(7) Celia Harland pretended that there should be a seance on the Tuesday, but she dressed as though she had in view an appointment with a lover, instead of a spiritualistic stance.

(8) Celia Harland has disappeared.

These eight points are strongly suggestive of Celia Harland’s complicity in the murder.  But I have no clue which will enable me to answer the following questions: 

(a) Who was the man who took part in the crime? (b) Who was the woman who came to the villa on the evening of the murder with Mme. Dauvray and Celia Harland?

(c) What actually happened in the salon?  How was the murder committed?

(d) Is Helene Vauquier’s story true?

(e) What did the torn-up scrap of writing mean? (Probably spirit writing in Celia Harland’s hand.)

(f) Why has one cushion on the settee a small, fresh, brown stain, which is probably blood?  Why is the other cushion torn?

Mr. Ricardo had a momentary thought of putting down yet another question.  He was inclined to ask whether or no a pot of cold cream had disappeared from Celia Harland’s bedroom; but he remembered that Hanaud had set no store upon that incident, and he refrained.  Moreover, he had come to the end of his sheet of paper.  He handed it across the table to Hanaud and leaned back in his chair, watching the detective with all the eagerness of a young author submitting his first effort to a critic.

Hanaud read it through slowly.  At the end he nodded his head in approval.

“Now we will see what M. Wethermill has to say,” he said, and he stretched out the paper towards Harry Wethermill, who throughout the luncheon had not said a word.

“No, no,” cried Ricardo.

But Harry Wethermill already held the written sheet in his hand.  He smiled rather wistfully at his friend.

“It is best that I should know just what you both think,” he said, and in his turn he began to read the paper through.  He read the first eight points, and then beat with his fist upon the table.

“No no,” he cried; “it is not possible!  I don’t blame you, Ricardo.  These are facts, and, as I said, I can face facts.  But there will be an explanation—­if only we can discover it.”

He buried his face for a moment in his hands.  Then he took up the paper again.

“As for the rest, Helene Vauquier lied,” he cried violently, and he tossed the paper to Hanaud.  “What do you make of it?”

Hanaud smiled and shook his head.

“Did you ever go for a voyage on a ship?” he asked.

“Yes; why?”

“Because every day at noon three officers take an observation to determine the ship’s position—­the captain, the first officer, and the second officer.  Each writes his observation down, and the captain takes the three observations and compares them.  If the first or second officer is out in his reckoning, the captain tells him so, but he does not show his own.  For at times, no doubt, he is wrong too.  So, gentlemen, I critcise your observations, but I do not show you mine.”