the light best, and if the screen is distant, may be employed to produce a large figure of the pattern on the back of the mirror, but the result is not nearly as beautiful as that obtained by either of the former three methods, the first two in particular of which, if the mirror is placed in a darkened room, at about fourteen feet distance from the luminous point produced by a tropical sun, cause the reflection on the wall to assume an appearance startling even to an educated mind, and which might well have brought to the feet of the magician the ignorant poor of the middle ages.

Referring to the arrangement of mirror and lens shown in fig. 4, and remembering the reasoning employed in the case of figs. 1, 2, and 3, we should conclude that if a portion, AB, of the mirror is more concave than the rest, this portion ought to appear as bright on a dark ground if the screen be held in the positions 1, 2, or 4, since, in all these, DE is less than CD or EF, but if it be held at any point, 3 in the region between the principal focus P and JJ, then, since here DE is greater than CD or EF, the concave portion ought to appear as dark on a relatively light ground, while at JJ, the image being uniformly illuminated, the appearance of the pattern ought to disappear altogether. We should expect, then, that the passage of the screen, either through P or through JJ, ought to produce an inversion of the phenomenon if the theory that we are here advocating of the Japanese mirror be correct.

Again, imagine the lens LL to gradually move up to the mirror until it attains a very near position, as in fig. 5, then an inspection of the direction of the rays shows that any concave part, AB, of the mirror must appear on the screen as light on a dark ground for all points between the lens and the principal focus P, but that it will be seen as dark on a relatively light ground for all positions of the screen

in the region beyond P. On arranging the light as in fig. 4, and placing the screen successively in the positions 1, 2, 3, JJ, and 4, afterwards moving the lens up to the Japanese mirror, until the distance between it and the mirror was less than the focal length of the lens, we found that the experiments bore out, in every detail, the results that must follow from the "inequality of curvature theory."

Returning now to fig. 3, in which it was first shown that a converging beam produced an inversion of the phenomenon, we find it impossible to obtain a distinct dark image of the pattern on a light ground by the employment of one converging lens only. This is partly due to the fact that here we are dealing with diverging pencils of light falling on the screen, so that no true image of the pattern is formed; and partly caused by the blurring effect arising from a beam of sunlight, consisting of a number of slightly diverging pencils. This latter may be, to a certain extent, corrected, either by allowing a very small beam of sunlight to fall on the single converging lens, or by causing the sunlight to be brought first to a focus by one lens, and then with a second lens at several feet distance, forming another convergent pencil of light, in which the convergent mirror is placed.

Guided by all that proceeds, we are led to the undoubted conclusion, that the third of the proposed explanations is the correct one, namely, that the whole action of the magic mirror arises from the thicker portions being flatter than the remaining convex surface, and even being sometimes actually concave.

The next question arises, why is there this difference in the curvature of the different portions of the surface? The experience that one gains from an examination of a large number of Japanese mirrors supplies, in part at any rate, the answer to the question. No thick mirror reflects the pattern on the back, not one of the many beautiful mirrors exhibited at the National Exhibition of Japan in 1877, and which we were so fortunate as to be able to experiment with in a darkened room with a bright luminous point at some twelve feet distance, shows the phenomenon in the slightest degree; some good old mirrors in the museum of the Imperial College of Engineering, and which belonged to the family of the late Emperor, the Shogun, of Japan, fail to reflect any trace of a design, and some old round mirrors without handles, which we have also tried, are, with the exception of one about six inches in radius, and for which the owner asked many pounds, equally unsuccessful. Now this in itself, independently of the erroneous idea regarding stamping, is almost sufficient to negative Mr. Prinsep's idea that part of the metal was by this stamping rendered in a degree harder than the rest, so that in polishing it was not worn away to the same extent." Again, it is not that the pattern is less clearly executed on the backs of these choice mirrors, since the better

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the mirror the finer and bolder is the pattern, but what is especially noticeable is that every one of these mirrors is as a whole far thicker than an ordinary Japanese mirror, and its surface is much less convex. This naturally led us to inquire, how are Japanese mirrors made convex? are they cast so, or do they acquire this shape from some subsequent process? In the article "Miroirs " in "Les Industries Anciennes et Modernes de l'Empire Chinois," nothing is said on this point, and the paper communicated by M. Julien on the Chinese Magic Mirror to the French Academy, is equally silent on this subject. Professor Pepper says, "Are the mirrors cast in a double mould one side of which is in intaglio and one side in relievo?" but has no information by which he can answer this question. We also were quite unable to gain any assistance from foreign or from Japanese books or manuscripts regarding the method by which the convexity observed in almost all Japanese mirrors is produced, and were consequently compelled to make inquiries ourselves among mirror makers. Now although shops where mirrors are sold are common enough in Tokio, workshops where they are made are very difficult to find. A workshop was said to exist at Oji, but after a long search in this suburb of Tokio we found only one old woman and a little mercury amalgam in a small hovel about six feet by four, as the representative of the mirror industry. As women are supposed to know nothing in Japan, it was useless to make inquiries of her: another search made on a subsequent occasion in a different direction only elicited the information that mirrors were not made at that time of the year, as the moulds were frostbitten. Mirror-sellers, mirror-polishers we could find, but nobody in Tokio seemed to cast mirrors. We have since found out that this is really the case, since all the common mirrors come from the ancient capital Kioto, about 400 miles to the south of Tokio, and it is only when some special order is given that mirrors are made in the capital. However, at last we lighted on some mirror makers and sellers combined, from whom Mr. Kawaguchi (one of the assistants to the Professor of Natural Philosophy at our College), in the course of many conversations, extracted much valuable information. As a large portion of this is not to be found, as far as we aware, in any books, and as it bears upon the explanation of the magic mirror given in this paper, it naturally finds a place here.

Composition used in Making Mirrors.—In regard to the composition of the mirrors the following seems to be the metal-mixture employed in Tokio:

Iyo shirome is the name given to a natural sulphide of lead and antimony taken out of the impurities of the lead ore from the mines of the province Iyo, in the island Shikoku. Tori shirome is a shirome containing an admixture of copper. In vol. iv of the "Transactions of the Asiatic Society of Japan," Dr. Geerts gives the metal-mixture employed in one of the largest mirror foundries in Kioto as follows:— Mirrors of First Quality.

MM. Champion and Pellet give as the result of their analysis of the material of Chinese mirrors :—

One of the chief of the Tokio mirror makers tells us he never puts ordinary lead into the mixture, since he finds this makes the face of

the mirror very difficult to be amalgamated; also that, in casting, the lead comes to the surface and spoils the mixture. Zinc he also finds has the same effect. But as a small amount of lead is required to be inserted in the composition to prevent the metal from becoming too brittle, the shirome or sulphide of lead and antimony is employed. The chief sources of this shirome arranged in order of merit are the provinces in the south of Japan, called—

1. Iyo, in the island Skikoku,

2. Shekishu,

3. Choshu,

4. Tosa, in the island Shikoku,

but the shirome coming from the last province, Tosa, cannot be used for mirrors, as it contains too much lead.

The mirrors of the first quality are only manufactured on receipt of a special order, and new mirrors of even the second and third qualities are rarely found ready made. The ordinary stock of the shops consists of mirrors of the fourth quality, in which there is no tin. The absence of both tin and the Iyo shirome in the composition of the fifth quality is found to make the mirrors give a pale reflection, from the difficulty of amalgamation, and so the fifth composition is not often used.

The composition for the common mirrors is made at the copper mines and forwarded to the various mirror foundries. Formerly the metal for mirrors was extensively prepared at Kioto, but the trade is dying out now, and is said to have been slowly diminishing for the last hundred and thirty years, at the commencement of which period it had reached its maximum.

Moulds for Mirrors.-The most striking feature of the moulds is that while practically all Japanese mirrors are convex, the surface of each half of the mould is quite flat. The material used for making the mould is a mixture of a special kind of clay (found near Tokio and Osaka) with water and straw-ash. Two suitable slabs having been formed from this plastic compound with the aid of wooden frames, a thick layer of half liquid mixture of powdered old crucibles, or of a fine powder called to-no-ko, made from a soft kind of whetstone, is spread on them. The design for the back of the mirror is then cut directly on one half of the mould, or a sketch drawn on paper is first stuck on and used as a guide in cutting the design in the clay. Sometimes, but rarely, the design is stamped in the clay with a pattern wood-block cut in relief like the proposed back of the mirror. After the design is complete a rim of the same material as that used in the construction of the mould, and having a thickness equal to that desired for the mirror, is attached to one half of the mould. The two halves are then dried in the smoke of a pine tree fire, pressed and tied together, and laid in the casting