have begun his preparations immediately after Belford saw him standing in the doorway of his room at eight minutes to eleven. To descend the wall; to enter the study; to hold Hoode in chaffing conversation for a moment to allay his curiosity regarding the unusual method of entry; to kill him; to reassemble the wood-rasp; to set the ‘struggle’ scene; arrange the clock; to climb back up the wall again; and all as noiseless as you please, cannot have taken him less than eight minutes at the very least. As I have shown, he was in all probability back in his room by four minutes past the hour (if not earlier) and it will be seen, therefore, that he must have begun descent of the wall by four minutes to at the latest.

“The witnesses I was after, therefore, were those who thought they had seen him between four minutes to and four minutes past the hour.

“Of these, as you can see from my statement of the alibi, Elsie Syme is the first, Mabel Smith the second, and Belford the third. (Elsie Syme, it is true, might be considered as barely coming within my rough-and-ready time-limit, but you must remember that all the times I fixed were calculations and not stopwatch records.)

“Separately, I questioned the three servants. It was not an easy task. I had to handle them gently, and I had to impress upon them the vital necessity to forget the conversation as soon as they had left me. I think I managed it.

“Their answers to my first important question were the same, though each was with me alone when I put it.

“I said: ‘You say you saw Sir Arthur at such and such a time in his room on the night of the murder, and that he was sitting in his chair and that that chair was by the window. Are you certain of this?’

“They said: ‘Yes, sir,’ and said it emphatically.

“I played my trump card. I played it in some fear; if the answers were not what I expected, my case fell.

“I said: ‘Now tell me: exactly how much of Sir Arthur did you see? What parts of him, I mean.’

“They goggled.

“I tried again: ‘Was the chair that big armchair? And was it facing the window with its back to the door?’

“ ‘Yes, sir,’ they said.

“I said: ‘Then all you saw of Sir Arthur was⁠—’

“They replied, after some further help but with conviction, that all they had seen was the top of his head, part of his trousers, and the soles of his shoes. Belford, who is an intelligent man, expanded his answer by saying: ‘You see, sir, we’re all so used-like to seein’ Sir Arthur sittin’ like that and in that chair as we just naturally thinks as how we’d seen all on ’im that night.’ Which, I think, is as lucid an explanation of the mistake as could well be given.

“I must explain here how I came in possession of this trump card of mine. It was through two casual observations, which at first never struck me as bearing in any way upon the matter I was investigating. The first was the annoying, almost impossible tidiness of Digby-Coates’s hair. It did not appear to be greased or pomaded in any way, and yet I never saw it other than as if he had just brushed it, and with care. The second was his curious trick of sitting on the edge of a chair with his feet thrust first backwards through the gateway formed by the front legs and then outwards until each instep is pressed against the back of each of those front legs. It is a trick most boys have, but it is unusual to find it persisting in a man of middle-age. Digby-Coates does not, of course, always sit like that, but frequently.

“What changed these two chance observations⁠—the sort of thing one idly notices about any man of one’s acquaintance without really thinking about them⁠—into perhaps the most important minor step in my case was a glimpse I had of Digby-Coates from the very point from which the servants who made his alibi had seen him. He was sitting as they had seen him sit (though I did not know this until I questioned them) in the big armchair, which was facing the window. All I could see from the passage was the long, solid back of the chair, the top of the well-tended head, six inches of each trouser-leg, and the soles of two shoes. On the open door was a notice: ‘Busy⁠—Please do not disturb.’

“The scene was, in fact, a replica of what I had gathered it to be on the night of the murder. I fell to thinking, and suddenly the most annoying pieces of my jigsaw puzzle fell into place. I went in and spoke to him. I looked, more carefully than ever before, at his head, and came to the conclusion that he was bald, but wore the most skilfully made toupee I had ever seen. I remembered that he had told me that he never used a valet. I pictured him⁠—he is the type⁠—as one to whom the thought that anyone else knew how unsavoury he appeared minus hair was abhorrent.

“When I discovered the toupee, I knew that I could smash the alibi if only the unknowing alibi-makers gave me, honestly, the answers I wanted.

“As you know, they did. I consider the matter clear, but I know it. Perhaps I had better show what Digby-Coates did that night; how he set his stage and played out his one-act show.

“He retires to his room, knowing that Hoode is in his study, Deacon busy or, as often of late, out, Miss Hoode and Mrs. Mainwaring in their beds, and some of the servants, as he wishes them, moving about the house⁠—he has studied their movements and knows that on this night of the week there is work to do which keeps them later than usual. Luckily for him, the night is

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