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and anyone who should examine those hats, as you suggest, might draw some very misleading deductions as to the personal habits of S. Löwe."

      Mr. Marchmont chuckled audibly, and then, remembering the gravity of the occasion, suddenly became portentously solemn.

      "So you think that the hat is of no use, after all?" said Mr. Löwe, in a tone of deep disappointment.

      "I won't say that," replied Thorndyke. "We may learn something from it. Leave it with me, at any rate; but you must let the police know that I have it. They will want to see it, of course."

      "And you will try to get those things, won't you?" pleaded Löwe.

      "I will think over the case. But you understand, or Mr. Marchmont does, that this is hardly in my province. I am a medical jurist, and this is not a medico-legal case."

      "Just what I told him," said Marchmont. "But you will do me a great kindness if you will look into the matter. Make it a medico-legal case," he added persuasively.

      Thorndyke repeated his promise, and the two men took their departure.

      For some time after they had left, my colleague remained silent, regarding the hat with a quizzical smile. "It is like a game of forfeits," he remarked at length, "and we have to find the owner of 'this very pretty thing.'" He lifted it with a pair of forceps into a better light, and began to look at it more closely.

      "Perhaps," said he, "we have done Mr. Löwe an injustice, after all. This is certainly a very remarkable hat."

      "It is as round as a basin," I exclaimed. "Why, the fellow's head must have been turned in a lathe!"

      Thorndyke laughed. "The point," said he, "is this. This is a hard hat, and so must have fitted fairly, or it could not have been worn; and it was a cheap hat, and so was not made to measure. But a man with a head that shape has got to come to a clear understanding with his hat. No ordinary hat would go on at all.

      "Now, you see what he has done—no doubt on the advice of some friendly hatter. He has bought a hat of a suitable size, and he has made it hot—probably steamed it. Then he has jammed it, while still hot and soft, on to his head, and allowed it to cool and set before removing it. That is evident from the distortion of the brim. The important corollary is, that this hat fits his head exactly—is, in fact, a perfect mould of it; and this fact, together with the cheap quality of the hat, furnishes the further corollary that it has probably only had a single owner.

      "And now let us turn it over and look at the outside. You notice at once the absence of old dust. Allowing for the circumstance that it had been out all night, it is decidedly clean. Its owner has been in the habit of brushing it, and is therefore presumably a decent, orderly man. But if you look at it in a good light, you see a kind of bloom on the felt, and through this lens you can make out particles of a fine white powder which has worked into the surface."

      He handed me his lens, through which I could distinctly see the particles to which he referred.

      "Then," he continued, "under the curl of the brim and in the folds of the hatband, where the brush has not been able to reach it, the powder has collected quite thickly, and we can see that it is a very fine powder, and very white, like flour. What do you make of that?"

      "I should say that it is connected with some industry. He may be engaged in some factory or works, or, at any rate, may live near a factory, and have to pass it frequently."

      "Yes; and I think we can distinguish between the two possibilities. For, if he only passes the factory, the dust will be on the outside of the hat only; the inside will be protected by his head. But if he is engaged in the works, the dust will be inside, too, as the hat will hang on a peg in the dust-laden atmosphere, and his head will also be powdered, and so convey the dust to the inside."

      He turned the hat over once more, and as I brought the powerful lens to bear upon the dark lining, I could clearly distinguish a number of white particles in the interstices of the fabric.

      "The powder is on the inside, too," I said.

      He took the lens from me, and, having verified my statement, proceeded with the examination. "You notice," he said, "that the leather head-lining is stained with grease, and this staining is more pronounced at the sides and back. His hair, therefore, is naturally greasy, or he greases it artificially; for if the staining were caused by perspiration, it would be most marked opposite the forehead."

      He peered anxiously into the interior of the hat, and eventually turned down the head-lining; and immediately there broke out upon his face a gleam of satisfaction.

      "Ha!" he exclaimed. "This is a stroke of luck. I was afraid our neat and orderly friend had defeated us with his brush. Pass me the small dissecting forceps, Jervis."

      I handed him the instrument, and he proceeded to pick out daintily from the space behind the head-lining some half a dozen short pieces of hair, which he laid, with infinite tenderness, on a sheet of white paper.

      "There are several more on the other side," I said, pointing them out to him.

      "Yes, but we must leave some for the police," he answered, with a smile. "They must have the same chance as ourselves, you know."

      "But surely," I said, as I bent down over the paper, "these are pieces of horsehair!"

      "I think not," he replied; "but the microscope will show. At any rate, this is the kind of hair I should expect to find with a head of that shape."

      "Well, it is extraordinarily coarse," said I, "and two of the hairs are nearly white."

      "Yes; black hairs beginning to turn grey. And now, as our preliminary survey has given such encouraging results, we will proceed to more exact methods; and we must waste no time, for we shall have the police here presently to rob us of our treasure."

      He folded up carefully the paper containing the hairs, and taking the hat in both hands, as though it were some sacred vessel, ascended with me to the laboratory on the next floor.

      "Now, Polton," he said to his laboratory assistant, "we have here a specimen for examination, and time is precious. First of all, we want your patent dust-extractor."

      The little man bustled to a cupboard and brought forth a singular appliance, of his own manufacture, somewhat like a miniature vacuum cleaner. It had been made from a bicycle foot-pump, by reversing the piston-valve, and was fitted with a glass nozzle and a small detachable glass receiver for collecting the dust, at the end of a flexible metal tube.

      "We will sample the dust from the outside first," said Thorndyke, laying the hat upon the work-bench. "Are you ready, Polton?"

      The assistant slipped his foot into the stirrup of the pump and worked the handle vigorously, while Thorndyke drew the glass nozzle slowly along the hat-brim under the curled edge. And as the nozzle passed along, the white coating vanished as if by magic, leaving the felt absolutely clean and black, and simultaneously the glass receiver became clouded over with a white deposit.

      "We will leave the other side for the police," said Thorndyke, and as Polton ceased pumping he detached the receiver, and laid it on a sheet of paper, on which he wrote in pencil, "Outside," and covered it with a small bell-glass. A fresh receiver having been fitted on, the nozzle was now drawn over the silk lining of the hat, and then through the space behind the leather head-lining on one side; and now the dust that collected in the receiver was much of the usual grey colour and fluffy texture, and included two more hairs.

      "And now," said Thorndyke, when the second receiver had been detached and set aside, "we want a mould of the inside of the hat, and we must make it by the quickest method; there is no time to make a paper mould. It is a most astonishing head," he added, reaching down from a nail a pair of large callipers, which he applied to the inside of the hat; "six inches and nine-tenths long by six and six-tenths broad, which gives us"—he made a rapid calculation on a scrap of paper—"the extraordinarily high cephalic index of 95·6."

      Polton now took possession of the hat, and, having stuck a band of wet tissue-paper round the inside, mixed a small bowl of plaster-of-Paris, and very dexterously ran

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