84 AVERAGE VALUES IN A CANONICAL 



du _du uty-e) udif, 

 d~d -- & + d' 



Setting u = 1 in this equation, we get 



d\f/ _ \i/ 

 d~ 



and substituting this value, we have 



du du ue ue 





If we differentiate equation (250) with respect to a (which 

 may represent any of the external coordinates), and write A 



for the force -^ , we get 



__ ail t *. 



du r r( du u dif/ u . \ 

 3-= /.../V-5- + ^^-+7 v ^) 

 da J J \da da / 



da 



phases 



du du 

 or = 



Setting w = 1 hi this equation, we get 



Substituting this value, we have 



du au uA uA 



du du 



or - r -- r = ^2-uI=(u-u)(A-2). (255) 



da aa 



Repeated applications of the principles expressed by equa- 

 tions (252) and (255) are perhaps best made in the particular 

 cases. Yet we may write (252) in this form 



