gthen nor shorten the curve during its production. To quote his
words: "This really involves the problem of the 'three bodies,' or
disturbing forces so celebrated in dynamical mathematics, and it is
further complicated by another quantity, the 'coefficient of
attrition,' or work done by the grinding material, as well as the
mischief done by capillary attraction and nodal points of superimposed
curves in the path of the tool. These complications tend to cause
rings or waves of unequal wear in the surface of the glass, and ruin
the defining power of the lens, which depends upon the uniformity of
its curve. As the outcome of much practical experiment, combined with
mathematical research, I settled upon the ratio of speed between the
sheave of the lens-tool guide and the turn-table; between whose limits
the practical equalization of wear (or cut of the emery) might with the
greater facility be adjusted, by means of varying the stroke and
eccentricity of the tool. As the result of these considerations in the
construction of the machine, the surface of the glass 'comes up'
regularly all over the lens; and the polishing only takes a few
minutes' work--thus keeping the truth of surface gained by using a
rigid tool."

The machine in question consists of a revolving sheave or ring, with a
sliding strip across its diameter; the said strip having a slot and
clamping screw at one end, and a hole towards the other, through which
passes the axis of the tool used in forming the lens,--the slot in the
strip allowing the tool to give any stroke from 0 to 1.25 inch. The
lens is carried on a revolving turn-table, with an arrangement to allow
the axis of the lens to coincide with the axis of the table. The ratio
of speed between the sheave and turn-table is arranged by belt and
properly sized pulleys, and the whole can be driven either by hand or
by power. The sheave merely serves as a guide to the tool in its path,
and the lens may either be worked on the turn-table or upon a chuck
attached to the tool rod. The work upon the lens is thus to a great
extent independent of the error of the machine through shaking, or bad
fitting, or wear; and the only part of the machine which requires
really first-class work is the axis of the turn-table, which (in this
machine) is a conical bearing at top, with steel centre below,--the
bearing turned, hardened, and then ground up true, and run in
anti-friction metal. Other details might be given,