The tool may overhang the lens by a quarter of the diameter of the latter as a maximum. The circuit may be completed in from twelve to thirty sweeps. The grinding tool should be lightly held by the fingers and the necessary force applied parallel to the surface. The tool itself must be slowly rotated about its axis of figure. If the tool be lightly held, it will be found that it tends to rotate by itself. I say "tends to rotate," for if the tool be touching evenly all over the surface it will rotate in a direction opposite to the direction of the circular sweep. For instance, if the tool be carried round its looped path clockwise, it will tend to rotate about its own axis of figure counter-clockwise. If it touch more in the middle, this rotation will be increased, while if it touches more along the edge, the rotation will be diminished, or even reversed in an extreme case. Every fifty sweeps or so the tool should be simply ground backwards and forwards along a diameter of the lens surface. This grinding should consist of three or four journeys to and fro along, say, eight different diameters. About one-quarter of the whole grinding should be accomplished by short straight strokes, during which the tool should only overhang about one-quarter of an inch. The object of the straight strokes is to counteract the tendency to a gradual accumulation of the emery in the centre, which results from the circular grinding. A great deal of the art of the process consists in knowing how to work the tool to produce any given effect. For instance, if the lens requires to be ground down near the centre, the epicycloidal strokes must be nearly central; the tool must never overhang very much. If, on the other hand, it is the edges which require attention, these must be dealt with by wider overhanging strokes. The tool must be frequently tested on its fellow, and, indeed, ground upon it if any marked unevenness of action (such as that just described) is required for the lens. A check by spherometer will be applied at intervals according to the judgment of the operator, but, in any case, the fellow tool and lens should be kept at very nearly the same figure. The emery should never be allowed to become anything like dry between the tool and the lens, for in some way (probably by capillary action increasing the pressure of the tool) this seems to lead to scratching and "rolling" of the emery. The channels in the glass tool between the squares are of the greatest importance in enabling the emery to distribute itself. Perhaps the best guide in enabling one to judge as to when it is time to wash off the emery and apply fresh is the "feel" of the tool; also when the mud gets light in colour we know that it is full of glass dust, and proportionately inoperative.