In the next form of clock, therefore, we find the pendulum introduced as a regulator. There was a crown wheel like the one in the balance clock, only instead of being vertical it was horizontal. This wheel was allowed to go round and the weight was allowed to fall by means of alternating pallets; it was in fact like that shown in Fig. 86, with the balance weights and the rod carrying them removed, and instead thereof there was a rod, attached at right angles to the end of that carrying the pallets, and hanging downwards, which, by means of a fork at its lower end, swung a pendulum to an extent equal to the go of the balance first used. Thus the pendulum was adapted by Huyghens. We have here something extremely different from the rough arrangement in which the weight was controlled by the horizontal oscillating bar carrying the weights, for the balance would go faster or slower as the crown wheel pressed harder or softer against the pallets, and so, if the weight acted at all irregularly the clock would go badly. But with the pendulum the control of the weight over it is small, for the bob can be made of considerable weight, because it swings from its suspending spring without friction, and such a heavy weight at the end of a long rod is scarcely altered in its rate by variations of pressure on the pallets. Galileo and Huyghens who followed him found that the oscillations of a simple pendulum are isochronous at all places where the force of gravity is equal, and that the time of oscillation depends on the length of the pendulum—the shorter the pendulum the shorter time of oscillation, and _vice versâ_. The time of oscillation varying as the square root of the length.