earth. They are attracted, but in a less degree, and so are driven
outwards by the heavy bodies; which being done, they stop, and are kept
by the earth in their own place. But although the attractive virtue of
the earth extends upwards, as has been said, so very far, yet if any
stone should be at a distance great enough to become sensible compared
with the earth's diameter, it is true that on the motion of the earth
such a stone would not follow altogether; its own force of resistance
would be combined with the attractive force of the earth, and thus it
would extricate itself in some degree from the motion of the earth." The
above passage from the Introduction to Kepler's "Commentaries on the
Motion of Mars," always regarded as his most valuable work, must have
been known to Newton, so that no such incident as the fall of an apple
was required to provide a necessary and sufficient explanation of the
genesis of his Theory of Universal Gravitation. Kepler's glimpse at such
a theory could have been no more than a glimpse, for he went no further
with it. This seems a pity, as it is far less fanciful than many of his
ideas, though not free from the "virtues" and "animal faculties," that
correspond to Gilbert's "spirits and humours". We must, however, proceed
to the subject of Mars, which was, as before noted, the first important
investigation entrusted to Kepler on his arrival at Prague.

The time taken from one opposition of Mars to the next is decidedly
unequal at different parts of his orbit, so that many oppositions must
be used to determine the mean motion. The ancients had noticed that what
was called the "second inequality," due as we now know to the orbital
motion of the earth, only vanished when earth, sun, and planet were in
line, i.e. at the planet's opposition; therefore they used oppositions
to determine the mean motion, but deemed it necessary to apply a
correction to the true opposition to reduce to mean opposition, thus
sacrificing part of the advantage of using oppositions. Tycho and