Pendulum

a weight hanging from a point of support in such a way that it is free to swing to and fro. A vibration is the trip from the highest point on one side to the highest point on the other. The length is the distance from the point of support to the center of mass. When a small string or light wire is used to suspend a heavy bob, the length is practically, but not quite, the distance from the point of suspension to the center of the bob. The time required for a vibration depends entirely on length, and has nothing to do with the kind of material, weight, or the length of arc through which the pendulum swings. This may be tested by watching a child's swing. It swings to and fro just as many times per minute when it goes high, as when it goes low. It makes no difference whether one child or two are swinging.

These facts are expressed in laws:

1. The time occupied by the vibration of a pendulum is independent of the length of the arc.

2. The time of one vibration of a pendulum varies as the square root of its length. Multiplying the length of a pendulum by four multiplies its time by two. If one pendulum be nine times as long as another, it will be three times as long in completing a vibration.

Since the time of a given pendulum does not change it is of great service in regulating the rate of motion of the works of a clock. It has been found by experiment that a pendulum 39.1 inches long will vibrate once per second at the sea level in the latitude of Boston. The greater the force of gravity, the less the time of vibration. If this standard pendulum be carried up a mountain where the force of gravity is less, it will take a little more than a second to a vibration, and must be shortened slightly to keep correct time. The same is true if it be carried toward the equator, while at the sea level very far north or south, being somewhat nearer the center of the earth, the action will be quickened and the pendulum must be lengthened slightly to keep correct time.

Another difficulty to be overcome is the lengthening of the pendulum rod in hot weather on account of the expansion due to heat and the corresponding shortening in cold weather. To obviate this change two plans have been devised. In a so-called gridiron pendulum a number of parallel rods are connected in a frame in such a way that the lengthening of one-half of them shortens the pendulum while the lengthening of the other half lengthens it by an equal amount. In a mercurial pendulum the bob is a vial of mercury. As heat expands the rod, thereby lowering the bob, it also swells the mercury, thereby raising its center of gravity. This leaves the length of the pendulum unchanged. In ordinary pendulum clocks the bob may be raised or lowered by means of a nut on the lower end of the pendulum wire. This should be turned up a half turn or so in hot weather, and turned down a little in cold weather to counteract the changing length of the wire.

See Clocks