On Cog or Toothed Wheels. 153 
the circular distance of two particles of mat- 
ter found in the serew-formed tooth ac, of the 
wheel Be, fig. 3, (referred to the circle ab, 
fig. 5), that distance 2 will be a mean propor- 
tional between the radius Dg of such wheel, 
and the double versed sine of this incon- 
ceivably small angle.* 
TE am aware that some mathematicians main- 
tain, that the smallest portion of a curve can- 
not strictly coincide with a right line; a doc- 
trine which I am not going to impugn. But 
however this may be, it appears certain that 
there is no such mathematical curve exhibited 
in the material world, but only polygons of 
a greater or less number of sides, according 
to the density of the various substances, that 
fall under our observation. I shall therefore 
proceed to apply the foregoing theory, not 
indeed to the ultimate particles of matter, 
(because I do not know their dimensions, ) 
but to those real particles which have been ac- 
tually measured. Thus, experimental phi- 
'* T ought perhaps to have introduced this reasoning on 
the 5th figure by observing, that every projection of every 
part of a screw, on a plane at right angles with the axis of 
such screw, is a circle; and that therefore the chord z, or 
the line gd, is the true projection of a proportionate part of 
any line, BC, fig. 4, when wrapped round a cylinder of 
equal diameter, with the circle a, fig. 6. 
VOL, III. U 
