Whence then the time of rotation of this body would be if the circle of rotation was small = 2π√(l/g). And if you try you will find that this is so. For instance, take a thread 39-1/7 inches long, that is 3·25 feet. Hang anything heavy from one end of it, and cause it to swing round and round in a _small_ circle. Now _g_ the acceleration of gravity = 32·2 feet per second. π the ratio of the circumference of a circle to its diameter = 3·14. From which it follows that the time of rotation = 2 × 3·14√(3·25/32·2) seconds = 2 seconds. But if we look at the rotating body sideways, it appears to act as a pendulum; it matters nothing whether we swing it round and round or to and fro. For in any case the accelerative force tending to bring it back to a position of rest is always proportional to the distance of displacement, and, therefore, its time of motion must always be 2π√(l/g) and its motion harmonic. The length of a seconds pendulum, that is a pendulum that makes its double swing in two seconds, will therefore be l = 4/((2π)²) × g feet = (g × 12)/π² inches = 39·14 inches. CHAPTER V. I have thus described the principal features of ordinary clocks. For the details many treatises must be studied, and knowledge acquired which is not in any books at all. I now, however, pass to watches. It will be remembered that a verge escapement consists of a crown wheel with teeth, engaging two pallets fixed upon a verge, furnished with balls at its extremities. As the crown wheel was urged forwards each pallet in succession was pushed till it slipped over the tooth which was engaging it. Then a tooth on the other side came into sharp collision with the other pallet, and drove the verge the other way, and so on. Now here we have a driving force, and a sort of pendulum. But how did the verge act as a pendulum to measure time? It is not a body rocking under the action of gravity, nor under the acceleration of a spring. How then can it act as a regulator of time, and what is the period of its swing? The answer to this is, that it is under the acceleration of gravity, but that gravity does not act freely on the bobs or weights, but only through the driving weight and teeth. The impulse that drives the verge is really also the accelerating force upon it, and the only accelerating force upon it.