“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 of {~FRACTION NUMERATOR ONE~}{~SUBSCRIPT ONE~}{~SUBSCRIPT THREE~}{~SUBSCRIPT FIVE~} 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.