times, the twenty-foot 900 times farther from us than the average first-magnitude star. As the light from such a star requires three years to reach us, the light from the faintest stars seen by the twenty-foot would require 2,700 years (3 x 900).
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
