VII. On an Apparatus for Grinding Telescopic Mirrors 
and Object Lenses. 
By tHe Rev. W. CECIL, M.A. 
OF MAGDALENE COLLEGE. 
[Read Dec. 11, 1822.] 
Tus grinding of telescopic mirrors by machinery has been 
considered nearly a hopeless attempt; partly from the degree 
of accuracy which is required, and partly from the supposed 
necessity of a parabolic figure. The condition of accuracy is 
indeed indispensable. If a reflecting telescope be not superior 
to the best achromatic refracting telescope that can be made, it 
may be considered, for the purposes of science, nearly useless. 
The inferior sort of reflecting telescopes are adopted chiefly on 
account of the great ease with which they may be constructed*. 
* One of the easiest telescopes to construct is that of Sir Isaac Newton, which requires 
very little accuracy except in the figure of the object mirror. The figure of the small plane 
mirror is quite indifferent for distinctness if only the polish be good: For if the image be 
thrown nearly on the surface of the small mirror, the foci of incident and reflected rays 
will coincide at the surface; and the rays will diverge accurately from the several points of the 
image, whatever be the form of the reflecting surface. To prevent distortion of the image, 
it is indeed necessary that the small mirror should be nearly plane ; but the distinctness of the 
several parts of the image will depend only on the polish. Yet, as the best polish must 
be imperfect, when its defects are magnified by the eye-piece, it is usual to throw the 
image at some short distance from the small mirror. 
