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 suggests the relation which Kepler bad discovered between the relative motions of the planets.

Every such discovery coming in this age of the rejuvenation of experimental science had a peculiar force in teaching men the all-important lesson that simple laws lie back of most of the diverse phenomena of nature, if only these laws can be discovered.
Galileo further observed that his pendulum might be constructed of any weight sufficiently heavy readily to overcome the atmospheric resistance, and that, with this qualification, neither the weight nor the material had any influence upon the time of oscillation, this being solely determined by the length of the cord.

Naturally, the practical utility of these discoveries was not overlooked by Galileo.

Since a pendulum of a given length oscillates with unvarying rapidity, here is an obvious means of measuring time.