SYSTEMS COMPOSED OF MOLECULES. 189 



ity of a generic phase is the sum of the probability-coefficients 

 of the specific phases which it represents. When these are 

 equal among themselves, the probability-coefficient of the gen- 

 eric phase is equal to that of the specific phase multiplied by 

 [z/i 1 1> 2 . . . \vg It is also evident that statistical equilibrium 

 may subsist with respect to generic phases without statistical 

 equilibrium with respect to specific phases, but not vice versa. 



Similar questions arise where one particle is capable of 

 several equivalent positions. Does the change from one of 

 these positions to another change the phase? It would be 

 most natural and logical to make it affect the specific phase, 

 but not the generic. The number of specific phases contained 

 in a generic phase would then be \v /e/ 1 . . . |z^ /c h \ where 

 K V . . . K h denote the numbers of equivalent positions belong- 

 ing to the several kinds of particles. The case in which a K is 

 infinite would then require especial attention. It does not 

 appear that the resulting complications in the formulae would 

 be compensated by any real advantage. The reason of this is 

 that in problems of real interest equivalent positions of a 

 particle will always be equally probable. In this respect, 

 equivalent positions of the same particle are entirely unlike 

 the [^different ways in which v particles may be distributed 

 in v different positions. Let it therefore be understood that 

 in spite of the physical equivalence of different positions of 

 the same particle they are to be considered as constituting a 

 difference of generic phase as well as of specific. The number 

 of specific phases contained in a generic phase is therefore 

 always given by the product \v^\v^ . [iy 



Instead of considering, as in the preceding chapters, en- 

 sembles of systems differing only in phase, we shall now 

 suppose that the systems constituting an ensemble are com- 

 posed of particles of various kinds, and that they differ not 

 only in phase but also in the numbers of these particles which 

 they contain. The external coordinates of all the systems in 

 the ensemble are supposed, as heretofore, to have the same 

 value, and when they vary, to vary together. For distinction, 

 we may call such an ensemble a grand ensemble, and one in 



