On Cog or Toothed Wheels. 145 
pressing points are in the exact ratio of their 
number of teeth respectively ; in which case 
there will be no sensible friction between the 
points in contact. ' 
8. In consequence of the properties above- 
mentioned, the epicycloidal or any other form 
of the teeth, is no longer indispensable; but 
many different forms may be used, without 
disturbing the principle of equable motion. 
With regard to the’ demonstration of the 
first. proposition, I must premise an observa- 
tion of M. Camus on this subject, in his Me- 
chanics; 3d part, page 306, viz. “ ifall wheels 
could have teeth infinitely fine, their geering, 
which might then be considered as a simple 
contact, would have the property required 
[that of acting uniformly,] since we have seen 
that a wheel and a pinion have the same tan- 
gential force, when the motion of one is com- 
municated to the other, by an infinitely small 
penetration of the particles of their respective 
circumferences.” 
Now suppose that on the cylindrical sur- 
face of aspur wheel Bc (Fig. 3), we cut ob- 
lique or rather screw formed teeth, of which 
two are shewn at ac, bd, so inclined to the 
plane of the wheel, as that the end c of the 
tooth ac may not pass the plane of the axes 
ABc, until the end 6 of the other tooth dd 
VOL. II. ed 
