He had accepted the identification of the remains, but on whose testimony? On that of the criminals, Mrs. Berlyn and the man whom he had thought was Jefferson Pyke. Of course at the time at which he interviewed them he had no idea of their connection with the crime, and therefore no reason to doubt their statements, but his error came in just here: that by the time he began to suspect them the identification was so firmly fixed in his mind that he overlooked the fact that it depended on them. If he had remembered that supremely important point he would have questioned the dead man’s identity. This would have led him to investigate, even more closely than he had, the movements of the Pykes and no doubt he would have thus discovered the impersonation which had been carried out. The first question, then, which demanded solution was: If the man whom he had thought was Jefferson Pyke was really his cousin, where was Jefferson himself? Like a man in a dream French went back to Kepple Street. Was Mrs. Welsh _absolutely_ sure that the Mr. Pyke who had engaged her rooms on the 22nd of July was the same man who had occupied them ever since? Mrs. Welsh, when at last she had been made to understand the question, was absolutely sure. If she were right, Stanley’s impersonation of Jefferson must have begun on that 22nd of July. They had both been at the Houston in the morning. By the evening Jefferson, the real Jefferson, apparently had vanished. Then suddenly French remembered the episode of the broken basin. It had not occurred to him before, but now he wondered if there was not more here than met the eye. The accident was unlikely. Had the basin been deliberately broken to help on some trick? He went back to the Houston and once again interviewed the reception clerk. But she could add nothing to her former statement. Then he reëxamined the chambermaid. From her at last he obtained a new fact, an apparently trifling fact, but what a difference it made in his conclusion! The girl had stated that the gentleman who broke the basin had told her that he had overslept himself and had asked her to see that his friend in No. 351 was awake. She had gone and found that the friend was already up. Now French learned that by “up” she had meant that the man was up and dressed and had left his room. At this a light shone into French’s mind. He retired to a corner of the smoking room, and after half an hour’s hard thinking he reached a detailed solution.