On Cog or Toothed Wheels. 147 
It is besides evident, that the difference 
between the lines BC and AB, depends on the 
angle ACB; in the choice of which, there 
is a considerable latitude. For general use 
however, I have chosen an angle of obliquity 
of 15°, which I shall now assume as the ba- 
sis of the following calculations. The tan- 
gent of 15°, pertables, is in round numbers 
268 to radius 1000; and the object now is to 
find the number of particles in the oblique 
line BC, when the line AB, contains any 
other number, ¢. 
By geometry, BC (x) = //7777= 1000/7 
268)” 1035 nearly ; and this last number is 
to 268, as the number of particlesin the oblique 
line BC is to the number contained in the cir- 
cumference AB, of the base of the cylinder. 
_Hence it appears, that a wheel cut into teeth 
of this form, contains (virtually) about four 
times as many teeth, as a wheel of the same 
diameter, but indefinitely thin, would contain. 
And the disproportion might: be increased, by 
adopting a smaller angle. 
be very small indeed ; but it will still act in the way here 
described, and give tendencies to the wheel it acts on, and 
to its axis precisely proportionate, to the quantities here 
mentioned, 
