On Cog or Toothed Wheels, 155 
is equal to the fraction 5-;32,>ths of an inch. 
And if that fraction be taken for the are gd 
(fig.'5), then to find the length of the line 
de, (on which the friction of this and all other 
geering depends,) we must use this analogy ; 
12 inch. (rad. of wheel): ,.,4>;> of an inch 
(chord gd)::=,32;- of an inch (gd): de, 
the line required — 555-¢52.037-295,250 Of an 
inch. This result is still short of the truth, 
as we do not know how much smaller the ul- 
timate molecules of gold are. 
To advert now to some of the practical 
effects of this system, I would beg leave to 
present a formof the teeth, the sole working of 
which would be a sufficient demonstration of 
thetruth of the foregoing theory. A, B, (fig.6) 
are two wheels of which the primitive circles 
or pitch-lines touch each other ato. As all 
the homologous points of any screw-formed 
tooth, are at the same distance from the cen- 
tres of their wheels, I am at liberty to give 
the teeth a rhomboidal form, 0 #7; and if the 
angle oexistsall round both wheels, (of which 
I have attempted graphically to give an idea 
at DG,) im this case, those particles only 
whichexist in the plane of the tangents fh, &c. 
and infinitely near that plane passing at right 
angles to it, through the centres A and B, 
will touch each other ; and there, as we have 
