It had, of course, far more elements of popularity. The victim was a young and good-looking girl to begin with. Also, it had taken place at a popular seaside resort.

All the details of the crime were reported fully and rehashed daily in thin disguises. The A.B.C. railway guide came in for its share of attention.

The favourite theory was that it had been bought locally by the murderer and that it was a valuable clue to his identity. It also seemed to show that he had come to the place by train and was intending to leave for London.

The railway guide had not figured at all in the meagre accounts of the Andover murder so there seemed at present little likelihood of the two crimes being connected in the public eye.

'We've got to decide upon a policy,' said the Assistant Commissioner. 'The thing is—which way will give us the best results? Shall we give the public the facts—enlist their cooperation—after all, it'll be the cooperation of several million people, looking out for a madman—'

'He won't look like a madman,' interjected Dr. Thompson.

'—looking out for sales of A.B.C.'s—and so on. Against that I suppose there's the advantage of working in the dark—not letting our man know what we're up to, but then there's the fact that he knows very well that we know. He's drawn attention to himself deliberately by his letters. Eh, Crome, what's your opinion?'

'I look at it this way, sir. If you make it public, you're playing A.B.C.'s game. That's what he wants— publicity—notoriety. That's what he's out after. I'm right, aren't I, doctor? He wants to make a splash.'

Thompson nodded.

The Assistant Commissioner said thoughtfully: 'So you're for baulking him. Refusing him the publicity he's hankering after. What about you, M. Poirot?'

Poirot did not speak for a minute. When he did it was with an air of choosing his words carefully.

'It is difficult for me, Sir Lionel,' he said. 'I am, as you might say, an interested party. The challenge was sent to me. If I say, 'Suppress that fact—do not make it public,' may it not be thought that it is my vanity that speaks? That I am afraid for my reputation? It is difficult! To speak out—to tell all—that has its advantages. It is, at least, a warning . . . . On the other hand, I am as convinced as Inspector Crome that it is what the murderer wants us to do.'

'Hm!' said the Assistant Commissioner, rubbing his chin. He looked across at Dr. Thompson. 'Suppose we refuse our lunatic the satisfaction of the publicity he craves. What's he likely to do?'

'Commit another crime,' said the doctor promptly. 'Force your hand.'

'And if we splash the thing about in headlines. Then what's his reaction?'

'Same answer. One way you feed his megalomania, the other you baulk it. The result's the same. Another crime.'

'What do you say, M. Poirot?'

'I agree with Dr. Thompson.'

'A cleft stick—eh? How many crimes do you think this—lunatic has in mind?'

Dr. Thompson looked across at Poirot. 'Looks like A to Z,' he said cheerfully. 'Of course,' he went on, 'he won't get there. Not nearly. You'll have him by the heels long before that. Interesting to know how he'd have dealt with the letter X.' He recalled himself guiltily from this purely enjoyable speculation. 'But you'll have him long before that. G or H, let's say.'

The Assistant Commissioner struck the table with his fist. 'My God, are you telling me we're going to have five more murders?''

'It won't be as much as that, sir,' said Inspector Crome. 'Trust me.'

He spoke with confidence.

'Which letter of the alphabet do you place it at, inspector?' asked Poirot.

There was a slight ironic note in his voice. Crome, I thought, looked at him with a tinge of dislike adulterating the usual calm superiority.

'Might get him next time, M. Poirot. At any rate I'd guarantee to get him by the time he gets to E.'

He turned to the Assistant Commissioner. 'I think I've got the psychology of the case fairly clear. Dr. Thompson will correct me if I'm wrong. I take it that every time he brings a crime off, his self-confidence increases about a hundred per cent. Every time he feels 'I'm clever—they can't catch me!' he becomes so overweeningly confident that he also becomes careless. He exaggerates his own cleverness and every one else's stupidity. Very soon he'll be hardly bothering to take any precautions at all. That's right, isn't it, doctor?'

Thompson nodded. 'That's usually the case. In non-medical terms it couldn't have been put better. You know something about such things, M. Poirot. Don't you agree?'

I don't think that Crome liked Thompson's appeal to Poirot. He considered that he and he only was the expert on this subject.

'It is as Inspector Crome says,' agreed Poirot.

'Paranoia,' murmured the doctor.

Poirot turned to Crome. 'Are there any material facts of interest in the Bexhill case?'

'Nothing very definite. A waiter at the Splendide at Eastbourne recognizes the dead girl's photograph as that of a young woman who dined there in company with a middle-aged man in spectacles. It's also been recognized at a roadhouse place called the Scarlet Runner, halfway between Bexhill and London. There they say she was with a man who looked like a naval officer. They can't both be right, but either of them's probable. Of course, there's a host of other identifications, but most of them not good for much. We haven't been able to trace the A.B.C..'

'Well, you seem to be doing all that can be done, Crome,' said the Assistant Commissioner. 'What do you say, M. Poirot? Does any line of inquiry suggest itself to you?'

Poirot said slowly: 'It seems to me that there is one very important clue—the discovery of the motive.'

'Isn't that pretty obvious? An alphabetical complex. Isn't that what you called it, doctor?'

'Me oui,' said Poirot. 'There is an alphabetical complex. A madman in particular has always a very strong reason for the crimes he commits.'

'Come, come, M. Poirot,' said Crome. 'Look at Stoneman in 1929. He ended by trying to do away with anyone who annoyed him in the slightest degree.'

Poirot turned to him. 'Quite so. But if you are a sufficiently great and important person, it is necessary that you should be spared small annoyances. If a fly settles on your forehead again and again, maddening you by its tickling—what do you do? You endeavour to kill that fly. You have no qualms about it. You are important—the fly is not. You kill the fly and the annoyance ceases. Your action appears to you sane and justifiable. Another reason for killing a fly is if you have a strong passion for hygiene. The fly is a potential source of danger to the community—the fly must go. So works the mind of the mentally deranged criminal. But consider now this case—if the victims are alphabetically selected, then they are not being removed because they are a source of annoyance to him personally. It would be too much of a coincidence to combine the two.'

'That's a point,' said Dr. Thompson. 'I remember a case where a woman's husband was condemned to death. She started killing the members of the jury one by one. Quite a time before the crimes were connected up. They seemed entirely haphazard. But as M. Poirot says, there isn't such a thing as a murderer who commits crimes at random.'

'Either he removes people who stand (however insignificantly) in his path, or else he kills by conviction. He removes clergymen, or policemen, or prostitutes because he firmly believes that they should be removed.'

'That doesn't apply here either as far as I can see. Mrs. Ascher and Betty Barnard cannot be linked as members of the same class. Of course, it's possible that there is a sex complex. Both victims have been women. We can tell better, of course, after the next crime—'

'For God's sake, Thompson, don't speak so glibly of the next crime,' said Sir Lionel irritably. 'We're going to do all we can to prevent another crime.'

Dr. Thompson held his peace and blew his nose with some violence. 'Have it your own way,' the noise seemed to say. 'If you won't face facts—'

The Assistant Commissioner turned to Poirot. 'I see what you're driving at, but I'm not quite clear yet.'

'I ask myself,' said Poirot, 'what passes in itself exactly in the mind of the murderer? He kills, it would seem from his letters, pour le sport—to amuse himself. Can that really be true? And even if it is true, on what principle does he select his victims apart from the merely alphabetical one? If he kills merely to amuse himself he would not advertise the fact, since, otherwise, he could kill with impunity. But no, he seeks, as we all agree, to make the

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