nvestigation of the basis on which they rest. If we are
going, from merely counting the stars, observing their magnitudes and
determining their proper motions, to draw conclusions as to the
structure of the universe in space, the question may arise how we can
form any estimate whatever of the possible distance of the stars, a
conclusion as to which must be the very first step we take. We can
hardly say that the parallaxes of more than one hundred stars have been
measured with any approach to certainty. The individuals of this one
hundred are situated at very different distances from us. We hope, by
long and repeated observations, to make a fairly approximate
determination of the parallaxes of all the stars whose distance is less
than twenty times that of a Centauri. But how can we know anything
about the distance of stars outside this sphere? What can we say
against the view of Kepler that the space around our sun is very much
thinner in stars than it is at a greater distance; in fact, that, the
great mass of the stars may be situated between the surfaces of two
concentrated spheres not very different in radius. May not this
universe of stars be somewhat in the nature of a hollow sphere?

This objection requires very careful consideration on the part of all
who draw conclusions as to the distribution of stars in space and as to
the extent of the visible universe. The steps to a conclusion on the
subject are briefly these: First, we have a general conclusion, the
basis of which I have already set forth, that, to use a loose
expression, there are likenesses throughout the whole diameter of the
universe. There is, therefore, no reason to suppose that the region in
which our system is situated differs in any essential degree from any
other region near the central portion. Again, spectroscopic
examinations seem to show that all the stars are in motion, and that we
cannot say that those in one part of the universe move more rapidly
than those in another. This result is of the greatest value for our
purpose, because, when we consider only the apparent motions, as
ordinarily observed, these are necessarily dependent upon the distance
of the star. We cannot, therefore, infer the actual speed of a star
from ordinary observations until we know its distance. But the results
of spectroscopic measurements of radial velocity are independent of the
distance of the star.

But let us not claim too much. We cannot yet say with certainty