. defense officials have said NATO's experience training Afghan and Iraqi security forces provides the expertise to do something similar with Libya.
Rasmussen said NATO is planning to coordinate with other national and international efforts and he expects a report from the expert group by the end of June, before more definite plans are made.
Libyan leaders have requested help from NATO, the U.S. and other nations. U.S. President Obama broadly indicated that he would support efforts by NATO to aid the Libyans.
French officials believe some jihadists may have fled Mali along traditional drug and other contraband trafficking routes through Niger and into Libya.
The vast, mostly barren southern two-thirds of Libya has largely gone its own way since the rebellion that overthrew longtime dictator Moammar Gadhafi in 2011, but now there are concerns that in addition to local tensions, the area might be drawn into larger regional conflicts involving al-Qaida.
French troops drove al-Qaida forces out of nearby Mali, and there are concerns that the militants might try to regroup in southern Libya.
|
{
"redpajama_set_name": "RedPajamaC4"
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|
Humanist Discussion Group, Vol. 23, No. 769.
Virtuel de la Connaissance sur l'Europe (http://www.ena.lu).
CNRS) organising THATCamp Paris (18-19 May).
Please feel free to forward to all interested parties.
behaviors, we will have to understand and explain narrative.
questions. What does narrative do for us? What exactly is narrative?
computational modeling and scientific understanding of narrative.
* How are narratives indexed and retrieved? Is there a "universal"
have on its form and content?
set? Is there a recipe for generating narratives?
of narrative schemas from experience?
* How can we evaluate computational models of narrative?
For the past nine years, the Renaissance Society of America program has featured a number of sessions that document innovative ways in which computing technology is being incorporated into the scholarly activity of our community. At the 2011 RSA meeting (Montreal, 24-26 March 2011), several sessions will continue to follow this interest across several key projects, through a number of thematic touchstones, and in several emerging areas.
Proposals for papers, panels, demonstrations, and/or workshop presentations that focus on these issues and others are welcome.
We are pleased to be able to offer several graduate student travel subventions for presentation on these panels. Those wishing to be considered for the subvention should indicate this in their abstract submission.
For details of the RSA conference see www.rsa.org http://www.rsa.org .
Please send proposals before May 15 to siemens_at_uvic.ca.
invigorating and important one for the STS.
and textual and literary theory.
This year the conference is introducing several new formats.
demonstrations of tools or projects are discouraged.
between the panel and audience following brief opening remarks.
material in a discussion under the guidance of the seminar leader(s).
attendees will be required to enroll with the workshop leader(s).
All participants in the STS 2011 conference must be members of STS.
see the STS website at http://www.textual.org .
Please post and recirculate this CFP as appropriate.
|
{
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| 103
|
var lastTime;
var scene;
var camera;
var renderer;
var WIDTH, HEIGHT;
var rot = 0.01;
var axis;
var camX = -10, camY = 5, camZ = 10;
var radius = 10;
var angle = Math.PI/2;
var objects = [];
var origin = new THREE.Vector3(0,0,0);
var edit = false;
var intersects;
var rotationInterval;
function init(){
scene = new THREE.Scene();
camera = new THREE.PerspectiveCamera(
60, // kąt patrzenia kamery (FOV - field of view)
16/9, // proporcje widoku
0.1, // min renderowana odległość
10000 // max renderowana odległość
);
renderer = new THREE.WebGLRenderer();
// kolor tła 0x zamiast #
renderer.setClearColor(0x000000);
WIDTH = 800//window.innerWidth;
HEIGHT = 400//window.innerHeight;
renderer.setSize(WIDTH, HEIGHT);
document.getElementById("div").appendChild(renderer.domElement);
document.addEventListener("keydown", onKeyDown, false);
document.addEventListener("mousedown", onMouseDown, false);
var geometry = new THREE.BoxGeometry(1,1,1, 32,32,32);
var materials = [];
materials.push(new THREE.MeshBasicMaterial({side: THREE.DoubleSide, map: THREE.ImageUtils.loadTexture('materials/diamond.png') }));
materials.push(new THREE.MeshBasicMaterial({side: THREE.DoubleSide, map: THREE.ImageUtils.loadTexture('materials/gold.png') }));
materials.push(new THREE.MeshBasicMaterial({ side: THREE.DoubleSide,map: THREE.ImageUtils.loadTexture('materials/iron.png') }));
materials.push(new THREE.MeshBasicMaterial({side: THREE.DoubleSide, map: THREE.ImageUtils.loadTexture('materials/diamond.png') }));
materials.push(new THREE.MeshBasicMaterial({side: THREE.DoubleSide, map: THREE.ImageUtils.loadTexture('materials/gold.png') }));
materials.push(new THREE.MeshBasicMaterial({ side: THREE.DoubleSide,map: THREE.ImageUtils.loadTexture('materials/iron.png') }));
var faceMaterial = new THREE.MeshFaceMaterial(materials);
for(var a = -5; a <= 5; a++){
for(var b = -5; b <= 5; b++){
var mesh = new THREE.Mesh(geometry, faceMaterial)
mesh.position.set(a, 0, b)
objects.push(mesh);
scene.add(mesh);
}
}
axis = new THREE.AxisHelper(50);
scene.add(axis);
camera.position.x = camX;
camera.position.y = camY;
camera.position.z = camZ;
camera.lookAt(origin);
rotate(angle)
loop();
}
function loop() {
var now = Date.now();
var deltaTime = (now - lastTime) / 1000.0;
update(deltaTime);
lastTime = now;
window.requestAnimationFrame(loop);
renderer.render(scene, camera);
};
function update(deltaTime){
camera.position.x = camX;
camera.position.z = camZ;
camera.position.y = camY;
camera.lookAt(origin);
};
function onKeyDown(event){
//esc - wylaczanie edycji
if(event.which == 27){
edit = false;
console.log("edit off");
}
//edycja wybranego obiektu
if(edit && intersects.length > 0){
//87 forward
if(event.which == 87)
intersects[0].object.position.z--;
//83 backward
if(event.which == 83)
intersects[0].object.position.z++;
//65 left
if(event.which == 65)
intersects[0].object.position.x--;
//68 right
if(event.which == 68)
intersects[0].object.position.x++;
//81 up
if(event.which == 81)
intersects[0].object.position.y--;
//69 down
if(event.which == 69)
intersects[0].object.position.y++;
//poruszanie kamera
} else {
//87 up
if(event.which == 87)
camY++;
//83 down
if(event.which == 83)
camY--;
//87 up
if(event.which == 87)
camY++;
//83 down
if(event.which == 83)
camY--;
//65 left
if(event.which == 65){
angle -= Math.PI/180;
rotate(angle);
}
//68 right
if(event.which == 68){
angle += Math.PI/180;
rotate(angle);
}
//obrot o 360 stopni
if(angle > Math.PI * 2)
angle = 0
if(angle < 0)
angle = Math.PI * 2;
}
//console.log(event.which);
};
//raycasting
function onMouseDown(event){
var raycaster = new THREE.Raycaster();
var mouseVector = new THREE.Vector2();
mouseVector.x = (event.clientX / WIDTH) * 2 - 1;
mouseVector.y = -(event.clientY / HEIGHT) * 2 + 1;
raycaster.setFromCamera(mouseVector, camera);
intersects = raycaster.intersectObjects(scene.children);
if (intersects.length > 0){
edit = true;
console.log("edit on")
}
};
//funkcja obracajaca kamere wokol srodka
function rotate(angle){
camX = origin.x + Math.cos(angle) * radius;
camZ = origin.z + Math.sin(angle) * radius;
};
|
{
"redpajama_set_name": "RedPajamaGithub"
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| 6,888
|
Sberbank Rosii (rusky Сбербанк России; dlouhá verze: сберегательный банк; česky: Ruská spořitelna) je největší ruská banka. Se svou hustou sítí 20 tisíc poboček je v mnohých oblastech Ruska jedinou dostupnou bankou.
Centrální banka Ruské federace drží dvoutřetinový podíl v bance, ostatní akcie jsou obchodovány na akciových trzích. Podle některých odhadů drží mimoruští investoři asi 20% podíl.
Historie
Vznik a počátky
I když svůj původ odvozuje od předrevolučních spořitelen fungujících od roku 1841, současná společnost byla založena v roce 1988 v rámci reorganizace sovětského bankovnictví jako spořitelna sbírající vklady od drobných vkladatelů. V roce 1991 byla přeměněna na akciovou společnost a částečně zprivatizována. Dále se zaměřovala na drobnou klientelu a vlastnila asi 50 procent ruských státních dluhopisů. Po ruské finanční krizi v roce 1998 banka ustupovala od investicí do státních dluhopisů a zaměřila se na firemní klientelu, zvláště velké těžařské společnosti.
Koncem 20. století, po privatizaci, byla banka kritizována za nízkou kvalitu služeb, které ale banka v následujících letech expandovala a zlepšila. Kolem roku 2010 byla banka považována za lídry odvětví co se kvality týče.
Banka v minulosti sponzorovala různé sporty a charity v ruských regionech. Banka také sponzoruje vzdělávací programy, zejména v oblasti finanční gramotnosti.
Rusko-ukrajinský konflikt
Ukrajinští představitelé roku 2014 obvinili banku z podporování proruských nepokojů. Tato tvrzení však banka zamítla, což potvrdila investigace Ukrajinské národní banky.
Krátce po ruské invazi na Ukrajinu 2022 byla banka zasažena sankcemi ze strany USA, které ji odřízly od amerického finančního systému a zmrazily její aktiva, jež se amerického finančního systému dotýkala. Počátkem června schválila Evropská unie v rámci 6. sankčního balíčku proti Rusku kromě jiného také odpojení Sberbank a dvou dalších ruských bank od systému SWIFT, který je zprostředkovatelem a vykonavatelem finančních transakcí v mezinárodním platebním styku.
Úpadek Sberbank Europe AG (2022)
Jednotný výbor pro řešení krizí (SRB) Evropské unie koncem února 2022 rozhodl, že východoevropská divize banky se sídlem ve Vídni Sberbank Europe AG a její dceřiné společnosti v Chorvatsku (Sberbank d.d.) a Slovinsku (Sberbank banka d.d.) jsou v důsledku rychlého zhoršení likvidity pravděpodobně v úpadku. Dále rozhodl o převedení chorvatské Sberbank d.d. na Chorvatskou poštovní banku (Hrvatska Poštanska Banka d.d.) a slovinské Sberbank banka d.d. na Nova ljubljanska banka d.d. V případě rakouské mateřské společnosti Sberbank Europe AG nepřijal SRB žádná opatření, takže úpadková řízení měla nadále probíhat podle vnitrostátních předpisů.
Sberbank CZ
V roce 2011 Sberbank odkoupila aktiva rakouské Volksbank v Bosně a Hercegovině, Česku, Chorvatsku, Maďarsku, na Slovensku, ve Slovinsku, Srbsku a na Ukrajině. Dohodnutá kupní cena činila 585 až 645 milionů eur (podle hospodářských výsledků společnosti v roce 2011). Transakce zahrnovala i českou Volksbank CZ, a.s., která proto od března 2013 změnila název na Sberbank CZ, a.s. Banky Sberbank ve střední Evropě a na Balkáně (včetně České republiky, ale již bez Slovenska a Ukrajiny) tak on února 2012 spadaly pod Sberbank Europe se sídlem ve Vídni, kterou majoritně vlastnila ruská Sberbank.
Z důvodu ruské invaze na Ukrajinu v únoru 2022 začaly soukromé osoby, firmy a samosprávy v České republice rušit své bankovní účty v této bance. Vzhledem ke skutečnosti, že Sberbank nebyla od 25. února schopna plnit závazky vůči klientům, zahájila 28. února Česká národní banka kroky k odejmutí bankovní licence Sberbank CZ, což nabylo právní moci 30. dubna. Městský soud v Praze počátkem května poslal banku do likvidace.
Reference
Externí odkazy
Ruské banky
|
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Movies Latest
By JuJu TeamPosted on February 25, 2021 May 9, 2021 0
The Netflix Movie Mank created an American biographical drama film created for Netflix by David Fincher. In fact, the Netflix Movie, Mank is an American Biography, Comedy, Drama genre Movie produced by Netflix International Pictures Moreover, the TV Series is Distributed by Netflix, Read more about the Netflix Movie, Mank age Rating, and parental guides for kids.
The Movie, Mank Official Poster, and Details
[su_table responsive="yes"]
Mank Age Rating 2020-21 – TV Show official Poster Netflix Images and Wallpapers
Movie Name –Mank
Genre – Biography, Comedy, Drama
Creator –David Fincher
Release Date –November 13, 2020(USA)
Age Rating – R
Runtime – 2h 11min
Mank Netflix Movie Overview
An anchorman called Michael meets a man called Isaac to account him about his activity post-Hurricane Katrina. Michael takes an absorption in one accurate account in Isaac's home of a woman called Christina Eames and wants to apperceive her backstory. In the present day Mae, Christina's daughter, inherits an assurance dropbox which includes the aforementioned account of herself and two letters. The aboriginal is to Mae and the additional is for Mae to bear to her father. Back in New York Michael meets Mae who works as an abettor curator. She pulls Christina's archival actual to appearance Michael.
What is Mank Age Rating
Details of Parental Guidance for Mank
Explained Why Mank Received R Age Rating
Mank Release date
What is Mank Runtime
Mank Age Rating – Wallpapers and Images
Official Trailer of Mank Movie
Summary Of Mank Cast
BBFC -12A
The Netflix Movie, Mank Age rating, is R
In fact, the age rating, fixed by MPAA( Motion Picture Association of America TV Movie rating system), CSM(common sense media), BBFC( British Board of Film Classification), and Netflix themselves. The board can decide who can watch the Movie and TV shows. He Mank is rated R for the content shown in the Netflix Movie. Including Blood contents, and Cigarette smoking, throughout the Movie. Notably, the R rating suggests that children under the age of 17 are restricted to watch the movie on Netflix. If you have watched the Movie, please provide the comments and thus help other kids/parents with the age rating and its contents.
Mank rating 12A in the United Kingdom and R in the United States and overseas. In addition, it is rated PG in Canada, M in Australia, and 12 in Germany. Other ratings include 12 in Spain and 15A in Ireland. Also, VM14 in Italy. This includes the age rating of Mank in the US, UK, NZ, Ireland, Canada, Singapore, etc…
no Sexual references
Eventually, these are the reasons for the R rating for the Netflix Movie, Mank.
The Movie Mank release date is November 13, 2020(USA), Distribution rights purchased by Netflix. You can see more info from the official site for the Movie.
Movie, Mank ,takes 2h 11min .
[youtube https://www.youtube.com/watch?v=aSfX-nrg-lI]
The Movie casting includes Gary Oldman, Amanda Seyfried, Lily Collins, Arliss Howard, Tom Pelphrey, Charles Dance, and others. In this Movie, Gary Oldman as Herman J. Mankiewicz, Amanda Seyfried as Marion Davies, Lily Collins as Rita Alexander, Arliss Howard as Louis B. Mayer, Tom Pelphrey as Joseph L. Mankiewicz, Charles Dance as William Randolph Hearst, Sam Troughton as John Houseman, Ferdinand Kingsley as Irving Thalberg
Stay tuned to get more updates on the age rating of all Netflix TV Movies, TV shows, books, and games. Finally, any suggestions always welcomed. Also, please make use of the comment box for your reviews. We are always providing the complete details on age rating for kids, We will make the easy and best way for your kids.
Tag: age rating 2020 Amanda Seyfried Biography Charles Dance Comedy David Fincher Drama Gary Oldman Tom Pelphrey
Toy Story 1995
Metal Skin Panic MADOX- 01 (1987)
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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
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Q: How to prevent line to extend across whole graph Currently, the below code (part of a more comprehensive code) generates a line that ranges from the very left to the very right of the graph.
geom_abline(intercept=-8.3, slope=1/1.415, col = "black", size = 1,
lty="longdash", lwd=1) +
However, I would like the line to only range from x=1 to x=9; the limits of the x-axis are 1-9.
In ggplot2, is there a command to reduce a line that is derived from a manually defined intercept and slope to only cover the range of the x-axis value limits?
A: You could use geom_segment instead of geom_abline if you want to manually define the line. If your slope is derived from the dataset you are plotting from, the easiest thing to do is use stat_smooth with method = "lm".
Here is an example with some toy data:
set.seed(16)
x = runif(100, 1, 9)
y = -8.3 + (1/1.415)*x + rnorm(100)
dat = data.frame(x, y)
Estimate intercept and slope:
coef(lm(y~x))
(Intercept) x
-8.3218990 0.7036189
First make the plot with geom_abline for comparison:
ggplot(dat, aes(x, y)) +
geom_point() +
geom_abline(intercept = -8.32, slope = 0.704) +
xlim(1, 9)
Using geom_segment instead, have to define the start and end of the line for both x and y. Make sure line is truncated between 1 and 9 on the x axis.
ggplot(dat, aes(x, y)) +
geom_point() +
geom_segment(aes(x = 1, xend = 9, y = -8.32 + .704, yend = -8.32 + .704*9)) +
xlim(1, 9)
Using stat_smooth. This will draw the line only within the range of the explanatory variable by default.
ggplot(dat, aes(x, y)) +
geom_point() +
stat_smooth(method = "lm", se = FALSE, color = "black") +
xlim(1, 9)
|
{
"redpajama_set_name": "RedPajamaStackExchange"
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\section{Introduction}
Poor data quality is an important and challenging problem in data analysis.
Outliers, which are data points that deviate from expected behavior are one of the four major categories of data quality errors
(the others being duplicates, rule violations, and pattern violations).
outlier detection is a fundamental data analysis task with widespread applicability in a number of critical domains such as cybersecurity, fraud detection, etc. Not surprisingly, there has been extensive prior work (see Section~\ref{sec:relWork} for summary) on identifying outliers under a wide variety of scenarios. However, many of these approaches do not scale well to large datasets that are now common.
Parametric methods assume an underlying data distribution (e.g.\ Gaussian mixture) $M$, estimate the parameters from the dataset and identify a given point $t$ as an outlier if $P(t|M)$ is smaller than a given threshold. Estimating these parameters on the entire dataset can be computationally expensive. Non-parametric methods using distance-based techniques often do not require distributional assumptions, and a data point is categorized as an outlier if it lies far away from other data points. Such approaches have scalability issues since they might require computation of all pairwise distances.
Adaptations such as indexes, approximations and pruning for distance computations only partially address scalability issues.
This problem cannot be solved by choosing the most scalable algorithm. The particular algorithm might not have the best detection rate or it might not be the most suitable for the problem at hand.
Furthermore, in outlier ensembles that combine multiple detection methods, even one non-scalable constituent algorithm affects the entire ensemble.
\begin{figure*}[!t]
\centering
\includegraphics[scale=0.25]{new-fig1.pdf}
\includegraphics[scale=0.25]{new-fig1-boxplot.png}
\caption{Generated data ($\times$) and a 10\% random sample ($\bullet$). We applied $3\sigma$ (left) and boxplot (right) methods. The two methods have different behaviors in terms of resilience: boxplot results are not preserved when sampling, while the $3\sigma$ limits for the original dataset (solid lines) and for the sample (dashed lines) are very similar.}\label{fig:monovariate}
\end{figure*}
{\bf Is Sampling the Silver Bullet?} A seemingly viable solution is to build models for outlier detection over samples of the entire dataset. While sampling reduces the amount of computations required for parameter estimation and pairwise distance calculations, it is not the panacea to our problems. This is because the results of detection methods on samples and on the entire dataset may not agree.
We illustrate this with an empirical example. We generated a bivariate distribution of 1,500 data points with mean $(-1,1)$ and variance $(1.015, 1.035)$, plotted ($\times$) in Figure \ref{fig:monovariate} (left), and extracted a 10\% random sample ($\bullet$). We used two {\em univariate} outlier detection methods on both sample and entire dataset.
The first univariate method, dubbed $3\sigma$, identifies all observations outside the interval between mean $\mu$ and $\pm 3\sigma$ as outliers. The second method uses the boxplot inner $(Q1-1.5\times IQR)$ and outer $(Q3+1.5\times IQR)$ fences, $Q1$ and $Q3$ being the first and third quartiles of the data and $IQR = Q3 - Q1$. Points beyond the inner and outer fences are deemed outliers. Figure~\ref{fig:monovariate} shows that the $3\sigma$ approach performs similarly with both sample and dataset while the boxplot method does not. Informally, this is because the sample mean and variance are better estimates of the population mean and variance than sample quartiles are of the population counterparts. We also found similar divergent behavior with two {\em multivariate} detection methods, $\chi^2$ and LOF (not shown).
{\bf Outline of Technical Contributions:} In this paper, we conduct a systematic study of how sampling impacts outlier detection algorithms. The paper has four contributions.
\noindent{\bf (1) Formalization of Resilience:}
The examples above show that while some outlier detection methods generalize well from samples to the entire dataset, others do not. We introduce and formalize the notion of {\em resilience to sampling} of outlier detection methods. Informally, resilience represents the extent to which the number and identification of detected outliers by a method applied to the whole dataset are preserved if it is actually applied to a sample. We emphasize that this property is orthogonal to traditional performance metrics such as specificity and sensitivity. We believe that understanding the notion of resilience is of paramount importance for practitioners. In many real-world scenarios, building outlier detection models over entire datasets is simply infeasible. Instead they are often built over samples where it is preferable to choose highly resilient methods over ones with lower resilience.
\noindent{\bf (2) Estimation of Resilience:}
If the ground truth is available, estimating the resilience of an outlier detection method is straightforward. For the more realistic case of no ground truth, we propose a novel method to estimate the resilience. This involves using multiple samples from the entire dataset to build outlier models and perform differential analysis.
\noindent{\bf (3) Resilience and Outlier Ensembles:}
If an algorithm is resilient to sampling, then an effective model can be built over the sample instead of the entire dataset. Such efficiency gains allows the use of more sophisticated models such as ensembles: a set of resilient detection algorithms can be combined effectively as outlier ensembles. Since detection methods capture different characteristics of the data, outlier ensembles can leverage the combined judgment of the different methods to produce a consensus.
While the weights of an ensemble model is easily determined in traditional classification, outlier ensembling without ground truth is not straightforward. Is it possible to infer the ``ground truth'' using some mild assumptions and the output of individual outlier detection methods? We investigate how the key ideas of resilience can be used to build outlier ensembles and adapt the classical Dawid-Skeene's EM-based approach to obtain a weighted majority.
\noindent{\bf (4) Extensive and Comprehensive Experiments:} We conducted an extensive study of resilience for seven diverse and representative outlier detection methods under two sampling schemes (uniform, block) and a subset-based partitioning approach over real-world and synthetic datasets. Our main finding is that the methods are not equally resilient to a given sampling scheme and hence it is important to
understand the impact of the joint selection of sampling scheme and outlier detection method.
\section{Notation and data model}
\label{sec:overview}
Let the dataset $\mathbf{D}$ be an $N\times V$ matrix with $N$ records and $V$ variables, with each row $\mathbf{D}_i \sim f_1 + \gamma f_2$, a mixture of two distributions, the regular distribution $f_1$ and the outlier distribution $f_2$, independently for $i=1, \ldots N$. The parameter $\gamma$ is the probability of any data point being an outlier, or equivalently, the proportion of outliers. The value of attribute $j$ for record $i$, noted $x_{ij}$ has an associated detection result vector $\mathbf{o}_{ij}$ with $M$ elements corresponding to the detection results of $M$ detection methods. If method $m$ identifies $x_{ij}$ as an outlier, then $\mathbf{o}_{ij}(m) \equiv o_{ijm} = 1$.
We note $O_m$ the set of outliers detected by method $m$ with size $|O_m|$.
\begin{table}[t]
\centering
\begin{tabular}{|l|p{7cm}|}
\hline
\multicolumn{2}{|c|}{ {\bf Notations} } \\
\hline
$\mathbf{D}$ & the whole dataset \\
\hline$S$ & the dataset sample of $\mathbf{D}$ \\
\hline $N$ & the number of records of $\mathbf{D}$\\
\hline $V$ & the number of variables of $\mathbf{D}$\\
\hline $M$ & the number of outlier detection methods\\
\hline $x_{ij}$& the value of attribute $j$ for record $i$\\
\hline $O_m$ & the set of outliers detected by method $m$ on $\mathbf{D}$ \\
\hline $O_m^S$ & the set of outliers detected by method $m$ on sample $S$ \\
\hline $O_m[S]$ & the subset of outliers detected by method $m$ on the whole dataset filtered to contain only the sampled records \\
\hline
\end{tabular
\caption{Notations}\label{tab:notations}
\end{table}
A sample $S$ has size $|S|$, consisting of $|S|$ rows of $\mathbf{D}$ and, in the context of massive datasets, usually we have $|S|\ll N$, so the sample can be loaded into the computer's memory. $O^S$ is the set of outliers detected from sample $S$ and $O[S]$ the subset of outliers detected from the whole dataset that are part of the sample $S$. Table \ref{tab:notations} summarizes our notation. We are interested in comparing $O^S_m$ and $O_m[S]$ for each method $m$. We use $\alpha_m$ for the probability that method $m$ detects a true outlier in the whole dataset, also known as its {\em sensitivity}, {\em recall} or {\em true positive rate (TPR)}: $\alpha_m=\big[\frac{TP}{TP+FN}\big]_m$ with {\it TP} being the proportion of true positives and {\it FN}, the proportion of false negatives. When applied to a sample $S$, this probability is denoted $\alpha_m^S$. We use $\beta_m$ to denote the {\em specificity}, the probability that method $m$ correctly identifies negatives in the full dataset (and $\beta_m^S$ in the sample $S$), i.e.\ $\beta_m=\big[\frac{TN}{FP+TN}\big]_m$ with {\it TN} the proportion of true negatives and {\it FP} the proportion of false positives.
\section{Resilience formalization} \label{sec:SingleAlgoSingleSample}
A method is said to be resilient to a sampling strategy if, when applied to the samples, it detects the same outliers as the ones the method would have detected if it was applied to the original whole dataset.
We consider resilience as an orthogonal notion to the traditional quality metrics of precision and recall.
Precision and recall are defined in an {\bf absolute} sense with respect to the ground truth. If the ground truth is not available, precision and recall cannot be computed. On the other hand, resilience is defined in a {\bf relative} sense as to what would have obtained if the method was applied to the whole dataset.
Notice that it is not necessary to have ground truth to estimate resilience, suggesting that the precision and recall of a method could have an orthogonal impact on its resilience. Hence, a method can have good recall and precision but low resilience to a given sampling scheme, e.g.\ if the model built over the sample is a poor approximation of the one built over the entire dataset resulting in divergence of the outliers detected. Conversely, a method can be resilient but have low precision and recall. This might occur if the data characteristic used by the method is not discriminative of the full outlier distribution, but is well captured well in the sample.
Resilience measures similarity of performance of an outlier detection method applied to samples to that applied to the whole dataset. A straightforward method to capture this property is to redefine the notion of precision and recall such that ``ground truth'' corresponds to whether a data point is categorized as an outlier by the method trained over the entire dataset. While the redefined metrics can be used directly, it is more meaningful to express this property as a single metric. The concept of F1-measure combines precision and recall as their harmonic mean and
we define the resilience as the harmonic mean of the redefined precision and recall metrics.
\noindent{\bf Definition 1. Resilience to sampling. }
Given a method $m$ and a sample $D_S$ of the full-sized dataset $\mathbf{D}$, the resilience, denoted $\rho_m(D_S)$ is defined as
\begin{eqnarray}\label{rho}
\rho_m(D_S)&=& \frac{2|O^S \cap O[S]|}{|O^S| + |O[S]|} \\
&=& \frac{2|O^S \cap O[S]|}{2|O^S \cap O[S]|+ |O^S \setminus O[S]|+ |O[S] \setminus O^S |}. \nonumber
\end{eqnarray}
\begin{figure}[!t]
\centering
\includegraphics[width=0.75\linewidth]{resilience.pdf}
\caption{Relationships between precision, recall, and resilience }\label{fig:resilience}
\end{figure}
Figure \ref{fig:resilience} illustrates the relationships between resilience and precision/recall when the method is applied to the full dataset and also when applied to samples, Resilience is a combination of two sets of metrics, on $TP$, $FP$, and $FN$ from both the whole dataset and the samples. Similarly, the sensitivity (or recall) and specificity (or true negative rate) of a method can be computed either from the sample or the whole dataset, when ground truth is available and the resulting sets of detected outliers can be quite different. The resilience definition precisely quantifies the extent to which a method's results (good or bad) are preserved through sampling.
When there is no ground truth, we express the expected values of the quantities in Eq. (\ref{rho}) in terms of the sensitivity and specificity. Here we omit the index of the method $m$ for notation simplicity. The expected number of records that are detected in both the whole dataset and the sample is
\begin{equation}\label{WP-hat}
\begin{aligned}
E(|O^S \cap O[S]|)&=|S|\left[ \gamma\alpha \alpha^S + (1-\gamma)(1-\beta)(1-\beta^S)\right],
\end{aligned}
\end{equation}
where the terms within the square brackets on the right-hand side refer respectively to records correctly detected as outliers both in the whole dataset and in the sample, and to records incorrectly detected as outliers both in the whole dataset and in the sample. They involve the sensitivities $\alpha$ and $\alpha^S$ of the method when applied to the whole dataset and to the sample respectively, as well as the corresponding specificities $\beta$ and $\beta^S$. Similarly, we have
\begin{equation}\label{noWN-hat}
\begin{aligned}
\mbox{E}(|\overline{O^S} \cap \overline{O[S]}|)
& = |S|\left[(1-\gamma)\beta\beta^S + \gamma(1-\alpha)(1-\alpha^S) \right].
\end{aligned}
\end{equation}
The terms on the right-hand side refer to records corrected or incorrectly detected as inliers both in the whole dataset and in the sample. Lastly, we have
\begin{equation}\label{noWP-hat}
\begin{aligned}
\mbox{E}(|O^S \cap \overline{O[S]}|)& =|S| \left[\gamma(1-\alpha)\alpha^S + (1-\gamma)\beta(1-\beta^S) \right],\\
\mbox{E}(|\overline{O^S} \cap O[S]|) & =|S| \left[\gamma\alpha(1-\alpha^S) + (1-\gamma)(1-\beta)\beta^S \right].
\end{aligned}
\end{equation}
If detection results from the whole dataset are available, the resilience can be trivially computed by comparing with the sample detections. In the more realistic scenario where this is not available, the resilience has to be estimated using only the sample detections.
In Section \ref{sec:MultipleAlgosSingleSample}, we present a procedure to estimate the resilience when the whole dataset detection is unavailable, focusing on estimating the resilience of outlier ensembles. We estimate the sensitivities and specificities, then use them in Eqs.\ (\ref{WP-hat}), (\ref{noWN-hat}), and (\ref{noWP-hat}), to finally estimate the resilience with Eq.\ (\ref{rho}).
%
\section{Resilience for outlier ensembles}
\label{sec:MultipleAlgosSingleSample}
The ability to build resilient models over small samples provides a number of advantages.
The computational benefits accrued by running on a small sample for model building
enables a user to invoke multiple outlier detection algorithms simultaneously.
The information gained can be richer than invoking a single outlier detection algorithm over the entire data. Different outlier detection algorithms are often customized for different characteristics of datasets and outliers. Hence, it is plausible that by incorporating the results of multiple algorithms, one can achieve better outlier detection performance.
In this section, we make two contributions.
First, we propose a mechanism to ``ensemble'' multiple detection algorithms where each is invoked on a single sample.
Second, we extend the notion of resilience for an outlier ensemble.
Ensemble analysis of outlier detection has received increasing attention from the research community. A common technique in building classifier ensembles is to combine the predictions of multiple classifiers using a weighted majority (or sum) rule. Classifiers that are more accurate are often provided with higher weights. However, adapting such a technique to outlier ensembles is much trickier since outlier detection is often an unsupervised learning problem with no ground truth. If we know the consensus of the outlier ensembles (say through weighted majority), we can easily compute the weight of an individual outlier detection algorithm based on its accuracy. However, to know the consensus of the outlier ensembles, we need the weight of each algorithm!
This conundrum is not specific to outlier ensembles and has been observed in other fields.
This chicken and egg issue is typically solved through iterative techniques such as EM (Expectation Maximization) that {\em jointly} estimate both the error rates and ground truth.
{\bf Two Coin Model for Outlier Ensembles.}
We use the Dawid-Skene model \cite{dawid1979maximum} to obtain ground truth
using noisy labels from individual outlier detection algorithms.
In Section~\ref{sec:overview} we described the performance of an outlier detection algorithm in terms of its sensitivity and specificity relative to an unknown ground truth.
We use a simple generative process by which each outlier detection algorithm determines if a data point is an outlier or an inlier.
Consider a data point $x$ with true label $y$. Suppose the outlier detection method $m_j$ produces output $y_j$ (assumed to be boolean, outlier or inlier, for simplicity) through the following stochastic process:
If $y=1$, $m_j$ flips a coin with bias $\alpha_j$ (representing its sensitivity).
If $y=0$, $m_j$ flips a coin with bias $\beta_j$ (its specificity).
In both cases, $m_j$ returns $y$ if the tossed coin returns heads and the alternate label if the coin returns tails.
This generative model is very simple and only depends on $y$.
However, we note that there are extensions of \cite{dawid1979maximum} that can take into account other relevant factors including the observation $x$.
{\bf Jointly Learning Sensitivity, Specificity and Ground Truth.}
To specify the algorithm, we first introduce the following notations.
Let $p_o$ and $p_i$ be the probability that a data point is an outlier and inlier respectively.
Ideally, $p_o = \gamma$, the outlier prevalence rate defined in Section \ref{sec:overview}. However, since the ground truth is unavailable, this value has to be estimated.
Each method has an associated confusion matrix, the probability that it outputs a particular label (say $b$) when the true label is $a$, denoted $\pi_{ab}^{m}$, where $a$ and $b$ can take values $o$ and $i$ (for outliers and inliers respectively).
Thus, $\pi_{io}^m$ and $\pi_{oi}^m$ are the probabilities that method $m$ mistakes an inlier for an outlier and vice-versa
while $\pi_{oo}$ and $\pi_{ii}$ are the probabilities that it will identify the outlier/inlier correctly.
Let $T_{ij}$ be an indicator variable equal to $1$ if $j$ is the true label for data point $i$ and $0$ otherwise, while $o_{ijm}$ be an indicator equal to $1$ if method $m$ assigned label $j$ to data point $i$.
We use an EM-like approach that iteratively performs the following:
(1) Estimate the outlier ground truth from different detectors taking into account their sensitivity and specificity; (2) Estimate the sensitivity and specificity of the detectors by comparing their results to the {\em inferred} ground truth.
Since the ground truth is unavailable, we treat it as a latent variable. Note that $\pi_{ab}^m$ can be computed as the fraction of data points for which method $m$
produces class label $b$ when the truth is $a$, to the total number of data points where $a$ is the true label. The prior probabilities $p_a$ can be computed as the fraction of the dataset that is assigned the label $a$ after ensembling. See Algorithm~\ref{alg:dawidSkene} below and \cite{dawid1979maximum} for additional details.
\begin{equation}
\label{eq:dsEstimatePi}
\pi_{ab}^m = \frac{ \sum_{i=1}^{|S|} T_{ia} \times o_{ibm}}{ \sum_{i=1}^{|S|} T_{ia}} \quad \text{with } a, b \in \{\mbox{outlier}, \mbox{inlier}\}
\end{equation}
\begin{equation}
\label{eq:dsEstimateP}
p_j = \frac{\sum_{i=1}^{|S|} T_{ij}}{|S|} \quad \mbox{where } j \in \{\mbox{outlier}, \mbox{inlier}\}
\end{equation}
\begin{equation}
\label{eq:dsEstimateGT}
p(T_{ij} = 1 | S) \propto \prod_{k=1}^{M} \prod_{\forall l \in \{\mbox{\footnotesize outlier}, \mbox{\footnotesize inlier}\}} \pi_{jl}^{k} \times p_j
\end{equation}
\begin{algorithm}
\caption{Outlier Ensembling Algorithm}
\label{alg:dawidSkene}
\begin{algorithmic}[1]
\STATE Initialize error rates $\pi^m_{a,b}$ for each method $m \in [1, m]$ and $a, b \in \{outlier, inlier\}$ (say to 0.5)
\STATE Initialize prior probabilities $p_i = p_o = 0.5$
\WHILE {estimated ground truth labels does not change between iterations }
\STATE Estimate label $L_i$ for each record $D_i$ using Eq.~(\ref{eq:dsEstimateGT})
\STATE Estimate error rates $\pi^m_{a,b}$ for each method $m$ using $L_i$ and $o_{iam}$ through Eq.~(\ref{eq:dsEstimatePi})
\STATE Estimate class prior probabilities using $L_i$ and the $o_{iam}$ through Eq.~(\ref{eq:dsEstimateP})
\ENDWHILE
\RETURN error rates $\pi^m_{a,b}$ for each method and estimated labels $L_i$ for each record
\end{algorithmic}
\end{algorithm}
Our proposed approach sidesteps a number of issues of prior outlier ensemble approaches such as outlier score normalization. By measuring the algorithm's error rates (through sensitivity and specificity), we can correct its bias and recover the ground truth with higher quality.
For example, detection algorithms that are conservative by rating more inliers as outliers can be easily identified and their bias corrected.
{\bf Resilience for Outlier Ensembles.}
Given an outlier ensemble $E_O$ and a sample $S$, we can readily extend the notion of resilience to ensembles. Our definition is orthogonal to the specific ensembling approach, so that it applies to outlier ensembles other than our EM-based algorithm for ensembling (see Section~\ref{sec:relWork} for other ensembling approaches).
Intuitively, we treat the ensemble as a complex black-box outlier detection algorithm and reuse the prior definition of resilience. Specifically, resilience for an outlier ensemble represents the extent to which the identification of outliers detected by the
ensemble is preserved between component models that were trained on the entire dataset versus single sample respectively.
Specifically, if the detection results from the whole dataset are available, we can use Eq.~(\ref{rho}) to compute the resilience by comparing outlier detection results for whole dataset versus the sample. Without this information, we instead estimate the sensitivity and specificity of the outlier
ensemble using Equations~(\ref{WP-hat}), (\ref{noWN-hat}), and (\ref{noWP-hat}) and then plug them into Equation~(\ref{rho}).
\section{Experiments and discussion}
\label{sec:discussion}
\subsection{Experimental Setting}
\noindent{\bf Datasets.} We set up extensive experiments with eight real-world datasets and their variants from UCI\footnote{\scriptsize{{https://archive.ics.uci.edu/ml/datasets.html}}}, ODDS\footnote{\scriptsize{{http://odds.cs.stonybrook.edu/}}}, and \cite{DAMI16}\footnote{\scriptsize{{http://www.dbs.ifi.lmu.de/research/outlier-evaluation/}}}. Their characteristics are shown in Table \ref{tab:datasets} and Figure
\ref{fig:syn-data} shows the synthetic data. The eight real datasets are diverse in terms of number of attributes, outlier injection rate, etc and often used in outlier detection research. We also used variants of the real datasets with and without ground truth ($GT$) outlier labels. The variants have different degrees of preprocessing which may have an impact on outlier detection performance. Synthetic datasets with 1,000, 5,000, and 10,000 records were generated from an independent bivariate normal with mean $(0,0)$ and standard deviations $1$ and $2$. Outliers were randomly inserted from two outlier distributions. One is an independent bivariate normal distribution with mean $(4,0)$ and equal standard deviations $0.25$ (Fig. \ref{fig:syn-data}, green), and the other has an additional independent bivariate normal component with mean $(0,6)$ and the same standard deviation (maroon). These are injected at three different rates (1\%, 5\%, and 10\%). We averaged results over 100 replications.
\begin{landscape}
\begin{table*}[!t]
\centering
\caption{Characteristics of the real-world dataset from UCI$^1$, ODDS$^2$ and [5]$^3$, and synthetic datasets used in the experiments ($N=$ number of observations, $V=$ number of variables, $GT=$ percentage of ground truth outliers, if available, $S=$ sample size, and $psize=$ percentage of sample size to whole dataset size).}
\small
\begin{tabular}{|p{1.7cm}|r|r|r||c|c|c|}
\hline
\multicolumn{1}{|c|}{{\bf Dataset name}}&\multicolumn{3}{|c||}{{\bf Dimensions} } & \multicolumn{3}{c|}{{\bf Sampling size $S$ }} \\
\cline{2-7}
\multicolumn{1}{|c|}{{}} & \multicolumn{1}{|c|}{$N$} & \multicolumn{1}{|c|}{$V$} &\multicolumn{1}{|c||}{$GT$}
& Random ($psize$) & \multicolumn{1}{c|}{ Blocking (number of blocks -- block size) } &Subsets\# \\
\hline
Arrhythmia$^1$&452&258&\multicolumn{1}{|c||}{-}&20 (4.425\%); 50 (11.062 \%)&(1-20) (5-4) (10-2) (1-50) (5-10) (10-5)&\\
Arrhythmia$^3$&452&274& 66 (15\%) &20 (4.425\%); 50 (11.062 \%)&(1-20) (5-4) (10-2) (1-50) (5-10) (10-5)&\\
\cline{1-6}
Diabetes$^1$ &768&9&\multicolumn{1}{|c||}{-}&50 (6.51 \%); 100 (13.021 \%)&(10-5) (25-2) (50-1) (10-10) (25-4), (50-2)&\\
Diabetes$^3$ &768&8&268 (35\%)&50 (6.51 \%); 100 (13.021 \%)&(10-5) (25-2) (50-1) (10-10) (25-4), (50-2)&\\
\cline{1-6}
Waveform$^1$&5,000&22&\multicolumn{1}{|c||}{-}&250 (5\%); 500 (10\%)&(10-25)(25-10)(50-5)(10-50)(25-20)(50-10)&\\
Waveform$^2$&3,443&21&100 (29\%)&250 (7.261\%); 500 (14.522\%)&(10-25)(25-10)(50-5)(10-50)(25-20)(50-10)&\\
\cline{1-6}
Spambase$^1$&4,601&58&\multicolumn{1}{|c||}{-}&200 (4.346\%); 400 (8.693\%)&(10-20) (25-8) (50-4) (10-40) (25-16) (50-8)&5; 10; 20\\
Spam$\_02^3$&2,479&57&51 (2\%)&200 (8.068\%); 400 (13.136\%)&(10-20) (25-8) (50-4) (10-40) (25-16) (50-8)&\\
Spam$\_05^3$&2,661&57&133 (5\%)&200 (7.516\%); 400 (15.032\%)&(10-20) (25-8) (50-4) (10-40) (25-16) (50-8)&\\
Spam$\_10^3$&2,808&57&280 (10\%)&200 (7.123\%); 400 (14.245\%)&(10-20) (25-8) (50-4) (10-40) (25-16) (50-8)&\\
Spam$\_20^3$&3,160&57&632 (20\%)&200 (6.329\%); 400 (12.658\%)&(10-20) (25-8) (50-4) (10-40) (25-16) (50-8)&\\
Spam$\_40^3$&4,207&57&1,679 (40\%)&200 (4.754\%); 400 (9.508\%)&(10-20) (25-8) (50-4) (10-40) (25-16) (50-8)&\\
\cline{1-6}
Australian &690&15&\multicolumn{1}{|c||}{-}&30 (4.347\%); 60 (8.696\%)&(1-30) (5-6) (10-3) (1-60) (5-12) (10-6)&\\
\cline{1-6}
Ionosphere &351&33& \multicolumn{1}{|c||}{-}&20 (5.698\%); 40 (11.396\%)&(1-20) (5-4) (10-2) (1-40) (5-8) (10-4)&\\
\cline{1-6}
Iris &150&4&\multicolumn{1}{|c||}{-}&10 (6.667\%); 20 (13.333\%)&(1-10) (5-2) (10-1) (1-20) (5-4) (10-2)& \\
\cline{1-6}
Isolet5 &1,559&618&\multicolumn{1}{|c||}{-}&75 (4.810\%); 150 (9.622\%)&(3-25) (5-15) (25-3) (5-30) (10-15) (25-6)& \\
\cline{1-6}
\cline{1-6}
Synth. Distrib. 1& 1,000; 5,000; 10,000& 2 & 1\%; 5\%; 10\%&5\%; 10\%&\multicolumn{1}{|c|}{-}&\\
Synth. Distrib. 2&1,000; 5,000; 10,000& 2 & 1\%; 5\%; 10\%&5\%; 10\%&\multicolumn{1}{|c|}{-}& \\
\hline
\end{tabular}
\label{tab:datasets}
\end{table*}
\end{landscape}
\noindent{\bf Outlier detection methods.} We considered seven well-known outlier detection methods, classified into four categories: \\
{\em (1) Statistical methods}: 3$\sigma$ where observations outside the mean and $\pm 3$ standard deviation are considered outliers; Boxplot with inner ($Q1 - 1.5\times IQR$) and outer ($Q3 + 1.5\times IQR$) fences \cite{tukey}, and Chi-Square ($\chi^2$) defined in \cite{grubbs}; \\
{\em (2) Deviation-based methods}: MAD using the median absolute deviation as defined in \cite{Carling};\\
{\em (3) Distance-based methods}: Mahalanobis distance which estimates how far each observation is from the center (centroid in multivariate space) \cite{Mahalanobis}, and K-Means \cite{Hartigan}; \\
{\em (4) Density-based methods}: LOF defined in \cite{Breunig2000}. \\
We use 10\% of the data size as the threshold for the number of outliers to be detected by Mahalanobis, LOF and K-Means.
\begin{figure}[!t]
\centering
\includegraphics[width=.5\linewidth]{Plot-indeptnorm-out24-forpaper.pdf}
\caption{Synthetic independent bivariate normal data (black) with outliers
injected at rates 1\%, 5\%, and 10\% from the $N((4,0);.25)$ (green) and $N((0,6);.25)$ (maroon).}
\label{fig:syn-data}
\end{figure}
\noindent{\bf Sampling.} We study three types of sampling schemes:
{\em (1) Random sampling} with 100 random samples with real-world sample sizes shown in Table \ref{tab:datasets} and for synthetic data, 1\%, 5\%, and 10\% of the data size;
{\em (2) Block sampling} with 100 block samples and six parameter pairs of block number and size (see Table \ref{tab:datasets});
{\em (3) Partitioning} where each dataset is divided into 5, 10, and 20 subsets.
\noindent{\bf Parameters:} We vary $psize$, the sample size percentage of the whole dataset size, and parameter settings of each sampling scheme. For the synthetic dataset, we vary the distributions and the rate of true outliers to understand how the resilience changes with an increasing number of true outliers.
\subsection{Summary of Experimental Results:}
In Section~\ref{section:resilienceVsF1}, we show that resilience to sampling is complementary to traditional metrics such as precision and recall. For example, some methods have high precision and/or recall when trained on the entire dataset but have poor performance when trained over a sample.
In Section~\ref{section:variety}, we note that resilience to sampling varies with method, dataset, sampling scheme and sample size. Most methods are not resilient to sampling thereby opening a promising research area of designing resilient algorithms.
In Section~\ref{section:size}, we show how sampling strategy and sample size affect resilience. Random sampling is often preferable to block sampling or partitioning. As expected, increasing sample size often improved resilience. Most algorithms are not resilient for small samples. Section \ref{section:true} shows that our resilience estimator is accurate and has low variance even for small samples.
Section \ref{section:em-based} shows that our two-coin idea for outlier ensemble using crowdsourcing is promising and provides good resilience estimates for ensemble performance.
\begin{figure*}[!t]
\centering
\includegraphics[width=1.05\linewidth]{F1-precision-recall-resilience-newRW.pdf}
\caption{Resilience wrt random sampling and quality metrics for real-world datasets with available Ground Truth}\label{fig:quality-metrics-vs-true-resilience}
\end{figure*}
\begin{figure}[!t]
\centering
\includegraphics[width=\linewidth]{new-radar-waveform.pdf}
\includegraphics[width=\linewidth]{new-radar-isolet.pdf}
\caption{Resilience estimates for Waveform and Isolet5 datasets. Univariate statistical methods consistently have higher resilience compared to multivariate methods. LOF and MAHA are least resilient for Waveform and Isolet5 respectively).
}\label{fig:waveform}
\end{figure}
\subsection{Resilience is complementary to quality metrics} \label{section:resilienceVsF1}
We used the real-world datasets with available ground truth and computed classical performance metrics (F1-measure, precision and recall) as well as resilience calculated with Eq. (\ref{rho}) for different sample sizes.
We find that outlier methods with relatively low F1-measure, precision and recall can have high resilience (e.g.\ univariate methods in Spam dataset) and vice-versa (e.g., CHISQ in Waveform and Spam datasets) (Fig. \ref{fig:quality-metrics-vs-true-resilience}).
Increasing the prevalence of outliers and data size logically increases the quality metrics but not necessarily the resilience (e.g., resilience decreased from Spam\_02 to Spam\_40). This suggests a need for better understanding of resilience and its estimation when ground truth is unavailable.
\subsection{Resilience of Outlier Methods}\label{section:variety}
Here, we consider only the real-world datasets without ground truth and computed the resilience estimates for each method using 100 samples from each sampling strategy.
Figure \ref{fig:waveform} shows the results for the Waveform and Isolet5 datasets, and Figure \ref{fig:RW-allmethods} for the other datasets.
We find that resilience to sampling varies greatly depending on sample size and data and outlier distributions. In the figures, resilience estimates
are represented as the distance from the center of the plot. Each axis represents a particular sampling strategy and sample size; a colored line in the plot shows the trend of the resilience estimate when both the sampling scheme and sample size change. The area defined by each colored line represents the resilience estimate of a method relative to the dataset and sampling scheme: the smaller the area, the less resilient.
Focusing on the Waveform and Isolet5 datasets, MAD has the highest resilience estimaates for all sampling strategies. LOF and MAHA had the lowest resilience for Waveform and Isolet5 respectively. Particularly for Isolet5, statistical and univariate methods such as MAD and $3\sigma$ seem to be more resilient to random and block sampling.
The resilience of BoxPlot, distance- and density-based multivariate methods seem to be affected by the data characteristics: Isolet5 has wide skewness (asymmetry) and kurtosis (shape) ranges of ([-2.22;31.05],[1.44;1220.16]). This affected MAHA which is less resilient than LOF in Isolet5. On the other hand, in Waveform which is more symmetric and flat, with ([-0.24;0.28],[1.49;3.11]) for (skewness, kurtosis) ranges, MAHA is more resilient than LOF. For each dataset, the ranking of the methods by resilience is generally preserved across sampling strategies.
The resilience estimates tend to slightly increase with sample size for all sampling schemes but at different rates. This suggests that the sampling scheme and sample size may have different impacts on a method's resilience.
\begin{figure*}[!t]
\begin{tabular}{ccc}
\includegraphics[width=.33\linewidth]{new-radar-spam.pdf} &
\includegraphics[width=.33\linewidth]{new-radar-iris.pdf} &
\includegraphics[width=.33\linewidth]{new-radar-diabetes.pdf} \\
\includegraphics[width=.33\linewidth]{new-radar-ionosphere.pdf}&
\includegraphics[width=.33\linewidth]{new-radar-australian.pdf}&
\includegraphics[width=.33\linewidth]{new-radar-arrhythmia.pdf}
\end{tabular}
\caption{Resilience estimates of outlier detection methods wrt sampling schemes and sample sizes for six real-world datasets.}
\label{fig:RW-allmethods}
\end{figure*}
\subsection{Impact of sample scheme and sample size}\label{section:size}
{\bf Random sampling}. From Fig.\ \ref{fig:random-resilience-size}, we find that mean resilience estimates increase with sample size. While all methods have relatively low resilience estimates, the $3\sigma$ method has the highest, consistently across datasets, sampling stratgegies and sample size percentage. $\chi^2$ and MAD have similarly high resilience estimates but are more dataset-dependent. LOF has the lowest estimates and is very dataset-dependent, with the greatest variability. This may be because LOF relies on local density properties which are lost in the sampling process.\\
{\bf Block sampling}.
LOF resilience estimates are again data dependent and impacted by block number and sample size, with no apparent trend (not shown).
$3\sigma$ still attains the highest resilience (except for Iris) and is stable across datasets, block number and sample size. The resilience estimates for MAHA, $\chi^22$, MAD and BoxPlot are more variable and data dependent. \\
{\bf Partitioning}. We used 5, 10 and 20 subsets, correspondingly reducing the size of each subset. The trend in Fig.\ \ref{fig:subset-resilience-size} is reversed and is more apparent for the multivariate methods (LOF and MAHA) for which intrinsic properties such as distance and density are not preserved in the samples: their resilience estimates decrease when the size of the subsets decreases; the resilience ranges of $3\sigma$, $\chi^2$, MAD, and BoxPlot are again compact and decreases slightly when the number of subsets decreases (and their sizes increase).
\begin{figure*}[!t]
\raggedleft \includegraphics[width=.99\linewidth]{new-random-resilience-psize.png}
\caption{Impact of random sampling and sample sizes (as percentage of the whole dataset size) on the resilience estimates of the methods applied to the real-world datasets.}
\label{fig:random-resilience-size}
\end{figure*}
\begin{figure*}[!t]
\raggedleft \includegraphics[width=.99\linewidth]{new-subset-resilience-psize.png}
\caption{Impact of partitioning and partition sizes (as percentage of the whole dataset size) on the resilience estimates of the methods applied to the real-world datasets.}
\label{fig:subset-resilience-size}
\end{figure*}
\begin{figure*}[!t]
\centering
\includegraphics[width=.8\linewidth]{Plot-ResilienceSynthetic.pdf}
\caption{Mean and standard deviation of resilience estimates for each method computed from five subsets (1/5 of the full dataset size) over 100 simulations for two outlier distributions and three rates of outlier injection.}\label{fig:resilience-synthetic}
\end{figure*}
The key observation is that statistical methods tend to be more resilient than multivariate density- and distance-based methods to random and block sampling.
Furthermore, $3\sigma$ has the highest resilience estimates and is not much affected by the data characteristics. Partitioning and block sampling work better for BoxPlot than random sampling. Block sampling with LOF should be avoided mainly due to the loss of the local density properties in the samples.
\subsection{Accuracy of Resilience Estimates} \label{section:true}
{\bf Accuracy wrt true outlier distribution and prevalence.}
We controlled the rate of true outliers injected in the synthetic datasets and, for each method, computed the resilience and checked its accuracy. Fig. \ref{fig:resilience-synthetic} shows resilience estimates for the two outlier distributions (same color scheme as Fig. 3) and three outlier rates (increasing line width) for the case of partitioning. Five subsets were used. The MAHA resilience seems to be high for all our settings of outlier distribution and prevalence rates. Using subsets for detection did not seem to affect this. To a lesser extent, this is also true for the MAD and BoxPlot methods as well, although there is some difference between the two outlier distributions. Their high resilience could be due to the symmetry and shape of the synthetic data distribution that are somehow preserved in the samples. This confirms our previous findings from real-world datasets. Both LOF and the $\chi^2$ methods seem to have lower detection power in our study, and exhibit noticeable low resilience when using outlier detection from subsets (in particular LOF for Distribution 1). This is mainly due to the fact that LOF is a density-based outlier detection method and the density property is somehow lost in the samples. Both the LOF and $3\sigma$ methods show large variation in resilience depending on the outlier prevalence rate, decreasing as the rate increases. With increasing full dataset size, LOF resilience significantly decreases in opposition with the other methods. This suggests a direction for future work to include density-based sampling such as that in \cite{Ros2016349} to fairly test the resilience of LOF. More importantly, it shows that a joint choice of outlier detection method with appropriate sampling scheme is crucial.
{\bf Accuracy wrt to the number of samples.} Tables III and IV show mean square errors (MSE) of resilience estimates for $3\sigma$ and BoxPlot using synthetic and real-world datasets. The low MSEs demonstrate that our model for computing resilience estimates is robust and has very good accuracy. Increasing the number of samples does not necessarily increase the accuracy of the estimates. Increasing the number of samples did not necessarily increase the accuracy of the estimates.
\begin{table}[ht]
\centering
\small
\begin{tabular}{cclcccc}
\hline
Outlier& Outlier & Data & \multicolumn{2}{c}{10 samples} & \multicolumn{2}{c}{20 samples} \\
distribution & rate & size & $3\sigma$ & Boxplot & $3\sigma$ & Boxplot\\
\hline
1 & 0.05 & 1000 & 1.2e-02 & 1.1e-03 & 1.8e-02 & 3.8e-03 \\
& & 10,000 & 3.8e-04 & 3.5e-05 & 7.1e-04 & 6.9e-05 \\
& 0.1 & 1000 & 2.8e-02 & 1.6e-03 & 2.0e-02 & 5.2e-03 \\
& & 10,000 & 2.1e-03 & 2.1e-05 & 5.0e-03 & 3.5e-05 \\ \hline
2 & 0.05 & 1000 & 5.7e-03 & 1.8e-03 & 1.0e-02 & 5.9e-03 \\
& & 10,000 & 1.4e-04 & 8.7e-05 & 2.8e-04 & 1.4e-04 \\
& 0.1 & 1000 & 1.1e-02 & 9.1e-04 & 1.8e-02 & 2.8e-03 \\
& & 10,000 & 4.0e-04 & 4.9e-05 & 6.5e-04 & 7.9e-05 \\
\hline
\end{tabular}\label{tab:MSEsynthetic}
\caption{MSE of resilience estimates for $3\sigma$ and Boxplot over multiple synthetic subset samples.}
\end{table}
\begin{table}[ht]
\centering
\small
\begin{tabular}{lcccccc}
\hline
& \multicolumn{2}{c}{5 samples} & \multicolumn{2}{c}{10 samples} & \multicolumn{2}{c}{20 samples} \\
& $3\sigma$ & Boxplot & $3\sigma$ & Boxplot & $3\sigma$ & Boxplot \\ \hline
arrhythmia & 1.3e-04 & 3.2e-05 & 1.9e-04 & 9.9e-05 & 3.7e-04 & 2.4e-04 \\
australian & 6.0e-03 & 1.0e-03 & 6.8e-03 & 1.7e-03 & 9.1e-03 & 3.3e-03 \\
diabetes & 4.0e-04 & 9.3e-04 & 7.3e-04 & 1.9e-03 & 1.9e-03 & 5.8e-03 \\
ionosphere & 1.2e-02 & 7.7e-04 & 2.5e-02 & 1.9e-03 & 3.6e-02 & 4.8e-03 \\
iris & 6.4e-02 & 1.9e-02 & NA & 7.7e-03 & NA & 1.7e-02 \\
isolet5 & 4.0e-05 & 8.4e-06 & 5.5e-05 & 1.0e-05 & 8.1e-05 & 2.2e-05 \\
spam & 2.0e-05 & 1.1e-07 & 2.3e-05 & 2.0e-07 & 5.1e-05 & 6.1e-07 \\
waveform & 3.5e-04 & 2.9e-04 & 5.6e-04 & 4.0e-04 & 9.5e-04 & 1.1e-03 \\
\hline
\end{tabular}\label{tab:MSEreal}
\caption{MSE of resilience estimates for $3\sigma$ and Boxplot over multiple real-world subset samples.}
\end{table}
\begin{figure}
\centering
\includegraphics[width=0.7\linewidth]{Plot-ResilienceSyntheticRandomSample.pdf}
\caption{Outlier Ensemble resilience for Random Sampling}
\label{fig:resilienceEnsembleRandomSample}
\end{figure}
\subsection{Evaluation of EM-Based Ensembling}\label{section:em-based}
With the synthetic data, we evaluate our EM-based ensembling approach on two aspects:
(a) its resilience compared to the component methods and
(b) its accuracy at estimating the sensitivity and specificity.
We varied data sizes (1,000, 5,000 and 10,000), outlier prevalence rate (1\%, 5\%, and 10\%) and considered two sampling schemes:
(a) random sampling with sampling fraction of 1\%, 5\%, and 10\% and
(b) partitioning with the data split into 5 and 10 equi-sized subsets.
For each scenario, we used 100 different samples and averaged the results.
While we only show the results for two representative distributions from Fig.~\ref{fig:syn-data}, the results were similar for the others.
{\bf Resilience of Outlier Ensembles:}
Fig.~\ref{fig:resilienceEnsembleRandomSample} for random sampling
and Fig.~\ref{fig:resilience-synthetic} (bottom right) for partitioning show high resilience compared to its component algorithms. As expected, increasing the sample size increases the resilience, an increase that quickly plateaus. This shows that it is feasible to build resilient outlier ensembles using only a fraction of the data size.
We also evaluated how the composition of the outlier ensembles affects the resilience by randomly choosing different subsets of outlier detection methods. We find that regardless of the mix of resilient and less resilient methods, the outlier ensemble retains its high resilience providing the best of both worlds in terms of both accuracy and resilience.
{\bf Accuracy of Resilience Estimation:}
Tables~\ref{tbl:emBasedExpResultsRandomSampling} and \ref{tbl:emBasedExpResultsSubsetting} show the RMSE of sensitivity and specificity estimates of the EM-based ensemble for random and subset sampling under different outlier distributions. The key observation is that the RMSE is very small for all settings suggesting that the EM-based algorithm can estimate the ground truth accurately from the ensembles.
\begin{landscape}
\begin{table*}[!t]
\centering
\caption{EM-based ensembling for Random Sampling: RMSE of sensitivity and specificity estimates of the ensemble
}
\small
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\cline{3-8}
\multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{6}{|c|}{RMSE($\alpha$), RMSE($\beta$)} \\
\hline
Outlier Distribution & $N$ & $s=5\%,pt=1\%$ & $s=5\%,pt=5\%$ & $s=5\%,pt=10\%$ & $s=10\%,pt=1\%$ & $s=10\%,pt=5\%$ & $s=10\%,pt=10\%$ \\ \hline
Distribution 1 & 1000 & 0.01, 0.03 & 0.01, 0.02 & 0.01, 0.02 & 0.01, 0.02 & 0.01, 0.02 & 0.01, 0.02 \\ \hline
Distribution 1 & 10000 & 0.01, 0.03 & 0.01, 0.02 & 0.01, 0.02 & 0.01, 0.02 & 0.01, 0.02 & 0.01, 0.02 \\ \hline
Distribution 2 & 1000 & 0.01, 0.03 & 0.01, 0.02 & 0.01, 0.02 & 0.01, 0.02 & 0.01, 0.02 & 0.01, 0.02 \\ \hline
Distribution 2 & 10000 & 0.01, 0.02 & 0.01, 0.02 & 0.01, 0.02 & 0.01, 0.02 & 0.01, 0.02 & 0.01, 0.02 \\ \hline
\end{tabular}
\label{tbl:emBasedExpResultsRandomSampling}
\end{table*}
\begin{table*}[!t]
\centering
\caption{EM-based ensembling for Subset Sampling: RMSE of sensitivity and specificity estimates of the ensemble.
}
\small
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\cline{3-8}
\multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{6}{|c|}{RMSE($\alpha$), RMSE($\beta$)} \\
\hline
Outlier Distribution & $N$ & $s=5,pt=1\%$ & $s=5,pt=5\%$ & $s=5,pt=10\%$ & $s=10,pt=1\%$ & $s=10,pt=5\%$ & $s=10,pt=10\%$ \\ \hline
Distribution 1 & 1000 & 0.06, 0.04 & 0.04, 0.06 & 0.04, 0.05 & 0.06, 0.04 & 0.04, 0.06 & 0.04, 0.05 \\ \hline
Distribution 1 & 5000 & 0.06, 0.04 & 0.04, 0.05 & 0.04, 0.05 & 0.06, 0.04 & 0.04, 0.05 & 0.04, 0.05 \\ \hline
Distribution 1 & 10000 & 0.06, 0.04 & 0.04, 0.06 & 0.03, 0.05 & 0.06, 0.04 & 0.04, 0.06 & 0.03, 0.05 \\ \hline
Distribution 2 & 1000 & 0.06, 0.04 & 0.04, 0.06 & 0.01, 0.07 & 0.06, 0.04 & 0.04, 0.06 & 0.01, 0.07 \\ \hline
Distribution 2 & 5000 & 0.06, 0.04 & 0.05, 0.06 & 0.01, 0.07 & 0.06, 0.04 & 0.05, 0.06 & 0.01, 0.07 \\ \hline
Distribution 2 & 10000 & 0.06, 0.04 & 0.05, 0.06 & 0.01, 0.07 & 0.06, 0.04 & 0.05, 0.06 & 0.01, 0.07 \\ \hline
\end{tabular}
\label{tbl:emBasedExpResultsSubsetting}
\end{table*}
\end{landscape}
\section{Related work}
\label{sec:relWork}
The outlier detection literature is vast and this section is not exhaustive.
A comprehensive survey can be found in \cite{Chandola:2009} and \cite{aggarwal2015outlier} and a recent comparative study in \cite{DAMI16}.
Prior research can be broadly categorized into three types.
The parametric approach builds statistical models based on some assumptions about the dataset. While conceptually simple, they suffer from shortcomings such as
simplifying assumptions about data distributions, less emphasis on interpretability and poor scalability.
An alternate approach involves distance-based techniques that do not make any prior assumption on data distribution.
However, this approach has scalability issues as it might require computation of distances between all pairs of points.
There has been slew of techniques to scale distance-based methods including indices (e.g.\ \cite{ramaswamy2000efficient}), pruning (e.g.\ \cite{bay2003mining}) and approximations. See \cite{knorr2000distance} for a summary of such techniques.
Yet another approach is based on ``local'' outliers that considers the distances (or densities) of observations in its neighborhood.
LOF \cite{Breunig2000} and LOCI \cite{Papadimitriou2003a} are canonical examples of this approach.
However, there is few prior work on sampling for speeding up outlier detection.
Most are focused on distance-based outlier detection techniques.
\cite{kollios2003efficient} showed that a biased sample where the sampling probability is proportional to the density of the dataset
often works well for diverse data mining tasks such as outlier detection and clustering.
\cite{wu2006outlier} proposed a sampling technique that efficiently approximated the distance to the $k$-th nearest neighbor.
\cite{sugiyama2013rapid} evaluated a number of distance-based outlier detection algorithms and found that sampling-based approaches
outperformed many state-of-the art algorithms in both efficiency and effectiveness.
Outlier ensembles is an emerging research topic with a number of challenging issues.
One the earliest work \cite{lazarevic2005feature} adapted the idea of (feature) bagging to outliers by repeatedly sampling different sets of dimensions of the data for outlier detection. Some theoretical foundation for outlier ensembles is provided in \cite{zimek2014ensembles} and \cite{aggarwal2015theoretical}.
\cite{zimek2013subsampling} introduced the idea of subsampling to include diversity in the outlier ensembles and found that running an outlier ensemble on subsamples is more efficient than other sophisticated methods to obtain diverse ensembles.
It has been found that outlier detection on subsamples is even more efficient than running a single outlier detector on the entire dataset.
\cite{aggarwal2015theoretical} and \cite{zimek2013subsampling} also proposed interesting techniques for model and score aggregation for outlier detection.
However, none of the previous work characterized, quantified or estimated the resilience of outlier detection methods to a particular sampling technique.
\balance
\bibliographystyle{abbrv}
|
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"redpajama_set_name": "RedPajamaArXiv"
}
| 1,372
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Q: Sequence to study Mathematics from beginning to Undergraduate Level I had the misfortune of a late diagnosed leaning impairment cause a few gaps in my knowledge which resulted in flawed foundational knowledge needed to progress efficiently and effectively.
I'm pursuing Applied Mathematics and Physics at Bachelor Degree Level and will possibly add Pure Mathematics later on.
My Question:
What is the best/easiest sequence to learn/relearn maths from Elementary/Primary level up to a Bachelor/Masters Level? My reason behind this is that I want to correct all gaps in my mathematical knowledge and progress to the highest level attainable.
My reasoning is that I am already aware that If your Algebra is flawed, You may struggle with Trigonometry etc.
Please list the items/ Topics/ Sub-topics
I would Appreciate any help.
A: I will assume that you've had basic schooling in math, since you refer to "a few gaps" in your knowledge, not a wholesale lack. In that case, the first thing to do is assess how good your current knowledge is.
I suggest starting with a pre-algebra book that has an answer key. Work the problems and see if you get the right answers. If you miss many, you should study the concepts needed for pre-algebra, because those will provide the foundational knowledge of topics you'll need for beginning algebra.
Once you're confident in pre-algebra, time to move on to beginning algebra. If you've had algebra, again try an assessment first. See if you can get the answers to problems, that'll let you know how thoroughly you'll have to study this topic.
After algebra, try introductory geometry, assessing your knowledge there and filling it in as necessary. Continue with more advanced high-school algebra, which should include trigonometry.
Precalculus is essentially advanced high-school algebra. Depending on which book(s) you use, you may cover some of the same topics as algebra/trigonometry but at a more advanced level.
Calculus is next. High-school calculus covers the same topics as introductory calculus at the college level, but at a slower pace. Calculus teaches about limits, derivatives, integrals, and various types of methods for evaluating and working with those with respect to different types of functions. Here you'll make use of concepts you learned in algebra/trigonometry/pre-caclulus.
Once you've got through calculus, you should consider differential equations, discrete math, linear algebra, and some kind of analysis (probably real analysis).
Mastering all of those should open things up for you to more advanced topics in math and physics.
|
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var rmentions = {};
for (var i = 0; i < m_id.length; i++) {
rmentions[m_id[i]] = (delta.deltaMessageReply.repliedToMessage.body || "").substring(
m_offset[i],
m_offset[i] + m_length[i]
);
}
//Mention block - 2#
callbackToReturn.messageReply = {
threadID: (delta.deltaMessageReply.repliedToMessage.messageMetadata.threadKey.threadFbId ?
delta.deltaMessageReply.repliedToMessage.messageMetadata.threadKey.threadFbId : delta.deltaMessageReply.repliedToMessage.messageMetadata.threadKey
.otherUserFbId).toString(),
messageID: delta.deltaMessageReply.repliedToMessage.messageMetadata.messageId,
senderID: delta.deltaMessageReply.repliedToMessage.messageMetadata.actorFbId.toString(),
attachments: delta.deltaMessageReply.repliedToMessage.attachments.map(function (att) {
var mercury = JSON.parse(att.mercuryJSON);
Object.assign(att, mercury);
return att;
}).map(att => {
var x;
try {
x = utils._formatAttachment(att);
} catch (ex) {
x = att;
x.error = ex;
x.type = "unknown";
}
return x;
}),
body: delta.deltaMessageReply.repliedToMessage.body || "",
isGroup: !!delta.deltaMessageReply.repliedToMessage.messageMetadata.threadKey.threadFbId,
mentions: rmentions,
timestamp: delta.deltaMessageReply.repliedToMessage.messageMetadata.timestamp,
};
}
if (ctx.globalOptions.autoMarkDelivery) {
markDelivery(ctx, api, callbackToReturn.threadID, callbackToReturn.messageID);
}
return !ctx.globalOptions.selfListen &&
callbackToReturn.senderID === ctx.userID ?
undefined :
(function () { globalCallback(null, callbackToReturn); })();
}
}
return;
}
}
if (v.delta.class !== "NewMessage" &&
!ctx.globalOptions.listenEvents
)
return;
switch (v.delta.class) {
case "ReadReceipt":
var fmtMsg;
try {
fmtMsg = utils.formatDeltaReadReceipt(v.delta);
} catch (err) {
return globalCallback({
error: "Problem parsing message object. Please open an issue at https://github.com/Schmavery/facebook-chat-api/issues.",
detail: err,
res: v.delta,
type: "parse_error"
});
}
return (function () { globalCallback(null, fmtMsg); })();
case "AdminTextMessage":
switch (v.delta.type) {
case "change_thread_theme":
case "change_thread_nickname":
case "change_thread_icon":
break;
case "group_poll":
var fmtMsg;
try {
fmtMsg = utils.formatDeltaEvent(v.delta);
} catch (err) {
return globalCallback({
error: "Problem parsing message object. Please open an issue at https://github.com/Schmavery/facebook-chat-api/issues.",
detail: err,
res: v.delta,
type: "parse_error"
});
}
return (function () { globalCallback(null, fmtMsg); })();
default:
return;
}
break;
//For group images
case "ForcedFetch":
if (!v.delta.threadKey) return;
var mid = v.delta.messageId;
var tid = v.delta.threadKey.threadFbId;
if (mid && tid) {
const form = {
"av": ctx.globalOptions.pageID,
"queries": JSON.stringify({
"o0": {
//This doc_id is valid as of ? (prob January 18, 2020)
"doc_id": "1768656253222505",
"query_params": {
"thread_and_message_id": {
"thread_id": tid.toString(),
"message_id": mid.toString(),
}
}
}
})
};
defaultFuncs
.post("https://www.facebook.com/api/graphqlbatch/", ctx.jar, form)
.then(utils.parseAndCheckLogin(ctx, defaultFuncs))
.then((resData) => {
if (resData[resData.length - 1].error_results > 0) {
throw resData[0].o0.errors;
}
if (resData[resData.length - 1].successful_results === 0) {
throw { error: "forcedFetch: there was no successful_results", res: resData };
}
var fetchData = resData[0].o0.data.message;
if (fetchData && fetchData.__typename === "ThreadImageMessage") {
(!ctx.globalOptions.selfListen &&
fetchData.message_sender.id.toString() === ctx.userID) ||
!ctx.loggedIn ?
undefined :
(function () { globalCallback(null, {
type: "change_thread_image",
threadID: utils.formatID(tid.toString()),
snippet: fetchData.snippet,
timestamp: fetchData.timestamp_precise,
author: fetchData.message_sender.id,
image: {
attachmentID: fetchData.image_with_metadata && fetchData.image_with_metadata.legacy_attachment_id,
width: fetchData.image_with_metadata && fetchData.image_with_metadata.original_dimensions.x,
height: fetchData.image_with_metadata && fetchData.image_with_metadata.original_dimensions.y,
url: fetchData.image_with_metadata && fetchData.image_with_metadata.preview.uri
}
}); })();
}
})
.catch((err) => {
log.error("forcedFetch", err);
});
}
break;
case "ThreadName":
case "ParticipantsAddedToGroupThread":
case "ParticipantLeftGroupThread":
var formattedEvent;
try {
formattedEvent = utils.formatDeltaEvent(v.delta);
} catch (err) {
return globalCallback({
error: "Problem parsing message object. Please open an issue at https://github.com/Schmavery/facebook-chat-api/issues.",
detail: err,
res: v.delta,
type: "parse_error"
});
}
return (!ctx.globalOptions.selfListen &&
formattedEvent.author.toString() === ctx.userID) ||
!ctx.loggedIn ?
undefined :
(function () { globalCallback(null, formattedEvent); })();
}
}
function markDelivery(ctx, api, threadID, messageID) {
if (threadID && messageID) {
api.markAsDelivered(threadID, messageID, (err) => {
if (err) {
log.error(err);
} else {
if (ctx.globalOptions.autoMarkRead) {
api.markAsRead(threadID, (err) => {
if (err) {
log.error(err);
}
});
}
}
});
}
}
module.exports = function (defaultFuncs, api, ctx) {
var globalCallback = identity;
return function (callback) {
globalCallback = callback;
//Reset some stuff
ctx.lastSeqId = 0;
ctx.syncToken = undefined;
//Same request as getThreadList
const form = {
"av": ctx.globalOptions.pageID,
"queries": JSON.stringify({
"o0": {
"doc_id": "1349387578499440",
"query_params": {
"limit": 1,
"before": null,
"tags": ["INBOX"],
"includeDeliveryReceipts": false,
"includeSeqID": true
}
}
})
};
defaultFuncs
.post("https://www.facebook.com/api/graphqlbatch/", ctx.jar, form)
.then(utils.parseAndCheckLogin(ctx, defaultFuncs))
.then((resData) => {
if (resData && resData.length > 0 && resData[resData.length - 1].error_results > 0) {
throw resData[0].o0.errors;
}
if (resData[resData.length - 1].successful_results === 0) {
throw { error: "getSeqId: there was no successful_results", res: resData };
}
if (resData[0].o0.data.viewer.message_threads.sync_sequence_id) {
ctx.lastSeqId = resData[0].o0.data.viewer.message_threads.sync_sequence_id;
listenMqtt(defaultFuncs, api, ctx, globalCallback);
}
})
.catch((err) => {
log.error("getSeqId", err);
return callback(err);
});
var stopListening = function () {
globalCallback = identity;
if(ctx.mqttClient)
{
ctx.mqttClient.end();
ctx.mqttClient = undefined;
}
};
return stopListening;
};
};
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 4,698
|
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