CAB* OP A i.C. :;J7 



ilarn be drawn from the new 

 directions of the force* acting at 

 r j>sition8 of equilibrium. tance be- 



tween the foot of any perpendicular and the * 



corresponding force, if called th< 

 tual vcl<>. that force, at 



atedjpofi nerpendicular 



fall* on the Hide of t! toward* wb torcc acta 



the iirincile ia thi< 



algeb, >he product of each force of the svtiem 



and the corretpondinq virtual velocity vanishes. And con- 



Before we proceed to a general demon 



caaea, that of a particle, and that of 

 a rigid rod acted on by forces at it* ends. 



250. Suppose that forces act on a single particle and 



t in equilibrium. Let P } , /*,, ... denote the forces; 



4 which their ii t ions respectively make 



osa-0. 



If . in of this equation be multiplied by the arbi- 



trary qua aye Z/V cos a = 0. out r cos a, 



. measured along the fixed line, on 



of the force 1\\ a similar meaning may be 



assigned to r cos o t , r cos a, , . . . Also r may be considered as 



the distance of the first p<> the particle from a second 



position arbitrarily chosen, and therefore, when r is indefi- 



-hed, r cos fl^, r cos a t , ...become the virtu:. 



. Hence, the 

 .-Ms in this can. 



Conversely. oaa = for all directions of displace- 



.3 a = for all directions, and the parti 

 in equilibrium unl( r the action of the given forces. 



case, we observe that thctical displacement 



of the particle may be of any magnitude we please, and that 

 the sum -i the products of each force into the projection of 

 the di-iplaceineiit on its dirccti'-u is n.-t milv t<:ViWi.v'v. l-u: 



