548 N0T2S'ON STATICS. 



13. If y denote the perpendicular distance between OA and tlie 

 central axis, we have 



G cos (j) 

 P = ; — ;^ — > 



G sin B cos X G cos (3 cot 9 

 y= ^ ■=P ^ 



G cos 3 

 Therefore (p — p') tan = — — - — , which is constant. 



14. To reduce the Resultant force H, and the Resultant couple A', 

 the origin being on the central axis, to two forces one of which 

 shall act along a given line. 



Let the given line be in the plane of the paper at a distance p^^ 



from and making an angle (?i with the central axis which may be 



supposed parallel to the plane of the paper. 



p Q 

 Resolve H into Q, R — Q, at distances j^i , — - — , respectively, from 



Ji — Q 



the central axis : and let the forces of X be each equal to — 5" A" at 



Px -"- 



p R 

 a distance --- — apart. Then taking one of the forces of the couple 

 R — Q 



to act with Q, and the other with R — Q, we have 



p,R 

 'Px 



.R—Q .g- 



R'-'Q K 

 tan 01 = ~1T • w ' 

 Pi K R 



tan 0, = =- J 



p^R 



where B^ is the angle which F^ makes with the central axis. Prom 

 these we find 



«-, KR sec 0j 



^ "" K ■\- p^ R tan 9^ ' 



F,=. ^^\ lK,^p\R'^)k, 



^ A" + j5i i2 tan 01 ^ ^ ' 



tan^/=^±^^-^!!A, 

 jOi A — A tan Q^ 



since ^', the angle between F^ and i^2> i^ equal to ^i + ^2 • 



