hat? Probably, if this supposition is true, because he either had not sufficient time to extract it, or else did not know how to extract it and therefore took the hat away with him to examine it at his leisure. Do you agree with me so far?”

The District Attorney nodded slowly. Queen sat still, his eyes vaguely troubled.

“Let us for a moment consider what the hat could possibly have contained,” resumed Ellery, as he vigorously polished his glasses. “Due to its size, shape and cubic content our field of speculation is not a broad one. What could be hidden in a tophat? The only things that present themselves to my mind are: papers of some sort, jewelry, banknotes, or any other small object of value which could not easily be detected in such a place. Obviously, this problematical object would not be carried merely in the crown of the hat since it would fall out whenever the wearer uncovered his head. We are led to believe therefore that, whatever the object was, it was concealed in the lining of the hat. This immediately narrows our list of possibilities. Solid objects of bulk must be eliminated. A jewel might have been concealed; banknotes or papers might have been concealed. We can, I think, discard the jewel, from what we know of Monte Field. If he was carrying anything of value, it would probably be connected in some way with his profession.

“One point remains to be considered in this preliminary analysis of the missing tophat. And, gentlemen, it may very well become a pivotal consideration before we are through.⁠—It is of paramount importance for us to know whether the murderer knew in advance of his crime that it would be necessary for him to take away Monte Field’s tophat. In other words, did the murderer have foreknowledge of the hat’s significance, whatever it may prove to be? I maintain that the facts prove deductively, as logically as facts can prove deductively, that the murderer had no foreknowledge.

“Follow me closely.⁠ ⁠… Since Monte Field’s tophat is missing, and since no other tophat has been found in its place, it is an undeniable indication that it was essential that it be taken away. You must agree that, as I pointed out before, the murderer is most plausibly the remover of the hat. Now! Regardless of why it had to be taken away, we are faced with two alternatives: one, that the murderer knew in advance that it had to be taken away; or two, that he did not know in advance. Let us exhaust the possibilities in the former case. If he knew in advance, it may be sanely and logically assumed that he would have brought with him to the theatre a hat to replace Field’s, rather than leave an obvious clue by the provocative absence of the murdered man’s hat. To bring a replacement hat would have been the safe thing to do. The murderer would have had no difficulty in securing a replacement hat, since knowing its importance in advance, he could certainly have armed himself with a further knowledge of Field’s head-size, style of tophat, and other minor details. But there is no replacement hat. We have every right to expect a replacement hat in a crime so carefully concocted as this one. There being none, our only conclusion can be that the murderer did not know beforehand the importance of Field’s hat; otherwise he would assuredly have taken the intelligent precaution of leaving another hat behind. In this way the police would never know that Field’s hat had any significance at all.

“Another point in corroboration. Even if the murderer didn’t desire, for some dark reason of his own, to leave a replacement hat, he certainly would have arranged to secure what was in the hat by cutting it out. All he had to do was to provide himself in advance with a sharp instrument⁠—a pocketknife, for example. The empty hat, though cut, would not have presented the problem of disposal that the missing hat would. Surely the murderer would have preferred this procedure, had he foreknowledge of the hat’s contents. But he did not do even this. This, it seems to me, is strong corroborative evidence that he did not know before he came to the Roman Theatre that he would have to take away a hat or its contents. Quod erat demonstrandum.

The District Attorney gazed at Ellery with puckered lips. Inspector Queen seemed sunk in a lethargy. His hand hovered midway between his snuffbox and his nose.

“Just what’s the point, Ellery?” inquired Sampson. “Why is it important for you to know that the murderer had no foreknowledge of the hat’s significance?”

Ellery smiled. “Merely this. The crime was committed after the beginning of the second act. I want to be sure in my own mind that the murderer, by not knowing in advance of the hat’s significance, could not have used the first intermission in any manner whatsoever as an essential element of his plan.⁠ ⁠… Of course, Field’s hat may turn up somewhere on the premises, and its discovery would invalidate all these speculations. But⁠—I don’t think it will.⁠ ⁠…”

“That analysis of yours might be elementary, boy, but it sounds quite logical to me,” said Sampson approvingly. “You should have been a lawyer.”

“You can’t beat the Queen brains,” chuckled the old man suddenly, his face wreathed in a wide smile. “But I’m going to get busy on another tack that ought to jibe somewhere with this puzzle of the hat. You noticed, Ellery, the name of the clothier sewed into Field’s coat?”

“No sooner said than done,” grinned Ellery. Producing one of the small volumes which he carried in his topcoat pocket, he opened it and pointed to a notation on the flyleaf. “Browne Bros., gentlemen⁠—no less.”

“That’s right; and I’ll have Velie down there in the morning to check up,” said the Inspector. “You must have realized that Field’s clothing is of exceptional quality. That evening-suit cost three hundred dollars,

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