16 



Scientific Proceedings, Royal Dublin Society, 



..(f.o.) = ..(^- 



EB.CN=ZB 



LB + LZ 



CN.EB tan^ = ZB sin^ 



LB + LZ 



2 cos ' 



. • . CN.BE = ZQ 5^^-t^= trapezium CAZB ; 



A Ci)iV= 4- trapezium C^ZS. q.b.d. 



The magnitude of P in tliis case can be easily expressed. Let 

 CL, AL, and CZ be denoted by H, h, and /, respectively : 



P = ^DJE% huiDE'-EBt&nrj> = {CB-CE)tm(l> 



( E \^ S ,, 



= ~. 1 tan 6 = I tan d» 



\sm^ J Gos,(p 



= ^sec - tan yH^ + h"^ cot^ ^ = £"860 ^ - v/^'^ tan^ + AS 



.\B = % [EBeG<p-yE' tan^0 + h']\ 



See Moseley's Engineering, p. 458. 

 This expression leads to a construction for the force P, which 



is useful in determining its point of application as well as its 

 magnitude. 



