clusion
drawn in this way would be that the stars having an apparent proper
motion of 10" per century or more are mostly contained within, or lie
not far outside of a sphere whose surface is at a distance from us of
200 light-years. Granting the volume of space which we have shown that
nature seems to allow to each star, this sphere should contain 27,000
stars in all. There are about 10,000 stars known to have so large a
proper motion as 10". But there is no actual discordance between these
results, because not only are there, in all probability, great numbers
of stars of which the proper motion is not yet recognized, but there
are within the sphere a great number of stars whose motion is less than
the average. On the other hand, it is probable that a considerable
number of the 10,000 stars lie at a distance at least one-half greater
than that of the radius of the sphere.

On the whole, it seems likely that, out to a distance of 300 or even
400 light-years, there is no marked inequality in star distribution. If
we should explore the heavens to this distance, we should neither find
the beginning of the Milky Way in one direction nor a very marked
thinning out in the other. This conclusion is quite accordant with the
probabilities of the case. If all the stars which form the groundwork
of the Milky Way should be blotted out, we should probably find
100,000,000, perhaps even more, remaining. Assigning to each star the
space already shown to be its quota, we should require a sphere of
about 3000 light-years radius to contain such a number of stars. At
some such distance as this, we might find a thinning out of the stars
in the direction of the galactic poles, or the commencement of the
Milky Way in the direction of this stream.

Even if this were not found at the distance which we have supposed, it
is quite certain that, at some greater distance, we should at least
find that the region of the Milky Way is richer in stars than the
region near the galactic poles. There is strong reason, based on the
appearance of the stars of the Milky Way, their physical constitution,
and their magnitudes as seen in the telescope, to believe that, were we
placed on one of these stars, we should find the stars around us to be
more thickly strewn than they are around our system. In other words,
the quota of space filled by each star is probably less in the region
of the Milky Way than it is near the centre where we seem to be
situated.

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