equator it should be about thirty-nine inches long, to "vibrate," or go from c to b in one second. At the latitude of Washington, where the force of gravity is greater, the length is thirty-nine and one tenth inches. At London, which is still farther north, the length is thirty-nine and one seventh inches. A pendulum of the right length in London would lose two and one quarter minutes a day at the equator. The pendulum that vibrates from c to b in two seconds must be four times the length of a one-second pendulum. The pendulum of the great clock at Westminster moves once in two seconds. It is nearly fifteen feet long, and it weighs seven hundred pounds—the heaviest in the world. The heavier and longer the pendulum, the more regularly will the clock move. But pendulums may be too long and too heavy. Almost all of the clocks that were made before the year 1800 had pendulums about 
Fig. 2. thirty-nine inches long, and they stood with their cases over five feet high—usually in the corner of the room. They were so clumsy that only the machinery was peddled about from place to place—the nearest cabinet-maker being called upon to make the case. By-and-by it was found that, if, in Fig. 1, the pendulum would go from c to b in one second, it would go from c to b, back again to c—or twice as fast—if it were one quarter as long. After that, clocks were made short enough to stand on a shelf.
It had also been found that the bob of the pendulum, when moving in the arc of a circle, was not reliable; but that all the trouble was avoided if it moved in the arc of a cycloid (or "like a circle"). This arrangement is shown in Fig. 2. The pendulum hangs from a fixed point, a, where it is fastened securely. The upper end of the wire is beaten into a very thin spring. When the bob b moves back and forth, it does not move in the arc of the circle c d, but on the dotted
