156 On Cog or Toothed Wheels. 
already proved, no sensible motion or the 
kind producing friction, exists between the 
points in actual contact. I might add, as 
the figure evidently indicates, that if any such 
motion did exist, the angles o would quit each 
other, and the figure of such teeth become 
absurd in practice; but on the other hand, 
if such teeth can exist and work usefully 
(which I assert they can, nay that all teeth 
have in this system a tendency to assume that 
form at the working points ;) this circum- 
stance is of itself a practical evidence of the 
truth of the foregoing theory, and of what F 
have said concerning it. 
It must have been perceived that I bave in 
some degree anticipated the demonstration 
of my third proposition, namely, that the 
epicycloidal or any other given form of the 
teeth, is not essential to this geering. It ap- 
pears that teeth formed .as epicycloids, will 
become more convex by working ; since the 
base of the curve is the only point where they 
suffer no diminution by friction ; whilst those 
of every other form, that likewise penetrate 
beyond the primitive circles of the wheels, 
will also assume a figure of the same nature, 
by the rounding off of their points, and the 
hollowing of the corresponding parts of the 
teeth they impel ; and that operation will con- 
