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.

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.