Telescopic Mirrors and Object Lenses. 99 
The chief difficulty is to find a suitable motion for grinding. 
To grind one paraboloid upon another by a rectilineal motion, 
or by any motion largely compounded with a rectilineal motion, 
is evidently impossible. And to grind only by a rotatory motion 
about the axes, would entirely destroy the surface, by producing 
rings. Still it may be possible to combine these motions, sufl- 
ciently for practical purposes, by making the crank, and therefore 
the rectilineal motion, extremely short, and the circular motion 
more rapid. The rotatory motion is increased by removing the 
cogged wheel (s), and putting in its place a small pully with a 
string passing round the circumference of the fly wheel. If the 
cogged wheel had twenty cogs, and the pully now substituted be 
one-fifth of the diameter of the fly wheel, the rotatory motion will 
be increased a hundred times; or the leaden tool will revolve ten 
times in a minute, and the mirror twenty times; hence their re- 
lative motion is thirty revolutions in a minute. The quantity 
of rectilineal motion should be the least possible, that is sufficient 
to prevent the formation of annular streaks on the mirror. 
As far as respects the grinding of conoids, this subject is only 
theoretical ; so that appropriate improvements and directions must 
be sought from a few experiments. 
