e smallest telescope of the set showed a large
number of stars; these must, then, be _twice_ as far from us, on the
average, as the stars just visible to the naked eye. But first-magnitude
stars, like _Sirius_, _Procyon_, _Arcturus_, etc., become just visible
to the eye if removed to twelve times their present distance. Hence the
stars seen in this first telescope of the set were between twelve and
twenty-four times as far from us as _Arcturus_, for example.

"At least," as HERSCHEL says, "we are certain that if stars of the size
and lustre of _Sirius_, _Arcturus_, etc., were removed into the
profundity of space I have mentioned, they would then appear like the
stars which I saw." With the next telescope, which collected nine times
more light than the eye, and brought into view objects three times more
distant, other and new stars appeared, which were then (3 x 12)
thirty-six times farther from us than _Arcturus_. In the same way, the
seven-foot reflector showed stars 204 times, the ten-foot 344 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 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 H