“But excellent—you have method. Let us hear them.”

I read out in a somewhat embarrassed voice.

“To begin with, one must look at the thing logically——”

“Just what my poor Hastings used to say,” interrupted Poirot, “but alas! he never did so.”

Point No. 1.—Mr. Ackroyd was heard talking to some one at half-past nine.

Point No. 2.—At some time during the evening Ralph Paton must have come in through the window, as evidenced by the prints of his shoes.

Point No. 3.—Mr. Ackroyd was nervous that evening, and would only have admitted some one he knew.

Point No. 4.—The person with Mr. Ackroyd at nine-thirty was asking for money. We know Ralph Paton was in a scrape.

These four points go to show that the person with Mr. Ackroyd at nine-thirty was Ralph Paton. But we know that Mr. Ackroyd was alive at a quarter to ten, therefore it was not Ralph who killed him. Ralph left the window open. Afterwards the murderer came in that way.

“And who was the murderer?” inquired Poirot.