ss to be ground, and are, say, half
an inch thick. These discs are turned convex or concave on one face
according as they are to be employed in the production of concave or
convex glass surfaces. The proper degree of convexity or concavity
may be approximated to by turning with ordinary turning tools, using a
circular arc cut from zinc or glass (as will be described) as a
"template" or pattern. This also is a mere matter of turning.

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