Pendulum
A body suspended from a fixed point in such a manner as to swing freely to and fro by the alternate action of gravity and momentum. The theoretical length of a pendulum, to beat seconds, or other time, depends upon its location, for the force that gravity exerts upon a body depends on the distance of the body from the center of the earth. The length of a seconds' pendulum at The Equator is __________39 inches Rio de Janeiro __________39.01 inches Madras __________________39.02 inches New York ________________39.1012 inches Paris ___________________39.13 inches London __________________39.14 inches Edinburgh _______________39.15 inches Greenland _______________39.20 inches North and South Pole_____39.206 inches Galileo's discovery of the law of pendulums was made in 1582 (See Galileo.). Observing the regularity of the swinging of a lamp, suspended from the roof of the cathedral of Pisa, he noticed that, whatever the arc of vibration, the time of vibration remained nearly the same. If a slight angular movement be given to a freely suspended pendulum, its oscillations, while gradually diminishing in extent, will occupy periods, which at first sight, Galileo affirmed to be equal. He was mistaken, however, as the difference, although very slight with short arcs, is none the less real, and Huyghens discovered and proved that the oscillation of a pendulum are only isochronal when its center of oscillation describes a cycloidal path. By experiment, Galileo also determined the law of the length of pendulums. He found that by increasing the length of the pendulum the time of vibration increased. The first application of the pendulum to clocks was made by Huyghens in 1657, although Galileo had some idea of this adaptation, and he even invented an escapement with a view to carrying it out.