ion might be
tested. It was claimed later on by Hooke that he had discovered a method
demonstrating the truth of the theory of inverse squares, and after
the full announcement of Newton's discovery a heated controversy was
precipitated in which Hooke put forward his claims with accustomed
acrimony. Hooke, however, never produced his demonstration, and it
may well be doubted whether he had found a method which did more than
vaguely suggest the law which the observations of Kepler had partially
revealed. Newton's great merit lay not so much in conceiving the law of
inverse squares as in the demonstration of the law. He was led to
this demonstration through considering the orbital motion of the moon.
According to the familiar story, which has become one of the classic
myths of science, Newton was led to take up the problem through
observing the fall of an apple. Voltaire is responsible for the story,
which serves as well as another; its truth or falsity need not in the
least concern us. Suffice it that through pondering on the familiar
fact of terrestrial gravitation, Newton was led to question whether this
force which operates so tangibly here at the earth's surface may not
extend its influence out into the depths of space, so as to include,
for example, the moon. Obviously some force pulls the moon constantly
towards the earth; otherwise that body would fly off at a tangent and
never return. May not this so-called centripetal force be identical with
terrestrial gravitation? Such was Newton's query. Probably many another
man since Anaxagoras had asked the same question, but assuredly Newton
was the first man to find an answer.

The thought that suggested itself to Newton's mind was this: If we make
a diagram illustrating the orbital course of the moon for any given
period, say one minute, we shall find that the course of the moon
departs from a straight line during that period by a measurable
distance--that: is to say, the moon has been virtually pulled towards
the earth by an amount that is represented by the difference between
its actual position at the end of the minute under observation and the
position it would occupy had its course been tangential, as, according
to the first law of motion, it must have been had not some force
deflected it towards the earth. Measuring the deflection in
question--which is equivalent to the so-called versed sine of the
arc traversed--we have a basis for determining the strength of the