194 SYSTEMS COMPOSED OF MOLECULES. 



respect to exchange of energy and exchange of particles, with 

 other grand ensembles canonically distributed and having the 

 same values of and of the coefficients p v ^ 2 , etc., when the 

 circumstances are such that exchange of energy and of 

 particles are possible, and when equilibrium would not sub- 

 sist, were it not for equal values of these constants in the two 

 ensembles. 



With respect to the exchange of energy, the case is exactly 

 the same as that of the petit ensembles considered in Chapter 

 IV, and needs no especial discussion. The question of ex- 

 change of particles is to a certain extent analogous, and may 

 be treated in a somewhat similar manner. Let us suppose 

 that we have two grand ensembles canonically distributed 

 with respect to specific phases, with the same value of the 

 modulus and of the coefficients ^ . . . fi h , and let us consider 

 the ensemble of all the systems obtained by combining each 

 system of the first ensemble with each of the second. 



The probability-coefficient of a generic phase in the first 

 ensemble may be expressed by 



e & (509) 



The probability-coefficient of a specific phase will then be 

 expressed by 



(510) 



since each generic phase comprises \v^ . . . [z^ specific phases. 

 In the second ensemble the probability-coefficients of the 

 generic and specific phases will be 



