the two media. When this is not the case, the particles of the first medium will move, after communicating motion to those of the second, and, in moving, give rise to the reflected wave. Thus refraction is always accompanied by reflexion; and this reflexion is greater, the greater the difference of the densities of the ether in the two media. It appears also, from what has been said, that the direction of the motions of the particles of the first medium, after they communicate motion to those of the second, will be different, according as the ether is denser or rarer in the first medium. In the former case the vibration of the particles is in the same direction that it was before; in the latter it is in the opposite direction. Thus there will be a reflected wave in both cases; but in one case this reflected wave is caused by a vibration in the same direction as that of the incident wave; in the other, by a vibration in an opposite direction.

The result of this difference is obviously the same as if one of the systems of waves were to gain or lose half an undulation on the other; so that when the two waves, reflected from the two surfaces of the plate, should be in complete accordance,-as far as depended on the difference of the lengths of their paths, they will actually be in complete discordance, and vice versâ. Thus the dark rings will be formed where the thickness of the plate is any even multiple of λ sec 0, and the bright ones where that thickness is an odd multiple of the same quantity; and the facts and the theory are reconciled.

(130) The principle which we have been illustrating has been experimentally established by M. Babinet, by an independent method. A pencil of rays diverging from a narrow aperture is separated into two, slightly inclined to one another, by means of the obtuse prism (85). These are allowed to fall on a thick plate of parallel glass, whose second surface is quicksilvered in one-half of its extent; and in such

a manner as to be both reflected by the transparent portion of that surface, or both by the opaque portion, or one by the former and the other by the latter. These two portions will interfere, and produce fringes after reflexion; and it is found that, in the two former cases, the central band is white, the two waves being in complete accordance: in the third case— i. e. when one of the pencils is reflected from the rarer, and the other from the denser medium-the central band is a black one; the two waves are, therefore, in complete discordance, and their phases differ by half an undulation.

It follows from the preceding, that in the system of rings formed between two object-glasses, the central spot will be white, if the thin plate is of a density intermediate to those of the two glasses; for it is evident that the reflexion takes place under the same conditions at the two surfaces-i. e. in both cases at the surface of a rarer, or in both at that of a denser medium. This anticipation of theory was verified by Young, by inclosing oil of sassafras between two object-glasses, one of which was of flint-glass, and the other of crown-glass.

(131) We have spoken of another set of rings visible by transmission. These are produced by the interference of the rays directly transmitted through the plate with those which penetrate it after two interior reflexions. It follows from the preceding considerations that they should be complementary to those seen by reflexion; and this is observed to be the case. The extreme paleness of the transmitted rings arises from the great difference in the intensities of the interfering pencils.

(132) The theory of thin plates, as it came from the hands of Young, laboured under an imperfection, which was, however, soon removed. It is obvious that the intensities of the two portions of light, reflected from the upper and under surfaces of the plate, can never be the same,-the light incident

on the second surface being already weakened by partial reflexion at the first. These two portions, therefore, can never wholly destroy one another by interference, and the intensity of the light in the dark rings can never entirely vanish, as it appears to do when homogeneous light is employed.

Poisson was the first to point out, and to remedy, this defect in the theory. It is evident, in fact, that there must be an infinite number of partial reflexions within the plate, at each of which a portion is transmitted; and that it is the sum of all these portions, and not the two first terms of the series only, which is to be considered in the calculation of the effect. When the problem is taken up in this more general form, it is found that, where the effective thickness of the plate is an exact multiple of the length of half a wave, the intensities of the reflected and transmitted lights will be the same as if it were removed altogether, and the bounding media placed in absolute contact. Hence, when these media are of the same refractive power, the reflected light must vanish altogether, and the transmitted light be equal to the incident.

Here then we have reached a point, with respect to which the two theories are completely opposed. According to both, a certain portion of light is reflected from the first surface of the plate. This portion, in the Newtonian theory, is left in all cases to produce its full effect, and there should therefore be a considerable quantity of light in the dark rings; while, in the wave-theory, it is, at certain intervals, wholly destroyed by the interference of the other portions, and the dark rings should be absolutely black in homogeneous light.

The latter of these conclusions seems to accord with phenomena, while the former is obviously at variance with them. This is clearly shown by an experiment of Fresnel. A prism was laid upon a lens having its lower surface blackened, a portion of the base of the prism being suffered to extend be

yond the lens. The light reflected from this portion, according to the Newtonian theory, should not surpass that of the dark rings in intensity. The roughest trial is sufficient to show that the intensities of the light in the two cases are widely different, and thus to prove that the dark rings cannot arise (as they are supposed to do in the theory of the fits) from the suppression of the second reflexion.

(133) When a pencil of light falls upon two plates in succession, some of the many portions into which it is divided by partial reflexion at the bounding surfaces, are frequently in a condition to interfere, and to give rise to the phenomena of colour.

Thus, when light is transmitted through two parallel plates, slightly differing in thickness, the colour is the same as that produced by transmission through a single plate, whose thickness is the difference of their thicknesses, and is found to be independent of the interval of the plates. This phenomenon was observed by Nicholson; and it has been shown by Young to arise from the interference of two pencils, one of which is twice reflected within the first plate, and the other twice reflected in the second. It is obvious, in fact, that if t be the thickness of the first plate, and t that of the second, the first pencil will have traversed the thickness 3t+t' in glass, and the second the thickness 3t' + t, the spaces traversed in air being the same; so that the interval of retardation is the time of describing the space 2(t - t') in glass. Sir David Brewster observed a similar case of interference, produced by two plates of equal thickness slightly inclined; the thickness traversed in the two plates being altered by their inclination.

In the foregoing cases, the interfering pencils are mixed up with, and overpowered by, the light directly transmitted, and some contrivance is necesssary to make the colours visible. The phenomena are much more obvious in

the light reflected from both plates, which, on account of their inclination, is thus separated from the direct light.

It

is obvious, in fact, that the direct image of a luminous object, seen through two glasses slightly inclined, will be accompanied by several lateral images, formed by 2, 4, 6, &c. reflexions. These images Sir David Brewster observed to be richly coloured; the bands of colour being parallel to the line of junction of the two glasses, and their breadth being greater, the less the inclination of the plates. The colours in the first lateral image are produced by the interference of the two pencils ABCDEFGH, ABCdefgh, into which the ray is divided at the first surface of the second plate;

one of these portions being reflected externally by the second plate, and internally by the first, -while the other is reflected in

ternally by the second, and externally by the first. The routes of these portions are obviously equal

G

H

h

F

E

A

D

B

C

when the plates are parallel, and differ in length only by reason of their inclination.

(134) The two preceding cases of interference may be produced with plates of any thickness. What are termed the colours of thick plates, however, are phenomena of another kind, and arise in circumstances wholly different. These phenomena were first observed by Newton.

In Newton's experiment a beam of light is admitted through a small aperture, and received on a concavo-convex mirror with parallel surfaces, the hinder of which is silvered. A screen of white paper being then held at the centre of the mirror, having a hole in the middle to let the beam pass and repass, a set of broad coloured rings will be depicted on it, similar to the transmitted rings of thin plates. The diame