142 On Cog or Toothed Wheels. 
‘known to mathematicians that the curve so 
modified will no longer be strictly an epicy- 
cloid; and it was on this account that I was 
careful above, to say that the teeth of wheels 
producing equable motion, depended upon 
that curve ; for if the curve of the teeth bea 
true epicycloid in the case of thick pins, the 
motion of the wheels will not be equable. 
I purposely omit other interesting cireum- 
stances in the application of this beautiful 
curve to rotatory motion; a curve by which 
I acknowledge that equable motions can be 
produced, when the teeth of the ordinary 
geering are made in this manner. But here 
is the misfortune :—besides the difficulty of 
executing teeth in the true theoretical form, 
(which indeed isseldom attempted ), this form 
cannot continue to exist ; and hence it is that 
the best, the most silent geering becomes at 
last imperfect, noisy and destructive of the 
machinery, and especially injurious to its more 
delicate operations. 
he cause of this progressive deterioration 
may be thus explained: Referring again to 
fig. 1, we there see the base of the curve AB 
divided into the equal parts, ab, be, and cd; 
and observing the passage of the generating 
circle D, from the origin of the curve at d, 
to the first division c on the base, we shall find 
