Clearly the effect of trimming away is correlated with the form and length of stroke, and the temper of the pitch, and in fact it requires the wisdom of the serpent to combine these various factors so as to produce the perfectly uniform and regular action required in polishing. Now and then, at brief intervals, the operation is stopped to supply rouge and to avoid changing the conditions by the heat of friction. Especially must heating be looked out for in hand polishing of lenses which is often done with the glass uppermost for easier inspection of the work. Polishing, if the fine grinding has been judiciously done is, for moderate sized surfaces, a matter of only a few hours. It proceeds quite slowly at first while the hills are being ground down and then rather suddenly comes up brilliantly as the polisher reaches the bottoms of the valleys. Large lenses and mirrors may require many days. Now begins the final and extraordinarily delicate process of figuring. The lens or mirror has its appointed form as nearly as the most precise mechanical methods can tell—say down to one or two hundred-thousandths of an inch. From the optical standpoint the result may be thoroughly bad, for an error of a few millionths of an inch may be serious in the final performance. The periphery may be by such an amount longer or shorter in radius than it should be, or there may be an intermediate zone that has gone astray. In case of a mirror the original polishing is generally intended to leave a spherical surface which must be converted into a paraboloidal one by a change in curvature totalling only a few hundred-thousandths of an inch and seriously affected by much smaller variations. The figuring is done in a fashion very similar to the polishing. The first step is to find out by optical tests such as are described in Chapter IX the location of the errors existing after the polishing, and once found, they must be eliminated by patient and cautious work on the surface. Every optical expert has his own favorite methods of working out the figure. If there is a hollow zone the whole surface must be worked down to its level by repolishing; if, on the other hand, there is an annular hump, one may repolish with stroke and tool-face adapted to cut it down, or one may cautiously polish it out until it merges with the general level. Polishing is commonly done with tools of approximately the size of the work, but in figuring there is great difference of practice, some expert workers depending entirely on manipulation of a full sized tool, others working locally with small polishers, even with the ball of the thumb, in removing slight aberrations. In small work where the glass can be depended on for homogeneity and the tools are easily kept true the former method is the usual one, but in big objectives the latter is often easier and may successfully reach faults otherwise very difficult to eliminate.