bable that the hypothesis of equal brilliancy for all stars
is still more erroneous than the hypothesis of equal distribution, and
it may well be that there is a very large range indeed in the actual
dimensions and in the intrinsic brilliancy of stars at the same order of
distance from us, so that the tenth-magnitude stars, for example, may be
scattered throughout the spheres which HERSCHEL would assign to the
seventh, eighth, ninth, tenth, eleventh, twelfth, and thirteenth
magnitudes. However this may be, the fact remains that it is from
HERSCHEL'S groundwork that future investigators must build. He found the
whole subject in utter confusion. By his observations, data for the
solution of some of the most general questions were accumulated, and in
his memoirs, which STRUVE well calls "immortal," he brought the
scattered facts into order and gave the first bold outlines of a
reasonable theory. He is the founder of a new branch of astronomy.

_Researches for a Scale of Celestial Measures.
Distances of the Stars._

If the stars are _supposed_ all of the same absolute brightness, their
brightness to the eye will depend only upon their distance from us. If
we call the brightness of one of the fixed stars at the distance of
_Sirius_, which may be used as the unity of distance, 1, then if it is
moved to the distance 2, its apparent brightness will be one-fourth; if
to the distance 3, one-ninth; if to the distance 4, one-sixteenth, and
so on, the apparent brightness diminishing as the square of the distance
increases. The distance may be taken as an order of magnitude. Stars at
the _distances_ two, three, four, etc., HERSCHEL called of the second,
third, and fourth magnitudes.

By a series of experiments, the details of which cannot be given here,
HERSCHEL determined the space-penetrating power of each of his
telescopes. The twenty-foot would penetrate into space seventy-five
times farther than the naked eye; the twenty-five foot, ninety-six
times; and the forty-foot, one hundred and ninety-two times. If the
seventh-magnitude stars are those just visible to the naked eye, and if
we still suppose all stars to be of equal intrinsic brightness, such
seventh-magnitude stars would remain visible in the forty-foot, even if
removed to 1,344 times the distance of _Sirius_ (1,344 = 7 x 192).
If, further, we suppose that the visibility of a star is strictly
proportional to the total intensity of th