198 SYSTEMS COMPOSED OF MOLECULES. 





phases 



or . (517) 



[vi . . . [1/5 



This may be called the probability of the petit ensemble 

 0>i, ... v h ). The sum of all such probabilities is evidently 

 unity. That is, 



(518) 



which agrees with (506). 



The average value in the grand ensemble of any quantity 

 u, is given by the formula 





phases 



If w is a function of i/ x , . . . i/ A alone, i. e., if it has the same 

 value in all systems of any same petit ensemble, the formula 

 reduces to 



8 ue 



= X "' 



Again, if we write ^ gr and an( i w] petit to distinguish averages in 

 the grand and petit ensembles, we shall have 



In this chapter, in which we are treating of grand en- 

 sembles, u will always denote the average for a grand en- 

 semble. In the preceding chapters, u has always denoted 

 the average for a petit ensemble. 



