SYSTEMS COMPOSED OF MOLECULES. 195 



The probability-coefficient of a generic phase in the third 

 ensemble, which consists of systems obtained by regarding 

 each system of the first ensemble combined with each of the 

 second as forming a system, will be the product of the proba- 

 bility-coefficients of the generic phases of the systems com- 

 bined, and will therefore be represented by the formula 



e (513) 



where ft"' = ft' + ft", e'" = e' + e", vi'" = vj + z>i", etc. It 

 will be observed that i//", etc., represent the numbers of 

 particles of the various kinds in the third ensemble, and e'" 

 its energy ; also that ft'" is a constant. The third ensemble 

 is therefore canonically distributed with respect to generic 

 phases. 



If all the systems in the same generic phase in the third 

 ensemble were equably distributed among the zV" | vjj" spe- 



cific phases which are comprised in the generic phase, the prob- 

 ability-coefficient of a specific phase would be 



In fact, however, the probability-coefficient of any specific 

 phase which occurs in the third ensemble is 



which we get by multiplying the probability-coefficients of 

 specific phases in the first and second ensembles. The differ- 

 ence between the formulae (514) and (515) is due to the fact 

 that the generic phases to which (513) relates include not 

 only the specific phases occurring in the third ensemble and 

 having the probability-coefficient (515), but also all the 

 specifier phases obtained from these by interchange of similar 

 particles between two combined systems. Of these the proba- 



