Telescopic Mirrors and Object Lenses. 89 
to each other, to receive particles of sand, emery, and other adven- 
titious substances; and lastly, are employed, the oxides of iron 
or tin (coleathar or putty) upon a surface of common pitch puri- 
fied by straining. 
This is a brief outline* of the process for grinding a spherical 
mirror ; we will now consider the mechanical conditions necessary 
to render this process as accurate as possible. 
The first condition is a due preportion between the surfaces 
of the two leaden tools. If these surfaces be made equal, it is 
observed in practice, that the radius of the sphere formed by grind- 
ing will continually diminish: and if the convex surface be much 
larger than the concave, it is manifest that the radius of the sphere 
must continually increase ; till at length the curvature will become 
inverted. There is therefore a certain proportion between the sur- 
faces, which will keep the curvature invariable; the length of the 
stroke being also given. This proportion is not very easily deter- 
mined by theory, but for practical purposes may be taken as above 
stated ; that is, ten for the diameter of the lower or conyex tool, 
and eight and a half for the diameter of the concave. Still the 
curvature may be made to increase, or to decrease, or to remain 
constant, merely by adjusting the length of the stroke. This 
circumstance furnishes a simple but important means for adjusting 
the focal length, which will be considered afterwards. It also 
points out the necessity of proper limits to the surfaces of the 
leaden tools. 
A considerable vertical pressure must be applied to the mirror, 
at least till the polishing commences; and this pressure, not at- 
tended with the inertia of a moving weight, must take place wholly 
at the centre of the mirror, so as to be equally effective on all parts 
of the surface. 
* Por more exact particulars of casting and polishing metallic specula, see Smith's Optics, 
Newton's Optics, also Mudge’s Paper in the Philosophical Transactions for the year 1777. 
Vol. Wl. Part [. M 
