feet per minute, and that the force acting on a stone or an apple
follows the same law as the force acting upon the heavenly bodies.[3]

The universality claimed for the law--if not by Newton, at least by
his commentators--was bold, and warranted only by the large number of
cases in which Newton had found it to apply. Its universality has been
under test ever since, and so far it has stood the test. There has
often been a suspicion of a doubt, when some inequality of motion in
the heavenly bodies has, for a time, foiled the astronomers in their
attempts to explain it. But improved mathematical methods have always
succeeded in the end, and so the seeming doubt has been converted into
a surer conviction of the universality of the law.

Having once established the law, Newton proceeded to trace some of its
consequences. He saw that the figure of the earth depends partly on
the mutual gravitation of its parts, and partly on the centrifugal
tendency due to the earth's rotation, and that these should cause a
flattening of the poles. He invented a mathematical method which he
used for computing the ratio of the polar to the equatorial diameter.

He then noticed that the consequent bulging of matter at the equator
would be attracted by the moon unequally, the nearest parts being most
attracted; and so the moon would tend to tilt the earth when in some
parts of her orbit; and the sun would do this to a less extent,
because of its great distance. Then he proved that the effect ought to
be a rotation of the earth's axis over a conical surface in space,
exactly as the axis of a top describes a cone, if the top has a sharp
point, and is set spinning and displaced from the vertical. He
actually calculated the amount; and so he explained the cause of the
precession of the equinoxes discovered by Hipparchus about 150 B.C.