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 There was a sympathetic silence, and then Poirot spoke in a detached manner.

"Let us arrange our facts with order and precision. According to our present theory, this is how they run. The Comte de la Roche knows of your purchase of these jewels. By an easy stratagem he induces Madame Kettering to bring the stones with her. He, then, is the man Mason saw in the train at Paris."

The other three nodded in agreement.

"Madame is surprised to see him, but she deals with the situation promptly. Mason is got out of the way; a dinner basket is ordered. We know from the conductor that he made up the berth for the first compartment, but he did not go into the second compartment, and that a man could quite well have been concealed from him. So far the Comte could have been hidden to a marvel. No one knows of his presence on the train except Madame; he has been careful that the maid did not see his face. All that she could say is that he was tall and dark. It is all most conveniently vague. They are aloneand the train rushes through the night. There would be no outcry, no struggle, for the man is, so she thinks, her lover."

He turned gently to Van Aldin.

"Death, Monseiur, must have been almost instantaneous. We will pass over that quickly. The Comte takes the jewel-case which lies ready to his hand. Shortly afterwards the train draws into Lyons."

M. Carrège nodded his approval.

"Precisely. The conductor without descends. It would be easy for our man to leave the train unseen;