“Then it was that you took out of your pocket a golf-ball—a golf-ball of a very common kind, by which you could not be traced. Leaning out of the window on the left-hand side of the train, you threw the ball backwards, in such a way as to hit the further window of Brotherhood’s carriage, the window on the side furthest from the engine, I mean. Your idea was that the ball, bouncing off with considerable speed, would fall into the valley below, where of course it would arouse no suspicion if it were found. As a matter of fact, it lodged at the top of the viaduct and was there found by me. “Brotherhood was startled at the noise, and, as you had hoped, he put his head out of the window. As you had hoped, he looked backwards in doing so, because it was the back window that the ball had hit. At that moment you brought down your stick with a violent blow over his skull, and he must have fallen doubled up over the window-frame. “It was not difficult, with the train stationary and the fog all around you, to climb along the foot-board, still on the left-hand side of the train. You had to be quick, though, for the train might move on at any moment. You removed his season-ticket, and substituted a third-class ticket for Paston Whitchurch. The train you were on did not stop at Paston Whitchurch; the ticket, then, would make people think that Brotherhood had fallen from the slow train that went past later. You changed the time of his watch, in order to confirm this impression. You put a wrist-watch on him, registering the same time, so as to make assurance doubly sure. There you over-reached yourself; there is no need to explain how. “All this you did while your victim, I suppose, still breathed. And still the train was held up by the signals. There was time to search the pockets. Your cipher-letter was still in his pocket; you thought there was no need to destroy that, because its secret could not be penetrated. You forgot that on the back of the sheet of note-paper on which you sent the cipher message you had jotted down some references to anthems, mattins, and so on, which helped me ultimately to trace the crime to you. You also found a coupon for a sleeping-carriage; that, too, you did not destroy, but you altered the dates, because your quick brain saw that a sleeping-carriage coupon for Tuesday would not have been held by a man travelling in the later train, the 4.50.