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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 a stream of the thick liquid on to the tissue-paper, where it quickly solidified. A second and third application resulted in a broad ring of solid plaster an inch thick, forming a perfect mould of the inside of the hat, and in a few minutes the slight contraction of the plaster in setting rendered the mould sufficiently loose to allow of its being slipped out on to a board to dry.

      We were none too soon, for even as Polton was removing the mould, the electric bell, which I had switched on to the laboratory, announced a visitor, and when I went down I found a police-sergeant waiting with a note from Superintendent Miller, requesting the immediate transfer of the hat.

      “The next thing to be done,” said Thorndyke, when the sergeant had departed with the bandbox, “is to measure the thickness of the hairs, and make a transverse section of one, and examine the dust. The section we will leave to Polton—as time is an object, Polton, you had better imbed the hair in thick gum and freeze it hard on the microtome, and be very careful to cut the section at right angles to the length of the hair—meanwhile, we will get to work with the microscope.”

      The hairs proved on measurement to have the surprisingly large diameter—fully double that of ordinary hairs, although they were unquestionably human. As to the white dust, it presented a problem that even Thorndyke was unable to solve. The application of reagents showed it to be carbonate of lime, but its source for a time remained a mystery.

      “The larger particles,” said Thorndyke, with his eye applied to the microscope, “appear to be transparent, crystalline, and distinctly laminated in structure. It is not chalk, it is not whiting, it is not any kind of cement. What can it be?”

      “Could it be any kind of shell?” I suggested. “For instance—”

      “Of course!” he exclaimed, starting up; “you have hit it, Jervis, as you always do. It must be mother-of-pearl. Polton, give me a pearl shirt-button out of your oddments box.”

      The button was duly produced by the thrifty Polton, dropped into an agate mortar, and speedily reduced to powder, a tiny pinch of which Thorndyke placed under the microscope.

      “This powder,” said he, “is, naturally, much coarser than our specimen, but the identity of character is unmistakable. Jervis, you are a treasure. Just look at it.”

      I glanced down the microscope, and then pulled out my watch. “Yes,” I said, “there is no doubt about it, I think; but I must be off. Anstey urged me to be in court by 11.30 at the latest.”

      With infinite reluctance I collected my notes and papers and departed, leaving Thorndyke diligently copying addresses out of the Post Office Directory.

      My business at the court detained me the whole of the day, and it was near upon dinner-time when I reached our chambers. Thorndyke had not yet come in, but he arrived half an hour later, tired and hungry, and not very communicative.

      “What have I done?” he repeated, in answer to my inquiries. “I have walked miles of dirty pavement, and I have visited every pearl-shell cutter’s in London, with one exception, and I have not found what I was looking for. The one mother-of-pearl factory that remains, however, is the most likely, and I propose to look in there tomorrow morning. Meanwhile, we have completed our data, with Polton’s assistance. Here is a tracing of our friend’s skull taken from the mould; you see it is an extreme type of brachycephalic skull, and markedly unsymmetrical. Here is a transverse section of his hair, which is quite circular—unlike yours or mine, which would be oval. We have the mother-of-pearl dust from the outside of the hat, and from the inside similar dust mixed with various fibres and a few granules of rice starch. Those are our data.”

      “Supposing the hat should not be that

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