“How, then, did you deduce the telegram?”

“Why, of course I knew that you had not written a letter, since I sat opposite to you all morning. I see also in your open desk there that you have a sheet of stamps and a thick bundle of postcards. What could you go into the post-office for, then, but to send a wire? Eliminate all other factors, and the one which remains must be the truth.”

“In this case it certainly is so,” I replied after a little thought. “The thing, however, is, as you say, of the simplest. Would you think me impertinent if I were to put your theories to a more severe test?”

“On the contrary,” he answered, “it would prevent me from taking a second dose of cocaine. I should be delighted to look into any problem which you might submit to me.”

“I have heard you say it is difficult for a man to have any object in daily use without leaving the impress of his individuality upon it in such a way that a trained observer might read it. Now, I have here a watch which has recently come into my possession. Would you have the kindness to let me have an opinion upon the character or habits of the late owner?”

I handed him over the watch with some slight feeling of amusement in my heart, for the test was, as I thought, an impossible one, and I intended it as a lesson against the somewhat dogmatic tone which he occasionally assumed. He balanced the watch in his hand, gazed hard at the dial, opened the back, and examined the works, first with his naked eyes and then with a powerful convex lens. I could hardly keep from smiling at his crestfallen face when he finally snapped the case to and handed it back.

“There are hardly any data,” he remarked. “The watch has been recently cleaned, which robs me of my most suggestive facts. ”

“You are right,” I answered. “It was cleaned before being sent to me.”

In my heart I accused my companion of putting forward a most lame and impotent excuse to cover his failure. What data could he expect from an uncleaned watch?

“Though unsatisfactory, my research has not been entirely barren,” he observed, staring up at the ceiling with dreamy, lack-lustre eyes. “Subject to your correction, I should judge that the watch belonged to your elder brother, who inherited it from your father.”

“That you gather, no doubt, from the H. W. upon the back?”

“Quite so. The W suggests your own name. The date of the watch is nearly fifty years back, and the initials are as old as the watch: so it was made for the last generation. Jewellery usually descends to the eldest son, and he is most likely to have the same name as the father. Your father has, if I remember right, been dead many years. It has, therefore, been in the hands of your eldest brother.”

“Right, so far,” said I. “Anything else?”

“He was a man of untidy habits — very untidy and careless. He was left with good prospects, but he threw away his chances, lived for some time in poverty with occasional short intervals of prosperity, and finally, taking to drink, he died. That is all I can gather.”

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