ed so as to gradually cut
off the light, and the observer notes the appearance of the mirror
surface. If the curves are perfect and spherical, the transition from
complete illumination to darkness will be abrupt, and no part of the
mirror will remain illuminated after the rest.

For astronomical purposes a parabolic mirror is required. In this
case the disc may be partially screened by zonal screens, and the
position of the image for different zones noted; the correctness or
otherwise of the curvature may then be ascertained by calculation. A
shorter way is to place the source just outside the focus, to be found
by trial, and then, moving the extinction screen (now a separate
appliance) to, say, five times the radius of curvature away, where the
image should now appear, the suddenness of extinction may be
investigated. This, of course, involves a corresponding modification
of the apparatus.

Whether the tests indicate that a deepening of the Centre, i.e.
increase of the curvature, or a flattening of the edges is required,
at least two remedial processes are available. The "chisel and
mallet" method of altering the size of the pitch, squares of the
polisher may be employed, or paper or small pitch tools may be used to
deepen the centre. The "chisel and mallet" method merely consists in
removing pitch squares from a uniformly divided tool surface by means
of the instruments mentioned. This removal is effected at those
points at which the abrasion requires to be reduced.

When some practice is attained, I understand that it is usual to try
for a parabolic form at once, as soon as the polishing commences.
This is done by dividing the pitch surface by V-shaped grooves, the
sides of the grooves being radii of the circular surface, so that the
central parts of the mirror get most of the polishing action. If
paper tools are used they must not be allowed much overhang, or the
edges of the mirror betray the effects of paper elasticity. Most
operators "sink" the middle, but the late Mr. Lassell, a most
accomplished worker, always attained the parabolic form by reducing
the curvature of the edges of a spherical mirror.

Sec. 72. Preparation of Flat Surfaces.

As Sir H. Grubb has pointed out, this operation only differs from
those previously described in that an additional condition has to be
satisfied. This condition refers to the mean curvature, which must be
exact (in the case of flats it is of course zero) to