In the absence of any _a priori_ knowledge of the actual clustering of the stars in space, Herschel chose the former of these two hypotheses; that is, he treated the apparent density of the stars on any particular part of the sky as a measure of the depth to which the sidereal systems extended in that direction, and interpreted from this point of view the results of a vast series of observations. He used a 20-foot telescope so arranged that he could see with it a circular portion of the sky 15′ in diameter (one-quarter the area of the sun or full moon), turned the telescope to different parts of the sky, and counted the stars visible in each case. To avoid accidental irregularities he usually took the average of several neighbouring fields, and published in 1785 the results of gauges thus made in 683[156] regions, while he subsequently added 400 others which he did not think it necessary to publish. Whereas in some parts of the sky he could see on an average only one star at a time, in others nearly 600 were visible, and he estimated that on one occasion about 116,000 stars passed through the field of view of his telescope in a quarter of an hour. The general result was, as rough naked-eye observation suggests, that stars are most plentiful in and near the Milky Way and least so in the parts of the sky most remote from it. Now the Milky Way forms on the sky an ill-defined band never deviating much from a great circle (sometimes called the =galactic= circle); so that on Herschel’s hypothesis the space occupied by the stars is shaped roughly like a disc or grindstone, of which according to his figures the diameter is about five times the thickness. Further, the Milky Way is during part of its length divided into two branches, the space between the two branches being comparatively free of stars. Corresponding to this subdivision there has therefore to be assumed a cleft in the “grindstone.” This “grindstone” theory of the universe had been suggested in 1750 by _Thomas Wright_ (1711-1786) in his _Theory of the Universe_, and again by Kant five years later; but neither had attempted, like Herschel, to collect numerical data and to work out consistently and in detail the consequences of the fundamental hypothesis.