Sweetwater hesitated.

"I am very fond of the one of your own choosing," he smiled, "but if you insist——"

Mr. Gryce was already writing.

In another moment the two slips were passed in exchange across the table.

Instantly, a simultaneous exclamation left the lips of both.

Each read a name he was in no wise prepared to see. They had been following diverging lines instead of parallel ones; and it took some few minutes for them to adjust themselves to this new condition.

Then Mr. Gryce spoke:

"What led you into loading up Correy with an act which to accept as true would oblige us to deny every premise we have been at such pains to establish?"

"Because—and I hope you will pardon me, Mr. Gryce, since our conclusions are so different—I found it easier to attribute this deed of folly—or crime, if we can prove it such—to a man young in years than to one old enough to know better."

"Very good; that is undoubtedly an excellent reason."

As this was said with an accent we will for want of a better word call dry, Sweetwater, hardy as he was, flushed to his ears. But then any prick from Mr. Gryce went very deep with him.

"Perhaps," he ventured, "you will give even less indulgence to what I have to add in way of further excuse."

"I shall have to hear it first."

"Correy is a sport, an incorrigible one; it is his only weakness. He bets like an Englishman—not for the money, for the sums he risks are small, but for the love of it—the fun—the transient excitement It might be"—here Sweetwater's words came slowly and with shamefaced pauses—"that the shooting of that arrow—I believe I said something like this before—was the result of a dare."

A halt took place in the quick tattoo which Mr. Gryce's fingers were drumming out on the table-top. It was infinitesimal in length, but it gave Sweetwater courage to add:

"Then, I hear that he wishes to marry a rich girl and shrinks from proposing to her on account of his small salary."

"What has that got to do with it?"

"Nothing so far as I can see. I am only elaborating the meager report lying there under your hand. But I recognize my folly. You ordered me to dream, and I did so. Cannot we forget my unworthy vaporings and enter upon the consideration of what may prove more profitable?"

Here he glanced down at the slip of paper he himself held—the slip which Mr. Gryce had handed him with a single word written on it, and that word a name.

"In a moment," was Mr. Gryce's answer. "First explain to me how, with the facts all in mind, and your chart before your eyes, you reconciled Correy's position on the side staircase two minutes after the shooting with your theory of a quick escape to the court by means of the door back of the tapestry? Haven't you hurried matters to get him so far in such a short space of time?"

"Mr. Gryce, I have heard you say yourself that this question of time has been, from the first, our greatest difficulty. Even with these three means of escape in our minds, it is difficult to see how it was possible for anyone to get from the gallery to the court in the minute or so elapsing between the cry of the dying girl and the appearance at her side of the man studying coins in the adjoining section."

"You are right. There was a delay somewhere, as we shall find later on. But granting this delay, a man would have to move fast to go the full length of the court from the Curator's room even in the time which this small delay might afford him. But perhaps you cut this inextricable knot by locating Correy somewhere else than where he placed himself at the making of the chart."

"No, I cut it in another way. You remember my starting to tell you just now how, in my dissatisfaction with a certain portion of my dream, I refused to believe in the escape of my Mr. X by the way of the Curator's office. The tapestry was lifted, the bow flung behind, but the man stepped back instead of forward. An open flight along the gallery commended itself more to him than the doubtful one previously arranged for. If you will accept that for fact, which of course you will not, it is easy to see how Correy might have been somewhere on that staircase when the inspiration came to turn the appearance of flight into a show of his own innocence, by a quick rush back into the further gallery and a consequent loud-mouthed alarm. But I see that I am but getting deeper and deeper in the quagmire of a bad theory badly stated. I am forgetting——"

"Many things, Sweetwater. I will only mention a very simple one. The man who shot the arrow wore gloves. You wouldn't attribute any such extraordinary precaution as that to a fellow shooting an arrow across the court on a dare?"

"You wouldn't expect it, sir. But in going about the museum that afternoon, I came upon Correy's coat hanging on its peg. In one of its pockets was a pair of kid gloves."

"You say the fellow is courting a rich girl," suggested Mr. Gryce. "Under those circumstances some show of vanity is excusable. Certainly he would not carry his folly so far as to put on gloves for the shooting match with which you credit him, unless there was criminal intent back of his folly—which, of course, would be as hard for you as for me to believe."

Sweetwater winced, but noting the kindly twinkle with which Mr. Gryce softened the bitterness of this lesson, he brightened again and listened with becoming patience as the old man went on to say:

"To discuss probabilities in connection with this other name seems futile this morning. The ease with which one can twist the appearances of things to fit a preconceived theory as exemplified by the effort you have just made warns us to be chary of pushing one's idea too far without the firmest of bases to support it. If you find a man's coat showing somewhere on its lining evidences that there had once been sewed to it a loop of the exact dimensions of the one I passed over to you last night, I should consider it a much more telling clue to the personality of X than a pair of gloves in the pocket of a man who in all probability intends to finish up the day with a call on the girl he admires."

"I understand." Sweetwater was quite himself again. "But do you know that this is no easy task you are giving me, Mr. Gryce. Where a man has but two coats, or three at best, it might not be so hard, perhaps, to get at them. But some men have a dozen, and if I don't mistake——"

"Sweetwater, I meant to give you a task of no little difficulty. It will keep you out of mischief."