James, white to the lips, looked steadily at his cousin.  “A very ingenious theory.  I’ve always complimented you on your imagination,” he said, a little hoarsely, as though from a parched throat.

“You do not desire to make any explanation?” Kirby asked.

“Thanks, no.  I’m not on trial for my life here, am I?” answered the oil broker quietly, with obvious irony.

His wife was sobbing softly.  The man’s arm went round her and tightened in wordless comfort.

From his pocket Kirby drew the envelope upon which he had a few hours earlier penciled the time schedule relating to his uncle’s death.

“One of the points that struck me earliest about this mystery was that the man who solved it would have to work out pretty closely the time element.  Inside of an hour ten people beside Uncle James were in his rooms.  They must ‘a’ trod on each other’s heels right fast, I figured.  So I checked up the time as carefully as I could.  Here’s the schedule I made out.  Mebbe you’d like to see it.”  He handed the envelope to James.

Jack rose and looked over his brother’s shoulder.  His quick eye ran down the list.  “I get the rest of it,” he said.  “But what does X mean?”

“X is the ten minutes of Uncle’s time I can’t account for.  Some of us were with him practically every other minute. X is the whole unknown quantity.  It is the time in which he was prob’ly actually killed.  It is the man who may, by some thousandth chance, have stepped into the room an’ killed him while none of us were present,” explained Kirby.

“If there is such an unknown man you can cut the time down to five minutes instead of ten, providing your schedule is correct,” James cut in.  “For according to it I was there part of the time and Mrs. Hull part of the rest of it.”

“Yes,” agreed his cousin.

“But you may have decided that Mrs. Hull is X or that I am,” jeered James.  “If so, of course that ends it.  No need for a judge or jury.”

Kirby turned to the man by the door.  “Chief, one of the queer things about this mystery is that all the witnesses had somethin’ to conceal.  Go right through the list, an’ it’s true of every one of us.  I’m talkin’ about the important witnesses, of course.  Well, Cole an’ I found a paper in the living-room of the apartment where Horikawa was killed.  It was in Japanese.  I ought to have turned it over to you, but I didn’t.  I was kinda playin’ a lone hand.  At that time I didn’t suspect my cousin James at all.  We were workin’ together on this thing.  At least I thought so.  I found out better later.  I took the paper to him to get it translated, thinkin’ maybe Horikawa might have written some kind of a confession.  James lost that paper.  Anyhow, he claimed he did.  My theory is that Horikawa had some evidence against him.  He was afraid of what that paper would tell.”