I know of no literature on the grinding of small lenses though the following memoirs on the making of large reflecting telescopes should be in the hands of any one interested in this work:
=On the Construction of a Five-foot Equatorial Reflecting Telescope.= By A. A. Common, LL. D., F. R. S. Memoirs of the Royal Astronomical Society, Vol. L., 1890-91.
=On the Construction of a Silvered Glass Telescope, Fifteen and a Half Inches in Aperture, and its Use in Celestial Photography.= By Henry Draper, M. D., Smithsonian Contributions to Knowledge, Vol. 34.
=On the Modern Reflecting Telescope and the Making and Testing of Optical Mirrors.= By George W. Ritchey. Smithsonian Contributions to Knowledge, Vol. 34.
In Fig. 6, A is a regular Brown & Sharpe Micrometer Head with the measuring point ground to an angle of 60° and slightly rounded; B is a round steel base all machined at one setting in which the micrometer head is clamped by a set screw not shown.
Let r be the radius of the spherical surface, MNO, and we will have at once r = (a^2 + d^2) / 2d. The advantage of this form of spherometer is that it is very easy to make the point of the micrometer exactly central with the base and the value of 2a can be accurately determined by means of an ordinary micrometer calliper. For a convex surface, 2a should obviously be the inside diameter of the base, B.
In using the instrument, two tables, one for concave and one for convex surfaces, should be prepared; these tables to give the power in dioptres for each one thousandth of an inch in the value of d. Using the American Optical Co.’s Standard Index, namely, μ equal to 1.5000 and one dioptre as being the power of a lens of 40 inches focus, we have, for a plano lens, p = 4/f = 40d/(a^2 + d^2) since f = r/(μ-1).
The advantage of forming the table in dioptres in place of radii directly is that the tabular differences are small at all parts of the table so that interpolation can be readily done and this is not the case in tables which give the radii directly.
If upon measuring the radius of the tool or lap being turned in the sphere turning machine, Fig. 4, with this spherometer, the tool is found to be in error by an amount Δp this may be corrected by changing the position of the cutting tool by an amount 20 (Δp / p^2).