He sat lost in thought for a little while and speaking now and then a phrase rather to himself than to his companion: "To run up here—to cut the arrow down—to round off the end as well as one can in a hurry—to stain it with some varnish—to mix it with the other pens in the tray. Not so bad!" He nodded his head in appreciation of the trick. "But nevertheless things begin to look black for that exquisite Mademoiselle Ann with her delicate colour and her pretty ways."

A noise of the shifting of furniture in the bedroom next door attracted his attention. He removed the nib from the arrow-head.

"We will keep this little matter to ourselves just for the moment," he said quickly, and he wrapped the improvised pen-holder in a sheet of the notepaper. "Just you and I shall know of it. No one else. This is my case, not Girardot's. We will not inflict a great deal of pain and trouble until we are sure."

"I agree," said Jim eagerly. "That's right, I am sure."

Hanaud tucked the arrow-head carefully away in his pocket.

"This, too," he said, and he took up Jim Frobisher's memorandum. "It is not a good thing to carry about, and perhaps lose. I will put it away at the Prefecture with the other little things I have collected."

He put the memorandum into his letter-case and got up from his chair.

"The rest of the arrow-shaft will be somewhere in this room, no doubt, and quite easy to see. But we shall not have time to look for it, and, after all, we have the important part of it."

He turned towards the mantelshelf, where some cards of invitation were stuck in the frame of the mirror, just as the door was opened and the Commissary with his secretary came out from the bedroom.

"The necklace is not in that room," said Monsieur Girardot in a voice of finality.