“After this we have Elsie Syme again. This time she is on her way to bed. Passing along the passage she again ‘saw Sir Arthur sitting by the window.’ The time in this instance is a little harder to get at, but cannot have been more than six minutes past the hour.
“Last we have the evidence of old Poole, who, after entering the study on hearing Miss Hoode scream, immediately fled to fetch his dead master’s friend. He found Sir Arthur sitting with a book, his arm-chair pulled close up to the open window. This, since Miss Hoode entered the study at approximately ten minutes past eleven, was probably at 11.13 or thereabouts.
“That is the alibi, and a very good one it is, too—too good. It was, of course, never recognised as being an alibi, since Digby-Coates was never suspected by police or public as being the murderer; but the very fact of its being there (it trickled out mixed up with unimportant and verbose evidence, and was very cleverly referred to by Digby-Coates himself on every possible occasion) must have had its sub-conscious effect. (I should perhaps explain here that, as Digby-Coates was never suspected and the alibi was therefore the nebulous but effective thing I have described, the times I have given were not mentioned otherwise than generally: such exactitude as appears above is the result of Superintendent Boyd’s and my own questioning, of which more came later.)
“I have shown that according to the witnesses, none of whom I could suspect of anything but honesty, Digby-Coates was seen there in his room at times which made it impossible that he should have done the murder. Yet I knew he was the murderer. Therefore some at least of these witnesses who had sworn to seeing him were mistaken.
“I had, then, to find out (a) which witnesses were thus in error, and (b) how they had been induced to make their common mistake.
“I got at (a) like this: (if the way seem long and roundabout, remember that it is far more difficult to find things out than to understand, when told, how they were so found out):—
“Digby-Coates, I reasoned, must 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 stop-watch 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.