144 On Cog or Toothed Wheels. 
curve, when this circle has made a semi-re- 
volution. 
Thus it appears that independently of the 
effects of percussion, the end of an epicy- 
cloidal tooth must wear out sooner than‘any 
part nearer its base, (and if so, much more 
may it be supposed of a tooth of another form ;) 
and that when its form is thus changed, the 
advantage it gave must cease, since nothing 
in the working of the wheel can afterwards 
restore the form, or remedy the growing 
evil. 
Having now shewn one great defect in the 
common system of wheels, I shall proceed 
to develope the principles of the new system, 
which may be understood through the medium 
of the three following propositions. 
1. The action of a wheel of the new kind 
on another with which it works or geers is the 
same at every moment of its revolution, so 
that the least possible motion of the circum- 
ference of one, generates an exactly equal 
and similar motion in that of the other. 
2. There are but two points, one in each 
wheel, that necessarily touch each other at 
the same time, and their contact will always 
take place indefinitely near the plane that 
passes through the two axes of the wheels, if 
the diameters of the latter, at the useful or 
