be essential, as in fig. 5. The reflected ray is seen to descend upon the plate A, which would have been polarised if the angles had been 35°, and consequently not reflected. But partial polarisation is produced by the plate B. The instrument shown at fig. 6 hardly requires description. It consists of a tube having a frame at each end, holding reflectors A and B, which are capable of being adjusted to any angle with the axis of the tube, and of being turned round the tube so that the planes of reflection may be at any angle to each other. Suppose the two mirrors (of unsilvered glass) inclined on their axis to the polarising angle 35°, remove the mirror B, and make a ray of natural light passing through the axis of the tube fall on the mirror A, it will be found that the light will be reflected equally in whatever direction the mirror is turned by the ring D, whether upwards or downwards, to the right or to the left. Let now the mirror B be replaced, and the apparatus so placed that the light reflected from it falls on the other mirror A, if the plane of reflection of the two mirrors coincide; that is, if the plane of each reflection is towards the same direction. To an eye placed opposite A there will be a reflection of a considerable part of the light incident on it. After being satisfied that there is in this position a partial reflection of the light, turn the ring D a quarter round either to the right or left, and with it the mirror A (the inclination of which to the axis remains the same), and on looking on the mirror there will be now found a total obscuration, that is, no light will be reflected, the whole passing through the glass. To be satisfied that this does not take place from any accidental derangement of the instrument, it is only necessary to turn the mirror slowly from one position to the other, and a gradual diminution of the intensity will be observed, passing from its maximum in the first position to complete obscuration in the last, or when the plane of the first reflection is at right angles to what would have been the plane of the second reflection had the light been direct.

202. A farther proof that this is no deception is afforded by substituting a metallic reflector in the place of the mirror B; in which case no such alteration takes place.

203. To return to the experiments. Continue to turn the mirror A gradually in the same direction, so that the reflection is again parallel to the first, but in an opposite direction, and the light will be again at a maximum; and, if the mirror be still turned in the same direction until it has made three-fourths of a revolution, the light reflected will again be reduced to nothing. 204. In this experiment we see that light, having been reflected from a surface at a certain angle, is entirely transmitted by another mirror, if the plane of incidence on the second mirror is perpendicular to the plane of incidence on the first, while natural light would have been equally reflected in every position.

205. It must be observed that, if the angle of reflection of either mirror be greater or less than the angle of polarisation, there will not be a total obscuration. The angle made by the two planes of reflection is often called the azimuth.

To succeed perfectly in this experiment the back of each mirror should be blackened, to prevent the admission of extraneous light. It will now be not difficult to show that the direction of polarity, in the reflected light, is to the plane of reflection, similar to the polarity of the ordinary ray in Iceland spar to its principal section, or an identity of the modification produced in the reflected ray and the modification produced by the action of the crystal on the ray ordinarily reflected; for if the ray reflected from water or glass at the polarising angle be received on a crystal of Iceland spar, the principal section of which coincides with the plane of reflection, the ray entering the crystal will proceed through it in the same direction that the ordinary ray, emerging from another crystal, would have proceeded. But, if the principal section of the crystal be placed perpendicular to the plane of reflection, the ray will be reflected extraordinarily; but in both positions there will be no bifurcation of the ray. If the principal section of the crystal be any otherwise situated, as to the plane of reflection, there will be two rays, but of equal Intensity, when the angle contained between these two planes is 45°. If, again, the ordinary ray emerging from a crystal be made to fall at the proper angle, on the surface of water, or any other reflecting surface capable of polarising light completely, it will be reflected when the principal section and plane of reflection co- . incide, but entirely transmitted when the planes are perpendicular to each other. But, if the extraordinary ray fall on the surface, the reflection will take place when the planes are at right angles, and a total transmission will result when the planes coincide.

206. We are therefore justified in assuming that the physical change the light has suffered is the same in the two cases. That whether an ordinary ray be examined by subsequent reflection, or the reflected ray by a doubly reflecting crystal, the influence is, that the polarity of each is in the same direction: the one in the plane of the principal section, and the other in the plane of reflection.

207. Light is not only reflected from the first surface of transparent bodies, but another portion is reflected from the second surface. We will suppose these two surfaces parallel, and it will not be difficult to see, that if the light be completely polarised by reflection from the first surface 'a, fig. 7, the portion reflected from the second surface will also be completely polarised, and in the same plane.

208. Let A I be the incident ray, and I R the reflected polar ray; II the refracted ray, partially reflected and refracted to R' and I'G, the remaining refracted light will be perpendicular to I' R', the reflected ray, a condition we have seen before producing complete polarisation.

209. From various experiments it has been proved that the quantity of light reflected, even from the two surfaces of a transparent body, is small in proportion to the incident light, and it is now convenient to enquire the condition of the refracted portion, under circumstances in which polarisation of the reflected light is produced. If the ray IG', fig. 7, be examined by a rhomboid,

it will be found divided into two rays, but not of equal intensity; for the ordinary or extraordinary ray will be found the more intense, as the section of the crystal is parallel or perpendicular to the plane of refraction. This condition of light is called partial polarisation, and is the same as the state of reflected light when the incidence is not such as to produce complete polarisation.

210. M. Arago gives the following experiments:-Let us suppose a plate of glass, ED, fig. 8, placed perpendicularly on a sheet of fine white paper A B, the eye placed at O will see at the same time the reflected ray a i o, and the refracted ray bio; interpose an opaque plate perforated with a small hole S; let the eye at O be furnished with a doubly refracting crystal C. If by a black screen, placed between b and i, we stop the ray bi, which would have been transmitted by the glass plate, the hole in the plate S is illuminated by the reflected light alone; and if the principal section of the crystal coincide with the plane of reflection, we see two images of the pole, of which the ordinary is the most brilliant. If the screen be now so placed as to intercept the reflected ray, a i o, there will be still two images, but now the extraordinary will be the most brilliant.

211. Now, if the screen be entirely removed, allowing both reflected and refracted light to reach the crystal, the intensity of the two images is found by actual experiment to be exactly equal. It is hence to be inferred, that the plane which contains the poles of light, polarised by transmission, is perpendicular to the plane which contains poles of light polarised by reflection; and that the quantity of polarised light, contained in the ray transmitted by a transparent plate, is exactly equal to the quantity of polarised light contained in the ray reflected from its surface, whatever the angle of incidence may be. M. Arago observes, that a body which, at its angle of complete polarisation, would reflect half the the incident light from its surface, would also completely polarise the transmitted ray; and that when there is no transmission of light there is no polarisation; and which seems proved experimentally, as no trace of partial polarisation is discoverable in the light reflected from the interior of a glass prism, when the reflection is

total.

212. As transparent substances reflect but a small portion of the incident rays, the quantity of polarised light in the transmitted ray is small in proportion to the light which has not undergone that modification. Dr. Brewster considers the transmitted ray as consisting of one portion. completely polarised in a plane at right angles to the plane of incidence, and another portion of light which has suffered a physical change more or less approaching to complete polarisation.' Light, having passed through a pile of plates, is at last polarised in a plane perpendicular to the plane of polarisation of the reflected light. This effect requires the agency of twenty-four plates at an incidence of 61°; consequently,' says Dr. Brewster, twelve plates will not polarise the whole pencil at that angle. Let us now suppose that the quantity not polarised amounts to twenty out of 100, then if these twenty were abso

lutely unpolarised, and in the same state as direct light, they would require to pass through twenty-four plates in order to be completely polarised. But experiments prove that they require to pass only through twelve other plates to be completely polarised; it therefore follows that the twenty rays have been half polarised by the first twelve plates, and the polarisation completed by the other twelve.'

213. This reasoning may be good; but as Malus, Biot, and Arago, consider this partially polarised light to consist of light completely polarised, and light in the state of direct or natural light-and as this view of the question admits of a ready explanation—we shall adopt it.

214. Let a, b, c, d, be supposed to represent the successive plates through which the incident ray 1000 is to pass, and at a given angle, fifty out of 100 be completely polarised by reflection, and a similar quantity of rays by refraction; the light emerging from the first lamina will consist of 900 in the state of direct light, and fifty of light polarised in a plane perpendicular to the plane of incidence. We have already seen that light polarised in one plane will not be reflected in a plane perpendicular to its plane of polarisation, and consequently the portion fifty of transmitted light will escape reflection from the lamina b, and therefore the light reflected from b, which we have supposed one-twentieth of the incident light, must be taken from the 900 of direct light. In this manner we may suppose the quantity of direct light constantly diminished, and the polarised light increased by each succeeding transmission.. According to this view, complete polarisation could never be produced, but the quantity of direct light, after a few transmissions, would be absolutely imperceptible.

215. It cannot be necessary to explain the result of submitting the ray emerging from a succession of plates to another pile of plates, to a doubly refractive crystal, or to a reflection from a polarising surface. It is in all respects similar in its polarisation relatively to the plane of incidence on the first surface to the extraordinary ray transmitted by a crystal, relatively to its principal section.

216. We will, however, mention one consequence of the foregoing laws; that polarised light, falling on the first surface of a pile of plates, will be partially reflected when the plane of incidence coincides with the plane of polarisation; and, a farther portion being also reflected at each successive plate, an eye placed at the back of the plates will receive no sensible quantity of light. If, on the contrary, the plane of polarisation be perpendicular to the plane of incidence, the whole light will be transmitted. It therefore follows that an apparatus may be constructed of the most transparent plates of glass, in two piles or bundles, forming a system perfectly transparent in one position of the piles, yet perfectly opaque in another. This effect is only to be produced by a great number of plates of glass, if the incidence be near the perpendicular; yet some substances possess this property of polarising transmitted light, whatever the incidence. A thin plate of tourmaline, cut parallel to the axis of the crystal, completely polarises the light at any incidence