that an image of the slit formed by light which has passed through the prism is seen through the telescope; and the prism is turned so as to make the image move nearer to the direction of direct light, the telescope following the image so as always to keep it in view. At length a position of the prism is obtained, such that if the prism be turned either way the image recedes from the direction of the direct light; this position of the prism is therefore the position of minimum deviation. The telescope is moved until the line of the spectrum coincides again with the cross-wires of the telescope. The angle through which the telescope has been turned from the position of direct light is read off the graduated circle, and this angle is the minimum deviation required.

163. To measure the refractive index of a liquid, it is enclosed in a hollow prism of glass, made by cementing plates of glass together. The two sides of the plates however are never accurately parallel, and from the observed deviation it is necessary to subtract the small deviation caused by the empty prism.

The refractive indices of gases in given conditions as to temperature and pressure have been measured by a similar process. They must be enclosed in a tube, the ends of which are closed by two plates of glass placed very obliquely with reference to the axis of the tube.

The experiments of Biot and Arago on the refractive indices of gases showed that for gases the quantity μ-1 is proportional to the density of the gas, a law which had been enunciated by Newton, who deduced it from his theory of emission.

164. To find the focal length of a thin convex lens.

This is usually measured by adjusting the lens and an object, until the distance between the object and the image is a minimum; this distance is then four times the focal length. For, if u, v be the distances of the object and image in front of, and behind, the lens, respectively,

while the distance between the object and the image is given by the equation

The quantity (u – v)2 is always positive, and therefore the least value of x is equal to 4f.

If the lens be concave, it is placed in contact with a convex lens, so that the whole combination may be collective; the focal length of the combination may be determined as before. If f, f' be the numerical focal lengths of the two lenses, F that of the combination,

165. It has been shown in § 5 that when an element of a surface is illuminated by light proceeding from a source of intensity I, at a distance r, so that the axis of the pencil makes an angle with the normal to the element of surface, then the intensity of illumination is proportional to

I cos 0

It is found that the eye is of itself unable to estimate the ratio of the intensities of two sources of light, but that it is an accurate judge of the equality of illumination

of two illuminated surfaces when they are placed side by side. All methods of photometry depend therefore on the equalising of two illuminations.

In order to compare the intensities of two sources of light, the two halves of a piece of thin porcelain are illuminated by the two sources, respectively, in such a way that either the light falls normally on the porcelain, or the lights from the two sources make equal angles with the plane of the porcelain. The distances of the lights are then adjusted so that the two halves of the porcelain are equally illuminated. Then the intensities of the sources are in the inverse proportion of the squares of their distances from the porcelain. This is the principle both of Ritchie's and of Foucault's photometers.

166. Ritchie's photometer consists of a rectangular box open at both ends. In the lid is a narrow strip of porcelain or oiled paper. The instrument is placed between the two sources to be compared, and the light is reflected up to the porcelain by two pieces of mirror (which must be cut from the same piece of glass) placed

B

at angles of 45° to the axis of the box. The box is then moved from one source towards the other until the two halves of the porcelain are equally illuminated, and the distances of the lights measured.

167. In Foucault's photometer the lights which are to be compared act separately on two different parts of the same vertical plate of thin transparent porcelain, PQ. RS is an opaque vertical screen which separates the two illuminations from one another. If this screen be so adjusted that the vertical planes ASm, BSn which limit the regions illuminated separately by the two sources A, B, intersect just in front of the lamina PQ, the dark

band mn can be made as narrow as we please. The

distances of A and B are then adjusted so that the two portions of the lamina are equally illuminated.

168. In Rumford's photometer the intensities of the two shadows on a screen of a vertical rod due to the two lights are compared. The lights are arranged so that the shadows fall close together, and the shadow formed by one light is lighted by the light from the other source. The distances being so adjusted that the shadows are of equal intensity, the distances of the lights are measured, and thus the intensities of the two sources can be compared.

Bunsen invented a very simple photometer. If a spot of grease be made on a sheet of paper, then if the paper be equally illuminated on its two sides, the transparent spot cannot be seen except by close inspection. The sources of light are placed on opposite sides of the paper and their distances are so adjusted that the grease spot disappears; then the intensities of the sources are inversely as the squares of their distances from the paper. The adjustment should first be made from the side on which one source lies, then the screen should be turned round and the adjustment made from the side on which lies the other source, the same side of the paper being observed each time. The mean of these two positions will give a fairly accurate result.

This is the photometer most usually employed to compare the illuminating power of different lights, such as gas and the electric light. A standard candle is a sperm candle burning 120 grains of sperm per hour. In stating the illuminating power of a particular gas-burner, it is supposed that the burner is consuming 5 cubic feet of gas per hour.

In all these comparisons the lights are supposed to be of the same quality, otherwise the comparison fails. A strict comparison of two compound lights of different qualities could only be arrived at after comparing the relative intensities of all the different coloured rays of the spectra given by the two lights, and tabulating the results.

Methods of determining the Velocity of Light.

169. There are two methods of determining the velocity of light by optical experiments, the one devised by Fizeau and the other by Foucault. Fizeau's experiments were repeated in 1876 by M. Cornu, and later a modification of Fizeau's method has been used by Dr Young and Professor Forbes in Scotland. The velocity of light has also been determined by A. A. Michelson, of the United States navy, who followed Foucault's method.

170. In Fizeau's experiments two astronomical telescopes several miles apart are arranged so that their axes are accurately parallel, the one telescope looking into the other. In one of the telescopes a mirror is placed at the focus of the object-glass, exactly perpendicular to the axis of the instrument. The observer stands at the other telescope; in this instrument a plate of glass, inclined at an angle of 45° to the axis of the telescope, is placed between the eye-piece and the principal focus of the object-glass. Light is admitted through the side of the instrument and reflected down the tube by the