“And yet there should be no combination of events for which the wit of man cannot conceive an explanation. Simply as a mental exercise, without any assertion that it is true, let me indicate a possible line of thought. It is, I admit, mere imagination; but how often is imagination the mother of truth?

“We will suppose that there was a guilty secret, a really shameful secret in the life of this man Douglas. This leads to his murder by someone who is, we will suppose, an avenger, someone from outside. This avenger, for some reason which I confess I am still at a loss to explain, took the dead man’s wedding ring. The vendetta might conceivably date back to the man’s first marriage, and the ring be taken for some such reason.

“Before this avenger got away, Barker and the wife had reached the room. The assassin convinced them that any attempt to arrest him would lead to the publication of some hideous scandal. They were converted to this idea, and preferred to let him go. For this purpose they probably lowered the bridge, which can be done quite noiselessly, and then raised it again. He made his escape, and for some reason thought that he could do so more safely on foot than on the bicycle. He therefore left his machine where it would not be discovered until he had got safely away. So far we are within the bounds of possibility, are we not?”

“Well, it is possible, no doubt,” said I, with some reserve.

“We have to remember, Watson, that whatever occurred is certainly something very extraordinary. Well, now, to continue our supposititious case, the couple - not necessarily a guilty couple - realize after the murderer is gone that they have placed themselves in a position in which it may be difficult for them to prove that they did not themselves either do the deed or connive at it. They rapidly and rather clumsily met the situation. The mark was put by Barker’s bloodstained slipper upon the windowsill to suggest how the fugitive got away. They obviously were the two who must have heard the sound of the gun; so they gave the alarm exactly as they would have done, but a good half hour after the event.”

“And how do you propose to prove all this?”

“Well, if there were an outsider, he may be traced and taken. That would be the most effective of all proofs. But if not - well, the resources of science are far from being exhausted. I think that an evening alone in that study would help me much.”

“An evening alone!”

“I propose to go up there presently. I have arranged it with the estimable Ames, who is by no means whole-hearted about Barker. I shall sit in that room and see if its atmosphere brings me inspiration. I’m a believer in the genius loci. You smile, Friend Watson. Well, we shall see. By the way, you have that big unbrella of yours, have you not?”

“It is here.”

“Well, I’ll borrow that if I may.”

“Certainly - but what a wretched weapon! If there is danger- -”

“Nothing serious, my dear Watson, or I should certainly ask for your assistance. But I’ll take the umbrella. At present I am only awaiting the return of our colleagues from Tunbridge Wells, where they are at present engaged in trying for a likely owner to the bicycle.”

It was nightfall before Inspector MacDonald and White Mason came back from their expedition, and they arrived exultant, reporting a great advance in our investigation.

“Man, I’ll admeet that I had my doubts if there was ever an outsider,” said MacDonald; “but that’s all past now. We’ve had the bicycle identified, and we have a description of our man; so that’s a long step on our journey.”

“It sounds to me like the beginning of the end,” said Holmes. “I’m sure I congratulate you both with all my heart.”