212 



>m (1) and (3) we obtain 



pTain = ^ JPcos a - Warn a sin 0; 



by (2) 



rt a cos a sin a sin 

 u tan = - . 



Bin a cos 6 



sin a sin 6 

 Therefore 



cos a sin a tan ft cos 6 



cot ft sin 6 

 ~~ cot a cot ft cos 6 * 



This result may then be developed in the manner already 

 exemplified in Art. 177. 



179. Lever with Friction. 



Suppose a solid body pierced with a cylindrical hole through 



Jf 



which passes a solid fixed cylindrical axis. Let the out. T 

 circle in the figure represent a section of the cylindrical hole 

 made by a plane perpendicular to its axis, and the inner circle 

 the corresponding section of the solid axis. In the plane of 

 section, we suppose two forces P and Q to act on the 

 solid body at the points A and B. Also at the point of con- 

 tact C there is a normal force E and a tangential force F. 

 These four forces keep the body in equilibrium* 



'e R and .Fhave a resultant passing through 6', it fol- 

 lows, by Art. 58, that the resultant of P and Q must also 



