104 OUTLINES OF NATUKAL PHILOSOPHY. 



Let the whole weight to be moved be W, the radius 

 of the wheel r ; ,/^the force which, drawing horizon- 

 tally, will raise the carriage over an immoveable ob- 

 stacle of the height h ; then 



or 



17%. When a machine is so loaded, that it 

 would be in equilibria if there were no friction, it 

 will not be ready to move till a part be added to 

 the power, having its momentum equal to the 

 momentum of the friction. 



The friction must be considered as a given force, op- 

 posed to the power, and having a momentum pro- 

 portional to its distance from the centre or axis of 

 motion. 



173. Let a lever turn on an axle of which the 

 radius is r; let a be the length of the arm to which 

 if the power P were applied, it would sustain the 

 weight W, supposing there were no friction ; and 

 let p be the addition to be made, in order to over- 

 come the friction, the ratio of the pressure to the 

 friction being that of n to 1 ; then is, 



jp= JL (P-fW). 

 na 



-a. The friction will cause the equilibrium to remain 

 while the power varies from P p to P +p. 



If 



