“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 pocket-knife, 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 snuff-box 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?”