“Next comes Belford again. You remember that he entered the study at a point between three and four minutes past eleven. On his way there from the upper part of the house he passed Digby-Coates’s room and ‘saw Sir Arthur by the window.’ Since he went straight to the study, the time at which he passed Digby-Coates’s door cannot have been earlier than 11.03. “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):—