VIRTUAL VELOCITIEH. B10ID BOOT. 



and &--y*, By-**; 



th,-rri.,v .r)-0; 



tore -0. 



'.irly, by suitable displacements, we may prove 



-0, i. /jc)-0. 



Hence, the six equation* of equilibrium h 



be a sy >*>dics, then, since 



th. j.rii! rtual velocities holds for any possible dis- 



placement of any one of the bodies, it holds for any possible 



854 In Art. 252 we have proof of the first 



part of t il velocities, by supposiii 



of s to . with that about whirli tin- body was 



an angular displace- 1: wing 



will IK- tin- process, if we suppose the displacement made 

 a straight line passing through the origin, and inclined 

 to the axis at angles who* >n cosines are /, TO, n. 



tance of a y, ) from the or 



is distance make* with the ^iven strai 

 perpendicular from (or, y, ) on the given straight 



.*- '+?; 



oforc p f or r" sin^-a^+^ + i*- (Ix -f niy-f *z)\ 



Suppose the body turned through a small angle 6 round 

 the given lii. - &r, y -f Sy, g + &, be the co-ordinates 



dy which was originally at (x, y, s). 



c r and p ar ired by the displacement, we have, 



(&r)', (o f , (&) in comparison with &r, o>, &, 



- fox + mfy + ties ; 



&r Sv 



fore- -= - --- -.-Xsupposc ...... (1). 



yn rm si xra xwi y ( 



