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.