s, and so on, as the cube of each distance. Since each
sphere includes all those within it, the volume of space between each
two spheres will be proportional to the difference of these
numbers--that is, to 1, 7, 19, etc. Comparing these volumes with the
number of stars probably within them, the general result up to the
present time is that the number of stars in any of these spheres will
be about equal to the units of volume which they comprise, when we take
for this unit the smallest and innermost of the spheres, having a
radius 400,000 times the sun's distance. We are thus enabled to form
some general idea of how thickly the stars are sown through space. We
cannot claim any numerical exactness for this idea, but in the absence
of better methods it does afford us some basis for reasoning.

Now we can carry on our computation as we supposed the farmer to
measure the extent of his wheat-field. Let us suppose that there are
125,000,000 stars in the heavens. This is an exceedingly rough
estimate, but let us make the supposition for the time being. Accepting
the view that they are nearly equally scattered throughout space, it
will follow that they must be contained within a volume equal to
125,000,000 times the sphere we have taken as our unit. We find the
distance of the surface of this sphere by extracting the cube root of
this number, which gives us 500. We may, therefore, say, as the result
of a very rough estimate, that the number of stars we have supposed
would be contained within a distance found by multiplying 400,000 times
the distance of the sun by 500; that is, that they are contained within
a region whose boundary is 200,000,000 times the distance of the sun.
This is a distance through which light would travel in about 3300 years.

It is not impossible that the number of stars is much greater than that
we have supposed. Let us grant that there are eight times as many, or
1,000,000,000. Then we should have to extend the boundary of our
universe twice as far, carrying it to a distance which light would
require 6600 years to travel.

There is another method of estimating the thickness with which stars
are sown through space, and hence the extent of the universe, the
result of which will be of interest. It is based on the proper motion
of the stars. One of the greatest triumphs of astronomy of our time has
been the measurement of the actual speed at which many of the stars are
moving to or from us in space. These