=100. The Simple Pendulum.=--Any body suspended so as to swing freely to and fro is a pendulum, as in Fig. 81. A simple pendulum is defined as a single particle of matter suspended by a cord without weight. It is of course impossible to construct such a pendulum. A small metal ball suspended by a thread is approximately a simple pendulum. When allowed to swing its vibrations are made in equal times. This feature of the motion of a pendulum was first noticed by Galileo while watching the slow oscillations of a bronze chandelier suspended in the Cathedral in Pisa. [Illustration: FIG. 81--A simple pendulum.] =101. Definition of Terms.= _The center of suspension_ is the point about which the pendulum swings. A _single vibration_ is one swing across the arc. A _complete_ or _double_ vibration is the swing across the arc and back again. The time required for a double vibration is called the _period_. The _length_ of a simple pendulum is approximately the distance from the point of support to the center of the bob. A _seconds pendulum_ is one making a single vibration per second. Its length at sea-level, at New York is 99.31 cm. or 39.1 in., at the equator 39.01 in., at the poles 39.22 in. A _compound pendulum_ is one having an appreciable portion of its mass elsewhere than in the small compact body or sphere called a bob. The ordinary clock pendulum or a meter stick suspended by one end are examples of compound pendulums. The _amplitude_ of a vibration is one-half the arc through which it swings, for example, the arc _DC_ or the angle _DAC_ in Fig. 81. =102. Laws of the Pendulum.=--The following laws may be stated: 1. The period of a pendulum is not affected by its mass or the material of which the pendulum is made. 2. For small amplitudes, the period is not affected by the length of the arc through which it swings. 3. The period is directly proportional to the square root of the length. Expressed mathematically, _t_/_t´_ = √_l_/√_l´_.