speed, forever. Contrariwise, a stationary body will remain forever at
rest unless acted on by some disturbing force.

This all-important law, which lies at the very foundation of all true
conceptions of mechanics, was thus worked out during the first half of
the seventeenth century, as the outcome of numberless experiments
for which Galileo's experiments with failing bodies furnished the
foundation. So numerous and so gradual were the steps by which the
reversal of view regarding moving bodies was effected that it is
impossible to trace them in detail. We must be content to reflect that
at the beginning of the Galilean epoch utterly false notions regarding
the subject were entertained by the very greatest philosophers--by
Galileo himself, for example, and by Kepler--whereas at the close of
that epoch the correct and highly illuminative view had been attained.

We must now consider some other experiments of Galileo which led to
scarcely less-important results. The experiments in question had to do
with the movements of bodies passing down an inclined plane, and
with the allied subject of the motion of a pendulum. The elaborate
experiments of Galileo regarding the former subject were made by
measuring the velocity of a ball rolling down a plane inclined at
various angles. He found that the velocity acquired by a ball was
proportional to the height from which the ball descended regardless of
the steepness of the incline. Experiments were made also with a ball
rolling down a curved gutter, the curve representing the are of a
circle. These experiments led to the study of the curvilinear motions of
a weight suspended by a cord; in other words, of the pendulum.

Regarding the motion of the pendulum, some very curious facts were soon
ascertained. Galileo found, for example, that a pendulum of a given
length performs its oscillations with the same frequency though the arc
described by the pendulum be varied greatly.(1) He found, also, that the
rate of oscillation for pendulums of different lengths varies according
to a simple law. In order that one pendulum shall oscillate one-half
as fast as another, the length of the pendulums must be as four to one.
Similarly, by lengthening the pendulums nine times, the oscillation
is reduced to one-third, In other words, the rate of oscillation of
pendulums varies inversely as the square of their length. Here, then, is
a simple relation between the motions of swinging bodies which suggest