: i! >. 



>f the motion of the particle, in pas< inir from i: 



to its second, makes an acute angle with that nlon-_r which 



we :r ating the Telocity. Tl, irtual v< 



particle estimated .-don-.: any -iv.n .-trai.irht line is found 

 in magnitude and sign, by multiply <>lutc 



virtual velocity by the cosine of the angle which it- direction 

 makes with the given straight line. 



The virtual moment of a force is the product of its inte 

 by the virtual velocity of its point of applicati* 

 f/,' </<',>< trnof the force. 



\\ e can now enunciate the principle of virtual velocities. 

 If any system of particles is in equilibrium! and 



a displacement of all the particles which is cons: 

 with the conditions to which they are subject, / 

 virtual moments of all the forces is zero, whatever be the dis- 

 placement. And conversely, if this relation hold for all the 

 ial displacements, the syst< 'ibrium. 



' The student will derive from the demonstrations 

 which follow a better notion of the mean i MI: of the principle 

 than from the mere enunciation of it; it is, in fact, necessary 

 to obtain a general view of the whole subi 

 tempting fully to comprehend the preliminary definition 



uients. One remark may be made for the purpose of 

 anticipating a difficulty ; each virtual ?// by dctinition 



an indefinitely null quantity, that is, ultimately vani 

 so that the principle seems to amount only to this, tnlcc each 

 force of the system <>,,,l ///////////// // Ay a <///</ /*?//// ?/7//VA 

 match/ vanishes, then the sum of these products vanishes. 



iple, however, implies more than this .stat. m< 

 shall see. 



The convenient term virtual moment is given by Duhamel ; 



y, however, be useful to enunciate the princijle of nrtuM 

 velocities without introducing this term, and we therefore give 

 the following. 



;)pose a material system held in equilibrium by any 

 forces, and suppose tin" points of application of the f 



1 through very small spaces in a manner consi 

 with the connexion of the parts of the system with each 



