\ 



\ 



56 AVERAGES IN A CANONICAL ENSEMBLE. 



/ ^p-fp 

 je & **d Pl ...dp n , (144) 



or again 



r r^=^ i 



I . . . / e < Ar^Ti 4i ( 145 ) 



for the fractional part of the systems of any given configura- 

 tion which lie within given limits of velocity. 



When systems are distributed in velocity according to these 

 formulae, i. e., when the distribution in velocity is like that in 

 an ensemble which is canonically distributed in phase, we 

 shall say that they are canonically distributed in velocity. 



The fractional part of the whole ensemble which falls 

 within any given limits of phase, which we have before 

 expressed in the form 



. dp n dqi . . . dq n , (146) 



may also be expressed in the form 



. . dq n dq l . . . dq n . (147) 



