Telescopic Mirrors and Objeet Lenses. 95 
with a file, and the grinding renewed till the marks of the file 
are erased. When the focal length is brought within a few inches 
of what is desired, it may be made perfect by a very simple process. 
It is observed in practice that the focal length will increase or 
decrease, or remam constant, according to the length of the stroke 
which the mirror performs. This depends wholly on the length 
of the crank, which may be adjusted at pleasure. A focal length 
of two feet may be varied several inches, in a short time, simply 
by grinding the leaden tools together in this manner*. 
It is one advantage of grinding mirrors by machinery, that the 
same workman may grind several mirrors at one time: and this 
even upon the same machine, provided the mirrors be of different 
dimensions. Thus in grinding two mirrors, for a telescope of Gre- 
gory’s or Cassegrain’s construction, the smaller mirror may be 
ground at a proportional distance from the centre of motion, on 
the same machine with the larger mirror, -and both will be ground 
in the same time and with the same accuracy. It is however the 
opinion of professional persons, that the rectilineal stroke is chiefly 
adapted for object mirrors, which have small curvature. The 
practice for grinding spherical mirrors of greater curvature is by 
a spiral stroke from the centre of the leaden tool towards the 
circumference; without much regard to any exact proportion of 
surfaces. 
It is obvious that the same machine may be employed in 
forming object glasses for refracting telescopes. A piece of plane 
glass being cemented upon a block similar to the convex leaden 
tool, the edges of the glass ate worn off by grinding with sand im 
a spherical basin of cast iron. It is then ground by the brass tool 
with emeries of different fineness, beginning with superfine corn 
* If the figure be impaired by this means, it may speedily be restored by adjusting 
the crank to produce constant curvature. 
