f glass does not
appear on the list, an application may be made to the Jena Factory of
Herr Schott. In order to give a definite example, I may mention that
for ordinary telescopic objectives good results may be obtained by
combining the hard crown and dense flint of Chance's list, using the
crown to form a double convex, and the flint to form a double concave
lens. The convex lens is placed in the more outward position in the
telescope, i.e. the light passes first through it.

The conditions to be fulfilled are:

(1) The glass must be achromatic;

(2) it must have a small spherical aberration for rays converging to
the principal focus.

It is impossible to discuss these matters without going into a
complete optical discussion. The radii of curvature of the surfaces,
beginning with the first, i.e. the external face of the convex lens,
are in the ratio of 1, 2, and 3; an allowance of 15 inches focal
length per inch of aperture is reasonable (see Optics in Ency.
Brit.), and the focal length is the same as the greatest radius of
curvature. Thus, for an object glass 2 inches in diameter, the first
surface of the convex lens would have a radius of curvature of 10
inches, the surface common to the convex and concave lens would have a
radius of curvature of 20 inches, and the last surface a radius of
curvature of 30 inches. This would also be about the focal length of
the finished lens. The surfaces in contact have, of course, a common
curvature, and need not be cemented together unless a slight loss of
light is inadmissible.

I will assume that a lens of about 2 inches diameter is to be made by
hand, i.e. without the help of a special grinding or polishing
machine; this can be accomplished perfectly well, so long as the
diameter of the glass is not above about 6 inches, after which the
labour is rather too severe. The two glass discs having been obtained
from the makers, it will be found that they are slightly larger in
diameter than the quoted size, something having been left for the
waste of working.

It is difficult to deal with the processes of lens manufacture without
entering at every stage into rather tedious details, and, what is
worse, without interrupting the main account for the purpose of
describing subsidiary instruments or processes. In order that the
reader may have some guide in threading the maze, it is necessary that
he should commence with a clear idea of the broad principles of
construc