rounding more opaque parts of the screen, so that the spot appears brighter than the surrounding paper. If, however, the screen is held against a dark background and illuminated from the front, the greasespot will appear dark, for more of the light which is incident on the screen is transmitted through the spot than through the rest of the screen, and hence less is reflected or diffused so as to reach the eye by the spot than by the surrounding parts. If the screen is equally illuminated on both sides, then the spot diffuses less of the light received from the one source than the surrounding parts, but i transmits more of the light from the other source, so that these two effects just neutralise one another, and the spot appears of the same brightness as the surrounding paper.

The screen with the grease-spot is placed between the two sources whose intensities have to be compared, and moved about till the greasespot can no longer be distinguished from the rest of the screen. If, when this adjustment has been made, the distances of the two sources from the screen are d, and do, we have, as before,

I _d 11⁄2 d

In using Bunsen's photometer, it is of assistance if both sides of the screen can be seen simultaneously. The usual arrangement employed to secure this end is a system of two mirrors inclined at 45° to the screen.

B

M

M2

S2

With this arrangement one side of the screen is seen with one eye and the other with the other, so that if, as is generally found to be the case, one eye is more sensitive than the other, a wrong setting may be made. This source of error is removed in the Lummer - Brodhum photometer, which consists of an opaque screen AB (Fig. 332), each side being illuminated by one of the sources which are to be compared. The two sides of the screen are viewed by means of two plane mirrors, M1 and M., and a double glass prism, CD. This prism consists of two right-angled prisms, the longest face of one being partly bevelled away, fastened together with Canada balsam. Owing to total internal reflection (§ 344), the central rays reaching an eye at E come from the left-hand face of the screen, and the surrounding rays come from the right-hand side, as is shown in the figure.

FIG. 332.

--->

E

R

Hence the observer moves the photometer till the central patch L and circumferential parts R appear of the same brightness, when the intensity of the illumination on the two sides of the screen is the same; the relative powers of the two sources is then as the square of their distances from the screen.

The relative illuminating powers of two sources is only strictly comparable when the colour of the light emitted is the same for both. If the colours differ, we can only compare their illuminating power for the lights of different wave-length which are included in the light given by both sources. In order to perform this comparison, a spectrum (§ 367) is formed with the light from each source, and the intensities of the dif ferent portions of the spectra which are common to both are compared. A rough comparison can be made by comparing the powers of the two sources, when a red, a yellow, and a blue-coloured glass is placed in turn between each source and the photometer screen. The three values for the relative illuminating powers thus obtained will give an idea as to the relative composition of the light given by the two sources.

CHAPTER V

VELOCITY OF LIGHT

362. Finite Velocity of Light-Römer.-An entirely new era in the history of the science of light was introduced by the Danish astronomer Römer in 1676, when he not only showed that light did not travel instantaneously, as had been previously supposed, but also measured the velocity with which light travels through interplanetary space.

The planet Jupiter has four moons, and as these revolve round the planet they disappear once in each revolution, for when they pass into the shadow of the planet cast by the sun they become invisible, and are said to be eclipsed, for we only see the planets and their satellites by the light of the sun which they reflect.

If any one of Jupiter's moons revolves round the planet with a uniform angular velocity, as is the case with our moon, then the time which elapses between one passage of the moon into the shadow and the next ought to be constant, since it would be equal to the periodic

time of the moon's revolution round the planet. However, if the times between successive eclipses of the planet are noted, as seen from the earth, it is found that they are not all equal.

Römer accounted for this phenomenon by supposing that light took an appreciable time to travel from Jupiter to the earth. Let S (Fig. 333) be the sun, E the earth, and J Jupiter; and suppose that when an eclipse of one of the moons occurs these three are in the relative positions shown, the earth being at its nearest point to Jupiter. When the next eclipse occurs, the earth will have moved round in its

orbit to some such position as E,, while Jupiter will have only moved a short distance round in its orbit. Hence the distance between the earth and Jupiter is now greater than before. If is the speed

with which light travels, then the observed time at which the eclipse occurs when the earth is at E will be at a time EJV, i.e. the time taken by the light to traverse the space EJ, after the actual eclipse. When the earth is at E1, the observed time will be EJ later than the actual time. Hence, if is the actual time between two successive eclipses, the observed interval is 0 + E1J/V ́ − EJ/ V, and since EJ is greater than EJ, the observed interval will be greater than the true interval; since, however, we cannot observe the true interval 0, the quantity cannot be calculated from the observation of a single interval in this way.

At each successive eclipse the earth will be further and further away from Jupiter, till finally they come into the positions J, En, when they are at their maximum distance apart. After this, at each successive eclipse the distance will diminish, and hence the observed interval be less than the true interval.

Suppose that ʼn eclipses occur between that which occurs when Jupiter and the earth are nearest together (at conjunction), and that which occurs when they are at their greatest distance (opposition), the actual interval between the first and last of these eclipses is n0. The observed interval is no + EnJn/ V – EJ/V, or if dis the diameter of the earth's orbit, so that EnJn-EJ = d, the observed interval 7, is n0+d\V.

The actual interval between the eclipse when the earth is at opposition and the one when it is again at conjunction will also be no. The observed interval, 7, since at the end of the series the earth is nearer Jupiter than at the commencement by a distance d, will be n0-d\V.

Hence if we know the diameter, d, of the earth's orbit, we can calculate the velocity of light, V, from the difference between the interval 7 which elapses between an eclipse at conjunction and the eclipse at the next opposition, and the interval 7 between this eclipse at opposition and the one which occurs at the next conjunction.

The moon chosen was the innermost, which makes a revolution in about 1 days, and it was found that, starting at conjunction, the interval between the first eclipse of this planet and the 113th (when the earth and Jupiter came into opposition) exceeded the interval between the 113th and the 225th (when the earth and Jupiter were again in conjunction) by 33.2 minutes, and hence 7- T-33.2 minutes. If d, or the diameter of

the earth's orbit, is taken as 195,600,000 miles, or 298,600,000 kilometres, this gives 186,300 miles per second, or 299,800 kilometres per second as the velocity of light.

363. Fizeau's Method of Measuring the Velocity of Light.— The accuracy of the determination of the velocity of light by Römer's method is limited by the accuracy with which we know the diameter of the earth's orbit, hence it is important to determine the velocity of light between two terrestrial points, the distance between which can be directly measured. The first to perform this experiment was Fizeau, who in 1849 measured the velocity of light by using a method depending on the eclipsing of a source of light by the teeth of a rapidly rotating wheel, the principle of the experiment resembling Römer's method.

A bright source of light was placed at I. (Fig. 334), and after passing through a lens A, a certain proportion of the rays of light was reflected from the surface of an unsilvered plate of glass, G, placed at an angle of 45°. The reflected rays came to a focus at F, this point being the

principal focus of a second lens B. Thus the light left B in a parallel beam, which, after traversing a distance of about four miles, fell on a lens C, and was brought to a focus at the surface of a spherical mirror D. The curvature of this mirror is such that the lens C is at its centre of curvature, and hence the rays are reflected back along their path, so that on emerging from the lens C they again form a parallel beam. This reflected beam falls on the lens B, is brought to a focus at F, and then falls on the plate of glass G, where some of the rays will be reflected, and some will be transmitted and enter the eye-piece E, so that a bright star will be seen by the observer, formed by light which has travelled to D and back again. A toothed wheel, H, which can be rapidly rotated round an axle, is so arranged that when a tooth passes F the light is intercepted, but when a space passes F the light is allowed to pass.

If the wheel is slowly rotated, an observer at E will see a bright star when a space passes F, while when a tooth passes there will be darkness, so that as the wheel rotates the star alternately appears and dis