prism. This image is illuminated only by light which has passed through s—that is, by light of a definite colour, and by moving the slit s2 a patch of light of any required colour can be thrown on to the screen at F E.

The lenses used will not, in general, be achromatic, and thus the images of s, formed by the different colours will not be at the same distance from L2, but by tilting the screen DD they can all be brought into focus. Again, since the face of the prism P2 is not at right angles to the

P

FIG. xxxiii.

S1

Sa

D

T2

E

direction in which the light travels from it to reach the slit S2, the lens L3 is also slightly tilted in order to form on FE a sharp image of the whole of this face.

To apply this to colour photometry, a vertical stick is placed in the path of this coloured beam, casting a shadow on the screen, while a second (standard) light (T2), mounted on a scale, casts a second shadow close by. This second shadow is coloured, being illuminated by the coloured beam from S2, while the first shadow receives the light from the standard; still, by moving the comparison light along the scale a point can be found at which the luminosities over the two appear equal. The determination of this point is,

however, attended with some difficulty, much of which is overcome by the adoption of the following oscillation method, the account of which is taken from the Bakerian Lecture for 1886 by Captain Abney and Major-General Festing.

The illuminating value of the spectrum varies greatly in its different parts, the maximum usually being in the yellow, and there is a gradation from this towards either end.

Now suppose that with the standard light at, say, 50 cm. from the screen it is approximately of the same intensity as the yellow light of the spectrum, then if the standard be moved to, say, 60 cm. distance there will be two parts of the spectrum, one towards the red the other towards the blue, which will have the same luminosity as the standard at a distance of 60 cm. ; this is, of course, 25/36 of its value when at 50 cm. To find these points, the card to which the slit S2 is attached is movable, and the slit can be made to slide along the spectrum, its position being determined by means of a scale. When the standard is at 60 cm. distance and the slit in the yellow, the shadow of the rod illuminated by the white light will be palpably darker than the other; when the slit has passed into the green-blue, it will be palpably lighter. Captain Abney finds that the best way of determining the intermediate point where the shadows balance is by oscillating the slide gently between two points where first one shadow and then the other is palpably too dark; the oscillations become shorter and shorter until the point of balance is determined.' The slide is then moved through the yellow to the red, and the same process is repeated. Two points in the spectrum whose illumination corresponds to that of the standard at the distance of 60 cm. are thus found. This distance is then varied, and another pair of points determined. In this manner a curve is drawn in which the abscissæ represent the position of the slit, while

the ordinates give the intensity of the light in terms of that of the standard.

By means of an independent series of observations the wave-length of the light which falls on the slit in any given position can be found, as in § 62, and thus a curve giving intensity in terms of wave-length can be determined. This curve is called a luminosity curve. The form of the curve, as found by Captain Abney, is given in fig. xxxiv. The

measurements are to some extent affected by the colour of the receiving screen; a card painted with two coats of zinc oxide gives the best results. A portion of this screen about 5 cm. square, limited by a sheet of black paper with a hole cut in it, should be used.

Instead of moving the standard light, the method of varying its intensity adopted by Captain Abney in some later experiments may be employed ('Proc. R. S.' vol. xliii. p. 249).

A circular disc is placed between the standard light and the screen. The disc is divided into four quadrantal sectors, and the alternate sectors are removed. If such a disc is rotated between the light and the screen, it is clear that half the light is cut off. To the disc a pair of movable sectors are fitted, and these can be adjusted so as to close

to a greater or less extent, as may be required, the open sectors of the main disc. If, for example, the open sectors be half closed by the adjustable sectors, the transmitted light has only half the intensity of that previously transmitted.

By means of suitable mechanism the position of these movable sectors can be adjusted relatively to the others while the apparatus is in motion, and thus the amount of light from the standard can be varied until the luminosity of the shadows is the same. In this method of making the: observations the slit is fixed in position and the sectors: adjusted. When the adjustment has been made the motor is stopped, and the position of the sectors determined; from this the intensity of the standard can be found.

The apparatus can be used to examine the effect of colour mixtures by placing two or more slits in the screen D D. A coloured image of the face of the prism will be formed by light passing through each slit, and these images are superposed. By opening each slit in turn and finding the luminosity, and then making measurements with the two or three slits open simultaneously, we can verify the law that the impression due to a mixed light is the sum of the impressions due to each light separately.

The apparatus has been employed by Captain Abney to study colour-blindness, by comparing the luminosity curves found by various observers, and also for experiments on the scattering of light by small particles. For this purpose a glass trough filled with pure water was placed between the source and the slit s1, and the luminosity curve found. Then a solution of mastic in alcohol was dropped in various quantities into the water, and the curve again determined.. It was found that the intensity of the transmitted light was very closely in accordance with the formula found by Lord Rayleigh, in accordance with which

Io being the intensity of the incident light, x the thickness of the absorbing medium, k a constant, and λ the wavelength.

Experiments.

(1) Determine the luminosity curve for the various components of the light from the given source, and compare the result with the normal curve.

(2) Shew that the intensity of a mixture of colours is the sum of the intensities of the components.

(3) Determine the absorption in different parts of the spectrum produced by the given solution of mastic, and compare your result with Lord Rayleigh's formula.

The curve can be drawn from these.

(2) Slits were placed in the red, green, and violet, and the

luminosities observed for each slit separately, and for the slits