the position of the single candle or the disc until the latter is equally illuminated on both sides (i.e. until the grease-spot disappears). When this is the case it will be found that the row of four candles is twice as far from the disc as the single candle is. What conclusion do you draw from this?

11. Note on Optical Benches, etc.-In working with the Bunsen photometer, as well as in many other optical experiments (e.g. in finding focal lengths of mirrors and lenses), it is convenient to have the various pieces of apparatus (candles, screens, etc.) mounted on suitable holders which slide on a graduated bar. Such an arrangement is called an optical bench. A short portion of a simple form of wooden bench is shown in Fig. 11, together with one of the sliding pieces. Each of these is furnished with an upright socket consisting of a piece of brass tube about 5 in. high and in. in diameter. The mirrors, lenses, etc., are mounted in wood or cork mounts, attached to iron rods which fit into the sockets; if these are provided with screws, the rods can be clamped at any convenient height. The bench should be about 6 ft. long, and a strip of stout white paper should be carefully pasted along the side of it. When this has dried thoroughly mark a graduated scale on it, the graduations coming right up to the edges of the slides. A centimetre scale is much more convenient than one in feet and inches. On the edge of each slide make a

vertical mark, corresponding to the centre of its socket.

Fig. 11.

The measurements required may also be made by using a beam-compass (Fig. 12), or even by holding a graduated scale alongside the apparatus.

But it is a great convenience to have some form of optical bench, especially when pieces of apparatus have to be moved backwards and forwards and always kept in the same straight line.

EXAMPLES ON CHAPTER II

1. A candle is placed at a distance of 1 ft. from a cardboard screen, and a lamp of nine candle-power is placed at a distance of 12 ft. on the other side. Compare the illumination on the two sides of the screen.

K

The intensity of the illumination on the side facing the candle is to that on the side facing the lamp as to

I

9

or as I to

(1)2 (12)2'

2. How near to the screen would the lamp in the last question have to be moved in order to reverse the proportion, i.e. to make the intensities of illumination as I to 16?

3. A standard candle and a gas-flame are placed 6 ft. apart, the gasflame being of four candle-power. Where would a Bunsen disc have to

be placed between them so as to make the grease-spot disappear?

Let x denote the distance of the disc from the candle; its distance from the gas-flame will then be 6 – x. The grease-spot disappears when the disc receives equal illumination from the candle and the lamp. When this is the case we must have

The disc must therefore be placed 2 ft. from the candle and 4 from the lamp.

ft.

4. What do you mean by the intensity of the illumination at a point, and how would you show, experimentally, that it is inversely proportional to the square of the distance of the point from the source?

5. In testing a night-light against a candle by means of a Rumford photometer it is found that the shadows are of equal depth when the night-light is 2 ft. from the screen and the candle 3 ft. Compare their illuminating powers.

6. Two equal sources of light are placed on opposite sides of a disc, one being 20 cm. from it and the other 30 cm. illumination on the two sides of the disc.

Compare the intensity of

7. In measuring the illuminating power of a gas-flame by a Bunsen photometer, the distance from the gas-flame to the grease-spot was 96 cm., and from this to the standard candle 30 cm. What was the candle-power of the gas-flame?

8. A Carcel lamp of nine candle-power is placed at a distance of 4 ft. from a standard candle: find, as in Example 3, the position in which a screen must be placed between them so as to receive equal amounts of light from each.

CHAPTER III

VELOCITY OF LIGHT

12. WHEN a gun at some distance from you is fired, you see the flash before you hear the report. The sound takes an appreciable time to travel from the gun to you. But how about the light? Is the flash seen at the very same instant when it is produced? or does the light travel with a definite velocity? If it does, by what method can this velocity be measured?

Suppose a gun to be fired at regular intervals, say every hour. An observer near at hand and provided with a delicate chronometer observes the times at which the flashes are seen. Now suppose the observer to move a very great distance off. If the distance were great enough, he would not now see the flashes exactly at the actual times of firing (ie. at the hour), but a short time afterwards; and by carefully measuring this time, knowing his distance from the gun, he would be able to calculate the speed with which light travels. As a matter of fact, this speed is so great that it would be exceedingly difficult to detect any retardation within any practicable distance on our earth. Astronomers have to deal with immensely greater distances, and so it is not surprising to find that the first observations on the velocity of light were made by astronomical methods.

13. Römer's Method. The first estimate of the velocity of light was made about the year 1675 by a Danish astronomer named Römer. It happens that one of Jupiter's satellites (or moons) passes into the shadow of the planet at regular intervals (48 hours), and is thus eclipsed. While the earth is in the neighbourhood of E, Fig. 13 (i.e. nearest to Jupiter),

its distance from Jupiter does not change rapidly, and the successive eclipses of the satellites are seen to occur at regular and equal intervals. The same holds good when the earth is

But

in the neighbourhood of E' (farthest from Jupiter). between these two positions, as the earth moves from E to E', its distance from the planet continually increases, and Römer observed that during this time the intervals between successive eclipses were always longer than the time mentioned. An eclipse seen at E' is 16 minutes 26 seconds later than if it had been observed at E. The difference is due to the time taken by the light in travelling from E to E', i.e. across the diameter of earth's orbit. This is a distance of about 184,000,000 miles, and since light traverses it in 986 seconds conclude that its velocity is 184,000,000

986

we

or about 186,600 miles per second. Some idea of this may be obtained by considering how long light would take to travel round our earth. The circumference of the earth is less than 25,000 miles. Light would therefore travel round it seven and a half times in a second.

14. Fizeau's Method. It might appear impossible to measure such an enormous velocity as this otherwise than by astronomical observations. The skill of modern experimenters has, however, proved equal to the task. The first experimental method was devised by Fizeau, and depends upon the following principle.

If a toothed wheel be made to revolve very rapidly about its axis, the time taken by a single tooth or a single space in passing a given point is extremely small. For example, it is

easy to make it as small as the ten-thousandth part of a second; during which time light would only travel about 18 miles. Now suppose that a beam of light passes between the two teeth of the mirror, parallel to its axis, and falls upon a distant mirror which reflects the beam back along its own path. When the light gets back again to the wheel it may be able to pass through a space, or it may be blocked by one of the teeth; and which of these two things happens will simply depend upon the distance of the mirror and the speed of rotation of the wheel.

Fizeau chose two stations 8633 metres apart. At one of these was placed the toothed wheel ww (Fig. 14), and a bright source of light; at the other the mirror m', which reflected the light back to the first station. The source of light was not

placed directly behind the wheel but to one side, at L, and the light from it was reflected to the distant mirror m' by means of a transparent mirror m (of unsilvered glass) inclined at an angle of 45°. Thus an observer looking through m towards the distant station would see a bright star or point of light-the image of L produced by reflection in m'.

I

Now it was found that when the wheel was made to rotate at a certain speed this bright star was eclipsed; and the speed of rotation at which this happened was such that the wheel only took of a second to move through the breadth of a tooth or space. During this short time the light had travelled through one of the spaces at ƒ to the distant mirror m' and back again, or through a distance of 2 × 8633, or

18,144