the earth, like a grain of sand at the centre of a mighty globe,
should turn round once in twenty-four hours, or that the whole of
that vast globe should complete a rotation in the opposite direction
in the same time? Obviously, the former is far the more simple
supposition. But the case is really much stronger than this. Ptolemy
had supposed that all the stars were attached to the surface of a
sphere. He had no ground whatever for this supposition, except that
otherwise it would have been well-nigh impossible to have devised a
scheme by which the rotation of the heavens around a fixed earth
could have been arranged. Copernicus, however, with the just
instinct of a philosopher, considered that the celestial sphere,
however convenient from a geometrical point of view, as a means of
representing apparent phenomena, could not actually have a material
existence. In the first place, the existence of a material celestial
sphere would require that all the myriad stars should be at exactly
the same distances from the earth. Of course, no one will say that
this or any other arbitrary disposition of the stars is actually
impossible, but as there was no conceivable physical reason why the
distances of all the stars from the earth should be identical, it
seemed in the very highest degree improbable that the stars should be
so placed.

Doubtless, also, Copernicus felt a considerable difficulty as to the
nature of the materials from which Ptolemy's wonderful sphere was to
be constructed. Nor could a philosopher of his penetration have
failed to observe that, unless that sphere were infinitely large,
there must have been space outside it, a consideration which would
open up other difficult questions. Whether infinite or not, it was
obvious that the celestial sphere must have a diameter at least many
thousands of times as great as that of the earth. From these