As a rule, when the watch repairer has to replace a pinion he selects one from the material dealer, finished in the leaves, but not on the ends or faces. The following operations are simple, and any one may finish these faces with little trouble. Having turned up your pivots and squared down the face of the leaves with the turning tool, grind it in the lathe by means of a ring of metal, the inside diameter being somewhat larger than the diameter of the staff. This ring is held between two centres, thus allowing it a vibratory motion, so that when it comes up to the face it accommodates itself to its plane, and thus has no tendency to force it out of a true flat; the ring, being larger than the staff or pivot, admits a small lateral motion, enough to effect a continuous change of surface. The same little tool may be used for polishing by substituting another polisher and using crocus and rouge. For the repairer, perhaps on general work the rouge would be superfluous. Vienna lime, used with a little slip of boxwood, brings up a very fine and brilliant polish, and in replacing new work in an injured time-piece, the steel may always be polished with great rapidity by using the lime on the gray surface left from the oil-stone dust; being quickly done and affording a very handsome finish. To resume the consideration of the pinion, the last stage is the polishing of the circular portions. Here again the wig-wag is the most useful tool, but it operates somewhat differently, for the grinder or polisher is pressed down by the finger of the operator, the pinion being held between the centres of a small lathe attached to the wig-wag; the staff is first ground and polished as the leaves have been before, and this is the last operation performed with the pinion between centres. From this stage it is chucked in a lathe very peculiarly fitted, the mandrel being hollow; and in it is fitted what is called a pump-centre, which is movable in direction of the axis of the mandrel, and capable of being securely fastened at any desired point. On the nose of the mandrel is secured a hollow steel chuck, the two sides of which have been filed out, thus leaving an open space between the end of the pump-centre and the end of the chuck. On this end a small steel plate, extremely thin, is fastened by means of shellac, and a hole drilled in the plate capable of taking in the chamfer on the shoulder of the pivot. The pump-centre being drawn back, the pinion is introduced into the chuck, the pivot placed in the hole in the steel plate, and the pump centre is drawn forward until it forces the chamfer to fill the hole; the pivot projecting from the chuck is now ready for all the grinding and polishing processes. Here the wig-wag steps in again, and from the delicacy of the pivots is modified to suit the case; this is done by having a polisher hung in the wig-wag on centres, so it may revolve; when in operation one