he
astronomer measures upon the celestial sphere.

Up to the present time, two stars have been found whose proper motions
are so large that, if continued, the bodies would make a complete
circuit of the heavens in less than 200,000 years. One of these would
require about 160,000; the other about 180,000 years for the circuit.
Of other stars having a rapid motion only about one hundred would
complete their course in less than a million of years.

Quite recently a system of observations upon stars to the ninth
magnitude has been nearly carried through by an international
combination of observatories. The most important conclusion from these
observations relates to the distribution of the stars with reference to
the Milky Way, which we have already described. We have shown that
stars of every magnitude, bright and faint, show a tendency to crowd
towards this belt. It is, therefore, remarkable that no such tendency
is seen in the case of those stars which have proper motions large
enough to be accurately determined. So far as yet appears, such stars
are equally scattered over the heavens, without reference to the course
of the Milky Way. The conclusion is obvious. These stars are all inside
the girdle of the Milky Way, and within the sphere which contains them
the distribution in space is approximately uniform. At least there is
no well-marked condensation in the direction of the galaxy nor any
marked thinning out towards its poles. What can we say as to the extent
of this sphere?

To answer this question, we have to consider whether there is any
average or ordinary speed that a star has in space. A great number of
motions in the line of sight--that is to say, in the direction of the
line from us to the star--have been measured with great precision by
Campbell at the Lick Observatory, and by other astronomers. The
statistical investigations of Kaptoyn also throw much light on the
subject. The results of these investigators agree well in showing an
average speed in space--a straight-ahead motion we may call it--of
twenty-one miles per second. Some stars may move more slowly than this
to any extent; others more rapidly. In two or three cases the speed
exceeds one hundred miles per second, but these are quite exceptional.
By taking several thousand stars having a given proper motion, we may
form a general idea of their average distance, though a great number of
them will exceed this average to a considerable extent. The con