196 SYSTEMS COMPOSED OF MOLECULES. 



bility-coefficient is evidently zero, as they do not occur in the 

 ensemble. 



Now this third ensemble is in statistical equilibrium, with 

 respect both to specific and generic phases, since the ensembles 

 from which it is formed are so. This statistical equilibrium 

 is not dependent on the equality of the modulus and the co-effi- 

 cients /Aj , . . . fx h in the first and second ensembles. It depends 

 only on the fact that the two original ensembles were separ- 

 ately in statistical equilibrium, and that there is no interaction 

 between them, the combining of the two ensembles to form a 

 third being purely nominal, and involving no physical connec- 

 tion. This independence of the systems, determined physically 

 by forces which prevent particles from passing from one sys- 

 tem to the other, or coming within range of each other's action, 

 is represented mathematically by infinite values of the energy 

 for particles in a space dividing the systems. Such a space 

 may be called a diaphragm. 



If we now suppose that, when we combine the systems of 

 the two original ensembles, the forces are so modified that the 

 energy is nc longer infinite for particles in all the space form- 

 ing the diaphragm, but is diminished in a part of this space, 

 so that it is possible for particles to pass from one system 

 to the other, this will involve a change in the function e ;// 

 which represents the energy of the combined systems, and the 

 equation e" f e f + e ff will no longer hold. Now if the co- 

 efficient of probability in the third ensemble were represented 

 by (513) with this new function e ;// , we should have statistical 

 equilibrium, with respect to generic phases, although not to 

 specific. But this need involve only a trifling change in the 

 distribution of the third ensemble,* a change represented by 

 the addition of comparatively few systems in which the trans- 

 ference of particles is taking place to the immense number 



* It will be observed that, so far as the distribution is concerned, very 

 large and infinite values of e (for certain phases) amount to nearly the same 

 thing, one representing the total and the other the nearly total exclusion 

 of the phases in question. An infinite change, therefore, in the value of e 

 (for certain phases) may represent a vanishing change in the distribution. 



