550 NOTES ON STATICS. 



where 8pl is the projection of BJJ.^ on the direction of P^ But if 

 5(Ti denote the projection oi A-fi-^ on the direction of P^, we have 



^(r ^ ^jo + Sp\ 

 Therefore from (1) and (2) we have 



S (P Sa) — 0, 

 the general equation which expresses the principle. 



17. When there is a system of bodies at rest under the forces 

 (jPi, P2, ■••■), (Qi, Q2, •••■)} &c, and the mutual actions between 

 the bodies, then supposing the whole system as stich to receive the 

 most general infinitesimal displacement, it follows that 



S(P^p) + S(Qog) + ==0, 



in which equation the virtual moments of the mutual actions betweeB 

 the bodies have disappeared. 



18. If one body only of the system is displaced, then 



S (P Sp) = 

 in which equation the virtual moments of the various reactions of the 

 other bodies on it will appear. 



19. If two bodies only be displaced around and along the sam^ 



-line, then 



S (P Sp) + S {Q 5q) = 0, 



in which equation the virtual moments of the mutual actions of the 

 two bodies only have disappeared, 



20. If all the bodies receive displacements around and along dif- 

 ferent lines, the virtual moments of the mutual actions appear in each 

 of the equations 



S (P ^jo) = 0, S (Q Sq) = 0, d:c,, 

 -and also in 



2{PSp) + 2iQSq)^ ....,, ^0. 



