“I grant it you – I grant it, mon vieux,” said M. Bouc with a gesture of irony.

Hercule Poirot was not at all put out. He continued calmly.

“I will pass over for the moment certain rather peculiar appearances which Dr. Constantine and I have already discussed together. I will come to them presently. The next fact of importance, to my mind, is the time of the crime.”

“That, again, is one of the few things we do know,” said M. Bouc. “The crime was committed at a quarter past one this morning. Everything goes to show that that was so.”

“Not everything. You exaggerate. There is, certainly, a fair amount of evidence to support that view.”

“I am glad you admit that at least.”

Poirot went on calmly, unperturbed by the interruption.

“We have before us three possibilities. “(1) – that the crime was committed, as you say, at a quarter past one. This is supported by the evidence of the watch, by the evidence of Mrs. Hubbard, and by the evidence of the German woman, Hildegarde Schmidt. It agrees with the evidence of Dr. Constantine.

“(2) – that the crime was committed later, and that the evidence of the watch was deliberately faked in order to mislead.

“(3) – that the crime was committed earlier, and the evidence faked for the same reason as above.

“Now if we accept possibility (1) as the most likely to have occurred, and the one supported by most evidence, we must also accept certain facts arising from it. If the crime was committed at a quarter past one, the murderer cannot have left the train, and the questions arise: Where is he? And who is he?

“To begin with, let us examine the evidence carefully. We first hear of the existence of this man – the small dark man with a womanish voice – from the man Hardman. He says that Ratchett told him of this person and employed him to watch out for the man. There is no evidence to support this; we have only Hardman’s word for it.

Let us next examine the question: Is Hardman the person he pretends to be an operative of a New York detective agency?

“What to my mind is so interesting in this case is that we have none of the facilities afforded to the police. We cannot investigate the bona fides of any of these people. We have to rely solely on deduction. That, to me, makes the matter very much more interesting. There is no routine work. It is all a matter of the intellect. I ask myself: Can we accept Hardman’s account of himself? I make my decision and I answer ‘Yes.’ I am of the opinion that we can accept Hardman’s account of himself.”

“You rely on the intuition? What the Americans call ‘the hunch’?” asked Dr. Constantine.

“Not at all. I regard the probabilities. Hardman is travelling with a false passport – that will at once make him an object of suspicion. The first thing that the police will do when they do arrive upon the scene is to detain Hardman and cable as to whether his account of himself is true. In the case of many of the passengers, to establish their bona fides will be difficult; in most cases it will probably not be attempted, especially since there seems nothing in the way of suspicion attaching to them. But in Hardman’s case it is simple. Either he is the person he represents himself to be, or he is not. Therefore I say that all will prove to be in order.”

“You acquit him of suspicion?”

“Not at all. You misunderstand me. For all I know, any American detective might have his own private reasons for wishing to murder Ratchett. No, what I am saying is that I think we can accept Hardman’s own account of himself. This story, then, that he tells of Ratchett’s seeking him out and employing him is not unlikely, and is most probably – though not of course certainly – true. If we are going to accept it as true, we must see if there is any confirmation of it. We find it in rather an unlikely place – in the evidence of Hildegarde Schmidt. Her description of the man she saw in Wagon Lit uniform tallies exactly. Is there any further confirmation of these two stories? There is. There is the button that Mrs. Hubbard found in her compartment. And there is also another corroborating statement which you may not have noticed.”

“What is that?”

“The fact that both Colonel Arbuthnot and Hector MacQueen mention that the conductor passed their carriage. They attached no importance to the fact, but, Messieurs, Pierre Michel has declared that he did not leave his seat except on certain specified occasions – none of which would take him down to the far end of the coach past the compartment in which Arbuthnot and MacQueen were sitting.

“Therefore this story, the story of a small dark man with a womanish voice dressed in Wagon Lit uniform, rests on the testimony, direct or indirect, of four witnesses.”

“One small point,” said Dr. Constantine. “If Hildegarde Schmidt’s story is true, how is it that the real conductor did not mention having seen her when he came to answer Mrs. Hubbard’s bell?”

“That is explained, I think. When he arrived to answer Mrs. Hubbard, the maid was in with her mistress. When she finally returned to her own compartment, the conductor was in with Mrs. Hubbard.”

M. Bouc had been waiting with difficulty until they had finished.

“Yes, yes, my friend,” he said impatiently to Poirot. “But whilst I admire your caution, your method of advancing a step at a time, I submit that you have not yet touched the point at issue. We are all agreed that this person exists. The point is, where did he go?”

Poirot shook his head reprovingly.

“You are in error. You are inclined to put the cart before the horse. Before I ask myself, ‘Where did this man vanish to?’ I ask myself, ‘Did such a man really exist?’ Because, you see, if the man were an invention – a fabrication – how much easier to make him disappear! So I try to establish first that there really is such a flesh-and-blood person.”

“And having arrived at the fact that there is – eh bien, where is he now?”

“There are only two answers to that, mon cher. Either he is still hidden on the train in a place of such extraordinary ingenuity that we cannot even think of it; or else he is, as one might say, two persons. That is, he is both himself – the man feared by M. Ratchett – and a passenger on the train so well disguised that M. Ratchett did not recognise him.”

“It is an idea, that,” said M. Bouc, his face lighting up. Then it clouded over again. “But there is one objection—”

Poirot took the words out of his mouth.

“The height of the man. It is that you would say? With the exception of Mr. Ratchett’s valet, all the passengers are big men – the Italian, Colonel Arbuthnot, Hector MacQueen, Count Andrenyi. Well, that leaves us the valet – not a very likely supposition. But there is another possibility. Remember the ‘womanish’ voice. That gives us a choice of alternatives. The man may be disguised as a woman, or, alternatively, he may actually be a woman. A tall woman dressed in men’s clothes would look small.”

“But surely Ratchett would have known—”

“Perhaps he did know. Perhaps, already, this woman had attempted his life, wearing a mares clothes the better to accomplish her purpose. Ratchett may have guessed that she would use the same trick again, so he tells Hardman to look for a man. But he mentions, however, a womanish voice.”

“It is a possibility,” said M. Bouc. “But—”

“Listen, my friend, I think that I should now tell you of certain inconsistencies noticed by Dr. Constantine.”

He retailed at length the conclusions that he and the doctor had arrived at together from the nature of the dead man’s wounds. M. Bouc groaned and held his head again.