154 On Cog or Toothed Wheels. 
losophy shews, that a cube of gold of 3 inch 
side, may be drawn upon silver to a length 
of 1442623 feet, and afterwards flattened to 
a breadth of ,2, of an inch, the two sides of 
which form a breadth of +, of an inch: so 
that if we divide the above length by 25, we 
shall have the length of a similar ribbon of 
metal of 4 aninchin breadth, namely, 47704 
feet; which cut into lengths of 4 of an inch 
(or multiplied by 24, the half inchesin a foot, ) 
give 1144896 such squares, which must con- 
stitute the number of lamina of a half inch 
cube of gold, or 2289792 for an. inch thick- 
ness. Let us suppose then a wheel of gold, 
of two feet indiameter, the friction of whose 
teeth it is proposed to determine. .. We must 
first seek what number, of particles. are con- 
tained in that part of the tooth or teeth, that 
are found in one inch of the wheel’s circum- 
ference ; this we have just seen to, be 2289792 
thicknesses of the leaves, or diameters of the 
particles, such as we are now contemplating, 
We shall now have this proportion (See 
Fig. 4,) 268 (AB) ; 1085. (BC) :: 2289792 
(no of particles in oneinch of circumference 
of base) : 2 = 8843040 particles in that part 
of the line BC, which corresponds with that 
inch of the circumference. Thus each of the 
latter particles. measured in the direction AB, 
