80 OUTLINES OF NATURAL PHILOSOPHY. 



wheel, will give the ratio of the power to the re- 

 sistance when an equilibrium takes place. 



The truth of the first part of this proposition is evi- 

 dent from 136. ; and the truth of the latter 

 part follows from the principle of the virtual velo- 

 cities. 



138. When wheels act by teeth working in one 

 another, notwithstanding that the length and po- 

 sition of the levers by which they act, are conti- 

 nually changing, the force of the one upon the 

 other will remain constant, if the line which is 

 drawn perpendicular to the surfaces of both teeth 

 at the point of contact, pass continually through 

 the same point of the line which joins the centres 

 of the wheels. 



It is here necessary to distinguish between what is 

 called the total, and the primitive radius of a wheel. 

 The total radius extends from the centre to the ex- 

 tremities of the teeth ; and the primitive extends only 

 to the point where the teeth would touch, if they 

 were to act merely by contact. If the distance be- 

 tween the centres of the wheels be divided by the 

 point O, (fig. 10.), in the ratio of the number of teeth 

 which the wheels are required to have, AO and 

 BO will be the primitive radii of the wheels, and O 

 is the point through which the perpendiculars in the 

 above proposition must be supposed to pass. 



139. There 



