[Illustration: Fig. 136.] 209. =Explanation of its Operation.=--A pendulum consists commonly of a ball or weight at the end of a rod suspended so as to vibrate with little friction at the point of the suspension. Let _a b_, Fig. 136, represent such a pendulum. When it is at rest it makes a plumb-line hanging toward the centre of the earth. If it be raised to _c_ and be left to fall, the force of gravity will not only carry it to _b_, but, by the accelerated velocity or accumulated momentum which it gives it in its descent, it will carry it to _d_. The same would be true of its return from _d_. And it would vibrate forever in this way if it could be entirely freed from the resistance of the air and friction. But, as it is, the pendulum left to itself gradually loses its motion from these obstacles. In the common clock the office of the weight is to counteract the influence of these obstacles, and keep the pendulum vibrating. In the watch the mainspring performs the same office to the balance-wheel. [Illustration: Fig. 137.] The times of the vibrations of a pendulum are nearly equal whether the arc it describes be great or small. For when the vibration is a large one the velocity which the pendulum acquires in falling is greater than when the vibration is of small extent. The reason is that the higher it rises the more steep is the beginning of its descent. Thus _a c_, Fig. 137, is steeper than _c b_. [Illustration: Fig. 138. Fig. 139.] 210. =Gridiron Pendulum.=--The longer a pendulum is the longer time does its vibration occupy. It requires a pendulum of the length of a little over thirty-nine inches to vibrate seconds. Cold weather, by contracting the pendulum, makes it vibrate quicker than in summer, and so makes the clock go faster. Various contrivances have been resorted to in order to counteract the variation of length in pendulums by heat and cold, but what is called the gridiron pendulum is the best. In this pendulum an ingenious use is made of the fact that heat expands brass nearly twice as much as it does steel. A simple form of this pendulum is given in Fig. 138. The middle rod is made of brass, and the side rods, _b_ and _c_, of steel. Suppose that the brass rod expands or increases in length half an inch. The rod _c_ would be drawn upward by it, and the rod _b_ downward, each one quarter of an inch; but this effect is counteracted by the expansion of each steel rod, which is half that of the brass, that is, one quarter of an inch. The ball _d_, therefore, always retains the same distance from the point of suspension, _e_. In Fig. 139 you have a gridiron pendulum of a more compound character, a part of the bars being steel, and a part brass.