stem is situated.[35] Thus we
should see a greater number of stars when we looked out through the
_length_ of such a disc in any direction, than when we looked out
through its _breadth_. This theory was, for a time, supposed to account
quite reasonably for the Milky Way, and for the gradual increase in the
number of stars in its vicinity.

It is quite impossible to verify directly such a theory, for we know the
actual distance of only about forty-three stars. We are unable,
therefore, definitely to assure ourselves whether, as the grindstone
theory presupposes, the stellar universe actually reaches out very much
further from us in the direction of the Milky Way than in the other
parts of the sky. The theory is clearly founded upon the supposition
that the stars are more or less equal in size, and are scattered through
space at fairly regular distances from each other.

Brightness, therefore, had been taken as implying nearness to us, and
faintness great distance. But we know to-day that this is not the case,
and that the stars around us are, on the other hand, of various degrees
of brightness and of all orders of size. Some of the faint stars--for
instance, the galloping star in Pictor--are indeed nearer to us than
many of the brighter ones. Sirius, on the other hand, is twice as far
off from us as [a] Centauri, and yet it is very much brighter; while
Canopus, which in brightness is second only to Sirius out of the whole
sky, is too far off for its distance to be ascertained! It must be
remembered that no parallax had yet been found for any star in the days
of Herschel, and so his estimations of stellar distances were
necessarily of a very circumstantial kind. He did not, however, continue
always to build upon such uncertain ground; but, after some further
examination of the Milky Way, he gave up his idea that the stars were
equally disposed in space, and eventually abandoned the grindstone
theory.

Since we have no means of satisfactorily testing the matter, through
finding out the various distances from us at which the stars are really
placed, one might just as well go to the other extreme, and assume that
the thickening of stars in the region of the Milky Way is not an effect
of perspective at all, but that the stars in that part of the sky are
actually more crowded together than elsewhere--a thing which astronomers
now believe to be the case. Looked at in this way, the shape of the
stellar universe might be that