SYSTEMS COMPOSED OF MOLECULES. 203 



experiment. Although the ensemble contains systems having 

 the widest possible variations in respect to the numbers of 

 the particles which they contain, these variations are practi- 

 cally contained within such narrow limits as to be insensible, 

 except for particular values of the constants of the ensemble. 

 This exception corresponds precisely to the case of nature, 

 when certain therm odynamic quantities corresponding to , 

 /ii, /A 2 , etc., which in general determine the separate densities 

 of various components of a body, have certain values which 

 make these densities indeterminate, in other words, when the 

 conditions are such as determine coexistent phases of matter. 

 Except in the case of these particular values, the grand en- 

 semble would not differ to human faculties of perception from 

 a petit ensemble, viz., any one of the petit ensembles which it 

 contains in which j^, j/ 2 , etc., do not sensibly differ from their 

 average values. 



Let us now compare the quantities H and 77, the average 

 values of which (in a grand and a petit ensemble respectively) 

 we have seen to correspond to entropy. Since 



__ 



, \b 



and *= 



(545) 



A part of this difference is due to the fact that H relates to 

 generic phases and 77 to specific. If we write ?7 gen for the 

 index of probability for generic phases in a petit ensemble, 

 we have 



^gen = ?! + ^g [Vl . . . [vfc , (546) 



H - r, = H - ^ + log |vi . . . [v , (547) 



.!^ (548) 



This is the logarithm of the probability of the petit en- 

 semble (v l . . . v h )* If we set 



* See formula (517). 



