box at an angle of 80° with the horizon, the half of the mould on which the design has been cut being uppermost. Finally, the molten speculum metal is run into a number of moulds at the same time, which, when cold, are broken up and the castings removed.

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Mirrors cast in a mould, in which the design has been cut by hand, are called ichi mai buki, "mould used once," and are regarded as artists' proofs," as the design on the back is well defined. To form subsequent moulds the two halves are pressed, when the clay is wet, on an ichi mai buki mirror, and the pattern is this way transferred, but the designs on the backs of the mirrors cast in such moulds are not as clear as on an ichi mai buki mirror, which therefore sells for a much higher price.

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Curving the Surface. The rough mirror is first scraped approximately smooth with a hand-scraping tool, and as this would remove any small amount of convexity, had such been imparted to it in casting, it is useless to make the mould slightly convex. If, however, a convex or concave mirror of small radius is required, then the surface of the mould is made concave or convex. On the other hand, to produce the small amount of convexity which is possessed by ordinary Japanese mirrors the following method is employed, if the mirror is thin, and it is with thin mirrors we have especially to deal, since it is only in these mirrors that the apparent reflection of the back is observed. The mirror is placed face uppermost flat on a wooden board, and then scraped or rather scratched with a rounded iron rod about half an inch in diameter and a foot long, called a megebo, “ distorting rod," so that a series of parallel scratches is produced, which causes the face of the mirror to become convex in the direction at right angles to the scratches, but to remain straight parallel to the scratches, in fact it becomes very slightly cylindrical, the axis of the cylinder being parallel to the scratches. This effect is very clearly seen by applying a straight-edge in different ways to the face of an unpolished mirror which has received a single set of scratches only. A series of scratches is next made with the megebo in a direction of right angles to the former, a third set intermediate between the two former, and so on, the mirror each time becoming slightly cylindrical, the axis of the cylinder in each case being parallel to the line of scratches, so that eventually the mirror becomes generally convex. Some workmen prefer to make the scratches with the megebo in the form of small spirals, others in the form of large spirals, but the general principle of the method employed with their mirrors appears to be always the same, the face of the mirror is scratched with a blunted piece of iron, and becomes slightly convex, the back, therefore, becoming

concave.

After the operation with the "distorting rod" the mirror is very slightly scraped with a hand-scraping tool to remove the scratches

and to cause the face to present a smooth surface for the subsequent polishing.

In the case of thick mirrors the convexity is first made by cutting with a knife, and the "distorting rod" applied afterwards. But in connection with this cutting process of thick mirrors there is one very interesting point. If the maker finds on applying from time to time the face of the mirror to a hard clay concave pattern, and turn-ing it round under a little pressure, that a portion of the surface has not been in contact with the pattern, in other words, that he has cut away this portion too much, then he rubs this spot round and round with the megebo until he has restored the required degree of convexity. Here again then scratching on the surface produces convexity.

Now, why does the scraping of the "distorting rod" across the face of the mirror leave it convex? During the operation it is visibly concave. The metal must receive then a kind of "buckle," and spring back again so as to become convex when the pressure of the rod is removed. It might in such a case reasonably be expected that the thicker parts of the mirror would yield less to the pressure of the rod than the thinner, and so would be made less convex, or even they might not spring back, on the withdrawal of the rod, and so remain actually concave. Again, since we find that scraping the face of a mirror is the way in which it is made convex, and the back therefore concave, we might conclude that a deep scratch on the back would make the back convex and the face slightly concave. Such a concavity, as we have proved, would explain the phenomenon of the bright line appearing in the reflection of sunlight on the screen which was observed by Professor Atkinson to correspond with the scratch on the back.

It appears then that the magic of the Eastern mirror results from no subtle trick on the part of the maker, from no inlaying of other metals, or hardening of portions by stamping, but merely arises from the natural property possessed by thin bronze of buckling under a bending stress, so as to remain strained in the opposite direction after the stress is removed. And this stress is applied partly by the "distorting rod," and partly by the subsequent polishing, which, in an exactly similar way, tends to make the thinner parts more convex than the thicker.

Polishing.-After the scratches produced by the megebo are removed the mirror is first polished with a whetstone called either iyodo, "whetstone from the province of Iyo," or shiroto, "white whetstone." Afterwards a whetstone called tenshimado, "whetstone from the province Tsushima," or the powder to-no-ko, previously described, is used. Thirdly, a piece of charcoal, prepared from the ho tree (Magnolia hypoleuca) is rubbed over the surface. The face now becomes fairly smooth, but it still generally contains some few cavities; these the maker fills up from a stock of copper balls of various sizes which he

has at hand, and which are obtained from the cinders of a copperfurnace. The cavities when thus filled up are well rubbed so as to escape notice, but they may usually be detected by looking at the mirror obliquely.

It was perhaps the presence of these bits of copper in the mirror which Ou-tseu-hing saw broken up in the 13th century, that misled him into concluding that the phenomenon of the magic mirror was produced by the inlaying of denser copper in a portion of the face exactly corresponding with the design on the back.

When the face of the mirror has been made quite smooth, an amalgam consisting, according to the Tokio makers, of half tin and half mercury, with perhaps a trace of lead, or of

according to the analysis of MM. Champion and Pellet (“Industries de l'Empire Chinois") is rubbed over the surface with a stiff straw brush or with the hand. The mirror is finally wiped clean with a soft kind of paper, mino-gami, " paper from the province Mino," which is considered to scratch the surface less than silk. Leather was formerly never employed in polishing, as it would have been considered impious to pollute so holy a thing as a mirror by touching it with the skin of an animal; for under the old feudal system in Japan, workers in skins, saddlers, and others, belonged to the Eta or pariah class.

When mirrors possessed by private people require brightening up, in consequence of the surface tarnishing, the paste produced when razors are sharpened on a hone is usually rubbed over the face of the mirror.

III. On the Torsional Strain which remains in a Glass Fibre after release from Twisting Stress." By J. HOPKINSON, D.Sc., F.R.S. Received October 4, 1878.

It has long been known that if a wire of metal or fibre of glass be for a time twisted, and be then released, it will not at once return to its initial position, but will exhibit a gradually decreasing torsion in the direction of the impressed twist. The subject has undergone n good deal of investigation, especially in Germany. The best method of approximating to an expression of the facts has been given by Boltzmann ("Akad. der Wissensch. Wien," 1874). He rests his theory upon the assumption that a stress acting for a short time wil

leave after it has ceased a strain which decreases in amount as time elapses, and that the principle of superposition is applicable to these strains, that is to say, that we may add the after-effects of stresses, whether simultaneous or successive. Boltzmann also finds that, if (t) be the strain at time t resulting from a twist lasting a very short time 7, at time t=0, $(t) = 4, where A is constant for moderate values

ta'

of t, but decreases when t is very large or very small. A year ago I made a few experiments on a glass fibre which showed a deviation from Boltzmann's law. A paper on this subject by Kohlrausch ("Pogg. Ann.," 1876) suggested using the results of these experiments to examine how Boltzmann's law must be modified to express them. Professor Kohlrausch's results indicate that in the cases of silver wire and of fibre of caoutchouc Boltzmann's principle of superposition is only approximate, and that in the case of a short duration of twisting A (t) = 4, where a is less than unity; in case of a long duration of twisting he uses other formulæ, which pretty successfully express his results, owing in part no doubt to the fact that in most cases each determination of the constants applies only to the results of one duration of twisting. In a case like the present it appears best to adopt a simple form involving constants for the material only, and then see in what way it fails to express the varying conditions of experiment. In 1865 Sir W. Thomson published ("Proceedings of the Royal Society ") the results of some experiments on the viscosity of metals, the method being to determine the rate at which the amplitude of torsional vibrations subsided. One of the results was that if the wire were kept vibrating for some time it exhibited much greater viscosity than when it had long been quiescent. This should guard us from expecting to attain great uniformity in experiments so roughly conducted as those of the present paper.

2. The glass fibre examined was about 20 inches in length. Its diameter, which might vary somewhat from point to point, was not measured. The glass from which it was drawn was composed of silica, soda, and lime; in fact, was glass No. 1 of my paper on "Residual Charge of the Leyden Jar" ("Phil. Trans.," 1877. In all cases the twist given was one complete revolution. The deflection at any time was determined by the position on a scale of the image of a wire before a lamp, formed by reflection from a light concave mirror, as in Sir W. Thomson's galvanometers and quadrant electrometer. The extremities of the fibre were held in clamps of cork; in the first attempts the upper clamp was not disturbed during the experiment, and the upper extremity of the fibre was assumed to be fixed; the mirror also was attached to the lower clamp. This arrangement was unsatisfactory, as one could not be certain that a part of the

VOL. XXVIII.

M

observed after-effect was not due to the fibre twisting within the clamps and then sticking. The difficulty was easily avoided by employing two mirrors, each cemented at a single point to the glass fibre itself, one just below the upper clamp, the other just above the lower clamp. The upper mirror merely served by means of a subsidiary lamp and scale to bring back the part of the fibre to which it was attached to its initial position. The motion of the lower clamp was damped by attaching to it a vane dipping into a vessel of oil. The temperature of the room when the experiments were tried ranged from 13° C. to 13.8° C., and for the present purpose may be regarded as constant. The lower or reading scale had forty divisions to the inch, and was distant from the glass fibre and mirror 383 inches, excepting in Experiment V, when it was at 37 inches. Sufficient time elapsed between the experiments to allow all sign of change due to after-effect of torsion to disappear. In all cases the first line of the table gives the time in minutes from release from torsion, the second the deflection of the image from its initial position in scale divisions.

t

Experiment I.-The twisting lasted 1 minute.

1 2 3 4 5 7 10 17 25 Scale divisions.. 22 13 9 7 5 4 3 2 1

Experiment II.-The twisting lasted 2 minutes.

t.....

1 2 3 4 5 7 10 20 40 Scale divisions.. 38 25 18 15 13 10 8 4 3