a degree which is
quite unnecessary in the manufacture of mirrors or lenses.

A little consideration will show that to get a surface flat the most
straightforward method is to carry out the necessary and sufficient
condition for three surfaces to fit each other impartially. If they
each fit each other, they must clearly all be flat. To carry out the
process of producing a flat surface, therefore, two tools are made,
and the glass or speculum is ground first on one and then on the
other, the tools being kept "in fit" by occasional mutual grinding.
The grinding and polishing go on as usual. If paper is employed, care
must be taken that the polisher is about the same size as the object
to be polished.

There is a slight tendency to polish most at the edges; but if the
sweeps are of the right shape and size, this may be corrected
approximately. The best surfaces which have come under my notice are
those prepared as "test surfaces" by Mr. Brashear of Alleghany, Pa,
U.S.A. These I believe to be pitch polished. A pitch bed is
prepared, I presume, in a manner similar to that described for
rocksalt surfaces; but the working of the glass is an immense art, and
one which I believe--if one may judge by results--is only known to
Mr. Brashear.

In general, the effect of polishing will be to produce a convex or
concave surface, quite good enough for most purposes, but distinctly
faulty when tested by the interference fringes produced with the aid
of the test plate. The following information therefore--which I draw
from Mr. 'Cook--will not enable a student to emulate Mr. Brashear,
but will undoubtedly help him to get a very much better surface than
he usually buys at a high price, as exhibited on a spectroscope prism.

The only difference between this process and the one described for
polishing lenses, lies in the fact that the rouge is put into the
paper surface while the latter is wet with a dilute gum "mucilage."
It is of course assumed that the object and the two tools have been
finely ground and fit each other impartially. The paper is rubbed
over with rouge and weak gum water. The tool, when dry, is applied to
the flat ground surface (of the object), and is scraped with the
three-cornered file chisel as formerly described. This process must
be very carefully carried out. The paper must be of the quality
mentioned, or may even be thinner and harder. The cross strokes
should be more employed than in the case of the