The problem sifted down to two factors. One was the time element. The other was the temperament of James. A man may be unprincipled and yet draw the line at murder. He may be a seducer and still lack the courage and the cowardice for a cold-blooded killing. Kirby had studied his cousin, but the man was more or less of a sphinx to him. Behind those cold, calculating eyes what was he thinking? Only once had he seen him thrown off his poise. That was when Kirby and Rose had met him coming out of the Paradox white and shaken, his arm wrenched and strained. He had been nonplussed at sight of them. For a moment he had let his eyes mirror the dismay of his soul. The explanation he had given was quite inadequate as a cause. Twenty-four hours later Kirby had discovered the dead body of the Japanese valet Horikawa. The man had been dead perhaps a day. More hours than one had been spent by Kirby pondering on the possible connection of his cousin's momentary breakdown and the servant's death. _Had James come fresh from the murder of Horikawa_? It was possible that the Oriental might have held evidence against him and threatened to divulge it. James, with the fear of death in his heart, might have gone each day into the apartment where the man was lurking, taking to him food and newspapers. They might have quarreled. The strained tendons of Cunningham's arm could be accounted for a good deal more readily on the hypothesis of a bit of expert jiu-jitsu than on that of a fall downstairs. There were pieces in the puzzle Kirby could not fit into place. One of them was to find a sufficient cause for driving Horikawa to conceal himself when there was no evidence against him of the crime. The time element was tremendously important in the solution of the mystery of Cunningham's death. Kirby had studied this a hundred times. On the back of an envelope he jotted down once more such memoranda as he knew or could safely guess at. Some of these he had to change slightly as to time to make them dovetail into each other. 8.45. Uncle J. leaves City Club. 8.55. Uncle J. reaches rooms. 8.55- 9.10. Gets slippers, etc. Smokes. 8.55- 9.20. Olson watching from W. fire escape. 9.10- 9.30. Hulls in Apt. 9.30- 9.40. _X_. 9.37- 9.42. Approximately time Olson heard shot. 9.20- 9.42. Olson busy on roof, with rope, etc. Then at window till 9.53. 9.40- 9.53. James in Apt. 9.44- 9.50. Jack and Phyllis in Apt. 9.55-10.05. Wild Rose in rooms. 10.00. I reach rooms. 10.20. Meet Ellis. 10.25. Call police.