either the wedge itself should be of a greenish hue, or green light
should be used in finding the scale-value (the constant B in the
formula m=A+Bw). In the second, star magnitudes obtained
by extinction with the wedge will agree better with those obtained
by photography than those obtained with other visual photometers,
since photographic action is chiefly produced by rays
from E to G in the spectrum, and the E light of ultimate importance
with the wedge photometer is nearer this light in character
than the D light with which other photometers are chiefly
concerned. It would also appear that results obtained with the
wedge photometer are independent of the aperture of telescope
employed, which is not the case with other photometers.
Passing now to the consideration of photographic methods, it is found that when a plate is exposed to the stars, the images of the brighter stars are larger and blacker than graphic those of the fainter ones, and as the exposure is prolonged the increase in size and blackness continues. Much of the light is brought to an accurate focus, but, owing to the impossibility of perfect achromatism in the case of refractors, and to uncorrected aberration, diffraction, and possibly a slight diffusion in both refractors and reflectors, there are rays which do not come bo accurate focus, grouped in rings of intensity gradually diminishing outwards from the focus. As the brightness of the star increases, or as the time of exposure is prolonged, outer and fainter rings make their impression on the plate, while the impression on the inner rings becomes deeper. Hence the increase in both diameter and blackness of the star disks. As these increase concurrently, we can estimate the magnitude of the star by noting either the increase in diameter or in blackness, or in both. There is consequently a variety in the methods proposed for determining star magnitudes by photography. But before considering these different methods, there is one point affecting them all which is of fundamental importance. In photography a new variable comes in which does not affect eye-observations, viz., the time of exposure, and it is necessary to consider how to make due allowance for it. There is a simple law which is true in the case of bright lights and rapid plates, that by doubling the exposure the same photographic effect is produced as by increasing the intensity of a source of light twofold, and so far as this law holds it gives us a simple method of comparing magnitudes. Unfortunately this law breaks down for faint lights. Sir W. Abney, who had been a vigorous advocate for the complete accuracy of this law up till 1893, in that year read a paper to the Royal Society on the failure of the law, finding that it fails when exposures to an amyl-acetate lamp at 1 ft. are reduced to 0s·001, and “signally fails” for feeble intensities of light; indeed, it seems possible that there is a limiting intensity beyond which no length of exposure would produce any sensible effect. This was bad news for astronomers who have to deal with faint lights, for a simple law of this kind would have been of great value in the complex department of photometry. But it seems possible that a certain modification or equivalent of the law may be used in practice. Professor H. H. Turner found that for plates taken at Greenwich, when the time of exposure is prolonged in the ratio of five star magnitudes the photographic gain is four magnitudes (Mon. Not. R.A.S. lxv. 775), and a closely similar result has been obtained by Dr Schwarzschild using the method presently to be mentioned.
Stars of different magnitudes impress on the plate images differing both in size and blackness. To determine the magnitude from the character of the image, the easiest quantity to measure is the diameter of the image, and when measurements of position are being made with a micrometer, it is a simple matter to record the diameter as well, in spite of the indefiniteness of the border. Accordingly we find that various laws have been proposed for representing the magnitude of a star by the diameter of its image, though these have usually been expressed, as a preliminary, m relations between the diameter and time of exposure. Thus G. P. Bond found the diameter to increase as the square of the exposure, Turner as the cube, Pritchard as the fourth power, while W. H. M. Christie has found the law that the diameter varies as the square of the logarithm of the exposure within certain limits. There is clearly no universal law-it varies with the instrument and the plate-but for a given instrument and plate an empirical law may be deduced. Or, without deducing any law at all, a series of images may be produced of stars of known brightness and known exposures, and, using this as a scale of reference, the magnitudes of other images may be inferred by interpolation. A most important piece of systematic work has been carried out by the measurement of diameters in the Cape Photographic Durchmusterung (Ann. Cape Obser. vols. iii., iv. and v.) of stars to the tenth magnitude in the southern hemisphere. The measurements were made by Professor J. C. Kapteyn of Groningen, on photographs taken at the Cape of Good Hope Observatory; he adopts as his purely empirical formula
magnitude＝B/(diameter+C),
where B and C are obtained independently for every plate, from comparison with visual magnitudes. C varies from 10 to 28, and B from go to 260. The part of the sky photographed was found to have an important bearing on the value of these constants, and it was in the course of this work that Kapteyn found a systematic difference between stars near the Milky Way and those far from it, which may be briefly expressed in the law, the stars of the Milky Way are in general bluer than the stars in other regions of the sky. It is intended, however, in the present article to discuss methods rather than results, and we cannot here further notice this most interesting discovery.
Of methods which choose the blackness of the image rather than the diameter for measurement, the most interesting is that initiated independently by Pickering at Harvard and C. Schwarzschild at Vienna, which consists in taking star images considerably out of focus. The result is that these images no longer vary appreciably in size, but only in blackness or density; and that this gradation of density is recognizable through a wide range of magnitudes. On a plate taken in good focus in the ordinary way there is a gradation of the same kind for the faintest stars, the smallest images are all of approximately the same size, but vary in tone from grey to black. But once the image becomes black it increases in size, and the change in density is not easy to follow. The images-out-of-focus method seems very promising, to judge by the published results of Dr Schwarzschild, who used a prepared comparison scale of densities, and interpolated for any given star from it. The most satisfactory photographic method would certainly be to take account of both size and blackness, i.e. to measure the total deposit in the film, as, for instance, by interposing the whole image in a given beam of light, and measuring the diminution of the beam caused by the obstruction. But no considerable piece of Work has as yet been attempted on these lines.
Even in a rapid sketch of so extensive a subject some notice must be taken of the application of photometry to the determination of the relative amount of light received on the earth from the sun. the moon and the planets. The methods by which these ratios have been obtained are as simple as they are ingenious; and for them Light of the Sun. Moon and Planets. we are mainly indebted to the labours of P. Bouguer and W. C. Bond (1789–1859). The former compared the light received from the sun with that from the moon in the following fashion in 1725. A hole one-twelfth of a Paris inch was made in the shutter of a darkened room, close to it was placed a concave lens, and in this way an image of the sun 9 in. in diameter was received on a screen. Bouguer found that this light was equal to that of a candle viewed at 16 in. from his eye. A similar experiment was repeated with the light of the full moon. The image now formed was only two-thirds of an inch in diameter, and he found that the light of this image was comparable with that of the same candle viewed at a distance of 50 ft. From these data and a very simple calculation it followed that the light of the sun was about 256,289 times that
