+ is a minimum; or, multiplying by v, and denoting the

v v

The constant factor, u, is the refractive index of the medium. In the case of reflexion, μ = 1, and 7+ l' is a minimum. The course pursued by a reflected ray is therefore such, that the sum of the paths described between any two points and the reflecting surface is the least possible.

(35) The intensity of the light, in the reflected and refracted waves, will depend on the relative densities of the ether in the two media. For we may compare the contiguous strata of ether in these media to two elastic bodies of different masses, one of which moves the other by impact; and it is easy to deduce, on this principle, the intensities of the reflected and refracted lights in the case of perpendicular incidence.

(36) On reviewing what has been said, we cannot but be struck by the remarkable fact, that theories so widely opposed as the theory of emission, and that of waves, should lead mathematically to the same result. According to both, we have seen, the ratio of the sines of incidence and refraction is equal to the ratio of the velocities of light in the two media, and is therefore constant. But there is this important difference between them in the wave-theory, the sines of these angles are in the direct ratio of the velocities, while, according to the theory of emission, they are in the inverse. In other words, the velocity of light in the denser medium is less according to the former theory; while, according to the latter, it is greater. Here, then, the two theories are directly at issue upon a point of fact, and we have only to ascertain how this fact stands, in order to be able to decide between

them. The important experiment by which this was first accomplished was made by Arago; and the result, as will be shown hereafter, is conclusive in favour of the wave-theory.

(37) The conclusion deduced from the experiment here referred to presupposes the laws of Interference of Light-laws which, in themselves, are intimately connected with the principles of the wave-theory. It was desirable, therefore, to deduce the same conclusion, if possible, by direct means. The experiment by which this is effected has been recently made by M. Fizeau, upon a method devised by Arago; its principle will be understood from the following description.

Let a ray of light, reflected by a heliostat, be admitted into a darkened chamber in a horizontal direction, and fall upon a mirror which revolves about a vertical axis situated in its own plane. It is manifest that, as the mirror revolves, the reflected ray will move, in the horizontal plane passing through the point of incidence, with an angular velocity double of that of the mirror itself. Now, in this plane let a second mirror be placed, perpendicular to the right line joining the centres of the two mirrors. Then, when the ray reflected by the revolving mirror meets the fixed mirror, in the course of its angular movement, it will be turned back on its course, and, after a second reflexion by the revolving mirror, return towards the aperture.

It is plain that if the revolving mirror were for a moment to rest in this position, the ray, after a second reflexion by it, would return precisely by the path by which it came. But, owing to the progressive movement of light, the mirror describes a certain small angle round its axis, in the interval between the two appulses of the ray; and the ray, after the second reflexion, will deviate from its first position, by an angle which is double of that described by the mirror in the interval. Hence, if this angle can be observed, the velocity of light is known.

For, if t be the time taken by the light to traverse the interval of the two mirrors, forwards and backwards, the angle described by the mirror in that time will be = wt, w denoting the angle described by the mirror in the unit of time. Hence, the angle described by the reflected ray in the time t, or the deviation, 2wt. Let this angle be denoted by a, and there is

=

But the corresponding space is double the distance between the two mirrors, or 2a. Consequently, the velocity of the light is

M. Fizeau has been enabled to observe an appreciable deviation of the reflected ray, when the distance of the two mirrors was 4 metres, and the revolving mirror made only 25 turns in a second. And as such a mirror has been made to revolve 1000 times in a second, it was obvious that the time taken by light to traverse even this short distance was capable of being measured with precision. It only remained to interpose a column of water between the mirrors, to observe the deviation, and to calculate the velocity. By these means M. Fizeau has established the fact, that the velocity of light is less in water than in air, in the inverse proportion of the refractive indices. The result is, therefore, decisive in favour of the wave-theory.

(38) The refractive index being equal to the ratio of the velocities of light in the two media (direct or inverse) it follows, whichsoever theory we adopt, that any change in the velocity of the incident ray must cause a variation in the amount of refraction, unless the velocity of the refracted ray be altered proportionally. Now the relative velocity of the light of a star is altered by the Earth's motion; and the amount of the change is obviously the resolved part of the Earth's velocity in

the direction of the star. It was, therefore, a matter of much interest to determine how, and in what degree, this change affected the refraction. The experiment was undertaken by Arago, at the request of Laplace. An achromatic prism was attached in front of the object-glass of the telescope of a repeating circle, so as to cover only a portion of the lens. The star being then observed, directly through the uncovered part of the lens, and afterwards in the direction in which its light was deviated by the prism, the difference of the angles read off gave the deviation. The stars selected for observation were those in the ecliptic, which passed the meridian nearly at 6 A.M. and 6 P. M., the velocity of the Earth being added to that of the star in the former case, and subtracted from it in the latter. No difference whatever was observed in the

deviations.

This remarkable and unexpected result can be reconciled to the theory of emission, as Arago has observed, only by the hypothesis already adverted to,*—namely, that the molecules are emitted from the luminous body with various velocities; but that among these velocities there is but one which is adapted to our organs of vision, and which produces the sensation of light. It is explained, in accordance with the principles of the wave-theory, on the same hypotheses which have been already made to explain the aberration of light;† and it is shown, on these suppositions, that both the laws, and the amount of refraction, are independent of the Earth's motion.

CHAPTER III.

DISPERSION.

(39) WE have hitherto supposed light to be simple or homogeneous. The light of the Sun, however, and most of the lights, natural or artificial, with which we are acquainted, are compound, each ray consisting of an infinite number of rays differing in colour and refrangibility. This important discovery we owe to Newton. We shall briefly describe the principal experiments by which it is established.

(40) When a beam of solar light is admitted into a darkened room through a small circular aperture, and received on a screen at a distance, a circular image of the Sun will be depicted there, whose diameter will correspond to that of the hole. If now the light be intercepted by a prism, having its refracting edge horizontal and perpendicular to the incident beam, the image of the Sun will be thrown upwards by the refraction of the prism, and will be no longer white and circular, but coloured and oblong; the sides which are perpendicular to the axis of the prism being rectilinear and parallel, and the extremities semicircular. The breadth of this image, or spectrum (as it is called), is equal to the diameter of the unrefracted image of the Sun, but its length is much greater.

Now if the solar beam consisted of rays having all the same refrangibility, the refracted image should be circular, and of the same dimensions as the unrefracted image, from which it should differ only in position. For the rays composing the beam, being parallel at their incidence on the prism, must (on this supposition) be equally refracted by it, and therefore continue parallel after refraction. This not being the case, we conclude