Poirot smiled, and unfolded the paper. It was a letter written in thin sloping handwriting. Poirot read it aloud.

“‘Chère Madame:

“‘It is with infinite pleasure that I look forward to the felicity of meeting you again. After your so amiable reply to my letter, I can hardly restrain my impatience. I have never forgotten those days in Paris. It is most cruel that you should be leaving London tomorrow. However, before very long, and perhaps sooner than you think, I shall have the joy of beholding once more the lady whose image has ever reigned supreme in my heart.

“‘Believe, chère madame, all the assurances of my most devoted and unaltered sentiments—

“‘Armand de la Rochefour.’”

Poirot handed the letter back to Halliday with a bow.

“I fancy, monsieur, that you did not know that your daughter intended renewing her acquaintance with the Count de la Rochefour?”

“It came as a thunderbolt to me! I found this letter in my daughter’s handbag. As you probably know, Monsieur Poirot, this so-called count is an adventurer of the worst type.”

Poirot nodded.

“But what I want to know is how you knew of the existence of this letter?”

My friend smiled. “Monsieur, I did not. But to track footmarks, and recognize cigarette-ash is not sufficient for a detective. He must also be a good psychologist! I knew that you disliked and mistrusted your son-in-law. He benefits by your daughter’s death; the maid’s description of the mysterious man bears a sufficient resemblance to him. Yet you are not keen on his track! Why? Surely because your suspicions lie in another direction. Therefore you were keeping something back.”

“You’re right, Monsieur Poirot. I was sure of Rupert’s guilt until I found this letter. It unsettled me horribly.”

“Yes. The Count says: ‘Before very long, and perhaps sooner than you think.’ Obviously he would not want to wait until you should get wind of his reappearance. Was it he who traveled down from London by the twelve-fourteen, and came along the corridor to your daughter’s compartment? The Count de la Rochefour is also, if I remember rightly, tall and dark!”