The steel wire having been selected, the first process is to cut it up in lengths a trifle larger than the required pinion. The separated pieces are then centred with care, and having been placed in a lathe, the staff and pivot are turned up to nearly the required gauge, leaving a portion of the whole piece the full size for the leaves. They are now taken to the milling tool to have the proper form given to the leaves. As this form is of the highest importance, it may be as well to give here the reasons. Supposing a wheel of 60 teeth, depthing into a pinion of 8 leaves, it can readily be seen that the arc of the motion of the wheel tooth is of greater radius than that of the leaf of the pinion, and it follows that if the teeth and the leaves are made in taper form with straight sections, there must occur a sliding motion on the surfaces of both--the power thus absorbed being totally wasted; but if we curve the surfaces we may approach a form so nearly perfect that the wheel teeth, being motors, really roll on the leaves, avoiding almost entirely the friction caused by sliding; the necessity for this curvature becoming greater the more the wheel exceeds the pinion in diameter. This curve, which has been demonstrated by very profound mathematical researches, is the “epicycloidal;” theoretically it should give no more sliding motion than the surfaces of two plain wheels revolving on each other. To obtain this perfect form, very great pains have been taken and expenses incurred, especially by the makers of the best time-keepers. In the American factories the cutters are very elaborately made, the section being an object of great solicitude--it being an exact counterpart of the space between any two leaves, and also of one-half the top of the leaf from the curvature to the point, so that in milling, the space made by the cutter is its shape, leaving the leaf of the proper form. Generally the pinion passes under two cutters; the first to strike down the rough stock, the other to dress it to size and shape, with a light cut. The care and skill required to make these is certainly very great, and it is a proof of the wonderful ingenuity of man that they are made so perfect as to shape and cutting power.