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of the night it should have easily penetrated to Mrs. Allen's room. She is, as she has told us, somewhat deaf; but none the less she mentioned in her evidence that she did hear something like a door slamming half an hour before the alarm was given. Half an hour before the alarm was given would be a quarter to eleven. I have no doubt that what she heard was the report of the gun, and that this was the real instant of the murder.

      "If this is so, we have now to determine what Barker and Mrs. Douglas, presuming that they are not the actual murderers, could have been doing from quarter to eleven, when the sound of the shot brought them down, until quarter past eleven, when they rang the bell and summoned the servants. What were they doing, and why did they not instantly give the alarm? That is the question which faces us, and when it has been answered we shall surely have gone some way to solve our problem."

      "I am convinced myself," said I, "that there is an understanding between those two people. She must be a heartless creature to sit laughing at some jest within a few hours of her husband's murder."

      "Exactly. She does not shine as a wife even in her own account of what occurred. I am not a whole-souled admirer of womankind, as you are aware, Watson, but my experience of life has taught me that there are few wives, having any regard for their husbands, who would let any man's spoken word stand between them and that husband's dead body. Should I ever marry, Watson, I should hope to inspire my wife with some feeling which would prevent her from being walked off by a housekeeper when my corpse was lying within a few yards of her. It was badly stage-managed; for even the rawest investigators must be struck by the absence of the usual feminine ululation. If there had been nothing else, this incident alone would have suggested a prearranged conspiracy to my mind."

      "You think then, definitely, that Barker and Mrs. Douglas are guilty of the murder?"

      "There is an appalling directness about your questions, Watson," said Holmes, shaking his pipe at me. "They come at me like bullets. If you put it that Mrs. Douglas and Barker know the truth about the murder, and are conspiring to conceal it, then I can give you a whole-souled answer. I am sure they do. But your more deadly proposition is not so clear. Let us for a moment consider the difficulties which stand in the way.

      "We will suppose that this couple are united by the bonds of a guilty love, and that they have determined to get rid of the man who stands between them. It is a large supposition; for discreet inquiry among servants and others has failed to corroborate it in any way. On the contrary, there is a good deal of evidence that the Douglases were very attached to each other."

      "That, I am sure, cannot be true." said I, thinking of the beautiful smiling face in the garden.

      "Well at least they gave that impression. However, we will suppose that they are an extraordinarily astute couple, who deceive everyone upon this point, and conspire to murder the husband. He happens to be a man over whose head some danger hangs—"

      "We have only their word for that."

      Holmes looked thoughtful. "I see, Watson. You are sketching out a theory by which everything they say from the beginning is false. According to your idea, there was never any hidden menace, or secret society, or Valley of Fear, or Boss MacSomebody, or anything else. Well, that is a good sweeping generalization. Let us see what that brings us to. They invent this theory to account for the crime. They then play up to the idea by leaving this bicycle in the park as proof of the existence of some outsider. The stain on the windowsill conveys the same idea. So does the card on the body, which might have been prepared in the house. That all fits into your hypothesis, Watson. But now we come on the nasty, angular, uncompromising bits which won't slip into their places. Why a cut-off shotgun of all weapons—and an American one at that? How could they be so sure that the sound of it would not bring someone on to them? It's a mere chance as it is that Mrs. Allen did not start out to inquire for the slamming door. Why did your guilty couple do all this, Watson?"

      "I confess that I can't explain it."

      "Then again, if a woman and her lover conspire to murder a husband, are they going to advertise their guilt by ostentatiously removing his wedding ring after his death? Does that strike you as very probable, Watson?"

      "No, it does not."

      "And once again, if the thought of leaving a bicycle concealed outside had occurred to you, would it really have seemed worth doing when the dullest detective would naturally say this is an obvious blind, as the bicycle is the first thing which the fugitive needed in order to make his escape."

      "I can conceive of no explanation."

      "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 window-sill 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 umbrella 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."

      "Well,

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