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 splash in the public eye—to assert his personality. In what way has his personality been suppressed that one can connect with the two victims he has so far selected? A final suggestion: Is his motive direct personal hatred of me, of Hercule Poirot? Does he challenge me in public because I have (unknown to myself) vanquished him somewhere in the course of my career? Or is his animosity impersonal—directed against a foreigner? And if so, what again has led to that? What injury has he suffered at a foreigner's hand?"

"All very suggestive questions," said Dr. Thompson.

Inspector Crome cleared his throat. "Oh, yes? A little unanswerable at present, perhaps."

"Nevertheless, my friend," said Poirot, looking straight at him, "it is there in those questions that the solution lies. If we knew the exact reason—fantastic, perhaps, to us—but logical to him—of why our madman commits these crimes, we should know, perhaps, who the next victim is likely to be."

Crome shook his head. "He selects them haphazard—that's my opinion."

"The magnanimous murderer," said Poirot.

"What's that you say?"

"I said—the magnanimous murderer! Franz Ascher would have been arrested for the murder of his wife—Donald Fraser might have been arrested for the murder of Betty Barnard—if it had not been for the warning letters of A.B.C.. Is he, then, so soft-hearted that he cannot bear others to suffer for something they did not do?"

"I've known stranger things happen," said Dr. Thompson. "I've known men who've killed half a dozen victims all broken up because one of their victims didn't die instantaneously and suffered pain. All the same, I don't think that that is our fellow's reason. He wants the credit of these crimes for his own honour and glory. That's the explanation that fits best."

"We've come to no decision about the publicity business," said the Assistant Commissioner.

"If I may make a suggestion, sir," said Crome. "Why not wait till the receipt of the next letter? Make it public then—special editions, etc. It will make a bit of a panic in the particular town named, but it will put everyone whose name begins with C on his guard, and it'll put A.B.C. on his mettle. He'll be determined to succeed. And that's when we'll get him."

How little we knew what the future held.

XIV.

The Third Letter

I well remember the arrival of A.B.C.'s third letter.

I may say that all precautions had been taken so that when A.B.C. resumed his campaign there should be no unnecessary delays. A young sergeant from Scotland Yard was attached to the house and if Poirot and I were out it was his duty to open anything that came so as to be able to communicate with headquarters without loss of time.