"During a series of experiments instituted many years since by Professor Barlow for verifying his methods of computing the curvatures of an achromatic object glass, in which I was practically engaged, it became necessary to ascertain with considerable accuracy the radii of curvature of the tools on which the lenses were ground. The method then adopted was that of grinding in the tool the edge of a plate of glass, till the edge accurately fitted the tool, and formed what is called a template. This was laid upon a board in which two pins were inserted, and the template, guided by the pins, was made to describe an arc of great extent. The chord and versed sine of this large arc being carefully drawn and measured afforded data for calculating the radius, by the well-known formula 2 R = ( δ/2)2/v + v, where R is the radius, c the chord, and v, the versed sine. This, though obviously not a very precise method, was sufficiently correct for verifying the theoretical deductions, and it was as accurate as the processes then employed in working the glasses for telescopes."
"With the view of improving these processes, and rendering their results more certain, I have, for more than two years, been carrying on a course of experiments to discover the causes of the discrepancies which were known to exist between theory and practice in this branch of optics. Every improvement in the processes rendered it indispensable to determine more correctly slight variations in the radii of curvature, to accomplish which I was led to invent the instrument which I now offer to the notice of the Society.
"Its principle and general features are explained in the accompanying sketch, where T, T, represents a portion of the convex tool to be measured; and as the tools are of necessity made in pairs we require to measure only one of each. A short cylinder C, C, nearly closed at one end has its edges very accurately turned and ground to a portion of a circle whose radius is known. In the cylinder is attached a carefully made square socket S, S, in which fits and moves the square index bar I, I, the extremities of which are finished with hard steel cones. Upon these conical terminations as centers the circular edge of the cylinder C, C, is ultimately turned and ground, so that all errors of workmanship in fitting and fixing the socket to the cylinder are completely obviated. The index bar I, I, is divided on one face to 1/50th of an inch, and a vernier V, is secured to the socket by which it may be read to 1/1000 th of an inch, or, by estimation, v = The apparent versed sine as indicated by the vernier.
"If the edge of the cylinder had been made square instead of circular, then the clear diameter of the cylinder would have been in all cases the value of the chord; but the difficulty of preserving a square angular edge perfectly true, and the different manner in which such a form would lie on spheres of small and large radii, induced me to adopt the circular edge, by which of course the value of the measured chord varies with every change of curvature in the tool." To obtain the value of the radius without determining the value of the varying chord Mr. A. Ross devised the formula R = v2+a2/2v - r a 3= The known semidiameter, or half the distance between the centers of the small circles which form the edge (which is determined by gently rubbing the cylinder on a perfectly flat surface and measuring the diameter of the ring thus marked on the circular edge).
r = The known radius of the edge of the spherometer.
R = The radius of the tool sought.
Diminutive microscopic lenses, whose diameter is sometimes as small as from one quarter, to one twentieth of an inch, are also ground and polished singly, as the radius of curvature is in general too small to allow of several being grouped together. The templates are made as small disks of steel, with slender stems turned in the lathe; for lenses, the radii of whose curvature are 5, 10 or 20 hundredths of an inch the diameters of the disks are 10, 20 or 40 hundredths. They are made with square edges and when hardened are applied diametrically as the finishing tools for turning the small metal cups or concave grinding tools. For measuring the diameters of the disks they are applied either in the sector gage, or one of the sliding gages often used for measuring the diameter of wire, and graduated decimally for reading the width of the opening to the hundredth or thousandth of an inch.
The cups when turned are charged with emery, and put in rapid revolution in the lathe, which for these minute lenses is in general very small, and worked with the drill bow. The lens is cemented with shell-lac upon a small wooden stick, and held against the grinding tool with a continual change of angle, the end of the stick being moved in the arc of a circle, while it is at the same time twisted on its axis.
The same succession of emeries is used as for grinding the larger lenses, but the polishing is usually done with bees-wax hardened with fine crocus, the wax is melted, and a sufficient quantity of the crocus stirred in to make it so hard that when cold the finger nail will only just indent it.' The smaller the lenses the harder the wax is made, as it should be of such a consistence that with moderate pressure the wax will yield sufficiently to assume the form of the lens, and at the same time be so hard as to retain the figure during the polishing. This composition has also been recommended for larger lenses, but is found to be less suitable than the pitch polisher, as when sufficiently hard to retain its figure, the adhesion is too great to be completely under the control of the fingers.
The brass cups for the polishing tools of small lenses, are turned in the lathe of a little larger radius than the grinding tool, and the surface is roughened that it may the better hold the wax, the tool is then heated, and the melted wax poured in, and when cold is either moulded to the form with a convex tool, or turned in the lathe, first with a thin scraping tool, and afterwards finished with a circular disk, just as in turning the grinding tool. In polishing the lens the surface of the wax is kept constantly wet with fine crocus and water, applied with a feather, and the lens is held in the same manner as for grinding. To separate the lenses from the runner or handle, they are warmed sufficiently to soften the shell-lac, and to prevent scratching the lenses in removing the last particles of cement, the latter is dissolved in spirits of wine.