94 Mr. Cecit on a Machine for Grinding 
times round it; and, to prevent confusion, to pass also as many 
times, wanting one, round a small beaded roller fixed in position. 
But the first construction is quite sufficient in practice to prevent 
the string from slipping, all grooves being made in the form of 
a V: the latter may be used when several mirrors are to be 
ground at once on the same machine. 
Another objection to this manner of producing the circular 
motion by a string, may seem to arise from the greatness of the 
resistance, by which the string might seem liable to be broken ; 
though the resistance, being overcome at a great mechanical ad- 
vantage, is hardly sensible as opposed to the moving power. This 
meconvenience is not found to arise in practice: on the contrary 
it is remarkable how thin a string will sustain the work during 
the whole formation of a mirror. The reason seems to be, that 
the tension of the string, which causes circular motion, enters into 
composition with the larger force which produces the rectilinear 
stroke: and it is obvious that two forces applied to the same body 
in different directions, may both take effect when compounded, 
though either force would be ineffective by itself. Much more 
if one force, namely the rectilineal, be adequate to produce motion, 
the other, however small, will enter mto composition with it, and 
will give an oblique motion to all points of the mirror except the 
centre. 
The sufficiency of the string in point of strength, depends 
chiefly on the comparative velocities of the circular and rectilineal 
motions, which are extremely disproportionate. The lower wheel 
with the convex leaden tool, is moved round once every ten 
minutes ; in which time the mirror revolves twice, and performs 
three or four thousand rectilineal strokes. 
While the mirror is being ground, the curvature is to be fre- 
quently examined by the gages. If the focal length is very far 
from what is wanted, the convex leaden tool may be corrected 
