ENSEMBLE OF SYSTEMS. 71 



= 



Combining this with (191), 



In precisely the same way, from the equation 



, 

 ^...^ n , (199) 



(200) 



config. 



we may obtain 



In the same way also, if we confine ourselves to a particular 

 configuration, from the equation 



/.all r ^ 1 



= // P e Ap dpi . . . dp M (201) 



J J 



we obtain 



r J 



veloc. 



which by (187) reduces to 



?=(!n+Jn). (203) 



Since this value is independent of the configuration, we see 

 that the average square of the kinetic energy for every configu- 

 ration is the same, and therefore the same as for the whole 

 ensemble. Hence e^ may be interpreted as the average either 

 for any particular configuration, or for the whole ensemble. 

 It will be observed that the value of this quantity is deter- 

 mined entirely by the modulus and the number of degrees of 

 freedom of the system, and is in other respects independent of 

 the nature of the system. 



Of especial importance are the anomalies of the energies, or 

 their deviations from their average values. The average value 



