I54 STATICS. [249. 



Thus the tension of an inelastic thread or rod being com- 

 posed of two equal and opposite forces does no work in any 

 infinitesimal displacement ; the work of the reaction of a fixed 

 point or fixed axis is zero, because the point of application 

 cannot move in the direction of the force ; the normal reaction 

 of a surface along which a body is constrained to slide does no 

 work, because any possible displacement is at right angles to 

 the force. If, however, the surface be rough, the friction will 

 in general do work. 



249. A full discussion of the principle of virtual work for 

 the most general case cannot be given in this place. It must 

 suffice to state it and to illustrate its application in a few 

 special cases. 



The necessary and sufficient condition of equilibrium of a 

 system of bodies the connections between which can be expressed 

 by forces is this, that the sum of the virtual works of all the 

 forces must vanish for all displacements consistent with the 

 geometrical conditions to which the system may be subject. 



The internal reactions between the different parts of the 

 system, with the exception of friction and elasticity, will in 

 general not enter into the equation of virtual work. Such 

 reactions can therefore be neglected while friction and elastic 

 tensions must be included among the forces acting on the 

 system. 



250. Let P be one of the forces, %p the projection on its 

 direction of the virtual displacement of its point of application ; 

 then the principle of virtual work requires that 



If X, Y, Z be the rectangular components of P, and x, y, z 

 the co-ordinates of its point of application, the same condition 

 can be expressed in the form : 



