combination of all such would give a representation of the shape of our stellar system. The more numerous and careful the observations, the more elaborate the representation, and the 863 gauges of Herschel are sufficient to mark out with great precision the main features of the Milky Way, and even to indicate some of its chief irregularities.
On the fundamental assumption of Herschel (equable distribution), no other conclusion can be drawn from his statistics but the one laid down by him.
This assumption he subsequently modified in some degree, and was led to regard his gauges as indicating not so much the depth of the system in any direction, as the clustering power or tendency of the stars in those special regions. It is clear that if in any given part of the sky, where, on the average, there are ten stars (say) to a field, we should find a certain small portion having 100 or more to a field, then, on Herschel's first hypothesis, rigorously interpreted, it would be necessary to suppose a spike-shaped protuberance directed from the earth, in order to explain
