o 2,000,000,000, of the number
of stars that have yet come within our faintest knowledge. Let us accept
the modest provisional estimate of 500,000,000. Now, if we had reason to
think that these stars were of much the same size and brilliance as our
sun, we should be able roughly to calculate their distance from their
faintness. We cannot do this, as they differ considerably in size and
intrinsic brilliance. Sirius is more than twice the size of our sun and
gives out twenty times as much light. Canopus emits 20,000 times as much
light as the sun, but we cannot say, in this case, how much larger it is
than the sun. Arcturus, however, belongs to the same class of stars as
our sun, and astronomers conclude that it must be thousands of times
larger than the sun. A few stars are known to be smaller than the sun.
Some are, intrinsically, far more brilliant; some far less brilliant.

Another method has been adopted, though this also must be regarded
with great reserve. The distance of the nearer stars can be positively
measured, and this has been done in a large number of cases. The
proportion of such cases to the whole is still very small, but, as far
as the results go, we find that stars of the first magnitude are, on the
average, nearly 200 billion miles away; stars of the second magnitude
nearly 300 billion; and stars of the third magnitude 450 billion. If
this fifty per cent increase of distance for each lower magnitude of
stars were certain and constant, the stars of the eighth magnitude would
be 3000 billion miles away, and stars of the sixteenth magnitude would
be 100,000 billion miles away; and there are still two fainter classes
of stars which are registered on long-exposure photographs. The mere
vastness of these figures is immaterial to the astronomer, but he warns
us that the method is uncertain. We may be content to conclude that the
starry universe over which our great telescopes keep watch stretches for
thousands, and probably tens of thousands, of billions of miles. There
are myriads of stars so remote that, though each is a vast incandescent
globe at a temperature of many thousand degrees, and though their
light is concentrated on the mirrors or in the lenses of our largest
telescopes and directed upon the photographic plate at the rate of more
than 800 billion waves a second, they take several hours to register the
faintest point of light on the plate.

When we reflect that the universe has grown with the gro