The first approximation to the desired convex or concave surface of the glass is attained (in the case of small lenses, say up to three inches diameter) by rotating the glass on the lathe as described above (for the purpose of giving it a circular edge) and holding the tool against the rotating glass, a plentiful supply of coarse emery and water, or sand and water, being supplied between the glass and metal surfaces. The tool is held by hand against the surface of the revolving glass, and is constantly moved about, both round its own axis of figure and to and fro across the glass surface. In this way the glass gradually gets convex or concave. The curvature is tested from time to time by a spherometer, and the tool is increased or decreased in curvature by turning it on a lathe so as to cause it to grind the glass more at the edges or in the middle according to the indications of the spherometer. This instrument, by the way--so important for lens makers--consists essentially of a kind of three-legged stool, with an additional leg placed at the centre of the circle circumscribing the other three. This central leg is in reality a fine screw with a very large head graduated on the edge, so that it is easy to compute the fractions of a turn given to the screw. The instrument is first placed on a flat plate, and the central screw turned till its end just touches the plate, a state of affairs which is very sharply discernible by the slight rocking which it enables the instrument to undergo when pushed by the hand. See the sketch. On a convex or concave surface the screw has to be screwed in or out, and from the amount of screwing necessary to bring all four points into equal contact, the curvature may be ascertained. Let a be the distance between the equidistant feet, and d the distance through which the screw is protruded or retracted from its zero position on a flat surface. Then the radius of curvature rho is given by the formula 2rho = a2/3d +d. Fig. 43. The process of roughing is not always carried out exactly as described, and will be referred to again. (4) The glass being approximately of the proper radius of curvature on one side, it is reversed on the chuck and the same process gone through on the other side. After this the glass is usually dismounted from the lathe and mounted by cement on a pedestal, which is merely a wooden stand with a heavy foot, so that the glass may be held conveniently for the workman. Sometimes a pedestal about four feet high is fixed in the floor of the room, so that the workman engaged in grinding the lens may walk round and round it to secure uniformity. For ordinary purposes, however, a short pedestal may be placed on a table and rotated from time to time by hand, the operator sitting down to his work.