“It is,” he agreed; “but it is the assumption that we have to act upon. We must not leave a loop-hole unwatched. He mustn’t get another chance.”

“No,” I concurred warmly; “he certainly must not—if we can help it. But it is an awful position. We carry that poor girl’s life in our hands, and there is always the possibility that we may be caught off our guard, just for a moment.”

He nodded gravely. “You are quite right, Gray. An awful responsibility rests on us. I am very unhappy about this poor young lady. Of course, there is the other side—but at present we are concerned with Miss D’Arblay’s safety.”

“What other side is there?” I demanded.

“I mean,” he replied, “that if we can hold out, this man is going to deliver himself into our hands.”

“What makes you think that?” I asked eagerly.

“I recognize a familiar phenomenon,” he replied. “My large experience and extensive study of crimes against the person have shown me that in the overwhelming majority of cases of obscure crimes the discovery has been brought about by the criminal’s own efforts to make himself safe. He is constantly trying to hide his tracks—and making fresh ones. Now this man is one of those criminals who won’t let well alone. He kills Van Zellen and disappears, leaving no trace. He seems to be quite safe. But he is not satisfied. He can’t keep quiet. He kills D’Arblay, he enters the studio, he tries to kill Miss D’Arblay; all to make himself more safe. And every time he moves he tells us something fresh about himself. If we can only wait and watch, we shall have him.”

“What has he told us about himself this time?” I asked.

“We won’t go into that now, Gray. We have other business on hand. But you know all that I know as to the facts. If you will turn over those facts at your leisure, you will find that they yield some very curious and striking inferences.”

I was about to press the question when the door opened and Mr. Polton appeared on the threshold. Observing me, he crinkled benevolently, and then, in answer to Thorndyke’s inquiring glance, said: “I thought I had better remind you, sir, that you have not had any supper.”