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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 of ⅟₁₃₅ of an inch—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 to-morrow 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."

      

TRANSVERSE SECTIONS OF HUMAN HAIR: A, OF A NEGRO; B, OF AN ENGLISHMAN; C, OF THE BURGLAR. ALL MAGNIFIED 600 DIAMETERS.

      "Supposing the hat should not be that of the burglar after all?" I suggested.

      "That would be annoying. But I think it is his, and I think I can guess at the nature of the art treasures that were stolen."

      "And you don't intend to enlighten me?"

      "My dear fellow," he replied, "you have all the data. Enlighten yourself by the exercise of your own brilliant faculties. Don't give way to mental indolence."

      I endeavoured, from the facts in my possession, to construct the personality of the mysterious burglar, and failed utterly; nor was I more successful in my endeavour to guess at the nature of the stolen property; and it was not until the following morning, when we had set out on our quest and were approaching Limehouse, that Thorndyke would revert to the subject.

      "We are now," he said, "going to the factory of Badcomb and Martin, shell importers and cutters, in the West India Dock Road. If I don't find my man there, I shall hand the facts over to the police, and waste no more time over the case."

      "What is your man like?" I asked.

      "I am looking for an elderly Japanese, wearing a new hat or, more probably, a cap, and having a bruise on his right cheek or temple. I am also looking for a cab-yard; but here we are at the works, and as it is now close on the dinner-hour, we will wait and see the hands come out before making any inquiries."

      We walked slowly past the tall, blank-faced building, and were just turning to re-pass it when a steam whistle sounded, a wicket opened in the main gate, and a stream of workmen—each powdered with white, like a miller—emerged into the street. We halted to watch the men as they came out, one by one, through the wicket, and turned to the right or left towards their homes or some adjacent coffee-shop; but none of them answered to the description that my friend had given.

      The outcoming stream grew thinner, and at length ceased; the wicket was shut with a bang, and once more Thorndyke's quest appeared to have failed.

      "Is that all of them, I wonder?" he said, with a shade of disappointment in his tone; but even as he spoke the wicket opened again, and a leg protruded. The leg was followed by a back and a curious globular head, covered with iron-grey hair, and surmounted by a cloth cap, the whole appertaining to a short, very thick-set man, who remained thus, evidently talking to someone inside.

      Suddenly he turned his head to look across the street; and immediately I recognized, by the pallid yellow complexion and narrow eye-slits, the physiognomy of a typical Japanese. The man remained talking for nearly another minute; then, drawing out his other leg, he turned towards us; and now I perceived that the right side of his face, over the prominent cheekbone, was discoloured as though by a severe bruise.

      "Ha!" said Thorndyke, turning round sharply as the man approached, "either this is our man or it is an incredible coincidence." He walked away at a moderate pace, allowing the Japanese to overtake us slowly, and when the man had at length passed us, he increased his speed somewhat, so as to maintain the distance.

      Our friend stepped along briskly, and presently turned up a side street, whither we followed at a respectful distance, Thorndyke holding open his pocket-book, and appearing to engage me in an earnest discussion, but keeping a sharp eye on his quarry.

      "There he goes!" said my colleague, as the man suddenly disappeared—"the house with the green window-sashes. That will be number thirteen."

      It was; and, having verified the fact, we passed on, and took the next turning that would lead us back to the main road.

      Some twenty minutes later, as we were strolling past the door of a coffee-shop, a man came out, and began to fill his pipe with an air of leisurely satisfaction. His hat and clothes were powdered with white like those of the workmen whom we had seen come out of the factory. Thorndyke accosted him.

      "Is that a flour-mill up the road there?"

      "No, sir; pearl-shell. I work there myself."

      "Pearl-shell, eh?" said Thorndyke. "I suppose that will be an industry that will tend to attract the aliens. Do you find it so?"

      "No, sir; not at all. The work's too hard. We've only got one foreigner in the place, and he ain't an alien—he's a Jap."

      "A Jap!" exclaimed Thorndyke. "Really. Now, I wonder if that would chance to be our old friend Kotei—you remember

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