We shall best understand the method employed by the Herschels if we first imagine all the stars in the sky to be intrinsically similar objects. Each would then emit the same amount of light, so that the nearer stars would appear bright, and the further stars faint, merely as an effect of distance. The way in which apparent brightness decreases with distance is of course well known; the law is that of the “inverse square of the distance,” which means that the apparent brightness decreases just as rapidly as the square of its distance increases; a star which is twice as distant as a second similar star appears only a quarter as bright, and so on. Thus if all stars emitted the same amount of light, we could estimate the relative distances of any two stars in the sky from their relative brightnesses. By cutting wires of lengths proportional to the distances of various stars, and pointing these in the directions of the stars to which they referred, we could form a model of the arrangement of the stars in the sky. We should, in fact, know the whole structure of the system of stars except for its scale. To represent the faint stars of the Milky Way, a great number of very long wires would be needed. In the model these would all point towards different parts of the Milky Way, forming a flat wheel-like structure. The problem which confronted Sir William Herschel was more intricate because he knew that the stars were of different intrinsic brightness as well as at different distances, and both factors combined to produce differences of apparent brightness. One of the main difficulties of astronomy, both to the Herschels and to the astronomer of to-day, is that these two factors have to be disentangled before any definite conclusions are reached. Herschel found that the number of stars visible in his telescope-field varied enormously with different directions in space. It was of course greatest when the telescope was pointed at the Milky Way, and fell off, steadily and rapidly, as the telescope was moved away from the Milky Way. Generally speaking, two telescope-fields which were at equal distances from the Milky Way contained about the same number of stars. In the technical language of astronomy, the richness of the star-field depended mainly on the galactic latitude, just as the earth’s climate depends mainly on the geographic latitude, and not to any great extent on the longitude. Fields at different distances from the Milky Way were found to differ in quality as well as in number of stars. The brightest stars of all occurred about equally in all fields, the difference in the fields resulting mainly from faint stars, and particularly the faintest stars of all, becoming enormously more abundant as the Milky Way was approached.