On Cog or Toothed Wheels. 149 
would be on the line BE, (which represents 
atooth of common geering:) let AD be drawn 
perpendicular to BC. If the point D can 
slide freely on the line BC, (and this is)the 
most favourable supposition for the objection, ) 
its pressure will be exerted perpendicularly 
to this line ; and if the point A, moves from 
A to B, the point D, leaving at the same 
aoment the point A, and moving in direction 
AD, will only arrive at D in the same time, 
its motion haying been slower than thatof A, 
in proportion of AB to AD ; whence by the 
principle of virtual velocities, its pressure on 
BC is to that on AC, as the said lines AB 
to DA. 
_ To convert these pressures into numbers, 
according to the above data; we have AC 
= 1000, AB = 268, BC = 1035;, then from 
the similar triangles BAC, BDA, it will be 
BC: AC:: AB: AD = 253°°* = 259 nearly. 
Therefore the pressure on BC, is to that.on 
AC, as 268 to 259, or as 1035: 1000. 
To find what part of the force tends to 
drive the point B, in the direction BE, (for 
this is what impels the wheels, in the direction 
of their axes, we may consider the triangle 
BAC as an inclined plane, of which BC is 
the length, and AB the height; and the total 
pressure on CB, which may be represented by 
