es more distant, but, by
chance, was seen along the same line, and made with A an _optical_
double. If the two stars were at the same distance from the earth, if
they made part of the same physical system, if one revolved around the
other, then this method of gaining a knowledge of their distance failed.
Even in his first memoir on the subject, a surmise that this latter
state might occur in some cases, was expressed by HERSCHEL. The notes on
some of the pairs declare that a motion of one of them was suspected.
But this motion might be truly orbital--of one star about the other as
a centre--or it might simply be that one star was moving by its own
_proper_ motion, and leaving the other behind. It was best to wait and
see. The first Catalogue of Double Stars contained two hundred and three
instances of such associations. These were observed from time to time,
and new pairs discovered. The paper of MICHELL, "An Inquiry into the
probable Parallax and Magnitude of the Fixed Stars, from the Quantity of
Light which they Afford, and the Particular Circumstances of their
Situation" (1767), was read and pondered. By 1802 HERSCHEL had become
certain that there existed in the heavens real pairs of stars, both at
the same distance from the earth, which were physically connected with
each other. The arguments of MICHELL have been applied by BESSEL to the
case of one of HERSCHEL'S double stars, in much the same order in which
the argument ran in HERSCHEL'S own mind, as follows:

The star _Castor_ (_[alpha] Geminorum_) is a double star, where A is of
the second, and B of the fourth, magnitude. To the naked eye these two
appear as one star. With a telescope this is seen to be two stars, some
5" apart. In the whole sky there are not above fifty such stars
as the brighter of the two, and about four hundred of the brilliancy of
B. These fifty and four hundred stars are scattered over the vault of
heaven, almost at random. No law has yet been traced by which we can say
that here or here there shall be a bright star like A, or a fainter one
like B. In general the distribution appears to be fortuitous. How then
can we account for one of the four hundred stars like B placed so close
to one of the fifty like A?

The chances are over four hundred thousand to one that the association
in position is not accidental. This argument becomes overwhelming when
the same association is found in many other cases. There were two
hundred and three doubles