has turned between letting the light through and cutting it off again is known; and thus can be found the time the light has taken to travel from F to M and back again; and so the velocity of light in air.

The chief objection to this method is that the exact speed of the wheel at which complete extinction of the light takes place cannot be directly determined; extinction appears to be complete at any speed which allows too small a quantity of light to pass to affect the eye.

Cornu has introduced improvements into this method. The speed of rotation of the wheel W was allowed to vary, its revolutions being registered electrically, so that its speed at any instant could be deduced. At the same time, the observer can, by means of a key, register any instant at which he desires to know the speed. Thus, by allowing the speed to vary continuously, and registering the instants at which the light disappears and reappears, the speeds at these two instants can be determined; and the speed for complete extinction is the mean between them. Cornu has found by this method for the velocity of light in air, 300,330,000; and in vacuo, 300,400,000 metres per second.

Foucault's Method. The figure shows a horizontal plan of Foucault's arrangement. Sunlight is directed through a

M

FIG. 130.

rectangular aperture, S, in the middle of which is a fine vertical wire. The light passes through a vertical plate of glass, G,

inclined at 45° to its path, and through an achromatic lens, L. At M is a small plane mirror which can be rotated about a vertical axis. At C is a concave mirror having its centre of curvature on the axis of rotation of M. The lens L is so adjusted that when M is suitably directed, an image of S is formed at C. Supposing M to be stationary, the light reflected back from C will form an image of S, which may be seen by reflexion from G, by means of a lens H; at A, say. Now, suppose M to be rotated with a moderate degree of rapidity. On account of the persistence of impressions, a continuous image of S will appear to be formed at A. The brightness of this image will depend upon the extent of the mirror C, for light is only being reflected back to L in the small portion of M's rotation in which it is sending light to C.

Suppose, now, that M is rotated very rapidly. During the time that light travels from M to C and back to M, M has turned through a small angle, and thus the light is reflected off from M by a slightly different path from that by which it arrived. This is true for each separate ray of light travelling from M to C; and whatever be the extent of C, all the rays on coming back to M are reflected back along paths inclined to their original paths at a common angle, equal to twice the angle through which M has turned during the passage of the light from M to C and back to M. This will cause the image of S formed by reflected rays, and seen by reflexion at the glass G, to appear displaced from A; to A', say.

Suppose that a denotes the distance SM; b, the distance M C; d, the displacement A A' of the image of S; n, the number of turns made by M per second; V, the velocity of light. The b time taken by light to travel to distance MCM is 2. b

2v་

In this time the mirror M turns through the angle 2 V X 2π1

b

= Απηγι

b

Thus the deflexion of the rays reflected from M

is 8. And a being small, this is also very nearlyThus

In Foucault's later experiments the distance M C was made

large by causing the light to undergo several reflexions between the mirrors M and C; the distance thus obtained was 20

metres.

The mirror M was carried on a well-made axis, and very carefully balanced. It was driven by a blast of air acting on a sort of siren to which it was attached. It was coated with silver on the reflecting side. It was in some experiments driven at a speed of some 800 revolutions per second.

Foucalt employed this apparatus to determine whether the velocity of light in air or in water is the greater. For this purpose another concave mirror, D, like C, is added to the apparatus, and a tube of water placed between it and M, so that the light had to traverse the water in its passage from M to D and back again. This would cause the light to come to a focus further off than D; and to correct for this, a convex lens had to be used along with the tube of water to focus the light on D. Each of the mirrors C and D would now, when M is rotating, give rise to an image of S by reflexion at G ; and when M is rotating slowly, these images would be superposed at A. Now, suppose that M is rotated very rapidly. It was found that the image produced by C, by means of rays that had passed entirely through air, was less displaced than that produced by D. It follows that the velocity of light in air is greater than that in water.

This experiment leads us to an important conclusion with regard to the nature of light. We shall see that the emission theory requires that the velocity, in a medium of greater refrangibility, shall be greater than in one of less refrangibility; but the undulatory theory requires that it shall be less. Now, water has a greater refrangibility than air, and we see that the velocity in it is less than in air. This experiment, then, shows that the emission theory, as it will be described, is untenable. Regarded as a crucial experiment to decide between the two theories, it decides in favour of the wave theory.

Captain A. A. Michelson, of the United States, has used the method of Foucault, modified in some respects, in a careful determination of the velocity of light. The distances between the aperture S and the revolving mirror M, and between this and the fixed mirror C, were made large-30 and 2000 feet respectively. The mirror C was plane, and the lens, which was of 150 feet focal length, was placed between iť and M. By using the lens in this way, an image of considerable brightness could be obtained, although the distance

MC was made so large. If the mirror C is of the same breadth as the lens, and M is at the principal focus of the lens, then, as long as light from M falls on any part of the lens, it I will reach C and return to M. In the experiment, in order to increase the distance S M, M was placed about 15 feet within the focus of the lens, and it was found that the light in this way reaching C gave a bright enough image when reflected back to S; although the light passing through the lens is then somewhat divergent, and all of it does not reach the mirror C.

In this, as in Foucault's experiment, it is necessary that an image of S should be formed exactly coinciding with S, when M is stationary. Now, L and M form an image of S, say I. An image of I,-say I-is formed by C; and I, acts as the source of the reflected light. For this to produce an image coinciding with S, it is necessary for I, and I to coincide. Thus I, must be formed on the surface of C. Then, whatever be the shape of C, I, coincides with I1.

The light returning to S was not reflected to the side, as in Foucault's experiment. This was unnecessary, as a large deflexion was produced. An eye-piece, which can be moved laterally along a scale which measures its motion, is placed so that it can be set behind the slit S, that is, on the side of S of the incident light, or it can be moved away to observe the deflected image of S when the mirror is spinning round. The difference of the readings on the scale when the eye-piece is focussed on S and on its image is the amount of the deflexion.

The mirror M was rotated by a sort of air turbine, the driving pressure being susceptible of nice regulation. Its speed was about 256 revolutions per second. This was measured by comparing it with a tuning-fork kept vibrating by electrical means. To the tuning-fork was attached a steel mirror, and the light from M falling on this is reflected to a plate of glass in the eye-piece inclined to its axis, and then to the eye. The fork made about 128 complete vibrations per second, its exact rate being determined by comparison, by the acoustical method of beats, with a standard fork of about an octave higher. Now, when the mirror rotates and the fork vibrates, the successive flashes of light from the mirror M will generally fall on the mirror of the fork when this is in different positions, and a spread-out image is seen in the eye-piece. When the mirror rotates in the same time as the fork vibrates, a single distinct image is seen; if twice as quickly, two images are seen, and so on. The speed of the mirror was regulated by adjusting the pressure while observing the reflected images

from the fork; and, when a steady speed was got, an observation of the displacement of the image was taken. A displacement of about 133 mm. as against mm. in Foucault's experiment, was obtained.

10

The result obtained for the velocity by these experiments was 299,944,000 ± 50,000 metres per second, in vacuo.

The question has been considered whether lights of various colours travel with the same or different velocities: and some observers have thought that they had detected differences in the velocities; but the weight of evidence is in favour of the velocities of lights of all colours, that is, of all wave-lengths, whether in air or in empty space, being the same.

Immediately after the eclipse of a star, if lights of different colours travelled with different velocities, the light of some colours would reach us before that of others, and the star would appear coloured.

On account of aberration, the lights of various colours would reach us along different directions, and the star would appear like a narrow spectrum, or, at least, would present coloured edges.

In Fizeau's experiment suppose, for instance, that the blue light travels faster than the red. Then as the speed of the rotating wheel is increased so as to begin to cut off the light, the red light is cut off first, and the image appears blue. When the eclipse is over, and the image begins to reappear, the red light begins to appear first, and the image appears red.

In Foucault's experiment the image of the aperture would consist of a series of coloured images having different positions. Thus the appearance would be that of a spectrum, or, at least, of an image having coloured edges.

It has not been proved that any of these appearances occur. Hence we infer that there is no appreciable difference, in air or in vacuo, between the velocities of lights of various

colours.

CHAPTER X.

WAVE MOTION.

IMAGINE a particle to be moving to and fro along a straight line A B, performing oscillations under the action of any forces, about the point O, which we may suppose to be the position of the particle when at rest, or its equilibrium position.