I had this fellow’s stride both on the clay outside and on the dust within. Then I had a way of checking my calculation. When a man writes on a wall, his instinct leads him to write above the level of his own eyes. Now that writing was just over six feet from the ground. It was child’s play.”

“And his age?” I asked.

“Well, if a man can stride four and a half feet without the smallest effort, he can’t be quite in the sere and yellow. That was the breadth of a puddle on the garden walk which he had evidently walked across. Patent-leather boots had gone round, and Square-toes had hopped over. There is no mystery about it at all. I am simply applying to ordinary life a few of those precepts of observation and deduction which I advocated in that article. Is there anything else that puzzles you?”

“The finger-nails and the Trichinopoly,” I suggested.

“The writing on the wall was done with a man’s forefinger dipped in blood. My glass allowed me to observe that the plaster was slightly scratched in doing it, which would not have been the case if the man’s nail had been trimmed. I gathered up some scattered ash from the floor. It was dark in colour and flaky—such an ash is only made by a Trichinopoly. I have made a special study of cigar ashes—in fact, I have written a monograph upon the subject. I flatter myself that I can distinguish at a glance the ash of any known brand either of cigar or of tobacco. It is just in such details that the skilled detective differs from the Gregson and Lestrade type.”

“And the florid face?” I asked.

“Ah, that was a more daring shot, though I have no doubt that I was right. You must not ask me that at the present state of the affair.”

I passed my hand over my brow. “My head is in a whirl,” I remarked; “the more one thinks of it the more mysterious it grows. How came these two men—if there were two men—into an empty house? What has become of the cabman who drove them? How could one man compel another to take poison? Where did the blood come from? What was the object of the murderer, since robbery had no part in it? How came the woman’s ring there? Above all, why should the second man write up the German word RACHE before decamping? I confess that I cannot see any possible way of reconciling all these facts.”

My companion smiled approvingly.

“You sum up the difficulties of the situation succinctly and well,” he said. “There is much that is still obscure, though I have quite made up my mind on the main facts. As to poor Lestrade’s discovery, it was simply a blind intended to put the police upon a wrong track, by suggesting Socialism and secret societies. It was not done by a German. The A, if you noticed, was printed somewhat after the German fashion. Now, a real German invariably prints in the Latin character, so that we may safely say that this was not written by one, but by a clumsy imitator who overdid his part. It was simply a ruse to divert inquiry into a wrong channel. I’m not going to tell you much more of the case, Doctor. You know a conjurer gets no credit when once he has explained his trick; and if I show you too much of my method of working, you will come to the conclusion that I am a very ordinary individual after all.”

“I shall never do that,” I answered; “you have brought detection as near an exact science as it ever will be brought in this world.”

My companion flushed up with pleasure at my words, and the earnest way in which I uttered them. I had already observed that he was as sensitive to flattery on the score of his art as any girl could be of her beauty.

“I’ll tell you one other thing,” he said. “Patent-leathers and Square-toes came in the same cab, and they walked down the pathway together as friendly as possible—arm-in-arm, in all probability. When they got inside, they walked up and down the room—or rather, Patent-leathers stood still while Square-toes walked up and down.