Here we shall take as our
standard a distance 400,000 times that of the sun from the earth.
Regarding this as a unit, we imagine ourselves to measure out in
any direction a distance twice as great as this--then another
equal distance, making one three times as great, and so
indefinitely. We then have successive spheres of which we take the
nearer one as the unit. The total space filled by the second
sphere will be 8 times the unit; that of the third space 27 times,
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.
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