That was the time schedule as well as he had been able to work it out. It was incomplete. For instance, he had not been able to account for Horikawa in it at all unless he represented _X_ in that ten minutes of time unaccounted for. It was inaccurate. Olson was entirely vague as to time, but he could be checked up pretty well by the others. Hull was not quite sure of his clock, and Rose could only say that she had reached the Paradox "quite a little after a quarter to ten." Fortunately his own arrival checked up hers pretty closely, since she could not have been in the room much more than five minutes before him. Probably she had been even less than that. James could not have left the apartment more than a minute or so before Rose arrived. It was quite possible that her coming had frightened him out. So far as the dovetailing of time went, there was only the ten minutes or less between the leaving of the Hulls and the appearance of James left unexplained. If some one other than those mentioned on his penciled memoranda had killed Cunningham, it must have been between half-past nine and twenty minutes to ten. The _X_ he had written in there was the only possible unknown quantity. By the use of hard work and common sense he had eliminated the rest of the time so far as outsiders were concerned. Kirby put the envelope in his pocket and went out to get some luncheon. "I'll call it a mornin'," he told himself with a smile. CHAPTER XXXIX KIRBY INVITES HIMSELF TO A RIDE The Twin Buttes man had said he would call it a morning, but he carried with him to the restaurant the problem that had become the pivot of all his waking thoughts. He had an appointment to meet a man for lunch, and he found his guest waiting for him inside the door. The restaurant was an inconspicuous one on a side street. Kirby had chosen it for that reason. The man who stepped into the booth with him and sat down on the opposite seat was Hudson, the clerk whom James had accused of losing the sheets of paper with the Japanese writing. "I've got it at last," he said as soon as he was alone. "Thought he never would go out and leave the key to the private drawer inside the safe. But he left the key in the lock--for just five minutes--while Miss Harriman came to see him about something this morning. He walked out with her to the elevator. I ducked into his office. There was the key in the drawer, and in the drawer, right at the bottom under some papers, I found what I wanted." He handed to Kirby the sheets of paper found in the living-room of the apartment where Horikawa had been found dead.