"I thought it best to have lunch served immediately in the restaurant car," he said. "Afterwards it will be cleared and M. Poirot can conduct his examination of the passengers there. In the meantime I have ordered them to bring us three some food here."

They found M. Bouc finishing an omelet.

Neither of the other two men was hungry, and the meal was soon eaten, but not till they were sipping their coffee did M. Bouc mention the subject that was occupying all their minds.

"An excellent idea," said Poirot.

"Eh bien?" he asked.

"Eh bien, I have discovered the identity of the victim. I know why it was imperative he should leave America."

"Who was he?"

"Do you remember reading of the Armstrong baby? This is the man who murdered little Daisy Armstrong -- Cassetti."

"I recall it now. A shocking affair -- though I cannot remember the details."

"Colonel Armstrong was an Englishman -- a V. C. He was half American, as his mother was a daughter of W. K. Van der Halt, the Wall Street millionaire. He married the daughter of Linda Arden, the most famous tragic American actress of her day. They lived in America and had one child -- a girl -- whom they idolized. When she was three years old she was kidnapped, and an impossibly high sum demanded as the price of her return. I will not weary you with all the intricacies that followed. I will come to the moment, when, after having paid over the enormous sum of two hundred thousand dollars, the child's dead body was discovered, it having been dead at least a fortnight. Public indignation rose to fever point. And there was worse to follow. Mrs. Armstrong was expecting another child. Following the shock of the discovery, she gave birth to a dead child born prematurely, and herself died. Her broken-hearted husband shot himself."

"Yes -- an unfortunate French or Swiss nursemaid. The police were convinced that she had some knowledge of the crime. They refused to believe her hysterical denials. Finally, in a fit of despair, the poor girl threw herself from a window and was killed. It was proved afterwards that she was absolutely innocent of any complicity in the crime."

"It is not good to think of," said M. Bouc.

"Mon Dieu, what a tragedy. I remember now," said M. Bouc. "There was also another death, if I remember rightly?"

"About six months later, this man Cassetti was arrested as the head of the gang who had kidnapped the child. They had used the same methods in the past. If the police seemed likely to get on their trail, they had killed their prisoner, hidden the body, and continued to extract as much money as possible before the crime was discovered.

"Now, I will make clear to you this, my friend. Cassetti was the man! But by means of the enormous wealth he had piled up and by the secret hold he had over various persons, he was acquitted on some technical inaccuracy. Notwithstanding that, he would have been lynched by the populace had he not been clever enough to give them the slip. It is now clear to me what happened. He changed his name and left America. Since then he has been a gentleman of leisure, travelling abroad and living on his rentes."

"Tout de même, it is not necessary that he should be killed on the Orient Express. There are other places."

"Ah! quel animal!" M. Bouc's tone was redolent of heartfelt disgust. "I cannot regret that he is dead -- not at all!"

"The question we have now to ask ourselves is this," he said. "Is this murder the work of some rival gang whom Cassetti had double-crossed in the past, or is it an act of private vengeance?"

"I agree with you."

"If I am right in my assumption, then the letter was burnt by the murderer. Why? Because it mentioned the word 'Armstrong,' which is the clue to the mystery."

"Are there any members of the Armstrong family living?"

He explained his discovery of the few words on the charred fragment of paper.

Poirot smiled a little. He realized that M. Bouc was biased in the matter.

"That, unfortunately, I do not know. I think I remember reading of a younger sister of Mrs. Armstrong's."

Poirot went on to relate the joint conclusions of himself and Dr. Constantine. M. Bouc brightened at the mention of the broken watch.

"That seems to give us the time of the crime very exactly."

"Not at all. Not at all," said Poirot.

There was a tap on the door, and the restaurant attendant entered.

"Yes," said Poirot. "It is very convenient."

"Mais non, après vous," they left the compartment.

Poirot did not reply. He sat looking thoughtfully in front of him.

Poirot related just what had occurred.

"I may accompany you?" asked Constantine.

After a little politeness in the matter of procedure, "Après vous, Monsieur."

"Twenty-three minutes to one, to be precise."

"The restaurant car is free now, Monsieur," he said.

"We will go there," said M. Bouc, rising.

"Certainly, my dear doctor. Unless M. Poirot has any objection?"

"You say that you yourself heard Ratchett speak to the conductor at twenty minutes to one?"

"Well," said M. Bouc, "that proves at least that Cassetti -- or Ratchett, as I shall continue to call him -- was certainly alive at twenty minutes to one."

"Then at twelve thirty-seven, to put it formally, M. Ratchett was alive. That is one fact, at least."

There was an indescribable something in his tone that made both the other two look at him curiously.