He leant back in his chair and smoked furiously. Yes, if there had been a murder, that must have been how it was committed. And that accounted for three, at any rate, of the puzzling circumstances—the place of the wound, the fact that only one empty shell had been found in Stanworth’s revolver although two shots had been fired that night, and the fact of the dead man’s grip upon the revolver being properly adjusted. It was only conjecture, of course, but it seemed remarkably convincing conjecture. Yet was it not more than counterbalanced by the facts that still remained? That the windows and door could be fastened, as they certainly had been, appeared to argue irresistibly that the midnight visitor had left the library while Mr. Stanworth was still alive. The confession, signed with his own hand, pointed equally positively to suicide. Could there be any way of explaining these two things so as to bring them into line with the rest? If not, this brilliant theorising must fall to the ground. Shelving the problem of the visitor’s exit for the time being, Roger began to puzzle over that laconically worded document. During the next quarter of an hour Roger himself might have presented a problem to an acute observer, had there been one about, which, though not very difficult of solution, was nevertheless not entirely without interest. To smoke furiously, with one’s pipe in full blast, betokens no small a degree of mental excitement; to sit like a stone image and allow that same pipe to go out in one’s mouth is evidence of still greater prepossession; but what are we to say of a man who, after passing through these successive stages, smokes away equally furiously at a perfectly cold pipe under the obvious impression that it is in as full blast as before? And that is what Roger was doing for fully three minutes before he finally jumped suddenly to his feet and hurried off once again to that happy hunting ground of his, the library. There Alec found him twenty minutes later, when the car had departed irrevocably for the station. A decidedly more cheerful Alec than that of the morning, one might note in passing; and not looking in the least like a young man who has just parted with his lady for a whole month. It is a reasonable assumption that Alec had not been wasting the last half hour. “Still at it?” he grinned from the doorway. “I had a sort of idea I should find you here.” Roger was a-quiver with excitement. He scrambled up from his knees beside the waste-paper basket, into which he had been peering, and flourished a piece of paper in the other’s face. “I’m on the track!” he exclaimed. “I’m on the track, Alexander, in spite of your miserable sneers. Nobody around, is there?” Alec shook his head. “Well? What have you discovered now?” he asked tolerantly. Roger gripped his arm and drew him towards the writing table. With an eager finger he stubbed at the blotter. “See that?” he demanded.