“But where does the hat-box come in?” asked the doctor, still puzzled.

“Ah! I am coming to that. As I say, these clues – the watch stopped at a quarter past one, the handkerchief, the pipe-cleaner – they may be genuine, or they may be faked. As to that I cannot yet tell. But there is one clue here which – though again I may be wrong – I believe has not been faked. I mean this flat match, M. le docteur. I believe that that match was used by the murderer, not by Mr. Ratchett. It was used to burn an incriminating paper of some kind. Possibly a note. If so, there was something in that note, some mistake, some error, that left a possible clue to the assailant. I am going to try to discover what that something was.”

He went out of the compartment and returned a few moments later with a small spirit stove and a pair of curling-tongs.

“I use them for the moustaches,” he said, referring to the latter.

The doctor watched him with great interest. Poirot flattened out the two humps of wire, and with great care wriggled the charred scrap of paper on to one of them. He clapped the other on top of it and then, holding both pieces together with the tongs, held the whole thing over the flame of the spirit-lamp.

“It is a very makeshift affair, this,” he said over his shoulder. “Let us hope that it will answer our purpose.”

The doctor watched the proceedings attentively. The metal began to glow. Suddenly he saw faint indications of letters. Words formed themselves slowly – words of fire.

It was a very tiny scrap. Only three words and part of another showed.

–member little Daisy Armstrong

“Ah!” Poirot gave a sharp exclamation.

“It tells you something?” asked the doctor.

Poirot’s eyes were shining. He laid down the tongs carefully.

“Yes,” he said. “I know the dead man’s real name. I know why he had to leave America.”

“What was his name?”

“Cassetti.”

“Cassetti?” Constantine knitted his brows. “It brings back to me something. Some years ago. I cannot remember… It was a case in America, was it not?”

“Yes,” said Poirot. “A case in America.”

Further than that Poirot was not disposed to be communicative. He looked round him as he went on:

“We will go into all that presently. Let us first make sure that we have seen all there is to be seen here.”

Quickly and deftly he went once more through the pockets of the dead man’s clothes but found nothing there of interest. He tried the communicating door which led through to the next compartment, but it was bolted on the other side.

“There is one thing that I do not understand,” said Dr. Constantine. “If the murderer did not escape through the window, and if this communicating door was bolted on the other side, and if the door into the corridor was not only locked on the inside but chained, how then did the murderer leave the compartment?”

“That is what the audience says when a person bound hand and foot is shut into a cabinet – and disappears.”

“You mean–?”

“I mean,” explained Poirot, “that if the murderer intended us to believe that he had escaped by way of the window, he would naturally make it appear that the other two exits were impossible. Like the ‘disappearing person’ in the cabinet, it is a trick. It is our business to find out how the trick is done.

He locked the communicating door on their side – “in case,” he said, “the excellent Mrs. Hubbard should take it into her head to acquire first-hand details of the crime to write to her daughter.”

He looked round once more.

“There is nothing more to do here, I think. Let us rejoin M. Bouc.”

They found M. Bouc finishing an omelet.

“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.”

“An excellent idea,” said Poirot.

None of the three 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.

“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, his mother having been 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 the parents had paid over the enormous sum of two hundred thousand dollars, the child’s dead body was discovered; it had been dead for at least a fortnight. Public indignation rose to fever point. And there was worse to follow. Mrs. Armstrong was expecting another baby. Following the shock of the discovery, she gave birth prematurely to a dead child, and herself died. Her broken-hearted husband shot himself.”

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

“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 had been absolutely innocent of any complicity in the crime.”

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

“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 killed their prisoner, hid 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 owing to 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.”

“Ah! quel animal!” M. Bouc’s tone was redolent of heartfelt disgust. “I cannot regret that he is dead – not at all!”

“I agree with you.”

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

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

“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?”

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

“If I am right in my assumption, then, the letter was burnt by the murderer. Why? Because it mentioned the name ‘Armstrong,’ which is the clue to the mystery.”

“Are there any members of the Armstrong family living?”

“That, unfortunately, I do not know. I think I remember reading of a younger sister of Mrs. Armstrong’s.”