ENSEMBLE OF SYSTEMS. 79 



But since identically 



the value of the corresponding expression for any index will 

 be independent of <*) and the formula reduces to 



we have therefore 



etc. 1 



It will be observed that when i/r or e is given as function of 

 O, all averages of the form e^ or (e T) ft are thereby deter- 



* In the case discussed in the preceding foot-notes we get easily 



and 



For the total energy we have in this case 



l h ~ 



x -Tx2 i 

 Ve-J = n' 



ft \ _ 2 



etc. 



