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Cellular neural networks and visual computing
Cellular Nonlinear/neural Network (CNN) technology is both a revolutionary concept and an
experimentally proven new computing paradigm. Analogic cellular computers based on CNNs are
set to change the way analog signals are processed and are paving the way to an entire new analog
computing industry.
This unique undergraduate-level textbook includes many examples and exercises, including CNN
simulator and development software accessible via the Internet. It is an ideal introduction to CNNs
and analogic cellular computing for students, researchers, and engineers from a wide range of
disciplines. Although its prime focus is on visual computing, the concepts and techniques described
in the book will be of great interest to those working in other areas of research, including modeling
of biological, chemical, and physical processes.
Leon Chua is a Professor of Electrical Engineering and Computer Science at the University of
California, Berkeley where he coinvented the CNN in 1988 and holds several patents related to CNN
Technology. He received the Neural Network Pioneer Award, 2000.
Tamás Roska is a Professor of Information Technology at the Pázmány P. Catholic University of
Budapest and head of the Analogical and Neural Computing Laboratory of the Computer and
Automation Research Institute of the Hungarian Academy of Sciences, Budapest and was an early
pioneer of CNN technology and a coinventor of the CNN Universal Machine as an analogic
supercomputer, He has also spent 12 years as a part-time visiting scholar at the University of
California at Berkeley.

Cellular neural networks
and visual computing
Foundation and applications
Leon O. Chua
and
Tamás Roska

         
The Pitt Building, Trumpington Street, Cambridge, United Kingdom
  
The Edinburgh Building, Cambridge CB2 2RU, UK
40 West 20th Street, New York, NY 10011-4211, USA
477 Williamstown Road, Port Melbourne, VIC 3207, Australia
Ruiz de Alarcón 13, 28014 Madrid, Spain
Dock House, The Waterfront, Cape Town 8001, South Africa
http://www.cambridge.org
First published in printed format
ISBN 0-521-65247-2 hardback
ISBN 0-511-04051-2 eBook
Cambridge University Press 2004
2002
(netLibrary)
©

To our wives, Diana and Zsuzsa

Contents
Acknowledgements page xi
1 Introduction 1
2 Notation,definitions,andmathematicalfoundation 7
2.1 Basic notation and deﬁnitions 7
2.2 Mathematical foundations 14
3 CharacteristicsandanalysisofsimpleCNNtemplates 35
3.1 Two case studies: the EDGE and EDGEGRAY templates 35
3.2 Three quick steps for sketching the shifted DP plot 49
3.3 Some other useful templates 50
4 SimulationoftheCNNdynamics 100
4.1 Integration of the standard CNN differential equation 100
4.2 Image input 101
4.3 Software simulation 102
4.4 Digital hardware accelerators 110
4.5 Analog CNN implementations 111
4.6 Scaling the signals 113
4.7 Discrete-time CNN (DTCNN) 114
vii

viii Contents
5 BinaryCNNcharacterizationviaBooleanfunctions 115
5.1 Binary and universal CNN truth table 115
5.2 Boolean and compressed local rules 122
5.3 Optimizing the truth table 124
6 UncoupledCNNs:unifiedtheoryandapplications 139
6.1 The complete stability phenomenon 139
6.2 Explicit CNN output formula 140
6.3 Proof of completely stable CNN theorem 142
6.4 The primary CNN mosaic 155
6.5 Explicit formula for transient waveform and settling time 156
6.6 Which local Boolean functions are realizable by uncoupled CNNs? 161
6.7 Geometrical interpretations 162
6.8 How to design uncoupled CNNs with prescribed Boolean functions 166
6.9 How to realize non-separable local Boolean functions? 173
7 IntroductiontotheCNNUniversalMachine 183
7.1 Global clock and global wire 184
7.2 Set inclusion 184
7.3 Translation of sets and binary images 188
7.4 Opening and closing and implementing any morphological operator 190
7.5 Implementing any prescribed Boolean transition function by not more than
256 templates 195
7.6 Minimizing the number of templates when implementing any possible
Boolean transition function 198
7.7 Analog-to-digital array converter 201
8 Backtobasics:Nonlineardynamicsandcompletestability 205
8.1 A glimpse of things to come 205
8.2 An oscillatory CNN with only two cells 205
8.3 A chaotic CNN with only two cells and one sinusoidal input 210
8.4 Symmetric A template implies complete stability 214
8.5 Positive and sign-symmetric A template implies complete stability 219

ix Contents
8.6 Positive and cell-linking A template implies complete stability 224
8.7 Stability of some sign-antisymmetric CNNs 231
A Appendix to Chapter 8 236
9 TheCNNUniversalMachine(CNN-UM) 239
9.1 The architecture 240
9.2 A simple example in more detail 244
9.3 A very simple example on the circuit level 246
9.4 Language, compiler, operating system 254
10 Templatedesigntools 258
10.1 Various design techniques 258
10.2 Binary representation, linear separability, and simple decomposition 260
10.3 Template optimization 264
10.4 Template decomposition techniques 265
11 CNNsforlinearimageprocessing 267
11.1 Linear image processing with B templates is equivalent to spatial convo-
lution with FIR kernels 267
11.2 Spatial frequency characterization 269
11.3 A primer on properties and applications of discrete-space Fourier trans-
form (DSFT) 272
11.4 Linear image processing with A and B templates is equivalent to spatial
convolution with IIR kernels 272
12 CoupledCNNwithlinearsynapticweights 276
12.1 Active and inactive cells, dynamic local rules 278
12.2 Binary activation pattern and template format 283
12.3 A simple propagating type example with B/W symmetrical rule 284
12.4 The connectivity problem 286
13 UncoupledstandardCNNswithnonlinearsynapticweights 290
13.1 Dynamic equations and DP plot 291

x Contents
14 StandardCNNswithdelayedsynapticweightsandmotionanalysis 296
14.1 Dynamic equations 296
14.2 Motion analysis – discrete time and continuous time image acquisition 297
15 Visual microprocessors – analog and digital VLSI implementation
of the CNN Universal Machine
304
15.1 The analog CNN core 304
15.2 Analogic CNN-UM cell 310
15.3 Emulated digital implementation 312
15.4 The visual microprocessor and its computational infrastructure 313
15.5 Computing power comparison 318
16 CNNmodelsinthevisualpathwayandthe‘‘BionicEye” 320
16.1 Receptive ﬁeld organization, synaptic weights, and cloning template 321
16.2 Some prototype elementary functions and CNN models of the visual
pathway 322
16.3 A simple qualitative “engineering” model of a vertebrate retina 329
16.4 The “Bionic Eye” implemented on a CNN Universal Machine 338
Notes 339
Bibliography 348
Exercises 361
Appendices 389
Index 390

Acknowledgements
We started to teach a formal course devoted entirely to CNN only in 1996, in the Spring
Semester, at Berkeley and in the Autumn Semester in Budapest. Since then, several
versions of Lecture Notes have been iterated. We are indebted to many of our former
students – some of whom have become our coworkers – who have helped us in various
forms we are thankful to all of them. Dr. Ákos Zarándy, Dr. Ken Crounse, Dr. Csaba
Rekecky, Dr. Chai-Wah Wu, Dr. László Kék, Dr. László Nemes, Dr. András Radványi,
and Dr. Péter Szolgay, as well as Tao Yang, An-Shan Huang, Dávid Bálya, Katalin
Keserű, István Petrás and István Szatmári made special efforts to help us during the
many years of forming the text to this present version. We are also grateful to Phil
Meyler for his kind initiative to publish this textbook.
Leon O. Chua and Tamás Roska
Berkeley–Budapest, May 2000
xi

1 Introduction
Scenario
Recent history of the electronic and computer industry can be viewed as three waves
of revolutionary processes.1 The first revolution, making cheap computing power
available via microprocessors in the 1970s, led to the PC industry of the 1980s. The
cheap laser and fiber optics, which resulted in cheap bandwidth at the end of the
1980s, led to the Internet industry of the 1990s. The third wave, the sensor revolution
at the end of the 1990s, will also provide for a new industry. Sensor revolution
means that cheap sensor and MEMS (micro-electro-mechanical system) arrays are
proliferating in almost all the conceivable forms. Artificial eyes, nose, ears, taste,
and somatosensory devices as well as sensing all physical, chemical, and biological
parameters, together with microactuators, etc. are becoming commodities. Thousands
and millions of generically analog signals are produced waiting for processing. A new
computing paradigm is needed. The cited technology assessment1 reads:
The long-term consequence of the coming sensor revolution may be the emergence of a newer analog
computing industry in which digital technology plays a mere supporting role, or in some instances
plays no role at all.
For processing analog array signals, the revolutionary Analogic Cellular Computer
paradigm is a major candidate. The core of this computer is a Cellular Nonlinear/neural
network2 (CNN), an array of analog dynamic processors or cells. The computer archi-
tecture is the CNN Universal Machine,3 with its various physical implementations. At
the same time, Analogic CNN computers mimic the anatomy and physiology of many
sensory and processing organs with an additional capability of stored programmability.
Recent studies on optical and nano-scale implementations open up new horizons on the
atomic and molecular levels.
The CNN was invented by Leon O. Chua and Lin Yang in Berkeley in 1988. Unlike
cellular automata, CNN host processors accepting and generating analog signals, the
time is continuous, and the interaction values are also real values. Unlike lattice
dynamics, the input of the CNN array plays an important role. Moreover, CNN
becomes a rigorous framework for complex systems exhibiting emergent behavior and
the various forms of emergent computations. The notion of the cloning template, the
1

2 Introduction
representation of the local interconnection pattern, is crucial. This allows not only
modeling but also engineering of complex systems.
Stored programmability, invented by John von Neumann, was the key for endowing
digital computers with an almost limitless capability within the digital universe of
signals, opening the door to human invention via digital algorithms and software.
Indeed, according to the Turing–Church thesis, any algorithms on integers conceived
by humans can be represented by Recursive functions/Turing Machines/Grammars.
The CNN Universal Machine is universal not only in a Turing sense but also on analog
array signals. Due to stored programmability, it is also open to human intelligence
with a practically limitless capability within the universe of analog array signals, via
analogic spatio-temporal algorithms and software.
The new world opened by the Analogic CNN computing paradigm is nowadays a
reality. There are operational focal plane visual microprocessors with 4096 or 16 000
processors, which are fully stored, programmable, and there are Walkman-size self-
contained units with image supercomputer speed.
The CNN Universal Chip4 highlighted on the cover of this book represents a mile-
stone in information technology because it is the ﬁrst operational, fully programmable
industrial-size brain-like stored-program dynamic array computer in the world. This
complete computer on a chip consists of an array of 64 × 64 0.5 micron CMOS cell
processors, where each cell is endowed not only with a photo sensor for direct optical
input of images and videos, but also with communication and control circuitries, as
well as local analog and logic memories. Each CNN cell is interfaced with its nearest
neighbors, as well as with the outside world. This massively parallel focal-plane array
computer is capable of processing 3 trillion equivalent digital operations per second (in
analog mode), a performance which can be matched only by supercomputers. In terms
of the SPA (speed, power, area) measures, this CNN universal chip is far superior to
any equivalent DSP implementation by at least three orders of magnitude in either
speed, power, or area. In fact, by exploiting the state-of-the-art vertical packaging
technologies, close to peta (1015) OPS CNN universal cube can be fabricated with
such universal chips, using 200 × 200 arrays.
There are many applications which call for TeraOPS or even PetaOPS in a
Walkman-size device. Some of these applications include high-speed target recogni-
tion and tracking, real-time visual inspection of manufacturing processes, intelligent
vision capable of recognizing context sensitive and moving scenes, as well as appli-
cations requiring real-time fusing of multiple modalities, such as multispectral images
involving visible, infrared, long wave infrared, and polarized lights.
In addition to the immense image and video processing power of the CNN universal
chip, we can exploit its unique brain-like architecture to implement brain-like informa-
tion processing tasks which conventional digital computers have found wanting. Such
brain-like processing operations will necessarily be non-numeric and spatio-temporal
in nature, and will require no more than the accuracy of common neurons, which is

3 Introduction
less than eight bits. Since the computation is a non-iterative wave-like process, the
input–output accuracy is not constrained by the iterative digital process. The CNN
universal chip is therefore an ideal tool for developing and implementing brain-like
information processing schemes. It is this vision of brain-like computing via the CNN
universal chip that makes the publication of this textbook both a timely and historic
event, the first undergraduate textbook on this new computing paradigm.
The textbook
Cellular Nonlinear/neural Networks (CNN) is an invention with rapid proliferation.
After the publication of the cited original paper by Chua and Yang in 1988, several
papers explored the rich dynamics inherent in this simple architecture. Indeed, many
artificial, physical, chemical, as well as living (biological) systems and organs can be
very conveniently modeled via CNN. Hence, the book is written in such a way that no
electronic circuit knowledge is needed to understand the first 14 chapters of this book.
Indeed, it is our teaching experience, at Berkeley and in Budapest, that undergraduate
students from different backgrounds and with a modest knowledge of mathematics and
physics taught in engineering, physics, and chemistry departments, as well as biology
students from similar backgrounds can understand the book.
In Chapter 2, the basic notations, definitions, and mathematical foundation are
presented. The standard CNN architecture is introduced. The cell, the interconnection
structure, the local connectivity pattern, the canonical equations and some useful
notations, and the biological motivation are described. The importance of the local
interconnection “synaptic weight” pattern, the cloning template, or gene, is empha-
sized. Indeed, these templates, mostly defined by 19 parameters, define the complete
array dynamics, which generate an output “image” from an input “image.”
In Chapter 3, after two examples, a simple technique for determining array dynam-
ics, based on cell dynamics, is introduced and explained. Next, 11 useful templates are
shown with examples and rigorous mathematical analysis.
Chapter 4 is devoted to the digital computer simulation of CNN dynamics. Nu-
merical integration algorithms, digital hardware accelerators, as well as the analog
implementation are discussed. An accompanying simulator CANDY is provided in
the Appendix.
In Chapter 5 the characterization of the simplest form of a CNN is explored and
the binary input binary output case is described. It is quite surprising that even this
very basic form with a 3 × 3 neighborhood template could implement 2512 ∼ 10134
different local Boolean functions.
Uncoupled CNN templates constitute a simple class of CNN. Their unified theory
and applications described in Chapter 6 provide a thorough understanding of this class
of CNN.

4 Introduction
In Chapter 7, we begin the introduction of the CNN computer represented by the
CNN Universal Machine architecture. We emphasize the need for local analog and
logic memory, a global clock and global wire, as well as a local logic unit. It is shown,
for example, that every local Boolean function can be realized by using these simple
elements in each cell processor.
In Chapter 8, “Back to Basics,” the mathematical analysis of the stability of CNN
in terms of cloning templates is presented. It turns out that, in most cases, simple
conditions are available to test the templates defining completely stable CNN.
The complete architecture of the CNN Universal Machine is shown in Chapter
9. Moreover, the computational infrastructure consisting of a high-level language, a
compiler, operating system, and a development system are introduced. An example
describing all the elementary details uncovers the basic implementation techniques.
Chapter 10 presents template design and optimization algorithms. The use of a
simple program TEMPO for template optimization and decomposition is prepared and
provided in the Appendix.
Many two-dimensional linear filters can be represented by CNN. These techniques
are shown in Chapter 11 which also introduces the discrete space Fourier transform.
Once we allow spatial coupling, the dynamics of the CNN becomes not only much
richer, but also exotic. The coupled CNN is described in Chapter 12 with a design
method for binary propagation problems. In particular, it turns out that the global
connectivity problem, long considered impossible by locally connected arrays, can
be solved by a quite simple coupled CNN.
Nonlinear and delay type synaptic weights and their use are introduced in Chapters
13 and 14, respectively. These types of CNN are typical in modeling living neural
networks as well as in solving more complex image processing problems.
In Chapter 15, we show the basics of the CMOS analog and digital implemen-
tation of the CNN Universal Machine. Indeed, the first visual microprocessor and
its computational infrastructure are described. A computing power comparison is
really breathtaking: about three orders of magnitude speed advantage for complex
spatio-temporal problems on the same area of silicon.
Finally, in Chapter 16, the surprising similarity between CNN architecture and
models of the visual pathway is highlighted. Models and some measurements in living
retina are compared.
In addition to the many examples in the text, exercises at the end of the book help
both students as well as lecturers to make practical use of the textbook.
The Appendices, provided via the Internet, contain a CNN template library
(TEMLIB), a simple yet efficient simulator (CANDY), and a template design and
optimization tool (TEMPO/TEMMASTER). These design tools provide for a working
environment for the interested reader as well as for the students to explore this new
field of modeling and computing. The text can be taught, typically, as a one-semester
course.

5 Introduction
New developments
More than 1000 reviewed papers and books have been published since the seminal
paper by Chua and Yang on CNN technology. Recently, the scope has started to
broaden in many directions. Various new forms of physical implementations have
started to emerge. Optical implementation is already emerging using molecular level
analog optical memory (Bacteriorhodopsine or polymer materials) and atomic5 and
molecular6 level implementation of the CNN array as well as of the CNN Universal
Machine may become feasible; the Analogic Cellular Computer represents a new
platform for computing. However, this notion of computing contains brand-new
elements and techniques, partially reflecting some forms of nature-made information
processing.
Nature-made information processing has several different manifestations. On the
molecular level this means the protein structures or interacting molecules on a two- or
three-dimensional grid; on the neuronal level it may mean the many sensory organs
and subsequent neural processing. On the functional neuronal level it may mean the
information representation in spatio-temporal memory, the functional laterality of the
brain, as well as the parallel processing places and functional units learned via PET,
NMR, fNMR, etc. On the mathematical-physical level it may mean several dynamic
spatio-temporal processes and phenomena represented by different nonlinear partial
differential equations (PDEs). Autowaves, spiral waves, trigger waves are just a few of
these exotic waves.
In modern image processing, PDE-based techniques are becoming the most chal-
lenging and important new directions. For the analogic CNN computer these are
the native, elementary instructions like the multiplication, addition, XOR, NAND,
etc. in digital computers. A new understanding about computing itself is emerging.
The striking intellectual and scientific challenge is how to combine these diverse
phenomena in useful algorithms running on a standard spatio-temporal computer,
based on the CNN Universal Machine.
The analogic cellular visual microprocessors, embedded in a complete program-
ming environment,7 offer surprising system performance. Two types of tasks are
becoming tractable:
Class K: Kilo real-time [K r/t] frame rate class.
The frame rate of the process in this class is in the order of about a thousand
times faster than the real-time video frame rate (30 frames per second). A typical
experiment is where a pattern classification with more than 10,000 frames per
second was tested (more than 0.33 K r/t). Using current CMOS technology, 1.5
K r/t, that is about 50,000 frame per second, is feasible.
In this Class K, the high frame rate is the key in the computation. Clearly, the sensing
and computing tasks are to be physically integrated. In standard digital technology,

6 Introduction
there is no time for A to D conversion and to complete the calculation, all within a few
microseconds.
Class T: TeraOPS equivalent computing power class.
Even if the frame rate is small, like real-time video (30 frames per second), the
required computing power (per chip) is enormous. Indeed, a trillion operations per
second are to be – and can be – achieved. These TeraOPS chips are capable of
solving a nonlinear PDE on a grid in a few microseconds. The detection of a moving
inner boundary of the left ventricle in an echocardiogram, via an analogic CNN
algorithm combining several waves, local logic, and morphology operators, took
only 250 microseconds on the ACE4K analogic Visual Microprocessor Chip made
in Seville. These chips hosted 4096 cell processors on a chip. This means about
3.0 TeraOPS equivalent computing power, which is about a thousand times faster
than the computing power of an advanced Pentium processor.
A major challenge, not yet solved by any existing technologies, is to build analogic
adaptive sensor-computers,8 where sensing and computing understanding are fully and
functionally integrated on a chip. Adaptive tuning of the sensors, pixel by pixel, is
performed based on the content and context of the dynamically changing scene under
sensing.

2 Notation, definitions, and mathematical
foundation
2.1 Basic notation and definitions
Definition 1: Standard CNN architecture
A standard CNN architecture consists of an M × N rectangular array of cells (C(i, j))
with Cartesian coordinates (i, j), i = 1, 2, . . . , M, j = 1, 2, . . . , N (Fig. 2.1).
Column
j N
C(i, j)
1
1
2
3
Row i
M
2 3
Fig. 2.1.
Remark:
There are applications where M = N. For example, a 5 × 512 CNN would be more
appropriate for a scanner, fax machine, or copy machine.
Definition 2: Sphere of influence of cell C(i, j)
The sphere of influence, Sr (i, j), of the radius r of cell C(i, j) is defined to be the set
of all the neighborhood cells satisfying the following property
Sr (i, j) = {C(k,l)| max
1≤k≤M,1≤l≤N
{|k − i|, |l − j|} ≤ r} (2.1)
where r is a positive integer.
7

8 Notation, definitions, and mathematical foundation
(a) (b)
C(i, j) C(i, j)
Fig. 2.2. (a) r = 1 (3 × 3 neighborhood), (b) r = 2 (5 × 5 neighborhood).
We will sometimes refer to Sr (i, j) as a (2r + 1) × (2r + 1) neighborhood. For
example, Fig. 2.2(a) shows an r = 1 (3×3) neighborhood. Fig. 2.2(b) shows an r = 2
(5 × 5) neighborhood.
Remarks:
1 In IC implementations, every cell is connected to all its neighbors in Sr (i, j) via
“synaptic” circuits.
2 When r N/2, and M = N, we have a fully connected CNN where every cell
is connected to every other cell and Sr (i, j) is the entire array. This extreme case
corresponds to the classic Hopfield Net. It is impractical to build any reasonable size
(several thousand cells) Hopfield Net in a VLSI chip. There exists a “commercial”
Hopfield-like chip by INTEL called “ETANN,” type 80170 ($500 in 1995). This
chip has 64 cells which makes it more of an expensive “toy.”
Definition 3: Regular and boundary cells
A cell C(i, j) is called a regular cell with respect to Sr (i, j) if and only if all
neighborhood cells C(k,l) ∈ Sr (i, j) exist. Otherwise, C(i, j) is called a boundary
cell (Fig. 2.3).
Remark:
The outermost boundary cells are called edge cells. Not all boundary cells are edge
cells if r 1.
Definition 4: Standard CNN
A class 1 M × N standard CNN is defined by an M × N rectangular array of cells
C(i, j) located at site (i, j), i = 1, 2, . . . , M, j = 1, 2, . . . , N. Each cell C(i, j) is
defined mathematically by:
1 State equation
ẋi j = −xi j +

C(k,l)∈Sr (i, j)
A(i, j; k,l)ykl +

C(k,l)∈Sr (i, j)
B(i, j; k,l)ukl + zi j (2.2)

9 2.1 Basic notation and definitions
Boundary cell (if r =1)
Corner cell
Fig. 2.3.
where xi j ∈ R, ykl ∈ R, ukl ∈ R, and zi j ∈ R are called state, output, input,
and threshold of cell C(i, j), respectively. A(i, j; k,l) and B(i, j; k,l) are called the
feedback and the input synaptic operators to be deﬁned below.
2 Output equation
yi j = f (xi j ) =
1
2
|xi j + 1| −
1
2
|xi j − 1| (2.3)
This is called standard nonlinearity (Fig. 2.4).
1
–1
–1 0 1 xij
yij
Fig. 2.4.
3 Boundary conditions
The boundary conditions are those specifying ykl and ukl for cells belonging to Sr (i, j)
of edge cells but lying outside of the M × N array.

10 Notation, definitions, and mathematical foundation
4 Initial state
xi j (0), i = 1, . . . , M, j = 1, . . . , N (2.4)
Remarks:
1 The input ukl is usually the pixel intensity of an M × N gray-scale image or picture
P, normalized without loss of generality, to have the range −1 ≤ ukl ≤ +1 where
“white” is coded by −1 and “black” is coded by +1. For a still image, ukl is a
constant for all time, for a moving image (video) ukl will be a function of time.
Other variables (x(0), y, z) can also be specified as images.
2 In the most general case, A(i, j; k,l), B(i, j; k,l), and zi j may vary with position
(i, j) and time t. Unless otherwise stated, however, we will assume they are space
and time invariant.
3 In the most general case both A(i, j; k,l) and B(i, j; k,l) are nonlinear operators1
which operate on xkl(t), ykl(t), ukl(t), xi j (t), yi j (t), and ui j (t), 0 ≤ t ≤ t0, to
produce a scalar (A(i, j; k,l) ◦ ykl)(t0) and (B(i, j; k,l) ◦ ukl)(t0), 0 ≤ t ≤ t0.
4 We may also introduce synaptic laws depending on the states (C template) and on
mixed variables (D template), respectively.
That is (C(i, j; k,l) ◦ xkl)(t0) and (D(i, j; k,l) ◦ (ukl, xkl, ykl)(t0).
Unless otherwise stated, however, A(i, j; k,l)ykl and B(i, j; k,l)ukl will denote
ordinary multiplication with real coefficients where they may be nonlinear functions of
states, inputs, and outputs of cells C(i, j), C(k,l) and may involve some time delays
(i.e., they may contain a finite time history, as in the case of having a time delay).
The following are some space and time invariant nonlinear examples chosen from
the CNN catalog of applications (CNN Software Library). See some of them in
TEMLIB (Appendix A).
EXAMPLE 2.1:
a(yij )
1
–1
–0.025 0.025 yij
Fig. 2.5.

11 2.1 Basic notation and definitions
A(i, j; k,l) = a(yi j ): depends on output (from TEMPLATE MajorityVoteTaker)
(Fig. 2.5).
EXAMPLE 2.2:
C(i, j; k,l) = c(xi j ): depends on state (from TEMPLATE LGTHTUNE) (Fig. 2.6).
c(xij)
xij
1
–3
0.2
0
Fig. 2.6.
EXAMPLE 2.3:
A(i, j; k,l) = a(ui j , ukl) and B(i, j; k,l) = b(ui j , ukl): depends on two inputs (from
TEMPLATE GrayscaleLineDetector) (Fig. 2.7).
a(uij, ukl)
–0.15 0.15 uij – ukl
1
0.25
1
uij – ukl
b(uij, ukl)
Fig. 2.7.
EXAMPLE 2.4:
A(i, j; k,l) = a(yi j , ykl): depends on two outputs (from TEMPLATE GlobalMaxi-
mumFinder) (Fig. 2.8).

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He had not yet escaped, however. He was resting in his inn
when a messenger entered with an invitation to an impromptu
banquet organized at the burgomaster's. In vain Harry pleaded that
he was in no trim for fine company. The burgomaster's own tailor
undertook to make him presentable; he had to sit through a long
Dutch feast and respond to the toast of his health. Even then his
labours were not ended. After the banquet the company adjourned
to the council chamber, where all the beauty of the town was
assembled. Harry had to lead off the dance with the burgomaster's
wife, a stout vrouw of forty-five years and fifteen stone. He did his
duty manfully, dancing the stately dances of the day with unflagging
spirit, and winning universal praise by the modesty with which he
wore his honours. The assembly broke up at a late hour; Harry was
dog-tired, and went to bed convinced that it was mighty hard work
to be a popular hero.
CHAPTER XII
Harry is Discharged
Rheum and Rum—Gall—Without Ceremony—A Question of Precedence—Res
Angustae—The Raw—To Scheveningen—Punctuality and Despatch—From the
Dutch Side—Temptation—Renunciation—Gretel—Misgivings
Atchew!—confusion! This pestilent country—atchew!—will be the
death of me. 'Tis one eternal—-atchew!—rheum! Stap my vitals! I
wish I were dead. Atchew! atchew!

Captain Aglionby sat in the topmost room of a high house in
one of the less savoury quarters of the Hague. His nose was redder
than ever; his cheeks more puffed; his eyes looked like boiled
oysters. A thick woollen comforter swathed his neck. Though it was
the height of summer, a big log fire blazed in the hearth; window
and door were fast shut; and in a temperature of something over
eighty degrees the captain was doing his best, according to his
lights, to cure a cold.
He was seated at a table drawn close to the fire. Upon the table
stood a bottle nearly empty, a beaker, a basin of sugar, an inkhorn, a
table-book of writing-paper, and a sheath containing quills. A kettle
sang on the fire. When his sneezing fit was over, the captain poured
the last of his rum into the beaker, sugared it, filled up with boiling
water, and gulped half of the mixture into a throat inured to fiery
passengers. Water streamed from his eyes, and his blotched brow
broke into a profuse perspiration. He wiped his face with a large red
handkerchief, smacked his lips, and, bending over the table, selected
a quill.
Hang writing! he muttered. I never writ a letter but I rued it.
Atchew! And with this cursed cold! Well, the sooner begun, the
sooner done; so here's to it. Atchew!
He cut his quill, dipped it in the ink, and began:
Mr. BARKLEY. Sir.
It would have been quite evident to an onlooker that the captain
was not a practised penman. He wrote very laboriously, frowning at
every stroke, and licking his lips often. Like most illiterate people, he

repeated half aloud the words as he wrote them, and being so
unused to giving visible expression to his thoughts, he commented
as he went along. He was never at a loss how to spell a word, for in
those days men spelt as they pleased, and bad spelling might almost
have been regarded as one of the marks of a gentleman.
Sir. This will, I hope, finde you well. For myself, I am afflicted
[atchew!] with a voilent Rheum, the wch I feare will turne to an
inflamatn of the Longs. [Egad! that'll please the old niggard!] I
command the sarvices of the best Potticary in the place, but finding
his nostrums vain, for three dayes have eate nought but Water
Gruel. 'Tis said that Rumm is a speedie Cure, but that I eschew.
[Atchew!] My Hande shakes with the feaver, I shd not rite to you
now had I not Surprizing Nuse to give. You must knowe that,
visitting at the house of Mme de Vodray, where your he sarvant is
ever an honour'd guest, [that's worth fifty guineas to me!] what was
my vaste Amazement to finde there that yonge Cockerell H—— R
—— swaggering it as one of the beste. It passes my wit to divine
how he escap'd from the Merrie Maide, hope y may recover the
Passage Money, the wch methinks will be difficult. [Atchew! He won't
get a penny o't.] 'Tis passing strange the boy is here, not lesse that
he is acquaint with the Vodrays; moreover with him is my pestilent
cozn S—— M——, of whom more hereafter, 'twill be easie to deal
with him, whereto I have already things in Traine. H—— R—— is
employ'd with one Grootz, a merchant of Substance, one that hath
large Contracks with the confederate armies. The boy being out of yr
way, y have belike no further cause against him, wd wish no
further stepps taken, comming going is like at any time to Cooke

his Goose, but if I mistake in this 'twould be well to sende 100
Guineas by the same Hande as wont, I wd endevour to bring the
matter to a safe and speedie End, in wch case I wd make bold to
aske for a further Summe of 200 Guineas for to requite my Zeale in
the sarvice of my honour'd Frende Patron.
Atchew! Writing is plaguily dry work, he muttered, breaking off at
this point, and the bottle's empty.
He tugged at a bell-pull, and resumed his letter.
'Twill be no light Taske, seeing the yonge man hath captured of late
a Partie of above 100 French in an Affaire near Breda, the wch I
doubte not will give him some Consekence with the Dutch no less
than himselfe, of the wch Affaire 'tis like an Account will be printed
in the Courant. [Sure 'twill give Nick a start.] I must add that Living
is verie Deare here. For my Creditt sake and the furtherance of youre
Ends, I have hired a Magnifficent Appartment, for the wch I have to
paye a sweete Rent. Hence it is verie nessessarie I have the Guineas
without delai. Waiting yr commands so subscribe myself yr ever
humble and obediant
RALPH AGLIONBY, Captain.
Atchew! There, 'tis done, and writ fair. He flung his pen on the
table. And I'd fain know what the squire has against the knave; 'tis
more than pique, I promise you. Where's Simmons, confound him!
He sanded the wet paper, folded it, sealed it with yellow wax,
and wrote the superscription:

For Nicolas Barkley Esqre
at his house
Winton St. Mary
nr Salisbury, England
This done, he tugged again at the bell-pull, blew his nose with
sounding ferocity, and stuck his legs into the hearth with the air of a
man who had successfully achieved a stupendous task.
The door opened, and John Simmons entered.
Hang you, sirrah! why don't you answer my bell at the very
moment, sir? Go get me a bottle of rum.
Simmons, pallid, frowsy, scared-looking, stood hesitating in the
doorway.
Are you deaf, clodpoll? roared the captain. A bottle of rum,
and instantly!
Yes, Captain, and the—and the money, sir?
The money, you dog! Where is the crown-piece I gave you this
morning?
I had to buy the dinner, sir, and——
Zounds! You'll answer me, will you? You're the most pestilent
knave man ever had to serve him. 'Tis money, money, all day with
you. Would that Sherry Minshull had left you to the hangman!
Begone, sirrah! and——
Pardon! said a voice in French from the door. If I am in the
way——

Come in, Monsieur, said Aglionby, springing to his feet. And
you, booby, be off and do my bidding.
Simmons vanished precipitately. Monsieur de Polignac gasped as
he entered the overheated room.
Phew! It would roast an ox.
Shut the door. I am nursing a pestilent rheum.
So it appears. You are in an ill humour, my friend; I fear my
news will not cheer you.
Spit it out and have done with it, then.
Well, this is it. A commission has been made out, I hear,
appointing your young Englishman a cornet in the Anspach
dragoons.
What young Englishman?
The young man whom we met at Madame de Vaudrey's.
The captain swore a hearty British oath.
Where learnt you that?
A la bonne heure! It is true. I have it on authority I cannot
doubt. Van Santen pressed it; his influence prevailed. There were
several vacancies in the regiment; it lost heavily in the action at
Eckeren a few weeks ago. This boy gets the senior cornetcy. We owe
it to ourselves, Monsieur le Capitaine, that the junior cornets get an
early step.
Peste! We do owe it to ourselves; or, I should rather say, we
owe it to yourself. For me, I have knocked about the world too long
to take umbrage easily; and look you, Monsieur, my family, although
gentle, indeed I may say noble, cannot compare with yours in
quartet-ings and such fal-lals. I understand your sentiments; as you
say, something must be done.

And at once, for which end I have come to see you. My
position, as you perceive, is delicate; for myself, I would seek a
quarrel with the bantling and spit him on my rapier without remorse.
But affairs of state—you understand me; that alters the case. I must
not appear. I propose to you this: to affront the boy, provoke him to
a duel; you a veteran, he a tyro; it will be a matter of seconds.
Voilà!
The captain gazed steadily at Polignac for a few moments, then
said:
Look you, Polignac, no man ever accused Ralph Aglionby, late
captain in the Preobrashenski Grenadiers, of lack of courage—no
man, that is to say, that lived to tell of it. Had you made the
proposition twenty years ago, I should by this time have been half-
way down the stairs on the way to kill this young springald. But
twenty years make a difference. My courage is the same, look you;
but the years have enlarged my girth—and my discretion. On the
point of honour I am as sensitive as ever I was, but I have learnt to
have patience—and consideration. Say I engage this peddling fool;
what happens? I kill him and baulk you of your revenge. Where are
you, my friend? Or suppose, by some vile contrivance, he kills me;
where am I? No, no, Monsieur; the right of place belongs to you.
Who am I, a broken soldier, a poor unnecessary captain of
grenadiers, to take precedence of you?
You have most admirable patience, sneered Polignac, and I
am overwhelmed by your consideration. I thank you, Monsieur le
Capitaine, and bid you adieu.
Stay, my friend; why this haste? I have consideration, as you
say. Would the world be better for the loss of you or me? are there

not more ways of getting even with a man than making one's self a
target for his pistol or a sheath for his sword? You remember
Marillier, and Aubin, eh? Sit down, and let us talk this over like
reasonable men.
Polignac sat on one of the rickety chairs in silence.
Your memory is jogged, eh? You remember the dark lane, and
the light in the window, and——
Enough! exclaimed the other impatiently. My memory is as
good as yours. This is different. I must be circumspect. Were we in
Paris—then! But here at the Hague, I am not my own master; I have
weightier interests to consider. An incautious step, even a chance
word, may ruin a dynasty. My own life—I do not consider it; but
when one is playing for a crown one has duties, responsibilities. If
you see your way—well, I am not one to dissuade you; and if a few
guilders——
Aglionby's red eyes gleamed.
Well, Monsieur, as you put it so, I own 'tis in a measure a
question of money. In truth 'tis desperate hard lines that I, who have
ruffled it with the best and got drunk with the Czar of Muscovy
himself, should be so hard driven as that I cannot offer due
hospitality to a friend. Look at this wretched lodging; was ever
gentleman, by no fault of his own, mark you, reduced to such
straits!
Polignac, glancing at the mean furniture and the empty bottle,
agreeably assented, but concealed a smile.
Well, he said, might I ask leave to send out for a bottle of
wine?
Aglionby jumped up with alacrity.

You say so? 'Tis the mark of a true friend. He pulled hard at
the bell-rope. My man will be here instantly; and, Monsieur, let it be
sack—sack, as you love me.
Simmons reappeared without delay, and was despatched for a
bottle of sack. With the energy of pleasurable anticipation the
captain pursued:
Now, my dear Polignac, mark—before attempting the house 'tis
well to poison the dog; aha! that is only my way of putting it, eh?
Of course. A figure of speech; but from the life!
Aglionby flung him a suspicious glance; at times he had an
uneasy feeling that Polignac was quizzing him. But after a
momentary pause he went on as before.
The dog in this case—and a low cur it is—is the young
cockerel's servant—the same that embraced you so cordially at
Madame de Vaudrey's. Ha! ha! I can relish the comical side of it e'en
though he embraced me also!—and before the charming
mademoiselle too!
He guffawed uproariously. He felt that he was now getting tit for
tat for Polignac's covert sneers, often rather suspected than
understood. But he was not a little startled by the effect of his words
and laughter. Polignac flushed purple with rage; his mouth took a
very decided twist towards his left eye. Springing up suddenly he
cried:
Morbleu, Monsieur, a truce to your pleasantries! and keep the
lady's name out of it, or by the——
No offence, no offence, my dear fellow, interposed the captain
hastily. I'm but a plain soldier—just an honest, bluff, outspoken old
campaigner; we blades don't pick and choose our words like you fine

gentlemen of the courts; though in truth when I was in Russia my
manners were as good as the best.
Polignac resumed his seat reluctantly without a word. After a
short, strained silence Aglionby went on:
The first thing, as I was saying, is to get this dog out of the
way. Burn him! he follows his master like a shadow. The man
removed, the rest is easy. A week from now, and he shall lie his
length in six feet of good Dutch soil, or my name isn't Ralph
Montacute Aglionby. Leave it to me, Monsieur; there will be
necessary expenses; say fifty guilders, a small sum, and at one time
——
Send to my chambers; you shall have the money. And by the
way, here is a packet for Captain Rudge of the Skylark. He sails with
this evening's tide. Bid him have the greatest care of it; should he
run into danger he must destroy it.—It is arranged, then? I shall
hear from you?
Within a week, on the word of a gentleman.
Then for the time, adieu!
When Polignac had gone, Aglionby looked curiously at the
packet entrusted to him. The address ran:
For Mistress Consterdine
to be left at the coffee-house,
by the Cockpitt, Whitehall, London.

It was carefully but not conspicuously sealed. The captain turned it
over and over in his dirty hands; they itched to open it. To judge by
his rage, he muttered, he's certainly smit with Mademoiselle de
Vaudrey. 'Tis not merely his interest is engaged. He sat musing for
a moment. Then his eye fell on a broadsheet, marked with many
circular stains, that lay on one of the chairs. He took it up and
searched for a passage which he had clearly already read. Lighting
upon it, he read:
The report goes that Coy's Horse embark at Harwich for Ostend on
Friday the 16th current. They will join the forces now operating
under General Lumley in Dutch Flanders.
With a fair wind they'll make port to-morrow. Then, Sherebiah
Minshull, my sweet coz, we shall begin to square accounts,—you and
I.
Stuffing the two packets into his capacious pocket, he clapped
on his hat, flung a cloak over his shoulders, wound the comforter
more tightly about his neck, and made his way out, sneezing half a
dozen times as he met the cooler air of the street. He walked along
the Lange Pooten, the chief business thoroughfare, into an open
space known as the Plein. As he was crossing this he caught sight of
a figure hastening into one of the larger houses, and almost
involuntarily he stepped aside into a doorway until all danger of
being seen was past.
What is the puppy doing here? he muttered, passing on his
way to the old road to Scheveningen. After a pleasant woodland
walk of two miles he reached that little fishing village, and found, as

he expected, Captain Rudge, owner and skipper of the sloop Skylark,
a fast sailer which ran to and fro between Scheveningen and
Harwich. To him Aglionby confided his own letter and Polignac's.
Then he retraced his steps, and at the Hague took horse for
Rotterdam. It was near midnight when he returned and wearily
climbed the lofty stair to his attic room; but though he was fatigued,
and his cold perceptibly worse, he seemed well satisfied with
himself, and chuckled many a time before he had drained to the
dregs the bottle of sack he had broached with Monsieur de Polignac.
The person from whose sight he had shrunk in the afternoon
was Harry Rochester himself, who had just returned from a visit to
Marlborough's camp at Hanneff. Mynheer Grootz was up to his eyes
in business, and the wide area over which the confederate forces
were spread taxed his resources to the utmost. He had now come to
the Hague to confer with a committee of the States General and
arrange further contracts, and had instructed Harry to meet him
there on the completion of his own errand.
Well, my boy, said Grootz on his arrival, I did not expect you
zo zoon. They were now on such friendly and familiar terms that
the Dutchman had dropped the formal address. How have you
fared?
Excellently, Mynheer, replied Harry. The commissary was well
content with your arrangements, and said—'tis no harm to repeat it
—that were all Dutchmen like Jan Grootz he would be spared a peck
of trouble.
Dat is goot, said Grootz, evidently well pleased. Dat is how I
do my business; always in time, always ready, always sure.

I had hoped to catch a glimpse of my lord Marlborough himself,
but 'twas not to be. Whatever may be said of his meanness and
selfishness, Mynheer, 'tis certain he is adored by his army. The
soldiers are full of courage, confident in my lord's genius, and all
afire to meet the French. They say, indeed, that if my lord were but
free of restraint, not bound to take counsel with your politicians
here, one campaign would see the end of the war.
Dey zay!—Yes, well, it may be zo. My lord is a fine soldier—
none would deny it—for all he dink little of de rules of war. But as for
de field deputies—my countrymen—dey alzo have reason. To Lord
Marlborough and you English, my boy, a defeat mean much; dat is
zo; but to my country—ah! much more. To us it mean ruin, every
village and town overrun, our polders spoiled, our homes destroyed,
everywhere black misery. Dis poor country know it all too well; we
have suffered—ah yes! we have suffered before too often. For my
lord, it is a game wherein he can noding lose but glory; for us it is a
struggle of life and death. True, for myself, I zay in war, as in
business, to follow a bold course is best; but I do not derefore blame
our statesmen dat dey move zlowly; no, I do not blame dem.
Harry had seen more than once lately that beneath the stolid
exterior of the merchant beat a heart warm toward his fatherland
and his friends. He could not but recognize much to sympathize with
in the Dutch point of view, and began to realize what it meant to the
Hollanders to have their country turned into a cockpit for the political
contentions of rival monarchs.
A slight pause followed Grootz's earnest speech; then suddenly,
with a change of tone, he said:

Now, Mynheer Harry, I have a ding to zay. Dere are reasons
why I find it now necessary to discharge you from my business.
Harry gasped and looked very blank. The merchant nodded
solemnly; up came his fat forefinger; and he continued with even
more deliberation than usual:
Dat is zo. I tell you dis; I find no fault wid you; none in de
world; but all de same, I zay dat it is necessary you go.
Harry was so much taken aback that he found it difficult to
speak.
Why—'tis sudden—what can—surely— his tongue stumbled
over half a dozen questions before, with an effort to command
himself, he said: Of course, Mynheer, if there is nothing more for
me to do, I must perforce seek other work. You have been very kind
to me; 'tis but poor thanks I can give you for what you have done.
What I have done! Gunst! it is noding. And you: it needs not to
zeek oder work; it is found. Hearken to dis.
He took up an official-looking paper that lay at his hand and
read in Dutch:

Mynheer Henry Rochester is appointed to a cornetcy in the Anspach
dragoons in succession to Mynheer Lodewyk van Monnen deceased.
Harry flushed to the eyes.
'Tis a mistake, Mynheer, surely. I have not sought this; I know
nothing of it.
A mistake! Not at all. General van Santen come to me and zay,
'Grootz, you have in your business a young man dat has no business
to be in your business; he is a soldier, noding less, and we have
need of such;' dat is what he zay, and more, and he go straight off
to put down your name for a commission. And here it is, in de
gazette. Dat is why I discharge you, before— (Mynheer Grootz
made a brave attempt to be jocular)—before you discharge
yourself.
Harry was silent. His nerves were tingling, his blood sang in his
veins. Here was the opening to a career after his own heart. All his
earlier longings came back to him; the inward struggle with which he
had acquiesced in his father's desire that he should enter the
Church; the light of hope that shone on him at his interview with
Marlborough; the agonizing dissolution of his castle in the air. And
now, unsought, what he had sought in vain had come to him, the
aspiration of his boyhood was about to be fulfilled. All this flashed
through his mind in a moment of time,—and there was Jan Grootz,
smiling out of his kindly little eyes. Jan Grootz!—what he owed to
him! But for Jan Grootz he might now be a hapless slave in the
Plantations, with no ray of light upon the endless vista of the years.
To Jan Grootz he owed his health and freedom, his training in

dealing with men; more than all, he had met in Jan Grootz a man
whose character compelled his respect and admiration, and whom
indeed he had begun to love. Would it not be the worst of
ingratitude to leave him now?
The temptation was strong, the inward struggle sharp. But it
was only a few moments after the staggering announcement when
he bent forward and said:
Mynheer, I cannot accept this offer—this splendid offer. 'Tis
exceeding kind of General van Santen; I owe him my hearty thanks;
but 'tis not to be thought of, save you yourself wish to be rid of me,
and that I must doubt, since 'tis but a week since you told me I was
useful to you. I will see the general, and explain to him the reason
why I decline this commission; I must do so at once.
He made towards the door, as though eager to avoid dalliance.
Grootz's broad plain face was transfigured by delight and pride and
gratification. Catching Harry by the arm, he drew him back, laid his
hand on his shoulder, and said:
No, Harry, my dear lad, I tell you dis; you must not do dis ding.
I do not zay I shall not feel your loss—there was an unusual note of
tenderness in his voice—true, it is not long dat we have worked
togeder, but already I regard you—jawohl, regard you as a son, and
to miss your bright face, your willing service——hoot! by den donder,
I am not myself to-day.
'Tis too kind of you, Mynheer.
Nay, nay; I am not zo weak. I am at one wid General van
Santen: you are made for a soldier. 'Tis de work you yourself would
have chosen; now 'tis de tide of fortune, dat you dare not miss. I tell

you dis; I am made up in my mind, fixed, noding can move me. I
salute you, Mynheer Rochester, cornet in de Anspach dragoons.
Indeed, 'tis too good of you, Mynheer.
Not zo. And dis I tell you alzo. You know me, Jan Grootz; I
prosper—God prospers me. I regard you as my son: well, 'tis a
fader's pleasure to provide for his son at de beginning of dings, just
as 'tis a skipper's pleasure to zee his ship sail taut and trim. You will
have heavy charges: clothes, equipment, a horse to buy. Dose
charges, you will permit me, zall be mine. 'Tis but right you should
take your place wid de best. I have no kith nor kin, nor like to have;
de pay for dragoons is little enough; I add a hundred guilders a
month; dat will suffice, dink you?
But, Mynheer——
Poof! no buts. I zall do as please me. Now, I am hungry: let us
go to de parlour. And dere is your man to tell; he will, no doubt,
continue to be your servant.
They went from the room, Grootz keeping his hand
affectionately on Harry's shoulder. The table in the parlour was
already laid, and in answer to the bell old Gretel appeared with a
tureen of soup.
Gretel, said the merchant, Mynheer Harry is about to leave
us.
There! Something inside told me, Mynheer, you would not keep
him long.
'Tis not of my own will, Gretel, said Harry at once.
No, added Grootz. The lad was not eager. He is to be an
officer of dragoons.
The old woman curtsied and grunted.

A rare exchange! she said. To my mind 'tis better to sell corn
than to stand up to be shot at, and a deal safer. But I wish you good
luck, Mynheer.
Thanks, Gretel, for that and for all your kindness to me. Is
Sherry downstairs?
Ja, Mynheer.
Send him up, if you please. I must tell him the news.
Oh! he will not be pleased. He has a scorn of soldiers, never a
good word to say for them. He is in the right.
Harry smiled as the privileged old housekeeper hobbled out.
Sherebiah soon appeared.
Sherry, said Harry, I have a thing to tell you. General van
Santen has recommended me to the heads of the Dutch army, and I
am made an officer of dragoons.
Zooks! was the man's astonished exclamation.
We shall still be together, you and I. I shall want a man, of
course; and you will not object to the place?
Well, sir, said Sherebiah slowly, looking down at his boots, 'tis
an awk'ard matter for a man o' peace. 'Tis a line o' life I ha' no love
for. To be sarvant to a man o' war is next to bein' a man o' war
yourself. Not but what I'd be proud to sarve 'ee, Master Harry; no
man more; but them as take the sword shall fall by the sword, as
the Book says, and I take that for a warnen to have none on 't.
A lame argument, Sherry.
True, sir, haven no larnen I feel it so. And will 'ee go shoulder
to shoulder with our English sojers?
There was a note of anxiety in his voice.

That I can't say. I hope that my regiment won't be left out in
the cold.
Well, sir, there's a providence in't. Them above knows what
they're about, to be sure, in a general way, and I bean't agwine to
set up for knowen better. I'll sarve 'ee, sir, polish your breastplate,
currycomb your horse, oil your boots, clean your pistols, keep an eye
on the sutlers, and——
You seem to have a good notion of your new duties, said
Harry, laughing.
Pretty good, sir, for a man o' peace, said Sherebiah
imperturbably. And when do 'ee mount your horse as a sojer,
Master Harry?
Zoon, put in Grootz. General van Santen himself will
introduce him to his broder officers; he tell me zo.
Ay, so. Well, 'tis a world o' changes. For you, sir, 'tis a change
for the better, barren 'ee bean't killed; for me,—well, the truth on't
is, I fear 'tis the beginnen o' the end for Sherebiah Stand-up-and-
Bless.
CHAPTER XIII
Concerning Sherebiah
A Summons—Coy's Horse—Vain Search—A Clue—Sentenced—Confession—A Quiet
Mind—A Friend in Camp—The Informer—Intercession—Who Goes There?—Hit—
The Mantle of Night—In a Ditch

One evening, a few days after he had received news of his
commission, Harry returned home somewhat later than usual from
his customary stroll. He was fond of walking through the pleasant
woods to Scheveningen, and watching the herring-boats as they
sailed out for the night's work. He would chat with the fishermen,
and had indeed by his frank manner, and perhaps an occasional gift
of tobacco, established himself as a favourite with them.
On this evening, feeling a little tired, he threw himself into a
chair in the parlour, and sat musing, gazing into the glowing sky as
the sun went down. By and by old Gretel entered and began to lay
the supper. She had gone in and out two or three times in silence
before Harry bethought himself and said:
Why, Gretel, how is it Sherry is not helping you to-night?
By den donder, Mynheer, you may well ask! He seems
bewitched since the great news. Not half so helpful to my poor old
bones as he was.
But where is he?
He has not returned yet.
Returned from where?
Why, Mynheer, he went out at once after receiving your
message, and——
My message!
Ja, Mynheer, the message sent by the boy.
What boy? Come, Gretel, I sent no message. I know nothing
about a boy. Tell me all you know.
It was about four o'clock, Mynheer, a boy of twelve or so came
to the door—a stranger to me. He asked for Sherry Minshull—no
mynheer to his tongue. I called to Sherry, and heard the boy say,

'Mynheer Rochester wishes you to come——' then the big bell of the
Groote Kerk tolled, and I heard no more. But Sherry reached down
his hat and said he was going to you, and he and the boy went away
together.
Harry was puzzled, and a little uneasy. He rose from his chair.
Are you sure you heard the boy mention my name?
Quite sure. And Sherry must have thought there was need for
haste, for he left his dish of coffee half full, and he is too fond of
mocha to do that without a reason.
Just then Mynheer Grootz came in to supper. When Harry had
informed him of the strange message and Sherebiah's continued
absence, he was at first disposed to make light of the matter.
Gretel is growing hard of hearing, he said. Maybe she
mistook de name.
Don't you think, Mynheer, 'twould be well to make enquiry
before it is dark? I am strangely uneasy about Sherry.
The merchant consented to accompany Harry into the streets.
Everybody knew him and answered his questions readily enough;
but none of the porters of the neighbouring houses, or the
watchmen who patrolled the streets, had seen Sherebiah or the boy,
though some of them owned that they knew the former well by
sight. By and by, however, they came upon an old soldier smoking
his evening pipe outside his cottage—the lodge to one of the larger
houses in Gedempte Spui. Grootz put the usual question.
Did you see an Englishman—stout, with a beard, and his hat
on one side, pass by a few hours ago with a boy of twelve or
thereabouts?

The soldier removed his long pipe, spat, and appeared to
meditate before replying.
Yes—now I think of it; I believe I did see a man of that cut,
though I would not be sure. He might not have been an Englishman.
He was stout, certainly, and had a beard; as for his hat, I didn't
notice it, for the truth is, I had been looking at some other
Englishmen, a party of Coy's Horse; my old corps served side by side
with them in '97. Yes, and there was a man among them I knew too;
a paymaster—Robins, I mind, was his name—donder! what a temper
he had! It was a curse and a blow with him. Ay, it is a hard life, the
soldier's. They halted at the inn over by there, and I was just going
over to drink a glass with them for old times' sake when the Baron's
coach came up and I had to open the gates. A lodge-keeper, see
you, is a sentry with no change of guard.
Ja, ja! But the Englishman and the boy—which way did they
go?
Which way? Let me see. They might have gone down the road:
no, now I bethink me, I believe they went up the road; but there, I
can't be sure. The sight of the English horse, men I fought side by
side with in '97, before I got my wound——
Ja, ja! Thank you!
They escaped his further reminiscences by walking on, past the
inn, past a row of cottages with the inevitable bright green shutters,
until they came to the watch-house at the cross-roads. Grootz put
the same question to the watchman.
No, he replied. I saw no Englishman with a boy. But I saw a
party of English horse; they had come in from Rotterdam, and I
heard afterwards at the inn they were on the track of a deserter.

It was now almost dark; to continue the search further would
be vain. They returned home to their belated supper, Grootz
promising to set exhaustive enquiries on foot in the morning.
That night, for the first time for many months, Harry was unable
to sleep. He was oppressed by perplexity and uneasiness. From
whatever point of view he looked at Sherebiah's disappearance it
seemed equally inexplicable. He could divine no motive for a
message sent to Sherebiah in his name; the man appeared to be on
very good terms with Dutchmen and was unlikely to have private
enemies. Harry was almost forced to the conclusion that Gretel had
been mistaken, after all, and that Sherebiah would by and by return
with a simple explanation of his absence. He might have met a
friend, and be spending a convivial evening with him. Perhaps—the
thought came like an illumination—one of the English troopers from
Rotterdam was a friend of his—a Wiltshire man, possibly. The
suggestion allayed his uneasiness, and he fell asleep half expecting
to be called by Sherebiah as usual next morning.
But Sherebiah did not return that night. It happened next day
that Mynheer Grootz was early summoned to a conference with a
committee of the States General, and when after a prolonged
discussion he was released he had to start at once for Leyden on
important business. It was late before he returned. Harry meanwhile
had lost no time in pursuing enquiries in every likely quarter, but in
vain. Sherebiah had not returned; nothing had been heard of him;
and there was nothing for it but to wait yet another day.
He was again wakeful, and his thoughts turned to the errand on
which the party of English horse had come. He pitied the
unfortunate wretch for whom they were in search—some poor

fellow, perhaps, who had escaped in the hope that he would be less
easily tracked in a foreign land. The punishment for desertion had
become much more stringent and summary of late owing to the
prevalence of the offence. Harry himself remembered one bleak
morning in London when, having gone early into Hyde Park, he had
been the unwilling spectator of the shooting of a deserter. Had they
caught the man? he wondered. I hope—— he thought, then
suddenly a strange suspicion flashed upon him. Surely it was
impossible; yet—— In a moment slumbering recollections awoke. He
remembered that many times, when approaching English soldiers in
London, Sherebiah had sidled away and disappeared. He
remembered how, more than once, Sherry had shown a knowledge
of military matters singularly intimate for a civilian; how insistently
he had always proclaimed himself a man of peace; how hardily he
had behaved in the fight at Lindendaal. These facts, and many a
slight hint scarcely regarded before, combined to convert a chance
surmise, almost dismissed as absurd, into a strong presumption little
short of certainty.
He sprang out of bed, dressed quickly, ran downstairs with his
slippers in his hands, and, noiselessly drawing the bolts, hurried
along the silent street towards the inn on the Rotterdam Road at
which the patrol had halted. Though it was late, the people of the
inn were still up. He asked for the landlord, and had not conversed
with him for more than a minute before he was convinced, from
what was said of the prisoner, that it was indeed Sherebiah. The
troopers had brought with them a led horse; on this they had
mounted the deserter, strapping him on each side to a dragoon, and
then ridden off at once towards Rotterdam, en route for Breda.

Returning to the house, Harry woke Mynheer Grootz, told him of
what he had learnt, and proposed to start at once for Breda to allay
or confirm his suspicion. From this the merchant dissuaded him. A
night ride would be attended with difficulty and danger; if he started
early in the morning, he might still overtake the dragoons before
they reached Breda. Accordingly he went back to bed for a few
hours. At dawn he rose, and by five o'clock was galloping towards
Rotterdam on the best horse in Grootz's stables.
At Rotterdam he learnt that a body of English horse, consisting
of units of several regiments, had left for Breda on the previous
afternoon. Waiting for an hour to rest and bait his horse he pushed
on to Breda, arriving there about one o'clock in the afternoon.
Without delay he sought out the officer to whom he had delivered
his convoy of provisions a few weeks before, and enquired whether
he knew of the arrest of an English deserter.
Ay, and a notorious character, it appears. 'Twas not merely
desertion they had against him, but mutiny, and a murderous attack
on an officer. He fought like a cat when he was arrested; 'twas a
foolish trick, for they were ten to one, and in a little he was
overpowered. He was tried by court-martial this morning at nine,
and the trial was short.
Was sentence pronounced?
Of course; he had no defence; he was sentenced to be shot.
There is no appeal?
None. The sentence will be laid before my lord Marlborough for
confirmation; a matter of form. But pray why do you take so much
interest in the man?

He is my servant, comes from my village, has done me right
faithful service. Good God! to think that he should come to this end!
The officer shrugged.
Unhappy chance indeed. 'Tis seven years or more since he
deserted; doubtless he felt secure. I am sorry for you. He'll get no
more than he deserves.
Could I see him?
Certainly; he is confined in the town-house; I will take you to
him myself.
In a few minutes Harry was ushered into a dark room in the
basement of the town-house. A candle was lit; he was left alone
with the prisoner, and the door was locked behind him.
Oh, Sherry, my poor fellow, who would have thought you
would come to this!
Master Harry, 'tis good of 'ee to come and see me. Ay; poor
feller! you med well say so; but to tell 'ee the truth, 'tis a load off my
back.
Yes, I understand. I know now why you always scouted the
soldiers in London. Why didn't you tell me? I would never have
brought you to this country, with our soldiers here, there, and
everywhere.
Tell 'ee! Not me. Why, you and me would 'a had to part
company that minute. Besides, 'twarn't zackly a thing to be proud
on, look at it how 'ee will. 'Twas ill-luck I were nabbed, to be sure;
but I've had nigh eight year as a man o' peace, and I s'pose 'twas
time the lid were putt on the copper.
And they'll shoot you!

Bless 'ee, I bean't afeard o' that. I've been shot at; ay, many's
the time: at Sedgemoor, and Walcourt, and other cities o'
destruction. I can stand fire wi' any man. Nay, the one thing as
troubles me is how poor old feyther o' mine'll take it. The poor
ancient soul never dreams I desarted; and zooks! 'tis that'll hurt un
more'n my bein' a corpse; his boy a desarter, and him a trooper of
old Noll's! Ay, that'll hurt un, 'twill so. And then there's you, sir; how
be I agwine to leave 'ee, wi' old Squire and Rafe Aglionby a-seeken
whom they may devour, and no one you can trust to polish your
breastplate and oil your boots? Ay, the way o' transgressors is hard;
the wages o' sin is death; many's the time I've yeard they holy
words from the lips of pa'son your good feyther, never thinken in my
feeble mind he were aimen at me.
Harry was at a loss for words. Sherebiah was so perfectly
resigned to his fate that any attempt at consolation would seem an
impertinence.
How came you to desert? he asked, to gain time.
Why, I'll tell 'ee about it. I was a corporal in Coy's horse; med
ha' been a sergeant long agoo, indeed. But there was a paymaster o'
that regiment, Robins by name; a good sojer, true, but with his
faults, like any other mortal man. He was hot in his temper, and
crooked in his dealens. Us men was bein' cheated, right and left; our
pay was small enough, but we never got it: a penny here and a
ha'penny there bein' took off for this or that. Ay, and he was a
knowen one, he was. All done so soft and quiet-like. We stood it a
long time; at long last, 'twas more'n Minshull blood could stomach,
and one mornen I up and spoke out; you see, I warn't a man o'
peace then. Well, Robins bein' fiery by nature, he got nettled; I

should myself; but 'tis one thing to get nettled, and another to use
yer fist. Robins he used his fist, and not bein' zackly meek as Moses,
I used mine, and he fell under. Two or three of my mates standen by
saw it all. Robins he raved and called on 'em to arrest me, but they
wouldn't. But 'twas all up wi' me; I knowed that well enough; if
Robins took a spite agen a man he med as well be a dead dog. I had
no mind to be a dead dog just then, so I bolted; and that's how I
come to be such a man o' peace.
But surely if you explained that, your punishment wouldn't be
so heavy.
Explain! Bless 'ee, 'twould be no good in the world. To strike a
officer be mortal sin. Nay, I've nowt to say for myself; I must just
take my wages.
How did you manage to elude them so long?
Oh! the regiment was out o' my way: been quartered this many
year in Ireland. 'Twas just my bad luck that they should ha' been
sent for on this campaign. Ah, well! a man can die but once; I've
kep' the commandments, and that's more'n Robins can say; and
there's no commandment 'Thee shall let a man hit 'ee and say thank
'ee'. I bean't afeard o' Them above, and I'll meet 'em with head up
and eye clear, like a English sojer.
When is it to be?
They didn't tell me that. 'Twill not be long, you may be sure.
My lord Marlborough has only got to scribble his name on the paper,
and he'll never remember 'twas me as held his horse at Salisbury in
'88 and got nowt but a smile.—Master Harry, belike I sha'n't see 'ee
again in this world. When you go home-along, you'll say a word o'
comfort to the old ancient gaffer, won't 'ee? Tell un all the truth; tell

un I be main sorry to vex his old gray hairs,—though not for
punchen Robins. Gi' him my dear love: his boy, he calls me, poor
soul: and say as how I were quite easy in mind and not a bit afeard.
He's a trooper of old Noll's, you see.
I'll give him your messages, said Harry with a gulp,—if ever I
get back alive.
Ay true, ye med not. The corn-dealen was a safer line o' life.—
What! time's up.—A sentry had thrown open the door.—Good-bye,
Master Harry; God bless 'ee! and I hope you'll get a man as'll polish
your 'coutrements to your mind. This time to-morrow, belike, I shall
be a true man o' peace.
Harry shook his hand in silence; he could not trust himself to
speak. He was angry at what he thought the essential injustice of
the sentence. Sherebiah had only struck the paymaster in self-
defence, and in the original cause of dissension had right on his
side. But Harry knew what military discipline meant; it was rigid as
iron. Still, he could not help asking himself whether even now it was
impossible to get the whole circumstances considered and the
sentence revised. He thought of making a personal appeal to
Marlborough, but soon dismissed the idea, for Marlborough had
doubtless forgotten him, and he had no force of persuasion to bring
to bear. Suddenly, as he walked slowly along the street, he
remembered Godfrey Fanshawe; he was an officer in a companion
regiment, Schomberg's Horse; he would ask his advice. He enquired
for the quarters of the regiment, found that it was encamped a short
distance out on the Tilburg road, and hastened thither with an
anxious heart.

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