transmitting polarised light through the crystal in the directions ac, bd, and subsequently analysing it, a system of rings round each of these axes. The system will exhibit the individual rings very plainly if the crystal is thin; but if it is thick we shall observe, when the plane abcdis perpendicular to the plane of primitive polarisation, some branches of blue and white light, diverging in the form of a cross from the centre of the system of rings, or the poles of no-polarisation, as shown at p and p', fig. 10, where the shaded branches represent the blue ones. The summits of the blue masses at p and p' are tipped with purple, and are separated by whitish light in some specimens and yellowish light in others. The white light becomes more blue from p and p' to o, where it is quite blue, and more yellow from p and p' to c and d, where it is completely yellow. When the plane abcd is in the plane of primitive polarisation, the poles p, p', are marked by spots of white light, but every where else the light is a deep blue.

226. In the plane cad b, fig. 10, the mineral, when we look through it at common light, exhibits no other color but yellow mixed with a small quantity of blue, polarised in an opposite plane. The ordinary image at c and d is yellowish-brown, and the extraordinary image faint blue; the former acquiring some blue rays, and the latter some yellow ones from c and d to a and b, where the difference of color is still highly marked. From a and b towards p and p' the yellow image becomes fainter till it changes into blue, and the weak blue image is reinforced by other blue rays, till the intensity of the two blue images is nearly equal. The faint blue image increases in intensity as the incident ray approaches from c and d to p and p', and the yellow one acquiring an accession of blue light, becomes bluish-white. From p and p' to o the ordinary image is whitish, and the other deep blue; but the whiteness gradually diminishes towards o, where they are both almost equally blue, the ordinary image being more luminous at o. From a and b to o the yellowish image becomes more blue, and the bluish image also more blue.

227. The principal axis of iolite is negative, and its greatest refracted image is purplish-blue, while the ordinary or least refracted image is yellowish-brown, passing into one another as above described. The index of the ordinary refraction is about 1-549; and the mineral belongs to the prismatic spectrum of Moh's, though both this mineralogist and M. Haüy place it under the rhomboidal system.

228. The splendid exhibition of colors which distinguishes mother-of-pearl from every other substance, and the successive development of fresh tints by every gentle inclination of the plate, have always been ascribed to the lamellated structure of the shell, and have been regarded as a fine proof of Newton's theory of the colors of natural bodies. Dr. Brewster has given an account of some experiments which he performed on this substance, in the Transactions of the Royal Society for 1814, and he observes, that he had no disposition to call in question this explanation, nor do the general train of his experiments lead him to such an enquiry. In examining the

colored rings which mother-of-pearl, like the topaz, exhibits by polarised light, and in ascertaining the relation between its refractive power and the angle at which it gives polarity to the reflected ray, he was under the necessity of grinding and polishing, with the utmost care, various plates of this substance. The development of new colors and the extinction of others, which took place during these processes, indicated the operation of some unknown and extraordinary cause, and encouraged him to pay the most minute attention to all the phenomena which were presented. The results of this investigation we shall endeavour to explain under the four following heads

1. On the optical properties peculiar to motherof-pearl.

II. On the communication of these properties to other bodies.

III. On the causes by which these phenomena are produced.

IV. On a new species of polarisation peculiar to mother-of-pearl."

229. I. Mother-of-pearl sometimes possesses a regular, and sometimes an irregular structure, and has a striking resemblance to the agate, in the immense variety of forms which it exhibits. Sometimes it is composed of parallel or concentric lamina: sometimes the veins are inflected in various successions, and sometimes it exhibits the same appearances as those which constitute what is called the hammered agate.

230. The regularly formed mother-of-pearl is of a uniform whiteness, somewhat resembling the pearl itself, and, in day light, scarcely exhibiting any of the prismatic colors; and, unless it is mentioned, this was the kind which Dr. Brewster employed in these experiments.

231. Let A B, fig. 1, plate IV., be a plate of mother-of-pearl, not polished, but having its two surfaces ground perfectly, either upon a blue hone or upon a plate of glass with the powder of schistus, and let the light Rr of a candle be incident at any angle on the point r, this ray will be reflected according to the ordinary law, so that the angle RrC is equal to Cr S, and the lines Rr, Cr, and Sr, in the same plane.

If the eye is now placed very close to the mother-of-pearl at B, so as to receive the reflected rays, it will perceive at S, in the direction rS', the common reflected image of the candle which will not be very bright, owing to the roughness of the reflecting surface. On the lower side of S' at the distance of some degrees there will also be seen a highly colored image of the candle at s, formed by rays reflected in the direction rs. In this spectrum the blue rays are nearest the common image, and the color is so great that it requires a prism of flint glass with a refracting angle of 65° to correct it, a large secondary spectrum being left, having the uncorrected green towards the vertex of the prism.

232. If the candle at R is kept steady, and the plate A B turned round r as a centre, so that the ray Rr may preserve the same angle of incidence, the colored ray rs will have a motion of rotation about r S, the common section A B of the plane srS and the surface of the motherof-pearl being invariable.

239. The line AB may be called the axis of extraordinary reflection; the extremity A, towards which the colored ray s is reflected, the primary pole of extraordinary reflection; r C the angle of extraordinary reflection; and srS the angle of aberration.

234. If the ray Rr is now reflected from the opposite surface of the mother-of-pearl, as represented in fig. 2, the same phenomena will be observed; but the colored ray rs will now be reflected towards B, and will be seen at s' above the common image S', being formed by rays reflected in the direction rs. The extremity B therefore of the axis A B will be the primary pole of extraordinary reflection for the lower surface. Hence the two surfaces of mother-of-pearl have always their poles in opposite directions, unless in specimens where a change of structure takes place.

235. Let the plate A B be now brought into

the position in fig. 1, where the plane rs S coincides with the plane of ordinary reflection RrS, and let it be placed upon a goniometer so that we may ascertain by measurement the changes which take place by varying the angle of incidence Rr C. It will then be found that the angle of aberration sr S regularly increases with the angle of incidence. The variations which it undergoes are represented with tolerable accuracy in the following table; but, owing to the elongation and indistinctness of the colored image at large angles of incidence, the measures are not susceptible of great correctness. The first column contains the angle of incidence; the second the complement of that angle; the third the angle of aberration as determined by experiment; and the fourth, formed by adding the second and third columns, contains the complement of the angle of extraordinary reflection."

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237. Assuming the numbers in columns third and fourth, Dr. Brewster has, upon this principle, computed those in the fifth, which are the calculated angles of aberration, and which agree very strikingly with the observed angles.

238. If we now turn round the mother-ofpearl 180°, so that the pole A may be brought into the position of B, the rays will be reflected towards the pole A, fig. 2, and the complement of the angle of extraordinary reflection will be equal to the difference between the angles of aberration and the complement of the angle of ordinary reflection. In this case we shall obtain the results given in the following table.

of Incidence.

gle of Extraordinary

Reflection.

Calculated

Angle of

Aberra-
tion.

239. By comparing the observed angles of aberration with the complements of the angles of extraordinary reflection, we shall find that

sin. r: sin. 'sin. A'-r': sin. A—r, which indicates the same relation as formerly between the angles of aberration and extraordinary reflection. Upon this principle Dr. Brewster has computed the numbers in the fifth column which agree very well with the observed angles. 240. While the primary pole A is describing a semicircle round r till it reaches B, and another semicircle from B to A again; a point s in the extraordinary ray rs will describe a curve round S composed of two semi-ellipses having the same conjugate axis, but having their semitransverse axes of different lengths. Thus, in fig. 3, if S be a point in the reflected ray r S, fig. 2, and S s, S N, St, S M, different values of the angles of aberration when the pole A is in the directions Ss, SN, &c.; then the point s will describe the semi-ellipse Ms N, and the semiellipse Mt N, which have their conjugate axis MN common, and their semi-transverse axes Ss, St, of unequal lengths. The conjugate axis M N is a constant quantity, while Ss, St, vary according to the law already mentioned. At different angles of incidence, therefore, the points will describe other curves such as M s'NT, which approach to a circle as the angle of incidence diminishes.

241. The angles of aberration vary in different pieces of mother-of-pearl, but there is no deviation from the laws which have just been explained.

242. On the outside of the extraordinary ray rs, fig. 1, a mass of colored light rp makes its appearance nearly at the same distance from the extraordinary image that the extraordinary image is from the common image: these three images are always in a straight line, but the angle of aberration of the mass of colored light varies according to a law different from that of the extraordinary ray. At great angles of incidence this mass of light is of a beautiful crimson color. At an angle of about 37° it becomes green, and at less angles of incidence it acquires a yellow hue, approaching to white, and becomes very luminous. These colors, which become more brilliant when the mother-of-pearl is polished, vary with the thickness of the plate.

243. The fracture of mother-of-pearl always reflects the extraordinary ray r s, as if the surface

of the fracture were parallel to the real surface; but, when the fracture is ground flat, no extraordinary reflection takes places.

244. When the extraordinary ray rs is reflected from another piece of mother-of-pearl, it experiences, as might have been expected, both an ordinary and an extraordinary reflection. In virtue of the ordinary reflection, an image is formed exactly like the extraordinary image; but in virtue of the extraordinary reflection, the highly colored image is sometimes rendered more highly colored, and at other times converted into a greenish white image, according as the second reflection conspires with, or opposes the first.

245. Hitherto we have attended to the phenomena only when the surface is rough and unpolished. When a slight degree of polish, however, is communicated to it, a new colored image appears on the opposite side of the common image formed by the rays r t, figs. 1 and 2. This new image resembles in every respect the other colored image, and follows the same laws; and, after a high degree of polish is induced upon the mother-of-pearl, it is almost as bright as the first colored image which has its brilliancy somewhat impaired by polishing. If the polish is removed by grinding, the second colored image vanishes, and the first resumes its former brilliancy. As this second image is reflected towards the pole A in fig. 1, and the pole B in fig. 2, they may. be called the secondary poles of extraordinary reflection.

246. If we now examine the light transmitted by the mother-of-pearl, we shall perceive phenomena analogous to those which have been described. A colored image will appear on each side of the common image, having the same angles of aberration as those seen by reflection, and resembling them in every respect, the blue light being nearest the common image, and the red light farthest from it.. These two images, however, are usually fainter than those seen by reflection, and, when the second extraordinary reflected image is extinguished by removing the polish, it is then the most brilliant when seen by transmission; and in general the image which is brightest by reflection is faintest by transmission.

247. In some irregularly formed pieces of mother-of-pearl which are ground very thin, and in which the axes of extraordinary reflection for the two surfaces are not coincident, four colored images are seen by transmission. Two of them

are produced by each surface, and the line which joins the two images formed by the same surface always coincides with its axis of extraordinary reflection. It is also deserving of notice that the transmitted extraordinary ray is bent towards the same pole as the extraordinary reflected ray to which belongs.

248. Like all other bodies, mother-of-pearl polarises light by reflection, and the angle at which the quantity of polarised light is a maximum is about 59°. The two extraordinary images are also polarised at the same angle, but the mass of green and crimson light exhibits no marks of polarity. This substance has also the property of depolarising light in every position like horn, tortoise-shell, caoutchouc, and gum arabic.

249. II. The phenomena which have now been described must be admitted to be very singular and instructive; and it is probable that some philosophers would have contented themselves with ascribing them to reflections from dierently inclined planes in the interior of the mother-of-pearl.

250. In order to measure the angles contained in the preceding tables, Dr. Brewster had occasion to fix the mother-of-pearl to a goniometer by a hard cement. Upon removing it from the cement the plate left a clean impression of its own surface, and he was surprised to observe that the cement had by this means received the property of producing the colors which were exhibited by the mother-of-pearl. This strange result he at first attributed to a thin film detached from the plate, but subsequent experiments soon convinced him that this was a mistake, and that the mother-of-pearl really communicated to the ceinent the properties which it possessed.

251. Dr. Brewster has also succeeded in imparting the same faculty of producing color to black and red wax, balsam of Tolu, gum arabic, gold leaf placed upon wax, tinfoil, the fusible metal composed of bismuth and mercury, and to lead by hard pressure, or by the blow of a hammer. When the impression is first made upon the fusible metal, the play of colors is singularly fine, but the action of the air corrodes the metal, and speedily destroys the configuration, as well as the polish of its surface. The same effect was produced when the metal was immersed in oil.

252. In order to show that in these cases no part of the mother-of-pearl is detached, he plunged the wax, after it had received the impression, into nitric acid, which had no effect either in destroying or diminishing the colorific property of the surface. In soft cements, made of bees' wax and rosin, the slightest degree of heat destroyed the superficial configuration by which the color is produced. In sealing-wax, gum arabic, and realgar, a much greater heat was requisite to remove the color; and in tinfoil and lead this could only be effected by the temperature at which they cease to become solid. 253. Let us now examine more minutely the phenomena which present themselves when the light is reflected from the surface of wax; and let us suppose that the impression upon the wax is made by the lower surface, when rough, of the mother-of-pearl, as represented in fig. 2, where

B is its primary and A its secondary pole When the light Rr of a candle is reflected from the surface of wax A B, fig. 4, the extraordinary image, instead of being reflected towards the pri mary pole B as in fig. 2, is reflected from it, and A is the primary pole of the wax, whereas B was the primary pole of the mother-of-pearl. By polishing the mother-of-pearl, and taking a new impression from it, the wax will now reflect the other extraordinary image in the direction rt, and therefore B is the secondary pole of the wax. Hence it follows that mother-of-pearl communicates to wax and other bodies the optical properties of the surface opposite to that from which the impression is taken.

254. At different angles of incidence the two colored images formed by the wax follow the same laws as those produced by the mother-ofpearl; but the mass of green and crimson light never appears, and is therefore caused by some internal structure which cannot be communicated to other bodies. When an impression is taken from the fracture of mother-of-pearl, its faculty of producing color is also communicated.

255. In imparting to gum arabic and balsam of Tolu the superficial configuration of mother-ofpearl, we are enabled, on account of their transparency, to observe the changes induced upon the transmitted light. The extraordinary images formed by reflection were both visible, the primary one being remarkably brilliant, and the secondary one scarcely perceptible; but, when the light was transmitted through the gum, the primary image was nearly extinct, while the secondary one was unusually brilliant and highly colored, far surpassing in splendor those which are formed by transmission through the motherof-pearl itself. When both the surfaces of gum arabic are impressed with mother-of-pearl, four images are seen. The colors seen by transmission are more brilliant in the gum than in the balsam, as the latter has the greatest reflective power; but the colored images produced by reflection do not seem to have suffered a greater dispersion when they are formed by the metals than when they are formed by cements.

256. When the impression is taken from a pearl, the wax receives a character similar to that which is possessed by the pearl. The image reflected from the surface of the pearl is enveloped in a quantity of unformed light, arising from a cause which will afterwards be explained; and the very same while nebulosity is reflected from the wax.

257. III. From a careful examination of the

preceding facts, we must now be prepared to infer that all the peculiar phenomena of motherof-pearl, as seen by reflection and transmission, are owing to a particular configuration of surface: that the communication of these properties to other bodies is the necessary consequence of the communication of its superficial structure; and that none of the light which is concerned in the production of these phenomena has penetrated the surface of the mother-of-pearl.

258. What this configuration of surface is, and in what manner it generates the colored images, are points of high interest, and of corresponding difficulty. The facts naturally lead us