surd, and therefore he was able to compare together the
plausibilities of the two rival schemes for explaining the diurnal
movement.

Once the issue had been placed in this form, the result could not be
long in doubt. Here is the question: Which is it more likely--that 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
wellnigh impossible to devise 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 considerations Copernicus
deduced the important fact that the stars and other important celestial
bodies must all be vast objects. He was thus enabled to put the question
in such a form that it would hardly receive any answer but the correct
one: Which is it more rational to suppose, that the earth should turn
round on