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. I could read all that in the dust; and I could read that as he walked he grew more and more excited. That is shown by the increased length of his strides. He was talking all the while, and working himself up, no doubt, into a fury. Then the tragedy occurred. I’ve told you all I know myself now, for the rest is mere surmise and conjecture. We have a good working basis, however, on which to start. We must hurry up, for I want to go to Halle’s concert to hear Norman Neruda this afternoon.”

This conversation had occurred while our cab had been threading its way through a long succession of dingy streets and dreary byways. In the dingiest and dreariest of them our driver suddenly came to a stand. “That’s Audley Court in there,” he said, pointing to a narrow slit in the line of dead-coloured brick. “You’ll find me here when you come back.”

Audley Court was not an attractive locality. The narrow passage led us into a quadrangle paved with flags and lined by sordid dwellings. We picked our way among groups of dirty children, and through lines of discoloured linen, until we came to Number 46, the door of which was decorated with a small slip of brass on which the name Rance was engraved. On inquiry we found that the constable was in bed, and we were shown into a little front parlour to await his coming.

He appeared presently, looking a little irritable at being disturbed in his slumbers. “I made my report at the office,” he said.