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Optimizing Engineering Problems through Heuristic
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Author(s): Kaushik Kumar, Divya Zindani, J. Paulo Davim
ISBN(s): 9781351049580, 1351049585
Edition: 1
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Year: 2019
Language: english

Optimizing
Engineering
Problems through

Heuristic Techniques

Science, Technology, and
Management Series
Series Editor:
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Department of Mechanical Engineering, University of Aveiro, Portugal
This book series focuses on special volumes from conferences, workshops, and

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Advanced Mathematical Techniques in Engineering Sciences
Edited by Mangey Ram and J. Paulo Davim
Soft Computing Techniques for Engineering Optimization
Edited by Kaushik Kumar, Supriyo Roy, and J. Paulo Davim
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Optimizing
Engineering
Problems through

Heuristic Techniques
Kaushik Kumar, Divya
Zindani, and
J.
Paulo
Davim

CRC Press
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v
Contents
Preface.......................................................................................................................ix
Authors.................................................................................................................... xiii
Section I Introduction to Heuristic Optimization
Chapter 1 Optimization Using Heuristic Search: An Introduction.......................3
1.1 Introduction................................................................................3
1.2
The Optimization Problem.........................................................4
1.2.1
Local Versus Global Optima.........................................4
1.3
Categorization of Optimization Techniques...............................4
1.4
Requirement of Heuristics and Their Characteristics................6
1.5
Performance Measures for Heuristics........................................7
1.6
Classification of Heuristics.........................................................8
1.7 Conclusion..................................................................................9
Section II Description of
Heuristic Optimization Techniques
PART I Evolutionary Techniques
Chapter 2 Genetic Algorithm...............................................................................13
2.1 Introduction..............................................................................13
2.2 Genetic Algorithm....................................................................13
2.3
Competent Genetic Algorithm................................................. 16
2.4
Improvements in Genetic Algorithms......................................20
2.5 Conclusion................................................................................21
Chapter 3 Particle Swarm Optimization Algorithm............................................23
3.1 Introduction..............................................................................23
3.2
Basics of Particle Swarm Optimization Approach...................23
3.2.1
Structure of Standard PSO..........................................24
3.2.2 Some Definitions.........................................................25
3.3 PSO Algorithm.........................................................................26
3.4
Some Modified PSO Algorithms..............................................27
3.4.1 Quantum-Behaved PSO..............................................27
3.4.2 Chaotic PSO................................................................28

vi Contents
3.4.3
Time Varying Acceleration Coefficient-Based PSO.....28
3.4.4 Simplified PSO............................................................29
3.5
Benefits of PSO Algorithm.......................................................30
3.6
Applications of PSO.................................................................30
3.7 Conclusion................................................................................ 31
PART II Nature-Based Techniques
Chapter 4 Ant Colony Optimization....................................................................33
4.1 Introduction..............................................................................33
4.2
Components and Goals of ACO...............................................34
4.3
Traditional Approaches of ACO...............................................36
4.3.1 Ant System..................................................................36
4.3.2
Max-Min Ant System..................................................37
4.3.3
Quantum Ant Colony Optimization............................37
4.3.4
Cooperative Genetic Ant System................................38
4.3.5
Cunning Ant System...................................................39
4.3.6
Model Induced Max-Min Ant System.........................40
4.3.7
Ant Colony System......................................................40
4.4
Engineering Applications of Ant Colony Optimization
Algorithm�� 41
4.5 Conclusion................................................................................ 41
Chapter 5 Bees Algorithm...................................................................................43
5.1 Introduction..............................................................................43
5.2
Basic Version of Bees Algorithm.............................................44
5.3
Improvements on Bees Algorithm............................................46
5.3.1
Improvements Associated with Setting and
Tuning of Parameters��46
5.3.2
Improvements Considered on the Local and
Global Search Phase��47
5.3.3
Improvements Made in the Initialization of the
Problem��50
5.4 Conclusion................................................................................50
Chapter 6 Firefly Algorithm................................................................................ 51
6.1 Introduction.............................................................................. 51
6.2 Biological Foundations.............................................................52
6.3
Structure of Firefly Algorithm.................................................53
6.4
Characteristics of Firefly Algorithm........................................54
6.5
Variants of Firefly Algorithm...................................................55
6.5.1
Modified Variants of Firefly Algorithm......................55

vii
Contents
6.5.2
Hybrid Variants of Firefly Algorithm.........................57
6.6
Engineering Applications of Firefly Algorithm.......................59
6.7 Conclusion................................................................................59
Chapter 7 Cuckoo Search Algorithm................................................................... 61
7.1 Introduction.............................................................................. 61
7.2
Cuckoo Search Methodology................................................... 61
7.3
Variants of Cuckoo Search Algorithm.....................................64
7.3.1
Adaptive Cuckoo Search Algorithm...........................64
7.3.2
Self-Adaptive Cuckoo Search Algorithm....................64
7.3.3
Cuckoo Search Clustering Algorithm.........................64
7.3.4
Novel Adaptive Cuckoo Search Algorithm.................65
7.3.5
Cuckoo Search Algorithm Based on
Self-Learning Criteria��65
7.3.6
Discrete Cuckoo Search Algorithm............................65
7.3.7
Differential Evolution and Cuckoo Search Algorithm....66
7.3.8
Cuckoo Inspired Fast Search.......................................66
7.3.9
Cuckoo Search Algorithm Integrated with
Membrane Communication Mechanism��66
7.3.10 Master-Leader-Slave Cuckoo......................................67
7.3.11
Cuckoo Search Algorithm with Wavelet Neural
Network Model��67
7.4
Engineering Applications of Cuckoo Search...........................67
7.5 Conclusion................................................................................69
Section III Application of Heuristic
Techniques Toward Engineering Problems
Chapter 8 Engineering Problem Optimized Using Genetic Algorithm...............73
8.1 Introduction..............................................................................73
8.2
Details of Ultrasonic Machining Process................................ 74
8.3
Details of the Experimentation Process................................... 74
8.4
Development of Empirical Models by Using Response
Surface Methodology��75
8.5
Optimization Using Genetic Algorithm...................................75
8.6 Conclusion................................................................................79
Chapter 9 Engineering Problem Optimized Using Particle Swarm
Optimization Algorithm...................................................................... 81
9.1 Introduction.............................................................................. 81
9.2
EDM Process Details............................................................... 81

viii Contents
9.3 Experimental Details................................................................82
9.4
Response Surface Method for Empirical Models....................83
9.5
Accuracy Check for the Model.................................................84
9.6
Optimization with PSO............................................................84
9.7 Conclusion................................................................................88
Chapter 10 Engineering Problem Optimized Using Ant Colony
Optimization Algorithm......................................................................89
10.1 Introduction..............................................................................89
10.2
Experimentation of the Milling Process..................................90
10.3 Optimization.............................................................................93
10.3.1
Set the Initial Values...................................................93
10.3.2 Selection......................................................................93
10.3.3
Dumping Operation and Pheromone Update
Mechanism��94
10.3.4 Random Search...........................................................94
10.4 Conclusion................................................................................97
Chapter 11 Engineering Problem Optimized Using Bees Algorithm...................99
11.1 Introduction..............................................................................99
11.2
Artificial Bee Colony Algorithm............................................100
11.3
Optimization of the Nd:YAG Laser Beam Machining
Process Using ABC��102
11.4 Conclusion.............................................................................. 105
Chapter 12 Engineering Problem Optimized Using Firefly Algorithm..............107
12.1 Introduction............................................................................107
12.2 Firefly Algorithm....................................................................107
12.3
Application of Firefly Algorithm to Electrochemical
Machining Optimization��109
12.4 Conclusion.............................................................................. 113
Chapter 13 Engineering Problem Optimized Using Cuckoo Search Algorithm..... 115
13.1 Introduction............................................................................ 115
13.2
Cuckoo Search Algorithm...................................................... 116
13.3
Application of Cuckoo Search Algorithm to Abrasive
Water Jet Machining�� 117
13.4 Conclusion.............................................................................. 119
References.............................................................................................................. 121
Index....................................................................................................................... 135

ix
Preface
The authors are pleased to present the book Optimizing Engineering Problems
through Heuristic Techniques under the book series Science, Technology, and
Management. The book title was chosen by looking at the present trend and notic-
ing a book in this area, covering various popular and recent heuristic optimization
techniques and its application to engineering problems to attain optimal solutions,
would come in handy for various academicians, students, researchers, industrialists,
and engineers.
Optimization is finding a solution or an alternative with the most cost effective or
highest achievable performance under the given constraints, by maximizing desired
factors and minimizing undesired ones. Optimization can be used in any field as it
involves in formulating process or products in various forms. It is the “process of
finding the best way of using the existing resources while taking into the account
of all the factors that influences decisions in any experiment.” The final product not
only meets the requirements from an availability standpoint, but also from a practi-
cal mass production criteria.
There are two distinct types of optimization techniques: one traditional
(statistical-
and calculus-based), which is deterministic in nature, and the other heuristic, which
is probabilistic in nature. The former has been in use for quite some time and has
been successfully applied to many engineering problems. The heuristic technique is
comparatively new and is gaining wide popularity due to certain
properties which
the traditional technique lacks. Due to complexity in engineering problems, an appli-
cation engineer cannot afford to rely on a particular method and should know the
advantages and limitations of various techniques, and therefore choose wisely the
most efficient technique for the problem at hand. Heuristic optimization techniques
are generally and presently being primarily utilized for non-engineering problems.
The book has 13 chapters categorized into three parts, namely Section I:
Introduction to Heuristic Optimization Techniques, Section II: Description of
Heuristic Optimization Techniques and Section III: Application of Heuristic
TechniquestowardsEngineeringProblems.SectionIcontainsChapter1,whereas
Section II comprises Two Parts. Part 1 has Chapter 2 and Chapter 3 describ-
ing the two most popular evolutionary techniques, namely Genetic Algorithm and
Particle Swarm Optimization. Part 2, dedicated to Nature-Based Techniques, of
this section has Chapter 4 to Chapter 7 describing four popular techniques, namely
Ant Colony Optimization, Bees Algorithm, Firefly Algorithm and Cuckoo
Search Algorithm, respectively. The last section, Section III, enlists Chapter 8 to
Chapter 13.
Section I, Chapter 1 introduces readers to the concept of heuristics and
presents
an overview of the same. Many real-life problems are modeled and solved for

optimality through classical optimization techniques. One such class of
optimization
techniques is that of Heuristic search. Although heuristics do not guarantee optimal-
ity, they produce concrete results. Heuristics have been widely applied in various
industries, such as business,
statistics,
environment, engineering, and sports.

x Preface
Chapter 2, the first chapter of Section II Part 1, illuminates its readers with the
fundamental concepts, mathematical models, and operators associated with genetic
algorithm (GA). It is, no doubt, one of the most well-known and popular evolution-
ary algorithms. GA mimics the Darwinian theory of survival of the fittest in nature.
The chapter also highlights improvements made in various components of GA, i.e.,
selection, mutation and crossover.
Particle swarm optimization (PSO) is discussed in the next chapter i.e., Chapter 3.
PSO was proposed by Kennedy and Eberhart in 1995 and is a heuristic global

optimization technique and now one of the most commonly employed. The
present
chapter delineates comprehensively an investigation into PSO and the advances
made. The authors think this chapter would be beneficial for researchers involved
directly or indirectly in the field of optimization.
Chapter 4, the first chapter of Section II Part 2, presents a brief overview of the
structure of Ant Colony Optimization (ACO), its variants and the engineering appli-
cations. ACO has received considerable attention and has therefore emerged as one
of the prominent Nature-Based Heuristic Optimization Techniques. ACO solves NP
hard problems inspired by ant foraging behavior i.e., searching for food, the heuris-
tics used by ants and the partial guidance of the other ants in indirect format. In this
chapter, the components and the goals of ACO have also been depicted.
Chapter 5 provides an overview of the Bees Algorithm. The foraging behavior
of honeybees is modeled by the Bees Algorithm and hence solves optimization prob-
lems. Exploitative neighborhood search in combination with the random explorative
search is performed by this algorithm to solve optimization problems. The Bees
Algorithm can be divided into four parts: tuning of parameter, initialization, the local
search process, and at last the global search processes. In the present chapter, various
improvements along with the application of the Bees Algorithm are discussed.
Chapter 6 presents a comprehensive outlook of firefly algorithm. The Firefly
Optimization Algorithm has gained its stature from a so-called swarm intelli-
gence. This algorithm has been applied to a number of domains including the field
of engineering. The Firefly Optimization Algorithm has been able to successfully
solve a variety of problems from different areas. Modified and hybrid
variants of
the Firefly Algorithm have been developed and hence its application scope has
grown exponentially. Biological foundations of the Firefly Algorithm are also dis-
cussed in this chapter. The structure, characteristics and modified variants of firefly
algorithms are discussed. Towards the end of the chapter, engineering
applications
to which firefly algorithms have been applied are discussed.
Chapter 7, the last chapter of Part 2 as well as Section II, provides a brief

overview of the Cuckoo Search Algorithm. Yang and Deb developed this in the year
2009 inspired by bird family. The present chapter also provides various
applications
of the optimization technique. From the chapter, it can be clearly observed that this
algorithm has been used to address a wide range of engineering problems. The
main objective of this chapter is to illuminate the readers with a definition of the
Cuckoo Search Algorithm and also provide an outlook of the application areas it has
addressed so far.
Section III, the section dedicated to solving engineering problems with heuristic
techniques, starts with Chapter 8. The chapter describes the application of genetic

xi
Preface
algorithm to a non-traditional machining process i.e., ultrasonic machining process,
which is one of the most extensively used non-traditional machining processes for
the machining of non-conductive brittle materials such as glasses, carbides and bio-
ceramics. The empirical models required for the optimization process were gener-
ated using the response surface methodology. Genetic algorithm has been applied
to minimize the roughness for a hole surface. For optimizing the process param-
eters, different parameters considered were, namely, power rating, concentration of
abrasive slurry and feed rate of the tool. As both the output parameters i.e., surface
roughness and material removal rate are equally important, this becomes a multi-
objective optimization.
The next chapter, Chapter 9, deals with the optimization problem for the electrical
discharge machining process, another non-traditional machining
technique. Setting
optimal parameters, maximizing the material removal rate and minimizing the
wear of the electrode tool, has been arrived at by employing the Particle Swarm
Optimization technique (PSO). Once again, response surface methodology has
been employed to arrive at the relationship between the inputs and outputs of the
machining process, and the effectiveness of PSO algorithm has been demonstrated
to address the
optimization problem in an engineering domain.
In Chapter 10, the Ant Colony Optimization (ACO) technique has been employed
to deal with the optimization problem in the multi-pass pocket milling process.
Milling has been considered to be one of the oldest material removal processes that
aids in removal of unwanted material through the use of rotating cutting tool. Setting
optimal parameters, considering process parameters like speed of the spindle, depth
of cut and feed rate, minimize surface roughness and machining time. The efficacy
and suitability of the optimization technique have been demonstrated to address the
optimization problem in the domain of a traditional machining process.
Following this trend, Chapter 11 demonstrates the
applicability of the Artificial
Bee Colony Optimization algorithm, in order to determine the optimal combination
of parameters for the Nd:YAG laser beam machining process by considering both
the single- and multi-objective optimization of the responses. Nd:YAG laser beam
machining process is one of the prominent non-conventional machining processes
which has the potential ability to manufacture intricately shaped
micro-products;
however, identification of a suitable combination of parameters in order to achieve
the desired machining performance is the key and the optimization technique
serves it well.
Chapter 12 describes the application of the Firefly Algorithm to find an optimal

solution for the electrochemical machining process. All the non-traditional machin-
ing
processes, including electrochemical process, produce complex parts with great
precision and are therefore time-consuming as well as expensive. Hence, it is nec-
essary to select optimal parameters so that performance parameters such as heat
affected zone (HAZ), radial overcut (ROC), and material removal rate (MRR) can
be optimized. The Firefly Algorithm discussed, in this chapter was revealed to be
robust and better in comparison to the results obtained by previous researchers.
Chapter 13, the final chapter of the book, illustrates the applicability of the
Cuckoo Search Algorithm to predict surface roughness in the case of abrasive water
jet machining. The Cuckoo Search Algorithm is one of the newest nature-based

xii Preface
algorithms. Various models of prediction have been developed with different
initial
eggs, and analysis was carried out to investigate the best predicted value for
surface
roughness. The validity of the results has been established by employing the t-test,
which ascertains applicability of the Cuckoo Algorithm for improving the perfor-
mance of abrasive water jet machining. The results have revealed that the Cuckoo
Algorithm is capable of optimizing process parameters that produce improved

surface finish of the abrasive water jet machining process.
First and foremost we would like to thank God for allowing us to pursue our
dreams. Almighty, without your support and blessings this work could not have been
done. We would like to thank our ancestors, parents, and relatives for allowing us to
follow our ambitions. Our families showed patience and tolerance while we took on
yet another challenge that decreased the amount of time we get to spend together.
They are our inspiration and motivation. We will be pleased if the readers of this
book benefit from our efforts.
We would also need to thank all our well-wishers, colleagues, and friends. Their
involvement in the development of this book cannot be overstated.
We owe a huge thanks to all of our technical reviewers and editorial advisory
board members, our book development editor, and the team at CRC Press, for their
work on this huge project. All of their efforts helped create this book. We couldn’t
have done it without their constant coordination and support.
Last, but definitely not least, we would like to thank everyone who took the time
to help us during the process of writing this book.
Kaushik Kumar
Divya Zindani
J. Paulo Davim

xiii
Authors
Kaushik Kumar,
B.Tech (Mechanical Engineering, REC (Now NIT), Warangal),
MBA (Marketing, IGNOU) and Ph.D. (Engineering, Jadavpur University), is pres-
ently an Associate Professor in the Department of Mechanical Engineering, Birla
Institute of Technology, Mesra, Ranchi, India. He has 18years of teaching research
experience and over 11years of industrial experience in a manufacturing unit of
global repute. His areas of teaching and research interest are Conventional and
Non-Conventional Quality Management Systems, Optimization, Non-Conventional
machining, CAD/CAM, Rapid Prototyping and Composites. He has 9 Patents, 28
Books, 19 Edited Book Volumes, 43 Book Chapters, 141 International Journal, 21
International and 8 National Conference publications to his credit. He is Editor-in-
Chief, Series Editor, Guest Editor, Editor, Editorial Board Member and Reviewer for
International and National Journals. He has been felicitated with many awards and
honors.
Divya Zindani,
(B.E., Mechanical Engineering, Rajasthan Technical University,
Kota), M.E. (Design of Mechanical Equipment, BIT Mesra), presently pursuing Ph.D.
(National Institute of Technology, Silchar). He has over 2years of industrial experi-
ence. His areas of interests are Optimization, Product and Process Design, CAD/
CAM/CAE, Rapid prototyping and Material Selection. He has 1 Patent, 4 Books,
6 Edited Books, 18 Book Chapters, 2 SCI Journal, 7 Scopus Indexed International
Journal and 4 International Conference publications to his credit.
J. Paulo Davim
received his Ph.D. degree in Mechanical Engineering in 1997,
M.Sc. degree in Mechanical Engineering (materials and manufacturing processes)
in 1991, Mechanical Engineering degree (5years) in 1986, from the University of
Porto (FEUP), the Aggregate title (Full Habilitation) from the University of Coimbra
in 2005 and the D.Sc. from London Metropolitan University in 2013. He is Senior
Chartered Engineer by the Portuguese Institution of Engineers with an MBA and
Specialist title in Engineering and Industrial Management. He is also Eur Ing by
FEANI-Brussels and Fellow (FIET) by IET-London. Currently, he is Professor at the
Department of Mechanical Engineering of the University of Aveiro, Portugal. He has
more than 30years of teaching and research experience in Manufacturing, Materials,
Mechanical and Industrial Engineering, with special emphasis in Machining
Tribology. He has also interest in Management, Engineering Education and Higher
Education for Sustainability. He has guided large numbers of postdoc, Ph.D. and
master’s students as well as has coordinated and participated in several financed
research projects. He has received several scientific awards. He has worked as evalu-
ator of projects for ERC European Research Council and other international research
agencies as well as examiner of Ph.D. thesis for many universities in different
countries. He is the Editor-in-Chief of several international journals, Guest Editor
of journals, Books Editor, Book Series Editor and Scientific Advisory for many

xiv Authors
international journals and conferences. Presently, he is an Editorial Board member
of 30 international journals and acts as reviewer for more than 100 prestigious Web
of Science journals. In addition, he has also published as editor (and
co-editor) more
than 100 books and as author (and co-author) more than 10 books, 80 book chapters
and 400 articles in journals and conferences (more than 250 articles in journals
indexed in Web of Science core collection/h-index 52+/9000+ citations, SCOPUS/
h-index 57+/11000+ citations, Google Scholar/h-index 74+/18000+).

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that you have in your hand?
It is a new collar and dog-chain, Walter explained. It suddenly
occurred to Venables just now that we had seen nothing of Bruno all
day. I have been whistling for him for half an hour, and though I am
almost certain he is hiding somewhere in the bracken on the
common, I can't get him to answer the call.
Probably afraid of a good thrashing for his work last night,
Ravenspur murmured. But you must manage to get hold of him,
Walter. It will never do for a big hound like that to be roaming about
the common. Those dogs are all right when they are well fed. But if
the beast gets really hungry I wouldn't answer for the
consequences. Whatever else happens, or whatever is neglected,
you must find Bruno, and that at once.
Walter and Venables went off in the direction of the common, and
for the next couple of hours sought everywhere for the dog. It
seemed to them they could hear him every now and then. Presently
Venables caught sight of his lean, dark-brown side as he crouched
behind a great thicket of gorse. Walter called softly, and held a
biscuit out in the direction of the bush. Then slowly, with his body
bent to the ground and his head hung down, the great beast came,
and Walter slipped the collar round his neck. He had hardly
congratulated himself upon his success when a hollow groan close
by attracted his attention. He turned eagerly to Venables. Oh, yes, I
heard it, the latter said with a smile. Can't you guess who it is? I
declare I had absolutely forgotten all about him. Unless I am greatly
mistaken, that is our friend Stevens whom Perks tied up so neatly
and artistically last night.

It was precisely as Venables had said. Stevens lay there groaning
and shivering, quite helpless and almost unable to move. Even after
his bonds were cut away it was some time before he had strength to
rise. His teeth were chattering with the cold, although the day was
quite a warm one. He was a mass of cramps and aches from head to
feet. When once his blood began to stir again, he turned an angry
face in the direction of his rescuers.
Oh, you need not laugh, he said. It is no laughing matter. I'll have
the law against you for this, see if I don't.
We will talk about that presently, said Venables coolly. In the
meantime, you had better come as far as the house and have
something to eat. And you will be wise if you say nothing, or know
nothing, of what happened last night. Your accomplice, Silva, lies in
bed at the point of death, so you have nothing to fear from him. If
you had gone straight with us, you would not have fallen into this
sorry plight. Have you got any money?
I spent it all in coming down last night, Stevens said.
Oh, well, we'll see you back to town again, Walter replied.
Meanwhile, we have other work to do. We will take you to the
house and see that you are properly fed, and then you can kill time
as best you can for the evening. You can return by the last train.
It was dark before Stevens reached the station with the few shillings
in his pocket necessary to get him back to London again. As he
stepped into a third-class carriage he did not realise that Walter and
Venables were taking their places at the end of the train. It was just
the same at Waterloo Station, where Stevens got out, and a moment
later he was being followed by the pair, who had been joined now by
Dallas.
What is the game, gentlemen? the Inspector asked. Surely that
man is the witness Stevens who gave such startling evidence at the
Delahay inquest?

That is right enough, Walter said. We are going to follow him and
see where he goes to. Unless I am greatly mistaken, he can give you
a great deal more information than he did at the inquest. And now,
perhaps, I had better tell you of the discovery which Lord Ravenspur
made last night. But, before doing that, I want to know if you
missed anything from Mr. Delahay's studio. For instance, did you find
a watch on the body?
There was no watch, Dallas said, after a moment's thought. We
found a purse in his trousers pocket with some gold in it, but
nothing besides. Was he wearing a watch?
I am sure if you ask Mrs. Delahay she will tell you so, Walter
replied. He was wearing a watch and chain, and on the chain was
an ornament which my uncle had given him. My uncle bought that
ornament yesterday from a man who is obviously a receiver of
stolen goods, and that ornament was sold to the shady individual in
question by John Stevens. In proof of what I say, here it is.
Dallas' eyes gleamed as he took the trinket in his hand. He said no
more as he walked thoughtfully by the side of his companions, till at
length Stevens turned into a shady street, where he entered a dingy
public-house. Without the slightest hesitation Dallas followed. He
had quite made up his mind what he was going to do. For the time
being, at any rate, the public-house was empty. Stevens was sitting
in an armchair behind a partition with a glass in his hand. He started
and his face changed colour as his eyes fell upon Dallas. The
Inspector's manner was genial enough, but there was a grimness on
his face that Stevens did not relish.
What can I do for you, gentlemen? he stammered.
Well, unless I am greatly mistaken, you can do a great deal, Dallas
replied. That matter of the Delahay murder, you know. You
remember what you told us at the inquest?

Yes, and every word of it was true, Stevens said tremulously. If it
is the last word I ever say, it was true.
And I believe it, Dallas went on. The only fault I find in your
evidence is that you did not tell us enough. Why didn't you finish
your story while you were about it?
Stevens looked stealthily at his tormentor. He gulped his glass of
liquor down hastily, for there was a queer dryness at the back of his
throat that almost choked him.
Come, Dallas said, with a quick and sudden sternness. Speak out,
or it will be all the worse for you. Tell us who it was who murdered
Mr. Louis Delahay?
CHAPTER XLIII.
THE WHOLE TRUTH.
Stevens stared helplessly at the speaker. He tried to speak, but his
jaw dropped. He mumbled something that was quite impossible to
understand. But, at the same time, he recognised the peril of his
position. There was a ghastly green tinge on his face, his hand
trembled. Dallas regarded him pleasantly enough. There was nothing
harsh or stern in the detective's manner. His quiet air of assured
triumph struck a greater terror into Stevens than any sternness
would have done. The shabby little man wriggled about in his seat
looking very much like a rat behind the bars of a cage.

Take your time, Dallas said quietly. You will find in the long run
that it will pay you a great deal better to tell the truth.
I have always told the truth, Stevens stammered.
Up to a certain point, yes. But you didn't go far enough. For
instance, you might have told the coroner that you saw Mr.
Delahay's lady visitor a second time. You might have gone further,
and told the court that Mr. Delahay had other visitors long after his
first one had gone. You see, that would have helped the police a
good deal, and it would have effectually cleared an innocent lady
whom we suspected of having a hand in the murder. Now who was
it that called at the studio in the early hours of the morning?
How should I know? Stevens said sullenly.
That, my good man, is for you to say. But you need not answer
unless you like. It so happens that you are waiting here for the
individual in question this very moment.
The greenish hue crept over Stevens' face again. He could only stare
at the speaker with open-mouthed astonishment. Dallas' manner
grew a little more stern and curt as he rose from his seat.
You will stay where you are, he said, and with these two
gentlemen I will go into the next box. I think I can trust you not to
betray our presence there. In fact, your safety, to a large extent,
depends upon your actions in the next hour or so.
I have done nothing, Stevens burst out. I swear I have done
nothing. I had no hand in it at all.
That I quite believe, Dallas replied. It was afterwards that you
began to see your way to make some money out of it. And now let
me tell you something. You don't deserve any consideration at my
hands, but I am prepared to spare you as far as possible. Oh, I
know you will play me false at the first chance. But let me tell you, I

know all about your visit to your friend, Perks, of Cannon Green. I
know how you disposed of certain stolen goods which, until the
night of the murder, were in the possession of Mr. Louis Delahay.
After that, I don't think you will deem it prudent to try any of your
nonsense with me.
Dallas turned away, and, with his two companions, entered the next
box. It was gloomy enough there, so that their presence was not
likely to be detected by anyone who came in. Walter turned eagerly
to Dallas. His curiosity was aroused now. He wanted to know how it
was that the inspector knew so much.
It was mere conjecture on my part, Dallas said. Of course, what
you told me gave me a great deal of assistance; but I did not begin
to see my way quite clearly until we followed Stevens here. The
landlord of this public-house has never got into trouble as yet. But
we know perfectly well that a good deal of stolen property is
disposed of, and when I saw Stevens turn in here, things became
plain enough. He was coming to meet his accomplice, and hand over
his share of the money which he had obtained from Perks. Before
half an hour is over, the real culprit will be here. Please stop talking
directly anybody comes in. It will spoil everything if our presence
here becomes known.
It was precisely as Dallas had said. Some twenty minutes later a
man lounged into the bar and called for something to drink. He
seemed to suspect nothing, he appeared to be perfectly at his ease.
He whistled some music-hall air merrily. The man was fairly well-
dressed. A gaudy cap on the back of his head disclosed a plaster of
greasy curls on a peculiarly low and retreating forehead. The
stranger might have been a street hawker in his best clothes.
Certainly he did not suggest a professional criminal.
He swallowed his drink and strolled towards the fireplace without
noticing the three occupants in the recesses of the box. Then he
caught sight of Stevens, and took a seat by his side. The

conversation was conducted in whispers, but it was possible for the
listeners to hear most of what was taking place.
Well, did you manage it all right? the newcomer asked.
Don't trouble about that, Stevens muttered. But I didn't get half
as much as you thought I should. Forty pounds was the price my
man offered, and he wouldn't give another penny.
The newcomer growled something incoherent. Then there was a
chink of money stealthily passed, followed by a volley of oaths from
Stevens' companion.
The game isn't worth playing, he muttered. Fancy, twenty quid for
a job like that, and the chance of hanging into the bargain. I wish I
had never gone there, John. I wish I had never met you that night,
when you told me all about the house in Fitzjohn Square. I wake up
in the night in a bath of cold sweat when I think of it. Fancy going
into what you take to be an empty house, and finding a dead body
staring up in your face from the floor! Yes, I took his watch and
chain all right, but I don't know where I got the pluck from. Took the
risk of being strung up for it, bli'me! And me ready to get married,
and the date fixed and all! Lord, if I could only see my way to get
clear of it all! Twenty quid against a man's life! You go and try it
yourself, and see what it's like, my ancient pal. When I recollect as it
was you as told me of the broken catch on the studio window, I
could bash your face in, I could. I can't forget it. I have tried drink,
but that is no use. You can stave it off for an hour or two, and then
it comes back worse than ever. And all for the sake of twenty quid!
Stevens made no reply. He sat there quivering from head to foot,
sick with suspense and anxiety, wondering in his mind when Dallas
was going to strike. At any other time the ghastly colour of his face
would have attracted the attention of his companion, but the other
man was occupied with his own thoughts. He was staring moodily
into the fireplace.

Don't talk about it, Stevens managed to say at length. If you had
told me about it at the time, I never should have touched that stuff.
But I had got it in my pocket, and I had given my word before ever I
had heard of the murder. And how was I to know that there was a
chance of Mr. Delahay coming back? If anything happens you will
say as much for me, won't you?
Stevens asked the question with trembling eagerness. He made his
request more with a view to impressing Dallas than anything else.
But the culprit by his side, apparently, had no idea of the drift of the
question, or why it was asked.
Oh, you have nothing to fear, he said moodily. At least, it is all
right as long as that stuff isn't traced. But what is the use of sitting
here jawing like this? Let us go to a music-hall or theatre or
something of that kind--anything to get away from one's thoughts.
Every now and again----
The speaker rose to his feet, and Stevens dragged his trembling
limbs from the settee. At the same moment, Dallas appeared upon
the scene and touched the stranger lightly on the shoulder.
I hope you know who I am, he said.
The other man heaved a sigh, which sounded almost like relief. Just
for a moment all the blood left his face. Then he recovered himself
and looked at Dallas steadily.
Dallas, of Scotland Yard, he said. Oh, I know you well enough, sir,
and I expect you know me.
Name of Cooney, Dallas said briskly. Jim Cooney. I arrest you for
burglary at the residence of Mr. Louis Delahay, in Fitzjohn Square.
Yes, that's right enough, Cooney said. I am not going to complain.
Upon my word, I am glad it is over. If you just let me have a
cigarette and another drink I'll tell you all about it; and a nice sort of

pal you are, Stevens. Oh, I'd give something to have you for five
minutes to myself. You sneaking rat!
I couldn't help myself, Stevens whined. Upon my word, I couldn't.
Besides, what does it matter? Inspector Dallas knows all about it. He
even knew you were coming here tonight, though I swear he never
had a single hint from me. Isn't that so, Inspector? Am I telling the
truth, or am I a liar?
It is perfectly true, Cooney, Dallas explained. I followed Stevens
here, knowing quite well that he was waiting for you.
The assurance seemed to be sufficient, for Cooney asked no further
questions. Nor was it for Dallas to explain that, till a few moments
ago, he had no idea of the real identity of the man whom Stevens
had come to meet. Cooney took a long whiff of his cigarette and
pitched the end of it into the fireplace.
I am quite ready for you now, he said, and I'll tell you all about it
if you like. Oh, I know everything I say will be taken down in
evidence against me; but it is little I mind that. I plundered the dead
body of Mr. Delahay, all right. He was dead when I got there, and if I
didn't tell you so, you overheard enough to jug me half a dozen
times. Don't look at me like that Mr. Dallas, sir. Don't think as I had
any hand in the murder, sir. May I die if I ain't as innocent of that as
a kid.
Better not say too much, Dallas suggested. Really, I am not
curious to hear. And now, come along. You can have a cab if you
like. Perhaps you may come out of this better than you expect--if
you are only candid.
Don't be in a hurry, Cooney pleaded. I'll tell you everything, sir, I
will--straight--everything from start to finish. Sit down and listen to
me; and you need not be afraid that I shall try and escape. I don't
want to.

CHAPTER XLIV.
THE STORY OF A CRIME.
Dallas shrugged his shoulders indifferently. Truth to tell he was both
annoyed and disappointed. He had looked forward with every
assurance to laying his hand on the actual culprit in the person of
Cooney. As it was now, the whole thing looked like beginning all over
again. A suspicion of the real truth was dawning on his mind. It was
like this, Cooney said, in a harsh, strained voice. I have been
pretty short of a job for some time, and I promised to pay for a lot
of furniture I bought for my house by a given time. I had the stuff
on the hire-purchase system, and I knew precious well what would
happen if I did not keep the instalments up. I had only a day or two
to spare, and I was getting pretty anxious. That same evening I met
Stevens in a public house. I hadn't seen him for some time, and,
naturally enough, I asked him what he had been doing. Then he told
me that on behalf of a party, whose name he didn't mention, he had
been shadowing a certain house in Fitzjohn Square. I wasn't
particularly interested until he let out that he could tell me a good
deal about the houses there, and how some of them would be easy
work for the likes of a chap such as me, for instance. Then I asks a
few questions, and hears all about Mr. Delahay's studio. Thinks I to
myself, here's a bit of luck for you, Jim Cooney. I had all the
information I wanted. The next night I goes round and has a look at
the studio. The thing was as easy as eating your dinner. I waited till
it got pretty late, and then I got into the house from the back. When
I did get there, I was rather alarmed to see a light in the studio. I

crept along to the door, and looked in. You can imagine my surprise
when I saw a gentleman painting there. When I looked at him again
I had no difficulty in recognising Lord Ravenspur.
What he was doing there, I don't know. But seeing it wasn't his
own house, I reckoned he wasn't likely to stay long, so I just sat
down to wait patiently for such a time as I could have the place to
myself. It wasn't more than an hour before I heard the door open,
and two other people came in. They were a lady and a gentleman,
but who the lady was I don't know from Adam. The gentleman, as
you will guess, was Mr. Delahay himself. I suppose the lady was
really Mrs. Delahay, too; I mean, the woman who is suspected of the
murder. But I am getting a bit away from the point. I had hardly
time to hide myself behind a recess with a curtain in front of it
before the newcomers came into the hall and began to talk. They
were conversing more or less in whispers, so that I could not follow
very well, but I could see that they were annoyed to find Lord
Ravenspur there, and they were casting about for some means of
getting rid of him. Presently the lady said something about the light
and the cable, and the gentleman seemed to fall in with her
suggestion. Anyway, I saw him take a knife from his pocket, and go
down into the basement. A moment later the whole place was
plunged in darkness----
You mean that the cable was cut? Dallas asked. Well, I am glad
that mystery is cleared up. I am bound to tell you, gentlemen, that
that cut cable has caused me no end of trouble. It started me on a
dozen, more or less impossible, theories. I see exactly what
happened now. Mr. Delahay and his companion doubtless thought
that if they cut off the light, they would get rid of Lord Ravenspur.
That is exactly what they did, Cooney resumed. I heard his
lordship fussing about, and trying the electric switches, but he gave
it up as a bad job, and after a bit left the house. Mr. Delahay
appeared presently from somewhere, with a lamp, which he carried
into the studio, and the lady followed him. I was close enough at

hand to see what took place. The lady had come, evidently for some
valuable jewelry, for Mr. Delahay produced a case from a safe, and
handed it over to her. My word, but those stones did sparkle! It
seemed to me that I was in luck that night. My game obviously was
to take no further heed of the studio, but to follow the lady as soon
as she left the house. It was nearly two o'clock in the morning, and
there wasn't a soul about. In my mind's eye I saw those stones
already in my pocket. But, unfortunately for me, Mr. Delahay walked
with his visitor as far as the front gate, and stood looking up the
road until the lady was safe in a hansom. It was as much as I could
do to get back to the house again without being discovered, but I
managed it all right. There were several valuable articles I had
marked down, and directly Mr. Delahay was back in the studio I
began to gather them together. I dropped one trinket, which tinkled
on the floor, and my heart was in my mouth. I thought that the
sound didn't reach the ears of Mr. Delahay. But I was mistaken. A
minute or two later I heard him coming, and I bolted through the
window into the garden. I waited there perhaps for an hour before it
seemed safe for me to go back, and then I went. I turned on the
light. . . . My heart was fair in my mouth. Then I looked down at the
floor. There lay Mr. Delahay as dead as a rabbit. I believe I howled
for a moment, I was taken to! But there he lay, and there was his
watch-chain a-shining in the light, and then it comes into my head
that, if I'd got pluck enough, here was a way to pay for them sticks
of furniture of mine. It was hard work, but I managed to screw
myself up to it at last. After all said and done, I'd only come here to
take what I could get, and it wasn't me that knifed the poor
gentleman. Besides, he might have died a natural death for all I
knew. There was no sign of blood about, and nothing that suggested
violence. All the same, I couldn't go through it again if you offered
me ten thousand of the best.
Cooney paused and shuddered. Great beads of perspiration poured
down his face. Then he resumed once more.

Well, he was dead, and there was an end of it. Just for the moment
I wasn't thinking about much besides my little happy home. I
pocketed all the valuables I could lay my hands upon, and carried
them away. You may say that that was a mad thing to do, but after I
saw Mr. Delahay lying dead at my feet, it seemed to me as if he
wasn't likely to miss 'em. Oh, I know as I stand in what the papers
call a serious position. But that's the gospel truth, and I can't tell you
any more. It seems to me I have said enough. And now, if you will
call a cab, sir, I am ready for you.
A cab was called, and Dallas drove off in the direction of Bow Street
with his prisoner. He stopped just a moment to exchange a few
words with Lance and Venables.
There is no reason why Mrs. Delahay should not know this just
yet? Walter asked. You may be sure that she feels her position
keenly. Would there be any objection to getting her to accompany us
as far as Cannon Green tonight? You will understand why.
None at all, Dallas said. I'll send a message to the man who is
watching outside the Grand Hotel, and let him know that his
presence there is needed no longer. All the same, we have still got to
find the culprit. It isn't Cooney. He told us the truth, I'm certain. The
culprit is at Cannon Green! What a fool I've been!
Mrs. Delahay received her visitors in a dull, apathetic way, which had
never left her since the night of the tragedy. But her face cleared,
and her manner became more soft and gentle as she listened to the
story which Walter had to tell. She dropped into a chair, and for
some moments the tears ran unrestrainedly down her cheeks. She
wiped her eyes presently. There was something like a smile on her
lips as she turned to Walter.
I believe those tears saved my reason, she said. I have not been
able to cry. I have not been able to feel the last few days. The death
of my husband was bad enough. The knowledge that I was

suspected of his murder was worse, but the feeling that my own
sister possibly had a hand in the tragedy was worse than all the rest.
There are one or two matters to be explained yet, but the great
truth is growing plain, and I feel like a living being once more. Oh,
yes; I will come down to Cannon Green with you; I am looking
forward to it with something like pleasure. I know that when I have
seen my sister everything will be cleared up.
It was a different woman who came down from her room half an
hour later, ready for the journey. She looked sad and pathetic
enough in her deep mourning. The trouble still brooded in her eyes,
but the look of stony despair was no longer there. They came at
length to the house on the common. The windows were lighted up,
the hall looked comfortable and cheery.
In the drawing-room were the Countess Flavio and Vera. They rose
as Mrs. Delahay entered.
I have brought your sister, Walter explained briefly. She has much
to say to you. Perhaps I had better leave you alone.
CHAPTER XLV.
COUNT FLAVIO'S DIARY.
It was getting exceedingly late now, but the two sisters Descarti,
together with Vera, were still in the drawing-room. Nobody cared to
disturb them. It was felt that they would have much to say to one
another. And no doubt, all they had to tell would be disclosed when

the proper time came. Valdo had not recovered consciousness again.
He lay there overhead, with a vigilant-eyed nurse watching him.
Venables had not come down with Mrs. Delahay and Walter. He had
excused himself on the plea of business, and on the understanding
that he would visit Cannon Green the following day. In the dining-
room for the last hour or two Walter had been seated, deeply
engrossed in the slim, parchment-covered volume which had been
sent him by Countess Flavio at the urgent request of her dying
servant.
Time was going on, and still Walter did not look up from the book. It
was long past two before he finished. Then with a firm step and a
determined air he went up to the little library where Lord Ravenspur
was busy writing letters. The latter looked up, and demanded to
know what his nephew wanted.
I want you to look at this, Walter said quietly. It is a diary written
by your late friend Count Flavio, whose handwriting you will, of
course, recognise. The diary came into the hands of Silva after his
master's death. Now Silva told me some time ago--in fact, during
that memorable interview in your studio--that he had in his
possession documentary evidence which would prove that his
mistress was an injured woman, and his master a scoundrel of the
deepest dye. When I asked him why he did not produce this book at
the trial, he shrugged his shoulders, and said that it would have
been useless. Public opinion against the Countess ran so high that
nobody would have believed that it was anything but a forgery. But
that will be for you to judge. Before we go any further, I want your
assurance that this is your dead friend's own handwriting.
Lord Ravenspur turned over the leaves of the manuscript, more or
less languidly. One leaf after another he fluttered over; then he
handed the book back to Walter again.
I am not going to contest the point, he said. Beyond question,
this is my unfortunate friend's handwriting; though the letters are

quite plain, the writing could not be easily forged. Indeed, to forge
such an amount as that would be the work of half a lifetime. But
what do you want me to do?
Walter signified that he would like his uncle to read the whole of the
volume, but Lord Ravenspur shook his head.
I am afraid I cannot, he said. I can speak Italian fairly enough, as
you know, but that is merely colloquial, and I had never time really
to master the language. But, seeing that you spent three years of
your life there, don't you think that you had better read it out to me.
I suppose it is interesting?
I never read anything that fascinated me more, Walter said. Mind
you, this is the secret diary of Count Flavio. He had no idea that
anybody would ever read it. I have gone through the volume from
start to finish, and I am forced to the conclusion that your friend was
the poisonous scoundrel that Silva declares him to be. I tell you, if
this book was published, it would cause a great sensation from one
end of Europe to the other. It is the work of a brilliant man with a
fine style and an imaginative mind--the history of an attempt to
deprive a woman of her will, and of her reason. For the three years
during which the Count and Countess Flavio lived together the
woman's life was one long, incessant torture. Mind you, there was
no actual violence, but the tortures were exquisite and cruel all the
same. And here we have them in the Count's own words. It is
absolutely necessary that you should listen to some extracts from
this amazing work.
Go on, Ravenspur said quietly; I am all attention.
Walter bent back the book, and began to read:
February 17th, 1887. What man is there who has ever succeeded in
penetrating the unfathomable depths of a woman's mind? What

fools we men are to assume a knowledge of the sex until we are
married, and have the object lesson before us day by day! There is
Carlotta, for example. Carlotta's prevailing trouble is that she is
jealous of me. She seems to think that because she cut herself off
from her family for my sake, I am to be at her beck and call
henceforth and for ever. This peculiar form of jealousy interests and
amuses me. It is a pleasure to study it from a scientific basis. This
morning I told her I was going to Florence for a day or two, and she
wept because I would not allow her to accompany me. I could see
that she does not trust me, wherefore I caused a friend of mine who
can imitate a woman's writing excellently, to write me a passionate
love-letter, which fell quite naturally into Carlotta's hands.
The scene which followed was exquisitely amusing. I have never
seen a woman weep to such an extent before. Positively my
charming Carlotta was enchanting. I was quite sorry at length when
she assumed a mantle of dignity, and left me. Still, this is only the
first of many such scenes if I engineered them properly. I see that
Carlotta is in possession of all the emotions, so that, by studying her
alone, I shall be in a position to add some really extraordinary
chapters to my great book on women and their ways.
March 19th, 1887. Carlotta has afforded me a month of absolute
enjoyment. Why do people pay money to sit in stuffy theatres and
watch comedies and tragedies when they can see and hear the real,
palpitating thing for nothing? Outwardly, Carlotta and myself are at
daggers drawn. She thinks I am unrepentant and angry, but, as to
myself, I have never been more cheerful and happy in my life. And
when Carlotta threatens to leave me, I ask her why she is going,
knowing perfectly well that she has not the slightest intention of
leaving me. Women are very much like cats in these matters--they
will make many sacrifices for the sake of the domestic hearth. I was
talking to Dr. Sacci, the great surgeon, the other day, and he was
telling me of the fierce joy that comes through some new discovery
which has been the outcome of vivisection. But, then, Sacci is only
working in the interests of humanity, whereas my vivisection allows

me to see the exquisite suffering of the patient. I can study the
nerves, and the palpitating wound, at the very moment when the
knife enters.
December 21st, 1887. The last chapter in my book is by far the
most brilliant and searching which I have yet added to that
fascinating volume. Whatever Carlotta suffers in the present, she
shall go down to posterity as the martyr of her sex. I will place her
on a pinnacle as high as my own. Indeed, I was almost sorry when I
had to tell her the story of the love-letter, and how I had been
playing on her feelings all these months. At the same time, I looked
forward to the explanation, because I knew that it would open up to
me a fresh phase of womanly nature. And I confess that it did with a
vengeance. Carlotta turned pale. She stood there looking as if she
were filled with the greatest physical agony, her eyes filled with tears
which did not fall. I don't know how many days it is since she spoke
to me last, but certainly it must be upwards of a fortnight. This is
not exactly what I expected. It is only when a woman talks that one
can judge of how the experiment is progressing. Tomorrow, all being
well, I am going to adopt a new scheme which I hope will have the
desired effect.
December 22nd, 1887. Our little Vera has disappeared. Evidently
she has been kidnapped with a view to a reward. The whole
neighbourhood is up in arms, and my wife is distracted. It has often
been a favourite theory of mine that every man takes a second place
in a woman's affections as soon as her first child is born. I look back
now with a vivid recollection of the early days when I first met
Carlotta. I look back to her passionate love scenes, and her
declarations that I should be first with her, then and always. Even
though I was very much enamoured, I had my doubts when I was
alone, and in a position to debate the matter clearly. The time has
come to put the question to a test, and thus it became necessary for
Vera to disappear. I might say at once that my theory has been
vindicated to the letter. I now know that Carlotta cares far more for
Vera than she does for me. The reflection is not soothing to one's

vanity, but there it is. There is a wildness and intensity in her grief,
which she never would have experienced had I been brought home
to her in the last stage of dissolution. I must keep this up. I must
work this phase as long as it lasts, which will not be an indefinite
time, because I must not drive my patient too far. She begins to
show signs of collapse already. I think at the end of a week I must
have Vera brought back again. By the expiration of that time, I fancy
I can add another chapter to my remarkable book.
Walter stopped for a moment, his voice was full of loathing and
disgust. An honest indignation almost choked him. He saw now that
his anger and contempt were reflected on the face of Ravenspur.
Do you want me to read any further, he said, or is that sufficient?
Shall I tell you, for instance, what happened after this inhuman
wretch brought his child home again? Shall I tell you of other
tortures and tyrannies, and how this scoundrel rejoices in the fact
that his neighbours like him and pity him because he is married to a
bad-tempered woman, who makes his life a burden? That is the note
that runs all through this extraordinary diary. The man uses it as a
weapon to play upon the feelings of his wife. If you are not yet
satisfied I will pick out----
No, no, Ravenspur cried, as he rose to his feet. I have heard
enough and more than enough. Flavio must have been a madman;
and yet I regarded him as one of the best and noblest of men. I
never dreamt he had an enemy. I never knew anybody say a word
against him. And to think that a man of the world like myself should
be deceived in this way! Everything is now growing wonderfully clear
before my eyes, Walter. I can even understand why the Countess left
her daughter behind her. Fancy suffering all that trouble and
humiliation to find, later on, that the child you had done so much for
was likely to turn out as her father had done! In the last ten minutes
you have proved that I was wrong, and the Countess was right; and

yet it seemed to me that I was justified in my actions. I don't know
what I am going to do. I don't know what steps I can take to
convince that unhappy woman that I acted for the best. At any rate,
I must make a beginning before I go to bed tonight.
Ravenspur took up the volume and went down the stairs. In the
drawing-room, the Countess, Mrs. Delahay, and Vera were still
seated, talking earnestly together. Ravenspur crossed the room to
the Countess's side and held out the book.
Do you know what this contains? he asked. I suppose you have
read it from cover to cover?
Once, said the Countess, with a shudder, but never again.
I can quite understand your feelings, Ravenspur said. I have only
heard extracts, but they have been quite sufficient for me. And now
let me do my best to try and convince you that I acted in what I
conceived to be the true interests of your child. I know now how
wrong I was. I know that you have been made the victim of a
scoundrel and a madman; and if you can forgive me for what I have
done, I will be your grateful servant in the future.
One moment, the Countess said. There is another, and yet more
painful thing to confess. I understand from your nephew that the
police think that they have a most important clue to the murder of
Louis Delahay. The police are all wrong. It is incredible to me that
they have not discovered the truth before; that they have not
blundered on it. Surely you can guess who it is who is responsible
for the death of my poor sister's husband?
I am afraid, Ravenspur murmured, that I cannot----
Not even after it was known that you were at work in the studio
that night?
No, unless, perhaps--good heavens, you don't mean to say Silva?

Nobody else. The man tracked you to Fitzjohn Square. There was
not one of your movements that he did not know. But come this
way. I dare say the nurse will not mind us talking to the patient for a
few moments alone. You shall hear Silva confirm what I have said to
you.
Ravenspur stumbled to his feet. He was dazed and numbed with
surprise; and yet the more he came to think of it, the more plausible
it seemed. No, the nurse had no objection, it would not harm the
patient. He was very near to his end now. Weak as he was, his eyes
gleamed as he caught sight of Lord Ravenspur, the old wolfish look
was on his face.
We have been mistaken, my dear Silva, the Countess said. Lord
Ravenspur has been one of my best friends if I had only known it.
He was deceived by my husband, as hundreds of others were. His
lordship was led to believe that the Count was a martyr to a dreadful
wife, a woman incapable of looking after a child. The kidnapping of
my daughter was part of his vengeance upon me, so that he could
reach me from the other side of the grave. Everything has been
explained, the diary has been read by Lord Ravenspur; and he has
forgiven you, he has come to your bedside to say so before you--
you----
Die, Silva said, with an effort. Curse his forgiveness. If I could
stand up now----
He could say no more, the malignant hate, the fire of madness, still
gleamed in his dark eyes. He would hold the same tradition to the
end. There was no chance of anything like a reconciliation here.
I expected nothing else, the Countess said sadly. Only a Corsican
could understand his feelings. It is his blood, his religion. But if you
can't forgive, my poor Silva, you can confess. It may be the means
of saving an innocent life. It was you who were responsible for the
death of Mr. Delahay?

Silva nodded quite coolly. There was an upward heave of his
shoulders that was very expressive. It was like one who confesses to
a mistake.
I understand, the Countess resumed. It was a misunderstanding.
You had traced Lord Ravenspur to the studio. You were going to kill
him there. Only Mr. Delahay and myself interrupted you. You were
probably hiding somewhere outside, waiting for your opportunity,
when we arrived. You did not see us, you were not aware of
anything till the lights were out. I may make errors in details, but in
the main I am quite correct. No, don't try and talk--a nod is
sufficient. When Mr. Delahay returned to the studio, after Lord
Ravenspur was driven away, and after I had gone, you were in the
studio. You mistook Mr. Delahay for Lord Ravenspur, and killed him
with a glass Corsican dagger. You did not know till you saw the
papers the next day that you had made a mistake?
Silva nodded again. He did not appear to feel the least remorse, but
his hungry eyes testified how he regretted that he had so signally
failed. The old wild spirit was still there, even the approach of death
could not quench it. Ravenspur turned away, filled with disgust and
sadness.
Really, there is nothing more to be said, he murmured. I should
like to put the heads of the confession down and get the unhappy
man to sign it.
Silva affixed a straggling signature to the confession. Then he turned
over on his side and refused to listen any more. Evidently he was
going to die as he had lived--hard, unfeeling, carrying his bitter
hatred to the grave.
According to his lights, Ravenspur murmured, let us hope that he
will not be judged too harshly where he is going so soon.

CHAPTER XLVI.
A WOMAN'S HEART.
The hard, cold face had softened slightly. It seemed to Ravenspur
that there was something akin to a smile in Countess Flavio's eyes
when once more they were alone in the drawing-room together.
Let us try and forget that dreadful scene, she said, as I will try
and forget what a hard, misunderstood life mine has been.
It must have been terrible, Ravenspur exclaimed; and yet there
was not a man in Europe for whom I had a higher regard than I had
for your husband. To me he was the soul of honour. I always found
him generous and liberal-minded. I have seen him do the most
spontaneous acts of kindness to strangers. It seemed hard to think
that he was wholly bad.
He was an enigma, the Countess replied. In his brain lay a curious
vein of madness, which vented itself upon me. No one else suffered,
and, indeed, no one knew that I suffered, with the solitary exception
of that poor lost soul who is lying at death's door upstairs. When I
fled from my father's house, knowing that I had cut myself off
entirely from my own flesh and blood, Silva followed me. From the
first he began to see how I was suffering. From the first he began to
entertain a malignant hatred of my husband.
And finally poisoned him, Ravenspur suggested.
Ah, there you are wrong, the Countess exclaimed. With all the
earnestness in my power I want to impress upon you that my

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