a screw, and then laid with the edge G H on a plate of hot iron, the heat will distribute itself as if the whole constituted one plate, and produce the effect shewn in Fig. 17; but the moment the plates are separated, the heat will distribute itself as in Fig. 20.

By combining a positive rectangular plate, or one in which the principal axis is positive, with another positive rectangular plate, so that the lines of no polarisation are parallel, the effect of each will be combined as if a plate had been used equal to the sum of their thicknesses, and the fringes on each side of the black lines will increase in number.

If we combine a positive rectangular plate with a similar negative rectangular plate, the effect of the one will counteract that of the other. If they have equal actions, the polarising structure of the one will destroy that of the other; but if their actions are unequal, the effect will be the same as if a plate had been used of the same thickness as the difference of their thicknesses, and having the structure of the thickest of the two combined plates.

When two positive or two negative rectangular plates are crossed, as shewn in Fig. 21, the tints are in some places raised in the scale, and in others depressed, according as opposite or similar structures are opposed to one another, the crossing of two positive or two negative structures sinking the tints in the scale, and the crossing of a positive with a negative structure raising them. By finding the tint at any given point in each plate from the preceding formulæ, and combining these tints according to the rule already given, it will be found that the isochromatic curves (or curves of equal tint) at the intersectional space A B C D are Hyperbolas, which will be equilateral when the breadths and the maximum tints of the two plates are the

same.

When a positive rectangular plate crosses a negative plate, it will be found, by the same process, that the isochromatic curves are Ellipses, as in Fig. 22, when the plates are of unequal breadths; and that they become circles when the plates and maximum tints are equal, as in Fig. 23.

All these different phenomena, which I first observed, are deducible mathematically from my formula in the Edinburgh Transactions, vol. viii, p. 357.

We have already seen that circular plates, or cylinders of

glass, have one positive axis, like zircon ; but when the cylinder has the form of a tube, like A CBD (Fig. 24), the polarising force is distributed in a very remarkable manner. A black circular fringe mpno forms the line of no polarisation, and the coloured fringes are placed on each side of this dark ring, and concentric with it. The structure on the outside of mpno is positive, like zircon, &c. and the structure on the inside negative, like calcareous spar.

If a tube of glass is brought to a red heat, and then cooled by inserting in its bore a cylinder of iron, or any other conducting body, the structure will then be the same as is represented in Fig. 25.

If a solid cylinder of glass which has only one structure is perforated in its centre, it will exhibit the appearance in Fig. 24.

When the tints are arranged in a glass cylinder, as in Fig. 24, take a file with a very sharp edge, and cut the tube entirely through by a notch E F (Fig. 25). By this operation the particles will be freed from the state of violence in which they are held, and will assume the very same arrangement which they never fail to take in rectangular plates of glass. By exposing the tube thus divided to polarised light, it will exhibit the appearance shewn in Fig. 25, where mpno, m' p' n' o', are two dark fringes having a negative structure on the outer side of each, and a positive structure between them, as in plates of glass with two axes.

SECT. X.-On the Communication of the Polarising Structure by Compression and Dilatation.

On the 3d of January 1815, I discovered that soft animal substances, such as calves' foot jelly and isinglass, acquire from simple pressure that peculiar structure which enables them to form two images polarised in an opposite manner, like those produced by doubly refracting crystals, and to exhibit the complementary colours of regularly crystallized minerals. This effect was observed in a cylindrical piece of calves' foot jelly which could scarcely support its own weight, and which had no action upon polarised light; but whenever it was pressed between the finger and the thumb, or even touched gently by the finger, it displayed the properties of the polarising structure.

During subsequent experiments on this subject, in October 1815, I observed that compression produced a negative po

larising structure, and dilatation a positive polarising structure; and by dilating isinglass I created a polarising structure more powerful than that which is possessed by beryl.

These experiments, which had been confined to soft substances, I extended, on the 1st November 1815, to plates of solid glass; but finding it difficult to apply regular forces to such a hard body, I thought of developing the polarising structure by bending plates of glass, whose edges were ground and polished. In this way I succeeded in exhibiting the phenomena in the most simple manner.

If we take any slip of glass, cut merely with a diamond, and holding one end of it in each hand, bend it slightly, we shall observe, through its edges, when exposed to polarised light, two separate structures A B NM, CDNM, Fig. 26, separated by a dark line MN; and each of them covered with coloured fringes, the scale of which commences at M N. When the axis of a plate of sulphate of lime is made to cross these fringes, those in CD N M on the concave side will rise in the scale, and will therefore be positive, while those in ABNM on the convex side will fall in the scale, and will therefore be negative. By measuring the breadth of the fringes, the tints were found to vary as their distance from the axis. By the application of great forces I ́succeeded also in altering the polarising structure of regularly crystallized bodies, and in communicating that structure where it did not previously

exist.

For a full account of these experiments, see the Phil. Trans. 1816, p. 156, and the Edin. Trans. vol. viii, p. 281.

SECT. XI. On the Polarisation of Light by Metals, and by the Second Surfaces of Transparent Bodies.

The discovery of the polarisation of light in two opposite planes by polished metals was independently made by Malus and myself, but the priority is due to Malus, who concluded from his observations, that while transparent substances refract all the light polarised in one plane, and reflect all the light polarised in the opposite plane, metallic bodies reflect what they polarise in both planes.

In examining the effects produced by successive reflexions from metallic surfaces, I discovered that they possessed the singular property of producing, when exposed to polarised light,

the phenomena of the complementary colours, and of moveable polarisation, like crystallized bodies.

Let us suppose that two parallel plates of highly polished silver, about three or four inches long, and half an inch broad, are fixed at the distance of about half an inch, and are interposed at ef, Fig. 10, between the polarising plane A B and the analyzing plate C D, and that the silver plates can be turned round, so that the plane of reflexion may form any angle with the plane of primitive polarisation A S T. If the plane of reflexion from the silver plates is either parallel or perpendicular to the plane of primitive polarisation, the action of the plates upon the polarised ray will be nothing, that is, the ray will retain its primitive polarisation, and will be colourless, however great be the number of reflexions. In every other position, however, of the plane of reflexion from the silver plates, and at every angle of incidence, the polarised ray will be divided into two portions, O and E, one of which, O, retains its primitive polarisation, while the other, E, is polarised in an angle equal to 2 a, or twice the azimuth of the plane of reflexion. When a is 45°, the tint E is a maximum, just as in plates of regularly crystallized bodies; the azimuthal angle of the plane of reflexion in the former, replacing the azimuth of the axis in the latter.

When a polarised ray is reflected from a single metallic surface in the manner now described, it experiences the same modification as if it had passed through a plate of any crystallized body of a certain thickness. If the action of the metallic surface is combined with that of a plate of sulphate of lime, having its axis coincident with the plane of reflexion, the colour polarised by the system will be that which is due to the sum of the thicknesses of the crystallized plate, and the equivalent plate of the same substance; but if the axis of the plate is at right angles to the plane of reflexion, the colour polarised by the system will be that which belongs to the difference of the thicknesses of the crystallized plate and the equivalent plate. The same is true of two or more metallic reflexions, each reflexion being equivalent to a plate of a crystallized body of a given thickness, their thickness varying with the angle of incidence; and if the angle of incidence varies, the thickness of the equivalent plate always increases as the angle of incidence upon the metal diminishes, or the depth to which the incident

ray penetrates the metallic surface increases as it approaches to the perpendicular.

The same effect is produced by successive reflexions from Gold, and, in an inferior degree, from Platinum, Steel, Brass, Copper, Tin, Lead, Mercury, Metal for specula, and Amalgam of Bismuth.

When a ray of common light has suffered a number of reflexions from polished plates of silver, I found, that even when the number of reflexions was thirty-six, the emergent pencil consisted of two pencils polarised in opposite planes. A portion of the most refrangible rays was absorbed at each reflexion, so that the resulting pencil was of a deep red colour. As one of the images was decidedly fainter than the other, the pencil would have ultimately been all polarised in the plane of reflexion. Hence it follows, that the intensity of the pencil polarised in the plane of reflexion is greater than that of the pencil polarised in the opposite plane; but these two intensities approach nearer to equality in silver than in any other metal.

If common light is incident upon Steel, and all the other metals except gold and silver, five or six reflexions at an angle of 70° are sufficient to polarise the whole of the incident pencil in the plane of reflexion. Hence it follows, that in all these metals the pencil polarised in the plane of reflexion exceeds greatly in intensity that which is polarised in an opposite plane, a great portion of this last pencil having been absorbed by the substance of the metal.

On the polarisation of

The discovery of the polarisation of light in two opposite pencils by the action of the forces which produce total reflexion, was made by me in 1814, light by total and explained in my paper on the Polarisation of Light by Reflexion.

reflexion.

The experiments by which I ascertained this property were conducted in a manner similar to those of Malus upon polished metals. A ray of polarised light was found to be depolarised by total reflexion, when the plane of total reflexion was inclined 45° to the plane of primitive polarisation, and in intermediate degrees at different azimuthal angles, excepting when the azimuths are 0°, 90°, 180°, and 270°, or when the plane of total reflexion is parallel or perpendicular to the plane of primitive polarisation.