"No, that is not true. We are more advanced. We know certain things. We have heard the evidence of the passengers."

"I am not a magician, mon cher. I am, like you, a very puzzled man. This affair advances in a very strange manner."

The three conductors and Hildegarde Schmidt had been dismissed.

"Explain to me then, quickly, what actually happened on the train last night."

"And what has that told us? Nothing at all."

"It does not advance at all. It stays where it was."

"A small dark man with a womanish voice," said M. Bouc.

"It is a good phrase that," said Poirot. "The impossible cannot have happened, therefore the impossible must be possible in spite of appearances."

Poirot shook his head.

"I would not say that, my friend."

"But I understand nothing -- but nothing of all this! The enemy that this Ratchett spoke of, he was then on the train after all? But where is he now? How can he have vanished into thin air? My head, it whirls. Say something, then, my friend, I implore you. Show me how the impossible can be possible!"

"I exaggerate, perhaps. The American, Hardman, and the German maid -- yes, they have added something to our knowledge. That is to say, they have made the whole business more unintelligible than it was."

M. Bouc turned upon him. "Speak, then, let us hear the wisdom of Hercule Poirot."

"No, no, no," said Poirot soothingly.

"Did I not tell you that I was, like you, a very puzzled man? But at least we can face our problem. We can arrange such facts as we have with order and method."

"Pray continue, Monsieur," said Dr. Constantine.

"Let us review the case as it stands at this moment. First, there are certain indisputable facts. This man Ratchett, or Cassetti, was stabbed in twelve places and died last night. That is fact one."

Poirot cleared his throat and straightened a piece of blotting-paper.

"I grant it to you -- I grant it, mon vieux," said M. Bouc with a gesture of irony.

"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."

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

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

"One: That the crime was committed, as you say, at a quarter past one. This is supported by the evidence of the German woman, Hildegarde Schmidt. It agrees with the evidence of Dr. Constantine.

"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 was so."

"I am glad you admit that at least."

"Possibility three: The crime was committed earlier and the evidence faked for the same reason as above.

"Now, if we accept possibility one as the most likely to have occurred and the one supported by most evidence, we must also accept certain facts arising from it. To begin with, if the crime was committed at a quarter past one, the murderer cannot have left the train, and the question arises: Where is he? And who is he?

"Possibility two: The crime was committed later and the evidence of the watch was deliberately faked.

Poirot went on calmly, unperturbed by the interruption. "We have before us three possibilities:

"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 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?" said 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 found in her compartment by Mrs. Hubbard. And there is also another corroborating statement which you may not have noticed."

"What is that?"

"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."

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

"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.

"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."

"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?"

"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 recognize him."

"Perhaps he did know. Perhaps, already this woman had attempted his life wearing men's 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 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 M. 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 man's clothes would look small."

"It is a possibility," said M. Bouc. "But --"

"But surely Ratchett would have known --"

"Exactly. It is absurd -- improbable -- it cannot be. So I myself have said. And yet, my friend, there it is! One cannot escape from the facts."

"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. "I know," said Poirot sympathetically. "I know exactly how you feel. The head spins, does it not?"

"The whole thing is a fantasy," cried M. Bouc.

The thought almost made him weep.

"Is it not? It is so mad, my friend, that sometimes I am haunted by the sensation that really it must be very simple… But that is only one of my 'little ideas.'…"

"Two murderers," groaned M. Bouc. "And on the Orient Express."

"And now let us make the fantasy more fantastic," said Poirot cheerfully. "Last night on the train there are two mysterious strangers. There is the Wagon Lit attendant answering to the description given us by M. Hardman, and seen by Hildegarde Schmidt, Colonel Arbuthnot and M. MacQueen. There is also a woman in a red kimono -- a tall, slim woman -- seen by Pierre Michel, by Miss Debenham, by M. MacQueen and by myself -- and smelt, I may say, by Colonel Arbuthnot! Who was she? No one on the train admits to having a scarlet kimono. She, too, has vanished. Was she one and the same with the spurious Wagon Lit attendant? Or was she some quite distinct personality? Where are they, these two? And, incidentally, where is the Wagon Lit uniform and the scarlet kimono?"

"It is madness!"

"But how --" began M. Bouc and stopped. "What is this noise that approaches?" he cried. "It resembles a locomotive in motion."

"Ah! that is something definite." M. Bouc sprang up eagerly. "We must search all the passengers' luggage. Yes, that will be something."

"It's too horrible," she cried. "It's just too horrible. In my sponge bag. My sponge bag. A great knife -- all over blood."

"Hildegarde Schmidt? You think --"

"You will find the scarlet kimono in the baggage of one of the men and you will find the uniform of the Wagon Lit conductor in the baggage of Hildegarde Schmidt."

"Not what you are thinking. I will put it like this. If Hildegarde Schmidt is guilty, the uniform might be found in her baggage -- but if she is innocent it certainly will be."

"Where, then?"

Poirot rose also.

"I will make a prophecy," he said.

The noise drew nearer. It consisted of shrill cries and protests in a woman's voice. The door at the end of the dining car flew open. Mrs. Hubbard burst in.

"I have a little idea."

"You know where they are?"

And, suddenly toppling forward, she fainted heavily on M. Bouc's shoulder.