YiKiTAi, vr.i.Mcn n.s. i.xA.Mri.i;. 

 have to fmd the dis])laccincnt uf 1> \ aloni 



the line of action of P. Now conceive the l>ram In 

 into its second position by two st< * it be moved 



parallel to itself till the lower end comes to A', ami m 

 it revolve round A' through a small an^lr tf. I>\ tl, 



// moves through a space parallel and rqn- 

 the second step B describes a small arc of a circle the i 

 Of which is AB.S6, that is Zcosec00. Thus the <li-: 

 ment of B estimated along the line of action of P is ultin. 

 c sin b cosec 6 80. 



Similarly by the first step G moves through a space equal 

 and parallel to A A, and by the second st.-p '/' <! 

 small arc of a circle the length of which is a&0. Tim 

 displacement of G resolved vertically downwards is ultin. 

 aw sin 6 c. 



Therefore, by the principle of virtual velocities, 



W (a sin 8W - c) + P(c sin 6 - 1 cosec 6W) = 0; 

 therefore, &0 (Wa sin 6 - PI cosec 6) - c (W- Psin 0) = 0; 

 and, since c and &0 may be any independent small quant 

 WaxrnO-Fb cosec = 0, W- Psin = 0; 



therefore 



(3) Suppose we wish to know R and the position of 

 ilibrium, and not J'. 



n we should displace the beam so as to give to A a 

 virtual velocity with respect to 11, but not one to B with 

 respect to /'. 



The beam must therefore still remain in contact with llic 

 peg. Let AA'= c, and let a be the angle which AA makes 



