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Graph Theoretic Methods in Multiagent Networks
Mehran Mesbahi Digital Instant Download
Author(s): Mehran Mesbahi; Magnus Egerstedt
ISBN(s): 9781400835355, 1400835356
Edition: Course Book
File Details: PDF, 2.13 MB
Year: 2010
Language: english

Graph Theoretic Methods in
Multiagent Networks

This page intentionally left blank

Graph Theoretic Methods in
Multiagent Networks
Mehran Mesbahi and Magnus Egerstedt
PRINCETON UNIVERSITY PRESS
PRINCETON AND OXFORD

Copyright c
2010 by Princeton University Press
Requests for permission to reproduce material from this work
should be sent to Permissions, Princeton University Press
Published by Princeton University Press,
41 William Street, Princeton, New Jersey 08540
In the United Kingdom: Princeton University Press,
6 Oxford Street, Woodstock, Oxfordshire OX20 1TW
press.princeton.edu
All Rights Reserved
Library of Congress Cataloging-in-Publication Data
Mesbahi, Mehran.
Graph theoretic methods in multiagent networks / Mehran Mesbahi and Magnus
Egerstedt.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-691-14061-2(hardcover : alk. paper) 1. Network analysis (Planning)–
Graphic methods. 2. Multiagent systems–Mathematical models. I. Egerstedt, Mag-
nus. II. Title.
T57.85.M43 2010
006.3–dc22
2010012844
British Library Cataloging-in-Publication Data is available
The publisher would like to acknowledge the authors of this volume
for providing the camera-ready copy from which this book was printed
Printed on acid-free paper. ∞
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1

v
To our very own multiagent systems
Maana, Milad, and Kathy (M.M.)
Annika, Olivia, and Danielle (M.E.)

Contents
Preface xi
Notation xv
PART 1. FOUNDATIONS 1
Chapter 1. Introduction 3
1.1 Hello, Networked World 3
1.2 Multiagent Systems 4
1.3 Information Exchange via Local Interactions 8
1.4 Graph-based Interaction Models 10
1.5 Looking Ahead 12
Chapter 2. Graph Theory 14
2.1 Graphs 14
2.2 Variations on the Theme 20
2.3 Graphs and Matrices 22
2.4 Algebraic and Spectral Graph Theory 27
2.5 Graph Symmetries 33
Chapter 3. The Agreement Protocol: Part I–The Static Case 42
3.1 Reaching Agreement: Undirected Networks 46
3.2 Reaching Agreement: Directed Networks 48
3.3 Agreement and Markov Chains 58
3.4 The Factorization Lemma 61
Chapter 4. The Agreement Protocol: Part II–Lyapunov and LaSalle 72
4.1 Agreement via Lyapunov Functions 72
4.2 Agreement over Switching Digraphs 76
4.3 Edge Agreement 77
4.4 Beyond Linearity 81
Chapter 5. Probabilistic Analysis of Networks and Protocols 90
5.1 Random Graphs 90
5.2 Agreement over Random Networks 93
5.3 Agreement in the Presence of Noise 100
5.4 Other Probabilistic Models of Networks 108

viii CONTENTS
PART 2. MULTIAGENT NETWORKS 115
Chapter 6. Formation Control 117
6.1 Formation Speciﬁcation: Shapes 118
6.2 Formation Speciﬁcation: Relative States 123
6.3 Shape-based Control 127
6.4 Relative State-based Control 130
6.5 Dynamic Formation Selection 143
6.6 Assigning Roles 151
Chapter 7. Mobile Robots 159
7.1 Cooperative Robotics 160
7.2 Weighted Graph-based Feedback 162
7.3 Dynamic Graphs 167
7.4 Formation Control Revisited 169
7.5 The Coverage Problem 176
Chapter 8. Distributed Estimation 191
8.1 Distributed Linear Least Squares 191
8.2 Pulsed Intercluster Communication 199
8.3 Implementation over Wireless Networks 208
8.4 Distributed Kalman Filtering 212
Chapter 9. Social Networks, Epidemics, and Games 226
9.1 Diffusion on Social Networks–The Max Protocol 226
9.2 The Threshold Protocol 229
9.3 Epidemics 233
9.4 The Chip Firing Game 243
PART 3. NETWORKS AS SYSTEMS 251
Chapter 10. Agreement with Inputs and Outputs 253
10.1 The Basic Input-Output Setup 253
10.2 Graph Theoretic Controllability: The SISO Case 260
10.3 Graph Theoretic Controllability: The MIMO Case 269
10.4 Agreement Reachability 276
10.5 Network Feedback 280
10.6 Optimal Control 282
Chapter 11. Synthesis of Networks 293
11.1 Network Formation 293
11.2 Local Formation Games 294
11.3 Potential Games and Best Response Dynamics 299
11.4 Network Synthesis: A Global Perspective 305
11.5 Discrete and Greedy 309
11.6 Optimizing the Weighted Agreement 312

CONTENTS ix
Chapter 12. Dynamic Graph Processes 319
12.1 State-dependent Graphs 319
12.2 Graphical Equations 323
12.3 Dynamic Graph Controllability 326
12.4 What Graphs Can Be Realized? 336
12.5 Planning over Proximity Graphs 338
Chapter 13. Higher-order Networks 344
13.1 Simplicial Complexes 344
13.2 Combinatorial Laplacians 347
13.3 Triangulations and the Rips Complex 350
13.4 The Nerve Complex 354
Appendix A. 362
A.1 Analysis 362
A.2 Matrix Theory 363
A.3 Control Theory 366
A.4 Probability 372
A.5 Optimization and Games 375
Bibliography 379
Index 399

Preface
“I don’t want to achieve immortality
through my work ... I want to achieve
it through not dying.” — Woody Allen
The emergence of (relatively) cheap sensing and actuation nodes, capable of
short-range communications and local decision-making, has raised a num-
ber of new system-level questions concerning how such systems should be
coordinated and controlled. Arguably, the biggest challenge facing this new
ﬁeld of research is means by which local interaction rules lead to desired
global properties, that is, given that the networked system is to accomplish
a particular task, how should the interaction and control protocols be struc-
tured to ensure that the task is in fact achieved?
This newly deﬁned area of networked systems theory has attracted wide
interest during the last decade. A number of sessions are devoted to this
problem at the major conferences and targeted conferences have emerged.
Moreover, graduate-level courses are beginning to be taught in this general
area, and major funding institutions are pursuing networked systems as in-
tegral to their missions due to the many applications where network-level
questions must be addressed. These applications include sensor networks,
multiagent robotics, and mobile ad hoc communication nets, in addition to
such areas as social networks and quantum networks.
The particular focus of this book is on graph theoretic methods for the
analysis and synthesis of networked dynamic systems. By abstracting away
the complex interaction geometries associated with the sensing and commu-
nication footprints of the individual agents, and instead identifying agents
with nodes in a graph and encoding the existence of an interaction between
nodes as an edge, a powerful new formalism and set of tools for networked
systems have become available. For instance, the graph theoretic framework
described in this book provides means to examine how the structure of the
underlying interaction topology among the agents leads to distinct global
behavior of the system. This graph theoretic outlook also allows for exam-
ining the correspondence between system theoretic features of networked
systems on one hand, and the combinatorial and algebraic attributes of the

xii PREFACE
underlying network on the other. By doing this, one can, for example, ad-
dress questions related to the robustness of networked systems in terms of
the variation of the network topology, as well as the network synthesis prob-
lem in the context of embedded networked systems.
This book builds on the foundation of graph theory and gradually paves
the way toward examining graph theoretic constructs in the context of net-
worked systems. This target is laid out in the first part of the book, which
focuses on the interplay between the agreement protocol (also known as
the consensus algorithm) and graph theory. Specifically, in Chapter 3, the
correspondence between the network structure and the convergence prop-
erties of the agreement protocol is shown for both undirected and directed
networks using the spectral properties of the graph. This is followed by es-
tablishing an explicit correspondence between the agreement protocol and
the general area of Markov chains. The latter chapters in Part I delve into the
extension of the basic setup in Chapter 3 to consider the effect of random-
ness, noise, and nonlinearities on the behavior of the consensus coordination
protocols. This is accomplished by introducing the powerful machinery of
Lyapunov theory in deterministic (Chapter 4) and stochastic (Chapter 5) set-
tings, which provides the flexibility for analyzing various extensions of the
basic agreement protocol.
In Part II, we provide various dynamical, system theoretic, and applied
facets of dynamic systems operating over networks. These include forma-
tion control (Chapter 6), mobile robot networks (Chapter 7), distributed es-
timation (Chapter 8), and social networks, epidemics, and games (Chapter
9).
Part III provides an introduction to a perspective of viewing networks as
dynamic systems. In Chapter 10, we discuss the controllability and observ-
ability of agreement protocols equipped with input and output nodes. In
particular, this chapter is devoted to the study of how control theoretic prop-
erties of the system are dictated by the algebraic and combinatorial structure
of the network. This is followed by the problem of synthesizing networks
(Chapter 11), with particular attention to the dynamic, graph theoretic, and
game theoretic aspects that such an endeavor entails. Another novel ramifi-
cation of the graph theoretic outlook on multiagent systems is in the context
of graph processes, where the network topology itself is given a dynamic
role that lends itself to analysis via system theoretic methods (Chapter 12).
Higher-order interconnections conclude the book (Chapter 13), demonstrat-
ing how the graph theoretic machinery can be extended to simplicial com-
plexes, for example, in order to address sensor-coverage problems.
Pictorially, one can view the chapters in this book as nodes in a directed
graph, shown below, whose edges suggest dependencies between the vari-
ous chapters.

PREFACE xiii
2
3
4
5 6
7
8 9 10 11
12
13
One can also think of these edges as suggesting possible routes through
the book. For example, the 2 → 3 → 4 → 6 → 7 branch constitutes a
natural graduate level course on multiagent robotics, while the branch 2 →
3 → 4 → 11 → 12 → 13 provides a more mathematical treatment of the
underlying theme of the book. Ideas for teaching from the book, additional
examples and exercises, as well as other comments will be posted on the
book website at https://sites.google.com/site/mesbahiegerstedt.
The book is suitable for graduate students and researchers in systems,
controls, and robotics across various engineering departments, as well as
those in applied mathematics and statistics whose work is network-centric.
Part of this book is also suitable for senior undergraduate students in en-
gineering and computer science programs. As such, we hope that it fills
a niche by providing a timely exposition of networked dynamic systems
with emphasis on their graph theoretic underpinnings. We enjoyed count-
less hours discussing and thinking about the topics that have found their way
into the book; along the way, we have been humbled by gaining a better
glimpse of the research creativity that has been expressed through schol-
arly works by many researchers in the general area of networks and system
theory. Since our goal was expanded at some point to cover a rather broad
set of topics related to graph theoretic methods for analysis and synthesis
of dynamical systems operating over networks, we had to make a few com-
promises on the style. As such, we decided to offer proofs for most of the
presented results, yet only state the results that we felt played a supportive
role in each chapter. In most cases, results that are stated without a proof are
discussed in the exercises and can be found in the references discussed at the
end of each chapter. Our hope is that researchers and students who are new
to this field will find in this book a welcoming and readable account of an

xiv PREFACE
active area of research- and for the experts–to stumble across new insights
that further complements their research horizons.
Throughout the development of this book, we have been fortunate to be
supported by a number of funding agencies, including NSF, ONR, ARO,
AFOSR, Boeing, NASA/JPL, and Rockwell Collins. Their support is grate-
fully acknowledged.
On a final note, this book would not have been possible without help,
support, and suggestions from a number of colleagues. In particular, Randy
Beard, Richard Murray, and Panagiotis Tsiotras provided feedback on the
book that certainly helped make it stronger. Parts of this book are based on
results obtained by our current and former students and post-docs, some of
whom graciously helped us proofread parts of the book. Special thanks go to
Dan Zelazo, Amir Rahmani, Airlie Chapman, Marzieh Nabi-Abdolyousefi,
Meng Ji, Musad Haque, Brian Smith, Patrick Martin, Philip Twu, Arindam
Das, Yoonsoo Kim, Peter Kingston, Simone Martini, Mauro Franceschelli,
and Abubakr Muhammad. We would like to thank Vickie Kearn at Princeton
University Press for shepherding this book, from its initial conception to
the final product. And finally, we are forever grateful to our parents for
cultivating in us a sense of appreciation for what is beautiful yet–at times–
enigmatic.
M.M. (Seattle), M.E. (Atlanta)
April 2010

xv
Notation
Graph Theory
G: undirected graph; also referred to as graph
D: directed graph; also referred to as digraph

D: graph obtained after removing the orientation of the directed edges
of D; also referred to as disoriented digraph
G: complement of undirected graph G
Go
: oriented version of graph G
V : vertex set; when necessary, also denoted by V (G) or V (D)
∂S: boundary of vertex set S (with respect to an underlying graph)
cl S: closure of vertex set S (with respect to an underlying graph)
vi, i = 1, . . . , n: vertex i; also used for denoting the ith entry of
vector v
E: edge set; when necessary, also denoted by E(G) or E(D)
eij = {vi, vj}: edge in a graph; also denoted by vivj or ij
i ∼ j: edge {vi, vj} is present in the graph
dist(i, j): the length of the shortest path between vertices vi and vj
eij = (vi, vj): edge in a digraph
Ge: graph G with edge e removed
G + e: graph G with edge e added
N(i): set of agents adjacent to i
N(i, t): set of agents adjacent to i at time t

xvi
d(v): degree of vertex v
din(v): in-degree of vertex v
dmin(G): minimum vertex degree in G
dmax(G): maximum vertex degree in G
¯
din(D): maximum (weighted) in-degree in D
diam(G): diameter of G
A(G): adjacency matrix of G
A(D): in-degree adjacency matrix of D
∆(G): degree matrix of G
∆(D): in-degree matrix of D
L(G): graph Laplacian of G
Le(G): edge Laplacian of G
L(D): in-degree Laplacian of D
Lo(D): out-degree Laplacian of D
L(G): line graph of G
D(D): incidence matrix of D
Cn: cycle graph on n vertices
Pn: path graph on n vertices
Kn: complete graph on n vertices
Sn: star graph on n vertices
G(n, p): set of random graphs on n vertices, with edge probability p
G(n, r): set of random geometric graphs on n vertices, with edge
threshold distance r
G1 G2: Cartesian product of two graphs G1 and G2

xvii
Linear Algebra
Rn: Euclidean space of dimension n
Rn
+: nonnegative orthant in Rn
Rm×n: space of m × n real matrices
Sn: space of n × n symmetric matrices over reals
Sn
+: space of n × n (symmetric) positive semidefinite matrices
In: n × n identity matrix; also denoted as I if the dimension is clear
from the context
0m×n: m × n zero matrix; also denoted as 0 if the dimension is clear
from the context
M−1, M†: respectively, inverse and pseudo-inverse of M
MT , M−T : respectively, transpose and inverse transpose of M
N(M): null space of M
R(M): range space of M
[A]ij: entry of matrix A on ith row and jth column
det(M): determinant of (square) matrix M
rank M: rank of M
trace M: trace of M
eM : matrix exponential of square matrix M
M1 ⊗ M2: Kronecker product of two matrices M1 and M2
L[i,j]: matrix obtained from L by removing its ith row and jth column
diag(M): vector comprised of the diagonal elements of M
Diag(v): diagonal matrix with the vector v on its diagonal
Diag(vk), k = 1, 2, · · · , n: Diag([v1, · · · , vn]T )
M 0 (M a symmetric matrix): M is positive definite
M ≥ 0 (M a symmetric matrix): M is positive semidefinite

xviii
λi(M): ith eigenvalue of M; M is symmetric and its eigenvalues are
ordered from least to greatest value
vi: ith entry of the vector v; also used for denoting vertex i in a graph
ρ(M): spectral radius of M, that is, the maximum eigenvalue of M
in magnitude
span{x}: span of vector x, that is, the subspace generated by scalar
multiples of x
x, y: inner product between two vectors x and y; real part of the
inner product x∗y if x and y are complex-valued
1: vector of all ones
1n: n × 1 vector of all ones
1⊥
: subspace orthogonal to span{1}
x : 2-norm of vector x; x = (xT x)1/2 unless indicated otherwise
Other
dist: distance function
j:
√
−1
|z|: modulus of complex number z = α+jβ, that is, 2-norm of vector
[α, β]T
V W: elements in set V that are not in set W

i αi: product of αis

i αi: sum of αis
≈: approximately equal to
: much less than
x∗: complex conjugate transpose for complex-valued vector x
xi(t) ∈ Rp
: state of agent i at time t
A: agreement set, equal to span{1}
E{x}: expected value of random variable x

xix
var{x}: variance of random variable x

x: estimate of random variable (vector) x
[n] (n a positive integer): set {1, 2, . . . , n}
mod p: a = b (mod p) if a − b is an integer multiple of p
2V (V a ﬁnite set): the power set of V , that is, the set of its subsets
n
m

: number of ways to choose m-element subsets of [n], that is,
n!/(m!(n − m)!)
card(A): cardinality of set A
arg min f: argument of the function f that minimizes it over its do-
main or constraint set
arg max f: argument of the function f that maximizes it over its do-
main or constraint set
R[x1, . . . , xn]: set of polynomials over the reals with indeterminants
x1, . . . , xn
O(f(n)): g(n) = O(f(n)) if g(n) is bounded from above by some
constant multiple of f(n) for large enough n
Ω(f(n)): g(n) = Ω(f(n)) if g(n) is bounded from below by some
constant multiple of f(n) for large enough n

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'Everybody knows, Fru Thyregod, that you are the life and soul of
Herakleion.'
They had wandered into a little wood, and sat down on a fallen tree
beside the stream. She began again prodding at the ground with her
parasol, keeping her eyes cast down. She was glad to have captured
Julian, partly for her own sake, and partly because she knew that
Eve would be annoyed.
'How delightful to escape from all our noisy friends,' she said; 'we
shall create quite a scandal; but I am too unconventional to trouble
about that. I cannot sympathise with those limited, conventional folk
who always consider appearances. I have always said, One should
be natural. Life is too short for the conventions. Although, I think
one should refrain from giving pain. When I was a girl, I was a
terrible tomboy.'
He listened to her babble of coy platitudes, contrasting her with Eve.
'I never lost my spirits,' she went on, in the meditative tone she
thought suitable to tête-à-tête conversations—it provoked intimacy,
and afforded agreeable relief to her more social manner; a woman,
to be charming, must be several-sided; gay in public, but a little
wistful philosophy was interesting in private; it indicated sympathy,
and betrayed a thinking mind,—'I never lost my spirits, although life
has not always been very easy for me; still, with good spirits and
perhaps a little courage one can continue to laugh, isn't that the way
to take life? and on the whole I have enjoyed mine, and my little
adventures too, my little harmless adventures; Carl always laughs
and says, You will always have adventures, Mabel, so I must make
the best of it,—he says that, though he has been very jealous at
times. Poor Carl,' she said reminiscently, 'perhaps I have made him
suffer; who knows?'
Julian looked at her; he supposed that her existence was made up of
such experiments, and knew that the arrival of every new young
man in Herakleion was to her a source of flurry and endless

potentialities which, alas, never fulfilled their promise, but which left
her undaunted and optimistic for the next affray.
'Why do I always talk about myself to you?' she said, with her little
laugh; 'you must blame yourself for being too sympathetic.'
He scarcely knew how their conversation progressed; he wondered
idly whether Eve conducted hers upon the same lines with Don
Rodrigo Valdez, or whether she had been claimed by Miloradovitch,
to whom she said she was engaged. Did she care for Miloradovitch?
he was immensely rich, the owner of jewels and oil-mines,
remarkably good-looking; dashing, and a gambler. At diplomatic
gatherings he wore a beautiful uniform. Julian had seen Eve dancing
with him; he had seen the Russian closely following her out of a
room, bending forward to speak to her, and her ironical eyes raised
for an instant over the slow movement of her fan. He had seen them
disappear together, and the provocative poise of her white
shoulders, and the richness of the beautiful uniform, had remained
imprinted on his memory.
He awoke with dismay to the fact that Fru Thyregod had taken off
her hat.
She had a great quantity of soft, yellow hair into which she ran her
fingers, lifting its weight as though oppressed. He supposed that the
gesture was not so irrelevant to their foregoing conversation, of
which he had not noticed a word, as it appeared to be. He was
startled to find himself saying in a tone of commiseration,—
'Yes, it must be very heavy.'
'I wish that I could cut it all off,' Fru Thyregod cried petulantly. 'Why,
to amuse you, only look....' and to his horror she withdrew a number
of pins and allowed her hair to fall in a really beautiful cascade over
her shoulders. She smiled at him, parting the strands before her
eyes.

At that moment Eve and Miloradovitch came into view, wandering
side by side down the path.
Of the four, Miloradovitch alone was amused. Julian was full of a
shamefaced anger towards Fru Thyregod, and between the two
women an instant enmity sprang into being like a living and visible
thing. The Russian drew near to Fru Thyregod with some laughing
compliment; she attached herself desperately to him as a refuge
from Julian. Julian and Eve remained face to face with one another.
'Walk with me a little,' she said, making no attempt to disguise her
fury.
'My dear Eve,' he said, when they were out of earshot, 'I should
scarcely recognise you when you put on that expression.'
He spoke frigidly. She was indeed transformed, her features
coarsened and unpleasing, her soft delicacy vanished. He could not
believe that he had ever thought her rare, exquisite, charming.
'I don't blame you for preferring Fru Thyregod,' she returned.
'I believe your vanity to be so great that you resent any man
speaking to any other woman but yourself,' he said, half persuading
himself that he was voicing a genuine conviction.
'Very well, if you choose to believe that,' she replied.
They walked a little way in angry silence.
'I detest all women,' he added presently.
'Including me?'
'Beginning with you.'
He was reminded of their childhood with its endless disputes, and
made an attempt to restore their friendship.

'Come, Eve, why are we quarrelling? I do not make you jealous
scenes about Miloradovitch.'
'Far from it,' she said harshly.
'Why should he want to marry you?' he began, his anger rising
again. 'What qualities have you? Clever, seductive, and entertaining!
But, on the other hand, selfish, jealous, unkind, pernicious, indolent,
vain. A bad bargain. If he knew you as well as I.... Jealousy! It
amounts to madness.'
'I am perhaps not jealous where Miloradovitch is concerned,' she
said.
'Then spare me the compliment of being jealous of me. You wreck
affection; you will wreck your life through your jealousy and
exorbitance.'
'No doubt,' she replied in a tone of so much sadness that he became
remorseful. He contrasted, moreover, her violence, troublesome,
inconvenient, as it often was, with the standardised and distasteful
little inanities of Fru Thyregod and her like, and found Eve
preferable.
'Darling, you never defend yourself; it is very disarming.'
But she would not accept the olive-branch he offered.
'Sentimentality becomes you very badly, Julian; keep it for Fru
Thyregod.'
'We have had enough of Fru Thyregod,' he said, flushing.
'It suits you to say so; I do not forget so easily. Really, Julian,
sometimes I think you very commonplace. From the moment you
arrived until to-day, you have never been out of Fru Thyregod's
pocket. Like Alexander, once. Like any stray young man.'
'Eve!' he said, in astonishment at the outrageous accusation.

'My little Julian, have you washed the lap-dog to-day? Carl always
says, Mabel, you are fonder of your dogs than of your children—you
are really dreadful, but I don't think that's quite fair,' said Eve, in so
exact an imitation of Fru Thyregod's voice and manner that Julian
was forced to smile.
She went on,—
'I expect too much of you. My imagination makes of you something
which you are not. I so despise the common herd that I persuade
myself that you are above it. I can persuade myself of anything,' she
said scathingly, wounding him in the recesses of his most treasured
vanity—her good opinion of him; 'I persuade myself that you are a
Titan amongst men, almost a god, but in reality, if I could see you
without prejudice, what are you fit for? to be Fru Thyregod's lover!'
'You are mad,' he said, for there was no other reply.
'When I am jealous, I am mad,' she flung at him.
'But if you are jealous of me....' he said, appalled. 'Supposing you
were ever in love, your jealousy would know no bounds. It is a
disease. It is the ruin of our friendship.'
'Entirely.'
'You are inordinately perverse.'
'Inordinately.'
'Supposing I were to marry, I should not dare—what an absurd
thought—to introduce you to my wife.'
A truly terrible expression came into her eyes; they narrowed to little
slits, and turned slightly inwards; as though herself aware of it, she
bent to pick the little cyclamen.
'Are you trying to tell me, Julian....'
'You told me you were engaged to Miloradovitch.'

She stood up, regardless, and he saw the tragic pallor of her face.
She tore the cyclamen to pieces beneath her white fingers.
'It is true, then?' she said, her voice dead.
He began to laugh.
'You do indeed persuade yourself very easily.'
'Julian, you must tell me. You must. Is it true?'
'If it were?'
'I should have to kill you—or myself,' she replied with the utmost
gravity.
'You are mad,' he said again, in the resigned tone of one who states
a perfectly established fact.
'If I am mad, you are unutterably cruel,' she said, twisting her
fingers together; 'will you answer me, yes or no? I believe it is true,'
she rushed on, immolating herself, 'you have fallen in love with some
woman in England, and she, naturally, with you. Who is she? You
have promised to marry her. You, whom I thought so free and
splendid, to load yourself with the inevitable fetters!'
'I should lose caste in your eyes?' he asked, thinking to himself that
Eve was, when roused, scarcely a civilised being. 'But if you marry
Miloradovitch you will be submitting to the same fetters you think so
degrading.'
'Miloradovitch,' she said impatiently, 'Miloradovitch will no more
ensnare me than have the score of people I have been engaged to
since I last saw you. You are still evading your answer.'
'You will never marry?' he dwelt on his discovery.
'Nobody that I loved,' she replied without hesitation, 'but, Julian,
Julian, you don't answer my question?'

'Would you marry me if I wanted you to?' he asked carelessly.
'Not for the world, but why keep me in suspense? only answer me,
are you trying to tell me that you have fallen in love? if so, admit it,
please, at once, and let me go; don't you see, I am leaving Fru
Thyregod on one side, I ask you in all humility now, Julian.'
'For perhaps the fiftieth time since you were thirteen,' he said,
smiling.
'Have you tormented me long enough?'
'Very well: I am in love with the Islands, and with nothing and
nobody else.'
'Then why had Fru Thyregod her hair down her back? you're lying to
me, and I despise you doubly for it,' she reverted, humble no longer,
but aggressive.
'Fru Thyregod again?' he said, bewildered.
'How little I trust you,' she broke out; 'I believe that you deceive me
at every turn. Kato, too; you spend hours in Kato's flat. What do you
do there? You write letters to people of whom I have never heard.
You dined with the Thyregods twice last week. Kato sends you notes
by hand from Herakleion when you are in the country. You use the
Islands as dust to throw in my eyes, but I am not blinded.'
'I have had enough of this!' he cried.
'You are like everybody else,' she insisted; 'you enjoy mean
entanglements, and you cherish the idea of marriage. You want a
home, like everybody else. A faithful wife. Children. I loathe
children,' she said violently. 'You are very different from me. You are
tame. I have deluded myself into thinking we were alike. You are
tame, respectable. A good citizen. You have all the virtues. I will live
to show you how different we are. Ten years hence, you will say to
your wife, No, my dear, I really cannot allow you to know that poor
Eve. And your wife, well trained, submissive, will agree.'

He shrugged his shoulders, accustomed to such storms, and
knowing that she only sought to goad him into a rage.
'In the meantime, go back to Fru Thyregod; why trouble to lie to
me? And to Kato, go back to Kato. Write to the woman in England,
too. I will go to Miloradovitch, or to any of the others.'
He was betrayed into saying,—
'The accusation of mean entanglements comes badly from your lips.'
In her heart she guessed pretty shrewdly at his real relation towards
women: a self-imposed austerity, with violent relapses that had no
lasting significance, save to leave him with his contemptuous
distaste augmented. His mind was too full of other matters. For Kato
alone he had a profound esteem.
Eve answered his last remark,—
'I will prove to you the little weight of my entanglements, by
dismissing Miloradovitch to-day; you have only to say the word.'
'You would do that—without remorse?'
'Miloradovitch is nothing to me.'
'You are something to him—perhaps everything.'
'Cela ne me regarde pas,' she replied. 'Would you do as much for
me? Fru Thyregod, for instance? or Kato?'
Interested and curious, he said,—
'To please you, I should give up Kato?'
'You would not?'
'Most certainly I should not. Why suggest it? Kato is your friend as
much as mine. Are all women's friendships so unstable?'
'Be careful, Julian: you are on the quicksands.'

'I have had enough of these topics,' he said, 'will you leave them?'
'No; I choose my own topics; you shan't dictate to me.'
'You would sacrifice Miloradovitch without a thought, to please me—
why should it please me?—but you would not forgo the indulgence
of your jealousy! I am not grateful. Our senseless quarrels,' he said,
'over which we squander so much anger and emotion.' But he did
not stop to question what lay behind their important futility. He
passed his hand wearily over his hair, 'I am deluded sometimes into
believing in their reality and sanity. You are too difficult. You ... you
distort and bewitch, until one expects to wake up from a dream.
Sometimes I think of you as a woman quite apart from other
women, but at other times I think you live merely by and upon
fictitious emotion and excitement. Must your outlook be always so
narrowly personal? Kato, thank Heaven, is very different. I shall take
care to choose my friends amongst men, or amongst women like
Kato,' he continued, his exasperation rising.
'Julian, don't be so angry: it isn't my fault that I hate politics.'
He grew still angrier at her illogical short-cut to the reproach which
lay, indeed, unexpressed at the back of his mind.
'I never mentioned politics. I know better. No man in his senses
would expect politics from any woman so demoralisingly feminine as
yourself. Besides, that isn't your rôle. Your rôle is to be soft, idle; a
toy; a siren; the negation of enterprise. Work and woman—the
terms contradict one another. The woman who works, or who
tolerates work, is only half a woman. The most you can hope for,' he
said with scorn, 'is to inspire—and even that you do unconsciously,
and very often quite against your will. You sap our energy; you sap
and you destroy.'
She had not often heard him speak with so much bitterness, but she
did not know that his opinions in this more crystallised form dated
from that slight moment in which he had divined her own
untrustworthiness.

'You are very wise. I forget whether you are twenty-two or twenty-
three?'
'Oh, you may be sarcastic. I only know that I will never have my life
wrecked by women. To-morrow the elections take place, and, after
that, whatever their result, I belong to the Islands.'
'I think I see you with a certain clearness,' she said more gently, 'full
of illusions, independence, and young generosities—nous passons
tous par là.'
'Talk English, Eve, and be less cynical; if I am twenty-two, as you
reminded me, you are nineteen.'
'If you could find a woman who was a help and not a hindrance?'
she suggested.
'Ah!' he said, 'the Blue Bird! I am not likely to be taken in; I am too
well on my guard.—Look!' he added, 'Fru Thyregod and your Russian
friend; I leave you to them,' and before Eve could voice her
indignation he had disappeared into the surrounding woods.

IV
On the next day, the day of the elections, which was also the
anniversary of the Declaration of Independence, Herakleion
blossomed suddenly, and from the earliest hour, into a striped and
fluttering gaudiness. The sun shone down upon a white town
beflagged into an astonishing gaiety. Everywhere was whiteness,
whiteness, and brilliantly coloured flags. White, green, and orange,
dazzling in the sun, vivid in the breeze. And, keyed up to match the
intensity of the colour, the band blared brassily, unremittingly,
throughout the day from the centre of the platia.
A parrot-town, glaring and screeching; a monkey-town, gibbering,
excited, inconsequent. All the shops, save the sweet-shops, were
shut, and the inhabitants flooded into the streets. Not only had they
decked their houses with flags, they had also decked themselves
with ribbons, their women with white dresses, their children with
bright bows, their carriages with paper streamers, their horses with
sunbonnets. Bands of young men, straw-hatted, swept arm-in-arm
down the pavements, adding to the din with mouth organs,
mirlitons, and tin trumpets. The trams flaunted posters in the colours
of the contending parties. Immense char-à-bancs, roofed over with
brown holland and drawn by teams of mules, their harness hung
with bells and red tassels, conveyed the voters to the polling-booths
amid the cheers and imprecations of the crowd.
Herakleion abandoned itself deliriously to political carnival.
In the immense, darkened rooms of the houses on the platia, the
richer Greeks idled, concealing their anxiety. It was tacitly considered
beneath their dignity to show themselves in public during that day.
They could but await the fruition or the failure of their activities
during the preceding weeks. Heads of households were for the most

part morose, absorbed in calculations and regrets. Old
Christopoulos, looking more bleached than usual, wished he had
been more generous. That secretaryship for Alexander.... In the
great sala of his house he paced restlessly up and down, biting his
finger nails, and playing on his fingers the tune of the many
thousand drachmæ he might profitably have expended. The next
election would not take place for five years. At the next election he
would be a great deal more lavish.
He had made the same resolution at every election during the past
thirty years.
In the background, respectful of his silence, themselves dwarfed and
diminutive in the immense height of the room, little knots of his
relatives and friends whispered together, stirring cups of tisane.
Heads were very close together, glances at old Christopoulos very
frequent. Visitors, isolated or in couples, strolled in unannounced
and informally, stayed for a little, strolled away again. A perpetual
movement of such circulation rippled through the houses in the
platia throughout the day, rumour assiduous in its wake. Fru
Thyregod alone, with her fat, silly laugh, did her best wherever she
went to lighten the funereal oppression of the atmosphere. The
Greeks she visited were not grateful. Unlike the populace in the
streets, they preferred taking their elections mournfully.
By midday the business of voting was over, and in the houses of the
platia the Greeks sat round their luncheon-tables with the knowledge
that the vital question was now decided, though the answer
remained as yet unknown, and that in the polling-booths an army of
clerks sat feverishly counting, while the crowd outside, neglectful of
its meal, swarmed noisily in the hope of news. In the houses of the
platia, on this one day of the year, the Greeks kept open table. Each
vast dining-room, carefully darkened and indistinguishable in its
family likeness from its neighbour in the house on either side,
offered its hospitality under the inevitable chandelier. In each, the
host greeted the new-comer with the same perfunctory smile. In
each, the busy servants came and went, carrying dishes and jugs of

orangeade—for Levantine hospitality, already heavily strained,
boggled at wine—among the bulky and old-fashioned sideboards. All
joyousness was absent from these gatherings, and the closed
shutters served to exclude, not only the heat, but also the strains of
the indefatigable band playing on the platia.
Out in the streets the popular excitement hourly increased, for if the
morning had been devoted to politics, the afternoon and evening
were to be devoted to the annual feast and holiday of the
Declaration of Independence. The national colours, green and
orange, seemed trebled in the town. They hung from every balcony
and were reproduced in miniature in every buttonhole. Only here
and there an islander in his fustanelle walked quickly with sulky and
averted eyes, rebelliously innocent of the brilliant cocarde, and far
out to sea the rainbow islands shimmered with never a flag to stain
the distant whiteness of the houses upon Aphros.
The houses of the platia excelled all others in the lavishness of their
patriotic decorations. The balconies of the club were draped in green
and orange, with the arms of Herakleion arranged in the centre in
electric lights for the evening illumination. The Italian Consulate
drooped its complimentary flag. The house of Platon Malteios—
Premier or ex-Premier? no one knew—was almost too ostentatiously
patriotic. The cathedral, on the opposite side, had its steps carpeted
with red and the spaciousness of its porch festooned with the
colours. From the central window of the Davenant house, opposite
the sea, a single listless banner hung in motionless folds.
It had, earlier in the day, occasioned a controversy.
Julian had stood in the centre of the frescoed drawing-room, flushed
and constrained.
'Father, that flag on our house insults the Islands. It can be seen
even from Aphros!'
'My dear boy, better that it should be seen from Aphros than that we
should offend Herakleion.'

'What will the islanders think?'
'They are accustomed to seeing it there every year.'
'If I had been at home....'
'When this house is yours, Julian, you will no doubt do as you
please; so long as it is mine, I beg you not to interfere.'
Mr Davenant had spoken in his curtest tones. He had added,—
'I shall go to the cathedral this afternoon.'
The service in the cathedral annually celebrated the independence of
Herakleion. Julian slipped out of the house, meaning to mix with the
ill-regulated crowd that began to collect on the platia to watch for
the arrival of the notables, but outside the door of the club he was
discovered by Alexander Christopoulos who obliged him to follow
him upstairs to the Christopoulos drawing-room.
'My father is really too gloomy for me to confront alone,' Alexander
said, taking Julian's arm and urging him along; 'also I have spent the
morning in the club, which exasperates him. He likes me to sit at
home while he stands looking at me and mournfully shaking his
head.'
They came into the sala together, where old Christopoulos paced up
and down in front of the shuttered windows, and a score of other
people sat whispering over their cups of tisane. White dresses, dim
mirrors, and the dull gilt of furniture gleamed here and there in the
shadows of the vast room.
'Any news? any news?' the banker asked of the two young men.
'You know quite well, father, that no results are to be declared until
seven o'clock this evening.'
Alexander opened a section of a Venetian blind, and as a shaft of
sunlight fell startlingly across the floor a blare of music burst equally
startlingly upon the silence.

'The platia is crowded already,' said Alexander, looking out.
The hum of the crowd became audible, mingled with the music;
explosions of laughter, and some unexplained applause. The shrill
cry of a seller of iced water rang immediately beneath the window.
The band in the centre continued to shriek remorselessly an
antiquated air of the Paris boulevards.
'At what time is the procession due?' asked Fru Thyregod over
Julian's shoulder.
'At five o'clock; it should arrive at any moment,' Julian said, making
room for the Danish Excellency.
'I adore processions,' cried Fru Thyregod, clapping her hands, and
looking brightly from Julian to Alexander.
Alexander whispered to Julie Lafarge, who had come up,—
'I am sure Fru Thyregod has gone from house to house and from
Legation to Legation, and has had a meal at each to-day.'
Somebody suggested,—
'Let us open the shutters and watch the procession from the
balconies.'
'Oh, what a good idea!' cried Fru Thyregod, clapping her hands
again and executing a pirouette.
Down in the platia an indefinite movement was taking place; the
band stopped playing for the first time that day, and began shuffling
with all its instruments to one side. Voices were then heard raised in
tones of authority. A cleavage appeared in the crowd, which grew in
length and width as though a wedge were being gradually driven
into that reluctant confusion of humanity.
'A path for the procession,' said old Christopoulos, who, although not
pleased at that frivolous flux of his family and guests on to the

balconies of his house, had joined them, overcome by his natural
curiosity.
The path cut in the crowd now ran obliquely across the platia from
the end of the rue Royale to the steps of the cathedral opposite, and
upon it the confetti with which the whole platia was no doubt strewn
became visible. The police, with truncheons in their hands, were
pressing the people back to widen the route still further. They wore
their gala hats, three-cornered, with upright plumes of green and
orange nodding as they walked.
'Look at Sterghiou,' said Alexander.
The Chief of Police rode vaingloriously down the route looking from
left to right, and saluting with his free hand. The front of his uniform
was crossed with broad gold hinges, and plaits of yellow braid
disappeared mysteriously into various pockets. One deduced
whistles; pencils; perhaps a knife. Although he did not wear feathers
in his hat, one knew that only the utmost self-restraint had
preserved him from them.
Here the band started again with a march, and Sterghiou's horse
shied violently and nearly unseated him.
'The troops!' said old Christopoulos with emotion.
Debouching from the rue Royale, the army came marching four
abreast. As it was composed of only four hundred men, and as it
never appeared on any other day of the year, its general
Panaïoannou always mobilised it in its entirety on the national
festival. This entailed the temporary closing of the casino in order to
release the croupiers, who were nearly all in the ranks, and led to a
yearly dispute between the General and the board of administration.
'There was once a croupier,' said Alexander, 'who was admitted to
the favour of a certain grand-duchess until the day when,
indiscreetly coming into the dressing-room where the lady was
arranging and improving her appearance, he said, through sheer

force of habit, Madame, les jeux sont faits? and was dismissed for
ever by her reply, Rien ne va plus.'
The general himself rode in the midst of his troops, in his sky-blue
uniform, to which the fantasy of his Buda-Pesth costumier had
added for the occasion a slung Hussar jacket of white cloth. His gray
moustache was twisted fiercely upwards, and curved like a scimitar
across his face. He rode with his hand on his hip, slowly scanning
the windows and balconies of the platia, which by now were
crowded with people, gravely saluting his friends as he passed.
Around him marched his bodyguard of six, a captain and five men;
the captain carried in one hand a sword, and in the other—nobody
knew why—a long frond of palm.
The entire army tramped by, hot, stout, beaming, and friendly. At
one moment some one threw down a handful of coins from a
window, and the ranks were broken in a scramble for the coppers.
Julian, who was leaning apart in a corner of his balcony, heard a
laugh like a growl behind him as the enormous hand of Grbits
descended on his shoulder.
'Remember the lesson, young man: if you are called upon to deal
with the soldiers of Herakleion, a fistful of silver amongst them will
scatter them.'
Julian thought apprehensively that they must be overheard, but
Grbits continued in supreme unconsciousness,—
'Look at their army, composed of shop-assistants and croupiers. Look
at their general—a general in his spare moments, but in the serious
business of his life a banker and an intriguer like the rest of them. I
doubt whether he has ever seen anything more dead in his life than
a dead dog in a gutter. I could pick him up and squash in his head
like an egg.'
Grbits extended his arm and slowly unfolded the fingers of his
enormous hand. At the same time he gave his great laugh that was
like the laugh of a good-humoured ogre.

'At your service, young man,' he said, displaying the full breadth of
his palm to Julian, 'whenever you stand in need of it. The Stavridists
will be returned to-day; lose no time; show them your intentions.'
He impelled Julian forward to the edge of the balcony and pointed
across to the Davenant house.
'That flag, young man: see to it that it disappears within the hour
after the results of the elections are announced.'
The army was forming itself into two phalanxes on either side of the
cathedral steps. Panaïoannou caracoled up and down shouting his
orders, which were taken up and repeated by the busy officers on
foot. Meanwhile the notables in black coats were arriving in a
constant stream that flowed into the cathedral; old Christopoulos
had already left the house to attend the religious ceremony; the
foreign Ministers and Consuls attended out of compliment to
Herakleion; Madame Lafarge had rolled down the route in her
barouche with her bearded husband; Malteios had crossed the platia
from his own house, and Stavridis came, accompanied by his wife
and daughters. Still the band played on, the crowd laughed,
cheered, or murmured in derision, and the strident cries of the
water-sellers rose from all parts of the platia.
Suddenly the band ceased to play, and in the hush only the hum of
the crowd continued audible.
The religious procession came walking very slowly from the rue
Royale, headed by a banner and by a file of young girls, walking two
by two, in white dresses, with wreaths of roses on their heads. As
they walked they scattered sham roses out of baskets, the gesture
reminiscent of the big picture in the Senate-room. It was customary
for the Premier of the Republic to walk alone, following these young
girls, black and grave in his frock-coat after their virginal white, but
on this occasion, as no one knew who the actual Premier was, a
blank space was left to represent the problematical absentee.
Following the space came the Premier's habitual escort, a posse of

police; it should have been a platoon of soldiers, but Panaïoannou
always refused to consent to such a diminution of his army.
'They say,' Grbits remarked to Julian in this connection, 'that the
general withdraws even the sentries from the frontier to swell his
ranks.'
'Herakleion is open to invasion,' said Julian, smiling.
Grbits replied sententiously, with the air of one creating a new
proverb,—
'Herakleion is open to invasion, but who wants to invade
Herakleion?'
The crowd watched the passage of the procession with the utmost
solemnity. Not a sound was now heard but the monotonous step of
feet. Religious awe had hushed political hilarity. Archbishop and
bishops; archmandrites and papás of the country districts, passed in
a mingling of scarlet, purple and black. All the pomp of Herakleion
had been pressed into service—all the clamorous, pretentious pomp,
shouting for recognition, beating on a hollow drum; designed to
impress the crowd; and perhaps, also, to impress, beyond the
crowd, the silent Islands that possessed no army, no clergy, no
worldly trappings, but that suffered and struggled uselessly, pitiably,
against the tinsel tyrant in vain but indestructible rebellion.
* * * * * *
As five o'clock drew near, the entire population seemed to be
collected in the platia. The white streak that had marked the route
of the procession had long ago disappeared, and the square was
now, seen from above, only a dense and shifting mass of people. In
the Christopoulos drawing-room, where Julian still lingered, talking
to Grbits and listening to the alternate foolishness, fanaticism, and
ferocious good-humour of the giant, the Greeks rallied in numbers
with only one topic on their lips. Old Christopoulos was frankly biting
his nails and glancing at the clock; Alexander but thinly concealed

his anxiety under a dribble of his usual banter. The band had ceased
playing, and the subtle ear could detect an inflection in the very
murmur of the crowd.
'Let us go on to the balcony again,' Grbits said to Julian; 'the results
will be announced from the steps of Malteios' house.'
They went out; some of the Greeks followed them, and all pressed
behind, near the window openings.
'It is a more than usually decisive day for Herakleion,' said old
Christopoulos, and Julian knew that the words were spoken at,
although not to, him.
He felt that the Greeks looked upon him as an intruder, wishing him
away so that they might express their opinions freely, but in a spirit
of contrariness he remained obstinately.
A shout went up suddenly from the crowd: a little man dressed in
black, with a top-hat, and a great many white papers in his hand,
had appeared in the frame of Malteios' front-door. He stood on the
steps, coughed nervously, and dropped his papers.
'Inefficient little rat of a secretary!' cried Alexander in a burst of fury.
'Listen!' said Grbits.
A long pause of silence from the whole platia, in which one thin
voice quavered, reaching only the front row of the crowd.
'Stavridis has it,' Grbits said quietly, who had been craning over the
edge of the balcony. His eyes twinkled maliciously, delightedly, at
Julian across the group of mortified Greeks. 'An immense majority,'
he invented, enjoying himself.
Julian was already gone. Slipping behind old Christopoulos, whose
saffron face had turned a dirty plum colour, he made his way
downstairs and out into the street. A species of riot, in which the
police, having failed successfully to intervene, were enthusiastically

joining, had broken out in the platia. Some shouted for Stavridis,
some for Malteios; some railed derisively against the Islands. People
threw their hats into the air, waved their arms, and kicked up their
legs. Some of them were vague as to the trend of their own
opinions, others extremely determined, but all were agreed about
making as much noise as possible. Julian passed unchallenged to his
father's house.
Inside the door he found Aristotle talking with three islanders. They
laid hold of him, urgent though respectful, searching his face with
eager eyes.
'It means revolt at last; you will not desert us, Kyrie?'
He replied,—
'Come with me, and you will see.'
They followed him up the stairs, pressing closely after him. On the
landing he met Eve and Kato, coming out of the drawing-room. The
singer was flushed, two gold wheat-ears trembled in her hair, and
she had thrown open the front of her dress. Eve hung on her arm.
'Julian!' Kato exclaimed, 'you have heard, Platon has gone?'
In her excitement she inadvertently used Malteios' Christian name.
'It means,' he replied, 'that Stavridis, now in power, will lose no time
in bringing against the Islands all the iniquitous reforms we know he
contemplates. It means that the first step must be taken by us.'
His use of the pronoun ranged himself, Kato, Aristotle, the three
islanders, and the invisible Islands into an instant confederacy. Kato
responded to it,—
'Thank God for this.'
They waited in complete confidence for his next words. He had shed
his aloofness, and all his efficiency of active leadership was to the
fore.

'Where is my father?'
'He went to the Cathedral; he has not come home yet, Kyrie.'
Julian passed into the drawing-room, followed by Eve and Kato and
the four men. Outside the open window, fastened to the balcony,
flashed the green and orange flag of Herakleion. Julian took a knife
from his pocket, and, cutting the cord that held it, withdrew flag and
flag-staff into the room and flung it on to the ground.
'Take it away,' he said to the islanders, 'or my father will order it to
be replaced. And if he orders another to be hung out in its place,' he
added, looking at them with severity, 'remember there is no other
flag in the house, and none to be bought in Herakleion.'
At that moment a servant from the country-house came hurriedly
into the room, drew Julian unceremoniously aside, and broke into an
agitated recital in a low voice. Eve heard Julian saying,—
'Nicolas sends for me? But he should have given a reason. I cannot
come now, I cannot leave Herakleion.'
And the servant,—
'Kyrie, the major-domo impressed upon me that I must on no
account return without you. Something has occurred, something
serious. What it is I do not know. The carriage is waiting at the back
entrance; we could not drive across the platia on account of the
crowds.'
'I shall have to go, I suppose,' Julian said to Eve and Kato. 'I will go
at once, and will return, if possible, this evening. Nicolas would not
send without an excellent reason, though he need not have made
this mystery. Possibly a message from Aphros.... In any case, I must
go.'
'I will come with you,' Eve said unexpectedly.

V
In almost unbroken silence they drove out to the country-house, in a
hired victoria, to the quick, soft trot of the two little lean horses,
away from the heart of the noisy town; past the race-course with its
empty stands; under the ilex-avenue in a tunnel of cool darkness;
along the road, redolent with magnolias in the warmth of the
evening; through the village, between the two white lodges; and
round the bend of the drive between the bushes of eucalyptus. Eve
had spoken, but he had said abruptly,—
'Don't talk; I want to think,' and she, after a little gasp of astonished
indignation, had relapsed languorous into her corner, her head
propped on her hand, and her profile alone visible to her cousin. He
saw, in the brief glance that he vouchsafed her, that her red mouth
looked more than usually sulky, in fact not unlike the mouth of a
child on the point of tears, a very invitation to inquiry, but, more
from indifference than deliberate wisdom, he was not disposed to
take up the challenge. He too sat silent, his thoughts flying over the
day, weighing the consequences of his own action, trying to forecast
the future. He was far away from Eve, and she knew it. At times he
enraged and exasperated her almost beyond control. His indifference
was an outrage on her femininity. She knew him to be utterly
beyond her influence: taciturn when he chose, ill-tempered when he
chose, exuberant when he chose, rampageous, wild; insulting to her
at moments; domineering whatever his mood, and regardless of her
wishes; yet at the same time unconscious of all these things. Alone
with her now, he had completely forgotten her presence by his side.
Her voice broke upon his reflections,—
'Thinking of the Islands, Julian?' and her words joining like a
cogwheel smoothly on to the current of his mind, he answered

naturally,—
'Yes,'
'I thought as much. I have something to tell you. You may not be
interested. I am no longer engaged to Miloradovitch.'
'Since when?'
'Since yesterday evening. Since you left me, and ran away into the
woods. I was angry, and vented my anger on him.'
'Was that fair?'
'He has you to thank. It has happened before—with others.'
Roused for a second from his absorption, he impatiently shrugged
his shoulders, and turned his back, and looked out over the sea. Eve
was again silent, brooding and resentful in her corner. Presently he
turned towards her, and said angrily, reverting to the Islands,—
'You are the vainest and most exorbitant woman I know. You resent
one's interest in anything but yourself.'
As she did not answer, he added,—
'How sulky you look; it's very unbecoming.'
Was no sense of proportion or of responsibility ever to weigh upon
her beautiful shoulders? He was irritated, yet he knew that his
irritation was half-assumed, and that in his heart he was no more
annoyed by her fantasy than by the fantasy of Herakleion. They
matched each other; their intangibility, their instability, were enough
to make a man shake his fists to Heaven, yet he was beginning to
believe that their colour and romance—for he never dissociated Eve
and Herakleion in his mind—were the dearest treasures of his youth.
He turned violently and amazingly upon her.
'Eve, I sometimes hate you, damn you; but you are the rainbow of
my days.'

She smiled, and, enlightened, he perceived with interest, curiosity,
and amused resignation, the clearer grouping of the affairs of his
youthful years. Fantasy to youth! Sobriety to middle-age! Carried
away, he said to her,—
'Eve! I want adventure, Eve!'
Her eyes lit up in instant response, but he could not read her inward
thought, that the major part of his adventure should be, not Aphros,
but herself. He noted, however, her lighted eyes, and leaned over to
her.
'You are a born adventurer, Eve, also.'
She remained silent, but her eyes continued to dwell on him, and to
herself she was thinking, always sardonic although the matter was of
such perennial, such all-eclipsing importance to her,—
'A la bonne heure, he realises my existence.'
'What a pity you are not a boy; we could have seen the adventure of
the Islands through together.'
('The Islands always!' she thought ruefully.)
'I should like to cross to Aphros to-night,' he murmured, with absent
eyes....
('Gone again,' she thought. 'I held him for a moment.')
When they reached the house no servants were visible, but in reply
to the bell a young servant appeared, scared, white-faced, and, as
rapidly disappearing, was replaced by the old major-domo. He burst
open the door into the passage, a crowd of words pressing on each
other's heels in his mouth; he had expected Julian alone; when he
saw Eve, who was idly turning over the letters that awaited her, he

clapped his hand tightly over his lips, and stood, struggling with his
speech, balancing himself in his arrested impetus on his toes.
'Well, Nicolas?' said Julian.
The major-domo exploded, removing his hand from his mouth,—
'Kyrie! a word alone....' and as abruptly replaced the constraining
fingers.
Julian followed him through the swing door into the servants'
quarters, where the torrent broke loose.
'Kyrie, a disaster! I have sent men with a stretcher. I remained in the
house myself looking for your return. Father Paul—yes, yes, it is he—
drowned—yes, drowned—at the bottom of the garden. Come, Kyrie,
for the love of God. Give directions. I am too old a man. God be
praised, you have come. Only hasten. The men are there already
with lanterns.'
He was clinging helplessly to Julian's wrist, and kept moving his
fingers up and down Julian's arm, twitching fingers that sought
reassurance from firmer muscles, in a distracted way, while his eyes
beseechingly explored Julian's face.
Julian, shocked, jarred, incredulous, shook off the feeble fingers in
irritation. The thing was an outrage on the excitement of the day.
The transition to tragedy was so violent that he wished, in revolt, to
disbelieve it.
'You must be mistaken, Nicolas!'
'Kyrie, I am not mistaken. The body is lying on the shore. You can
see it there. I have sent lanterns and a stretcher. I beg of you to
come.'
He spoke, tugging at Julian's sleeve, and as Julian remained
unaccountably immovable he sank to his knees, clasping his hands
and raising imploring eyes. His fustanelle spread its pleats in a circle

on the stone floor. His story had suddenly become vivid to Julian
with the words, 'The body is lying on the shore'; 'drowned,' he had
said before, but that had summoned no picture. The body was lying
on the shore. The body! Paul, brisk, alive, familiar, now a body,
merely. The body! had a wave, washing forward, deposited it gently,
and retreated without its burden? or had it floated, pale-faced under
the stars, till some man, looking by chance down at the sea from the
terrace at the foot of the garden, caught that pale, almost
phosphorescent gleam rocking on the swell of the water?
The old major-domo followed Julian's stride between the lemon-
trees, obsequious and conciliatory. The windows of the house shone
behind them, the house of tragedy, where Eve remained as yet
uninformed, uninvaded by the solemnity, the reality, of the present.
Later, she would have to be told that a man's figure had been
wrenched from their intimate and daily circle. The situation appeared
grotesquely out of keeping with the foregoing day, and with the wide
and gentle night.
From the paved walk under the pergola of gourds rough steps led
down to the sea. Julian, pausing, perceived around the yellow
squares of the lanterns the indistinct figures of men, and heard their
low, disconnected talk breaking intermittently on the continuous
wash of the waves. The sea that he loved filled him with a sudden
revulsion for the indifference of its unceasing movement after its
murder of a man. It should, in decency, have remained quiet, silent;
impenetrable, unrepentant, perhaps; inscrutable, but at least silent;
its murmur echoed almost as the murmur of a triumph....
He descended the steps. As he came into view, the men's
fragmentary talk died away; their dim group fell apart; he passed
between them, and stood beside the body of Paul.
Death. He had never seen it. As he saw it now, he thought that he
had never beheld anything so incontestably real as its irrevocable
stillness. Here was finality; here was defeat beyond repair. In the
face of this judgment no revolt was possible. Only acceptance was

possible. The last word in life's argument had been spoken by an
adversary for long remote, forgotten; an adversary who had
remained ironically dumb before the babble, knowing that in his own
time, with one word, he could produce the irrefutable answer. There
was something positively satisfying in the faultlessness of the
conclusion. He had not thought that death would be like this. Not
cruel, not ugly, not beautiful, not terrifying—merely unanswerable.
He wondered now at the multitude of sensations that had chased
successively across his mind or across his vision: the elections, Fru
Thyregod, the jealousy of Eve, his incredulity and resentment at the
news, his disinclination for action, his indignation against the
indifference of the sea; these things were vain when here, at his
feet, lay the ultimate solution.
Paul lay on his back, his arms straight down his sides, and his long,
wiry body closely sheathed in the wet soutane. The square toes of
his boots stuck up, close together, like the feet of a swathed
mummy. His upturned face gleamed white with a tinge of green in
the light of the lanterns, and appeared more luminous than they. So
neat, so orderly he lay; but his hair, alone disordered, fell in wet red
wisps across his neck and along the ground behind his head.
At that moment from the direction of Herakleion there came a long
hiss and a rush of bright gold up into the sky; there was a crackle of
small explosions, and fountains of gold showered against the night
as the first fireworks went up from the quays. Rockets soared,
bursting into coloured stars among the real stars, and plumes of
golden light spread themselves dazzlingly above the sea. Faint
sounds of cheering were borne upon the breeze.
The men around the body of the priest waited, ignorant and
bewildered, relieved that some one had come to take command.
Their eyes were bent upon Julian as he stood looking down; they
thought he was praying for the dead. Presently he became aware of
their expectation, and pronounced with a start,—
'Bind up his hair!'

Fingers hastened clumsily to deal with the stringy red locks; the limp
head was supported, and the hair knotted somehow into a
semblance of its accustomed roll. The old major-domo quavered in a
guilty voice, as though taking the blame for carelessness,—
'The hat is lost, Kyrie.'
Julian let his eyes travel over the little group of men, islanders all,
with an expression of searching inquiry.
'Which of you made this discovery?'
It appeared that one of them, going to the edge of the sea in
expectation of the fireworks, had noticed, not the darkness of the
body, but the pallor of the face, in the water not far out from the
rocks. He had waded in and drawn the body ashore. Dead Paul lay
there deaf and indifferent to this account of his own finding.
'No one can explain....'
Ah, no! and he, who could have explained, was beyond the reach of
their curiosity. Julian looked at the useless lips, unruffled even by a
smile of sarcasm. He had known Paul all his life, had learnt from
him, travelled with him, eaten with him, chaffed him lightly, but
never, save in that one moment when he had gripped the priest by
the wrist and had looked with steadying intention into his eyes, had
their intimate personalities brushed in passing. Julian had no genius
for friendship.... He began to see that this death had ended an
existence which had run parallel with, but utterly walled off from, his
own.
In shame the words tore themselves from him,—
'Had he any trouble?'
The men slowly, gravely, mournfully shook their heads. They could
not tell. The priest had moved amongst them, charitable, even
saintly; yes, saintly, and one did not expect confidences of a priest.
A priest was a man who received the confidences of other men.

Julian heard, and, possessed by a strong desire, a necessity, for self-
accusation, he said to them in a tone of urgent and impersonal
Justice, as one who makes a declaration, expecting neither protest
nor acquiescence,—
'I should have inquired into his loneliness.'
They were slightly startled, but, in their ignorance, not over-
surprised, only wondering why he delayed in giving the order to
move the body on to the stretcher and carry it up to the church.
Farther up the coast, the rockets continued to soar, throwing out
bubbles of green and red and orange, fantastically tawdry. Julian
remained staring at the unresponsive corpse, repeating sorrowfully,
—
'I should have inquired—yes, I should have inquired—into his
loneliness.'
He spoke with infinite regret, learning a lesson, shedding a particle
of his youth. He had taken for granted that other men's lives were as
promising, as full of dissimulated eagerness, as his own. He had
walked for many hours up and down Paul's study, lost in an audible
monologue, expounding his theories, tossing his rough head,
emphasising, enlarging, making discoveries, intent on his egotism,
hewing out his convictions, while the priest sat by the table, leaning
his head on his hand, scarcely contributing a word, always listening.
During those hours, surely, his private troubles had been forgotten?
Or had they been present, gnawing, beneath the mask of sympathy?
A priest was a man who received the confidences of other men!
'Carry him up,' Julian said, 'carry him up to the church.'
He walked away alone as the dark cortège set itself in movement,
his mind strangely accustomed to the fact that Paul would no longer
frequent their house and that the long black figure would no longer
stroll, tall and lean, between the lemon-trees in the garden. The fact
was more simple and more easily acceptable than he could have
anticipated. It seemed already quite an old-established fact. He

remembered with a shock of surprise, and a raising of his eyebrows,
that he yet had to communicate it to Eve. He knew it so well himself
that he thought every one else must know it too. He was
immeasurably more distressed by the tardy realisation of his own
egotism in regard to Paul, than by the fact of Paul's death.
He walked very slowly, delaying the moment when he must speak to
Eve. He sickened at the prospect of the numerous inevitable
inquiries that would be made to him by both his father and his uncle.
He would never hint to them that the priest had had a private
trouble. He rejoiced to remember his former loyalty, and to know
that Eve remained ignorant of that extraordinary, unexplained
conversation when Paul had talked about the mice. Mice in the
church! He, Julian, must see to the decent covering of the body. And
of the face, especially of the face.
An immense golden wheel flared out of the darkness; whirled, and
died away above the sea.
In the dim church the men had set down the stretcher before the
iconostase. Julian felt his way cautiously amongst the rush-bottomed
chairs. The men were standing about the stretcher, their fishing caps
in their hands, awed into a whispering mysticism which Julian's voice
harshly interrupted,—
'Go for a cloth, one of you—the largest cloth you can find.'
He had spoken loudly in defiance of the melancholy peace of the
church, that received so complacently within its ready precincts the
visible remains from which the spirit, troubled and uncompanioned
in life, had fled. He had always thought the church complacent,
irritatingly remote from pulsating human existence, but never more
so than now when it accepted the dead body as by right, firstly
within its walls, and lastly within its ground, to decompose and rot,
the body of its priest, among the bodies of other once vital and
much-enduring men.

'Kyrie, we can find only two large cloths, one a dust-sheet, and one
a linen cloth to spread over the altar. Which are we to use?'
'Which is the larger?'
'Kyrie, the dust-sheet, but the altar-cloth is of linen edged with lace.'
'Use the dust-sheet; dust to dust,' said Julian bitterly.
Shocked and uncomprehending, they obeyed. The black figure now
became a white expanse, under which the limbs and features
defined themselves as the folds sank into place.
'He is completely covered over?'
'Completely, Kyrie.'
'The mice cannot run over his face?'
'Kyrie, no!'
'Then no more can be done until one of you ride into Herakleion for
the doctor.'
He left them, re-entering the garden by the side-gate which Paul had
himself constructed with his capable, carpenter's hands. There was
now no further excuse for delay; he must exchange the darkness for
the unwelcome light, and must share out his private knowledge to
Eve. Those men, fisher-folk, simple folk, had not counted as human
spectators, but rather as part of the brotherhood of night, nature,
and the stars.
He waited for Eve in the drawing-room, having assured himself that
she had been told nothing, and there, presently, he saw her come
in, her heavy hair dressed high, a fan and a flower drooping from
her hand, and a fringed Spanish shawl hanging its straight silk folds
from her escaping shoulders. Before her indolence, and her
slumbrous delicacy, he hesitated. He wildly thought that he would
allow the news to wait. Tragedy, reality, were at that moment so far
removed from her.... She said in delight, coming up to him, and

forgetful that they were in the house in obedience to a mysterious
and urgent message,—
'Julian, have you seen the fireworks? Come out into the garden.
We'll watch.'
He put his arm through her bare arm,—
'Eve, I must tell you something.'
'Fru Thyregod?' she cried, and the difficulty of his task became all
but insurmountable.
'Something serious. Something about Father Paul.'
Her strange eyes gave him a glance of undefinable suspicion.
'What about him?'
'He has been found, in the water, at the bottom of the garden.'
'In the water?'
'In the sea. Drowned.'
He told her all the circumstances, doggedly, conscientiously, under
the mockery of the tinsel flames that streamed out from the top of
the columns, and of the distant lights flashing through the windows,
speaking as a man who proclaims in a foreign country a great truth
bought by the harsh experience of his soul, to an audience
unconversant with his alien tongue. This truth that he had won, in
the presence of quiet stars, quieter death, and simple men, was
desecrated by its recital to a vain woman in a room where the very
architecture was based on falsity. Still he persevered, believing that
his own intensity of feeling must end in piercing its way to the
foundations of her heart. He laid bare even his harassing conviction
of his neglected responsibility,—
'I should have suspected ... I should have suspected....'

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