ny desired ratio of
motion to the tool-holder, which simply consists of two pins
projecting vertically downwards from the spokes of wheel K.

These pins form a fork, and each prong engages in a corresponding hole
in the back of the slate-grinding tool (not shown in figure). The
connection with the tool is purposely loose. The wheel E, of course,
cannot rotate about the crank-pin D. Provision for changing the ratio
of tool rotation is achieved by mounting the wheels composing the
train on pins capable of sliding along a long slot in the bar
supporting them. The farther end of this bar is caused to oscillate
to and fro very slowly by means of an additional crank-pin S and
crank-shaft, the projecting face of the bed-plate W being placed
so as to allow V to slide about easily and smoothly.
Motion is communicated to this part of the system by means of
gears at 0 and P, and a belt working from P to Q.
Thus the vertical shaft R is set in motion and
communicates by gears with S. A pulley placed on the axle of the
wheel carrying the crank-pin S gives a slow rotation to the work which
is mounted on the table M. A small but important feature is the tray L
below the gear K. This prevents dirt falling from the teeth of the
wheel on to the work. The motion of S is of course very much less
than of B--say 100 times less. The work can be conveniently adjusted
as to height by means of the screw N.

The machine must be on a steady foundation, and in a place as free
from dust as possible. Though it looks complicated it is quite
straight-forward to build and to operate.

It is explained in Lord Rayleigh's article on Optics in the
Encyclopaedia Britannica that a very minute change in the form of the
curvature of the surface of a lens will make a large difference in the
spherical aberration. This is to be expected, seeing that spherical
aberration is a phenomenon of a differential sort, i.e. a measure of
the difference between the curvature actually attained, and the
theoretical curvature at each point of the lens, for given positions
of point and image. Sir H. Grubb gives an illustration of the
minuteness of the abrasion required in passing from a curve of one
sort to a curve of another, say from a spherical to a parabolic curve,
consequently the process of figuring by the slow action of a polishing
tool becomes quite intelligible. In making a large mirror or lens all
the processes hitherto described under grinding and polis