VICTUAL VELOCITIES. RIGID ft 



must be c<jual in magnitude and must act along the rod in 



is, or may be easily shewn 

 oe then 1* - P 9 we have by (5) 



+ /"(&r cosa + By cos + &' cos 7) - (6). 



o Pacts along the r ;< the product of 



!ar prod- ..-no-, the 



of holds in this case. 



convene of orcm IB trur in this CAAC, but we 



shall not give a separate demonstration of it; the general 

 demonstration of Art. 253 will sufficiently illustrate 

 point. 



If (5) were absolutely tru> , then in the case of a rod, as in 

 that of a single particle, the sum of the prod acts of each force 

 lie projection of the displacement of its point of applica- 

 tion n of the force would be zero, whether the 

 displacement were finite o, 5) instead of 

 being absolutely true is obtained from (3) by neglecting 

 squares and products of the resolved displacement!' < y,. . . 



253. We proceed to establish the truth of the principle in 

 ise of a rigid body. We shall assume that any possible 

 body may be produced, by first making 

 >ody rotate about some axis, and then moving all the 

 particles of the body through equal spaces in para 

 tions. dee Sphrrical Trigonometry, Chapter MIL Suppose, 

 for simjil the axis of s is made to coincide with tin- 



axis about \\liMi tiie body is turned; let be the angle 

 :i the body is turned. co-ordinates of a 



parti' :i were originally x and v will become, if we 



neglect the square and higher powers of 9, x -v0 and y + xd 

 respi co-ordinate z of the panicle remain* un- 



ohanged. 



Let the body be now further displaced, so that each particle 

 moves through a space of which a, b t c are the projections on 



