ent backward motion of the stone is really the actual forward motion of the car, the time was half a second; in that time the stone moved across the car, 10 feet, and its rate of motion was therefore 20 feet per second. Evidently we may, if more convenient, measure the angle AA'B, and the line AB, and by trigonometry find the sides AB, and AA', from which the velocities of both stone and car may be determined.

513. Application. Let AB be a telescope which. moves with the earth, and in a certain time takes the position A'B'. Let a ray of light from the star S meet the object glass at B, and suppose its velocity sufficient

Fig. 168.

to bring it to A' at the instant that the eye-piece comes to the same point. As the ray is in the line of collimation at B and at A', it must have followed that line through the tube, and there comes to the eye in the apparent direction A'S', its real path having been A'S. The star is therefore displaced by the amount of the angle SA'S' in the direction of the earth's motion.

The angle is 20" (510), and the length of the telescope is known; the solution of the triangle BAA' gives the distances AA', through which the telescope moved, and BA', through which the light moved. From the earth's rate of motion, the time of passing from A to A' is found, which is also the time of passage of light from B to A'; hence, the velocity of light is determined.

This method gives 192,600 miles per second.

FIZEAU'S EXPERIMENT.

514. Theory. Suppose a wheel which has 1000 teeth in its circumference rotates once in a second; evidently the time between the passage of two successive teeth is Too of a second. If the wheel turns 10 times a second, each tooth marks Too of a second.

Suppose a ray of light passes between two teeth of the rotating wheel, goes to a mirror at some distance, and is reflected back again. If the teeth are passing at the rate of 10,000 in a second, and the distance is such that the light can pass from the wheel to the mirror and back in Toooo of a second, the returning ray will find the second space in the precise position for it to pass through; but if it occupies less or more than 1 of a second, it

may find a tooth instead of a space, and be intercepted.

Fig. 169.

If the rate of the

wheel, and the distance of the mirror are so arranged that the ray will pass through the second space, doubling the velocity of the wheel will allow the light to pass through the third space; two teeth will have passed while the light is taking its journey. Three times the velocity

causes three teeth to pass, etc.

515. The apparatus.-A telescope, A, is fitted with a smaller tube, B, at right angles to the larger. The wheel,

E, is so placed that its teeth pass through a notch in the tube, across the line of collimation of the telescope. The clock-work which drives the wheel, and registers its revolutions, is omitted, for simplicity. A ray of light from a lamp passes into the small tube, B, is reflected at C along the large tube to a mirror, at a known distance, which returns it through the large tube to the observer at D. The observer can see no light which is not reflected from the distant mirror.

When the wheel turns slowly the reflected rays are all intercepted; when the velocity is such that the rays can return in the time between the passage of two successive teeth, each finds a space to pass through, and goes to the eye, a clear bright light like a star. At a more rapid rate, the star vanishes; at double the velocity it re-appears, and again, at three and four times the velocity.

The distance from the telescope to the mirror is twice traversed, in a part of a second which is known from the rate of the teeth as shown by the clock-work, hence the velocity of light is again determined.

The experiment was made with the most perfect machinery, and with the greatest care, by M. Fizeau, at Paris.

It gave 194,000 miles per second as the velocity of light. M. Foucault devised a still different experiment by which similar results were obtained.

The number generally adopted is 192,000 miles per second.

CHAPTER XVIII.

THE FIXED STARS.

517. The fixed stars are those which to the ordinary observer keep their places with reference to each other. They are distinguished from a few which, from their wandering, were called planets (117). The fixed stars form groups nearly the same as those which were seen two thousand years ago; careful observations with the telescope, compared after the lapse of many years, show that some of them do move. Probably none are abso

lutely fixed in space. Besides keeping its place, a fixed star usually maintains the same brightness and color from century to century.

518. Magnitudes.-The stars are classed by their brilliancy, the brightest being of the first magnitude. Stars larger than the seventh magnitude, and, under very favorable circumstances, even those of the seventh, may be seen without instruments. Smaller, or telescopic, stars are classed as low as the 18th, or even the 20th, magnitude. The only limit is the power of instruments.

Sirius is by far the brightest star in the sky, and no other is entitled to rank with it. Sixteen to nineteen other bright stars are usually classed with Sirius, in the 1st mag., although it is not easy to say why the division should be made either at the seventeenth, or at the twentieth.

519. The relative brightness of the magnitudes.-Herschel proposed to indicate the relative brightness by numbers. He placed two telescopes in such positions that he could pass very quickly from one eye-piece to the

other. He then prepared a series of pasteboard rings with openings of various sizes; with these rings, laid over the object-glass, he could admit more or less light, as he pleased. When comparing two stars, he reduced the light of the brighter, until it seemed no more than that of the less. Then he considered that the magnitude of the stars were proportioned inversely to the areas, through which their lights were received.

Thus, when he covered three-fourths of the objectglass, Arcturus, a star of the 1st mag., seemed no brighter than Polaris, of the 2d mag.; hence, Polaris is one-fourth as bright as Arcturus. In the same way, Polaris is found equal to four times Mu Pegasus, of the 4th mag., and Mu Pegasus is equal to four times q Pegasus, which is between the 5th and 6th mags. Hence, the brightness of Arcturus is

4 times that of a star of the 2d mag.;

16 times that of a star of the 4th mag.;

64 times that of a star between the 5th and 6th mag. Working by this method, he found the average brightness of the magnitudes as follows:

520. The number of the stars. In the whole heavens, about 6000 (5905) stars may be seen without a telescope. As but half the sky is visible at once, and only the brightest stars can be distinguished within several degrees of the horizon, probably not more than 2500 can be seen at once. That the "stars of heaven" should seem to be "countless" is due partly to their irregular