But HERSCHEL was now (1817) convinced that the twenty-foot telescope could not penetrate to the boundaries of the Milky Way; the faintest stars of the Galaxy must then be farther from us even than nine hundred times the distance of _Arcturus_, and their light must be at least 3,000 years old when it reaches us.
There is no escaping a certain part of the consequences established by HERSCHEL. It is indeed true that unless a particular star is of the same intrinsic brightness as our largest stars, this reasoning does not apply to it; in just so far as the average star is less bright than the average brightness of our largest stars, will the numbers which HERSCHEL obtained be diminished. But for every star of which his hypothesis is true, we may assert that his conclusions are true, and no one can deny, with any show of reason, that, on the whole, his suppositions must be valid. On the whole, the stars which we call faint are farther from us than the brighter ones; and, on the whole, the brilliancy of our brightest and nearest stars is not very far from the brilliancy of the average star in space. We cannot yet define the word _very_ by a numerical ratio.
The _method_ struck out by HERSCHEL was correct; it is for his successors to look for the special cases and limitations, to answer the question, At a certain distance from us, what are the variations which actually take place in the brilliancy and the sizes of stars? The answer to this question is to be found in the study of the clusters of regular forms, where we _know_ the stars to be all at the same distance from us.
Frequently in the course of his astronomical work, HERSCHEL found himself confronted by questions of physics which could not be immediately answered in the state of the science at that time. In his efforts to find a method for determining the dimensions of the stellar universe, he was finally led, as has been shown, to regard the brightness of a star as, in general, the best attainable measure of its distance from us. His work, however, was done with telescopes of various dimensions and powers, and it was therefore necessary to find some law for comparing the different results among themselves as well as with those given by observations with an unassisted eye. This necessity prompted an investigation, published in 1800, in which, after drawing the distinction between absolute and intrinsic brightness, HERSCHEL gave an expression for the _space-penetrating power_ of a telescope. The reasoning at the base of this conception was as follows.