PHOTOGRAPHIC PHOTOMETRY Here, we are dealing with a problem which differs considerably in detail from the visual procedure. We can no longer vary the light of a star by some device such as a Nicol prism until it is equal in brightness to a standard. But on a plate which has been exposed to a field of stars we can at any rate arrange the stars in order of brightness by measuring the diameters of the images, or by estimating their degrees of blackness, and we are then faced with the task of finding a means of relating our measures of blackness or of diameter to the true photometric scale defined as above.
Two principal methods have been employed, the in-focus method and the out-of-focus method. In the in-focus method a field of stars is photographed twice on the same plate, the intensity of the light being reduced in some known ratio for the second expo sure. This can be effected by stopping down the aperture of the telescope by a given amount. The plate is placed in the usual position, that is, in the focal plane of the object glass or mirror. For each star we then have two images on the plate whose dif ference in magnitude is known. Now suppose we measure the photographic effect of each image in some way and denote the measure by D. A simple measure of photographic effect is the diameter of the image, in which case D is the measured diameter. Suppose and D2 be the measures on the two images of the same star. The difference of magnitude between these two images depends only on the ratio in which the aperture has been stopped down and is consequently known. We thus get the magnitude difference corresponding to the difference of the measures and D2. In other words, we are relating the scale of our measures of photographic effect to the magnitude scale, and we thus have a means of converting the measures into magnitudes and of ob taining the relative magnitudes of all the stars on the plate.
The principle of the method is as follows. Select a sequence of stars on the plate such that the diameter (or any other measure of photographic effect that may be adopted) of the fainter image of any member of the sequence is equal to the diameter of the brighter image of the next succeeding member. We then have
a sequence of stars each member of which differs in magnitude from the following member by a known amount. In other words, the magnitudes of the stars of the sequence are known, but with an arbitrary zero point. If then, the measured diameters of these stars be plotted against their magnitudes obtained in this way, a curve would be obtained from which the magnitude of any star on the plate can be read off from its measured diameter. In actual practice a mathematical process is used instead of a graphical one. Furthermore, the equality between the fainter and brighter images of two consecutive members of the sequence will not be exact and this must be allowed for.
So far this method only gives a means of determining the rela tive magnitudes of stars in the same region of the sky and which can therefore be photographed on the same plate, but if we expose every plate a second time on some standard area, the time of exposure being the same, we can determine the magnitudes rela tively to some star or stars in the standard area (which may con veniently be the area of the Polar sequence) and it only remains to define the zero. This has been fixed, as already explained, so as to make the photographic magnitudes of the white stars of the 6th magnitude agree with their visual magnitudes on the Harvard scale. Instead of using a stop to reduce the light in a given ratio for a second exposure, it is preferable to use a coarse wire dif fraction grating placed over the aperture of the telescope. Each image is then flanked by fainter lateral images differing in magni tude from the main image by a known amount depending on the thickness and spacing of the wires. The subsequent procedure is unchanged, but only one exposure is necessary. In order to give some idea of the appearance of such gratings, it may be mentioned that one of the gratings used at Greenwich in conjunction with the 26-inch refractor consisted of wires o•69 mm. in diameter and spaced at intervals of 5 mm. (Monthly Notices R.A.S., 1913).