If we put a pinion of eight leaves on the minute hand arbor _c_, and engage it with a wheel of sixty-four teeth on another arbor _b_, then _b_ will obviously turn round once in eight hours, that is to say, twenty-four times in the period of eight days. And, if we fix on _b_ a “drum” or cylinder two inches long, the twenty-four turns of our cord will just fit upon it, since, as has been said, our cord is to be one-twelfth of an inch in diameter. The diameter of the drum must be such that a cord nine feet long can be wound twenty-four times round it. That is to say, each lap must take (9 × 12)/24 = 4½ inches of cord. From this it is easy to calculate that the diameter of the drum must be rather less than one and a half inches. From this then it results that we want for a “Grandfather’s” clock a drum two inches long and one and a half inches diameter, on this a cogwheel of sixty-four teeth working into a minute hand arbor, with a pinion wheel with eight leaves, and a cogwheel of sixty-four teeth, an intermediate or idle wheel with an eight-leaved pinion, and a cogwheel of sixty teeth, engaging with a seconds hand arbor with a pinion of eight leaves. This is called the “train of wheels.” With it a weight such as can be arranged in an ordinary “Grandfather’s” clock case will cause by its fall during eight days the second hand arbor to turn round once in each minute during the whole time, and the minute hand arbor to turn round once in each hour. [Illustration: FIG. 50.] We must next provide an arrangement for winding the clock up. It is obvious that we cannot do so by twisting the hands back. It is true that this could be done, but it would take about five minutes to do each time and be wearisome. In order to save this trouble, an arrangement called a ratchet wheel and pall must be provided. A ratchet wheel consists of a wheel with a series of notches cut in it, as shown in the figure _A_. A pall is a piece of metal, mounted on a pin, and kept pressed up against the ratchet wheel by a spring _C_. It is obvious that if I turn the wheel _A_ round, and thus wind up a weight, fastened to a cord wound round the drum _D_, that the pall _B_ will go click-click-click as the ratchet wheel goes round, but that the pall will hold it from slipping back again. When, however, I take my hands away, and let the ratchet wheel alone, then the weight _E_ will pull on the drum _D_, and try and turn the ratchet wheel back the opposite way to that in which I twisted it at first. If the pall _B_ is held fast, it is impossible to move it, but if the pall is fixed to a cogwheel _F_, which rides loose on the arbor of the drum _D_, then the pull of the weight _E_ will tend to twist the cogwheel _F_ round, and this, if engaged with a pinion wheel on the minute hand arbor, will therefore drive the clock. As the clock arbors move, of course the weight _E_ gradually runs down, and, at last all the string is unwound from the drum _D_.