On Cog or Toothed Wheels. 157 
tinue till an angle similar to that at 0 (fig. 6,) 
but generally more obtuse, prevails around 
both wheels; when all sensible change of 
figure or loss of matter will cease, as the 
wheels now before you will evince. 
On the right of the drawing (fig. 6,) the 
teeth of the wheel B are angular (suppose 
square, ) and those of the wheel C rounded off 
by any curves, within an epicycloid. All that 
. 1s necessary to remark in this case is, that the 
teeth of the wheel B must not extend beyond 
its primitive circle, whilst the round parts of 
those of the wheel C, do more or less extend be- 
yond its primitive circle; whence it becomes 
evident, that the contact of such teeth (if infinite 
in number,) can only take place in the plane 
of the common tangent at right angles to AB ; 
also that if these teeth are sufficiently hard 
to withstand ordinary pressure. without in- 
dentation in these circumstances, there is no 
perceptible reason for a sensible change of 
form; since this contact only takes place 
where thetwo motions are alike, both in swift- 
ness and direction. A fact I am going ‘to 
mention may outweigh this reasoning in the 
minds of some, but cannot invalidate it. I caus- 
ed two of these wheels made of brass, to be 
turned with rapidity under a considerable re- 
sistance for several weeks together, keeping 
