86 Mr. Ceci on a Machine for Grinding 
If spherical surfaces only be employed, the extreme accuracy re- 
quired does not exclude the use of machinery, but rather calls 
for the aid of machinery, provided that we are able to imitate 
or improve upon the methods used in grinding mirrors by the 
hand. With respect to the spherical aberrations, it has been 
proved in a paper lately read to the Society, that they may be 
effectually corrected by a combination of spherical surfaces afford- 
ing two refractions and two reflections: and even where the para- 
bolic figure is supposed necessary, as in the Newtonian telescope, 
(there being only one surface employed in forming the first image,) 
yet this figure is not attempted except in the last stage of the 
process, while the mirror is being polished, and after a spherical 
surface has been first obtained. To obtain only the spherical 
form is a very unpleasant and laborious operation, sufficient to 
discourage any but professed mechanics. To relieve this part of 
the work is the design of the machine about to be described : 
and the mirror may be entirely finished on such a machine, if it 
be thought that a correct sphere with a moderate aperture is pre- 
ferable to a paraboloid formed by methods purely tentative and 
very uncertain. An experiment was made, some years ago, with 
a machine of this kind, moved by a small steam engine; and 
the result was favourable. The figure of the mirror appeared 
correct, and would take high magnifying powers, with as much 
distinctness as could be expected from the quality of the 
metal. 
The machines employed for grinding lenses with a short focus 
will not at all assist us in grinding reflectors and object glasses. 
The greater degree of accuracy necessary to the latter, requires 
a totally different method of grinding. A brief description of this 
method will lead to an explanation of the machine by which the 
operation may be performed. 
We have first to procure two gages of plate brass, one convex 
