COD is equal to the complement of the sun's declination, that is, to the angle which the direction of the sun makes with the earth's axis. If, then, the clockwork being set going, CO is set to point towards the sun, it will continue to do so.

CO may be turned towards the sun by turning Cs till a needle, which is attached to the axis at D, indicates the hour of true time on the dial B B. The limb rr' is carried by a hollow support which surrounds the axis that connects CP s with the clockwork, and moves independently of this axis; by means of the two clamping-screws E and A, the rod can be set in any desired direction, the direction in which the light is to be reflected.

Attached to the limb C Ps are a pin-hole aperture s and a small screen P, such that the line Ps is parallel to CO.

M

These may be used in setting the apparatus. It is, for instance, unnecessary to know the meridian plane if the apparatus is set correctly in all other respects. For if this is the case, and the whole apparatus be turned about, keeping its base level, till the sun shines through s on P, then the axis must be in the meridian.

EXAMPLE.

If you were observing a small luminous object by a telescope not corrected for chromatic aberration, what appearances would present themselves on sliding the eye-piece in and out? (Lond. Int. Sci. Pass, 1881.)

CHAPTER IX.

VELOCITY OF LIGHT.

THE first successful attempt to measure the velocity of light was made by Roemer, a Danish astronomer, in about 1675. His method was based on observations of the eclipses of Jupiter's first satellite. The plane in which the satellite revolves round Jupiter is nearly the same as that of Jupiter's orbit about the sun; and the satellite becomes periodically eclipsed, passing into the shadow of Jupiter cast by the sun. The satellite revolves uniformly about Jupiter, as does Jupiter about the sun, so that successive eclipses should occur at equal intervals, and so should successive emergences. In the figure S denotes the sun, and the inner and outer circles the orbits of the earth and Jupiter. Suppose both to move in the plane of the paper, clockwise. Jupiter's period of revolution is 11 years and 10 months. Suppose the planets (E and J) to be in conjunction, that is, in the positions E, J1. In a little more than 6 months they will be in opposition, at E2, J1⁄2 And after another equal interval they will be in conjunction again at Eg, J. Now, while E moves from E, to E, the appearances of the satellite can be observed; and while E moves from E to E, its disappearances can be observed. It is found that the mean interval between successive appearances is longer than the mean interval between successive disappearances. This is because light takes a finite time to reach the earth from the satellite, and a longer time as the earth gets further away. If the interval between successive disappearances or appearances is calculated from observations made as the earth moves from conjunction to conjunction again, it is found

that the interval between appearances at E, and E, is 16 mins. 26 secs. longer than the calculated time, and the interval between disappearances at E, and E, is by the same amount shorter than the calculated time. Thus 16 mins. 26 secs. is

the time that light takes to travel over the diameter of the earth's orbit. And the velocity of light in space is found by dividing this diameter by 16 mins. 26 secs. The result that has been

obtained in this way is 308,000,000 metres per second.

C

Bradley, the English astronomer, in 1728, explained, by means of the finite velocity of light, the astronomical phenomenon called aberration; and deduced from the phenomenon the value of the velocity of light in space. This phenomenon is a small apparent periodic displacement of the fixed stars from the mean position. The period of the displacement is a year; and the displacement is always in the direction in which the earth is moving in its orbit. Now, suppose the earth to be at A, and let A B denote the velocity with which it is moving; let light be coming to A along the path CA and with a velocity denoted by CA; then the relative approach of the light towards the pounded of the two velocities CA and B A,

FIG. 128.

earth is comthat is, it is

represented by DA. That the light will appear to come along the path DA will, perhaps, be made clearer by the following illustration :

Suppose a telescope (and the same reasoning would apply to the eye) to be directed along AC. Then, if the light enters one end of the tube at C, by the time the light has arrived at A, the other end of the tube will have got to B, and the light will not be perceived. But if the telescope is directed along A D, the light coming along DB enters the tube at D, and by the time it arrives at B, the other end of the tube is there to receive it. Thus the light appears to come along DA. This explanation does not at all depend on the nature of light, but merely on the facts that light travels with finite velocity, and along straight lines, so that its path in the moving telescope tube is in a straight line with all the remainder of its path.

Let, then, a denote the angle which the apparent distance of the star is making with the earth's path, that is, the angle CAB; and let & denote the angular apparent displacement of the star from its true position. Let V and v be the velocities of light and of the earth. Then we have—

To find & it is necessary to know the true direction of the star. This, for many stars, is the same as its mean apparent direction, practically. The distances of some stars are so vast that the directions of one from all points of the earth's orbit are about the same. And in two intervals, separated by six months, when the earth is moving with equal velocities in opposite directions, a will have nearly equal values, and the displacements from the true position will be equal and opposite. The greatest value of d for any star is only about one-third of a minute of angular measure.

Fizeau's Experiment.-Suppose a source of light to send a pencil to a plane mirror at a great distance placed normally to the path of the pencil. Imagine a toothed wheel near the source, and so placed that the light goes and returns by the space between two teeth. Now, the wheel may be rotated at such a speed that the light goes to the mirror through an aperture, and on its return is intercepted by the next tooth; or, again, the wheel may be rotated faster, so that the light returns by the next aperture. On continuing to increase the speed, successive disappearances and reappearances would be observed.

This is the principle of Fizeau's method. The experiment was carried out in the following manner :—

At two stations, a considerable distance apart, are two telescopes, A B and C D. In Fizeau's experiment this distance was nearly three

is arranged by setting each telescope so that the image of the object-glass of the other is brought to the centre of its field of view. The eye-piece D is removed, and a plane mirror, M, is set at the focus of C, and at right angles to the axis of C, so that the rays entering C may return to B. It is clear that extremely accurate setting of M is not necessary, so long as the focus of C is in M. S is a source of light of which an image is formed at F, the focus of B, by means of a system of lenses and a plate of unsilvered glass, G, inclined at 45° to the axis of B. W is a toothed wheel, whose teeth pass over F, and which can be rotated at a known rate by means of clockwork and countingwheels. When the wheel rotates slowly, on looking through A an image of S will be seen, for the light will go through two teeth to M, and return through the same space. As the speed of W is increased, the light will be cut off; and on still further increasing it, the light will reappear, because it goes to M through one aperture and returns through the next; and so on. If, then, the speed of W giving complete extinction of the light is known, and the number of the extinction (whether it is the first second, third, etc.), the angle through which the wheel

M

FIG. 129.