CHAPTER XIII. 



EFFECT OF VARIOUS PROCESSES ON AN ENSEMBLE OF 



SYSTEMS. 



IN the last chapter and in Chapter I we have considered the 

 changes which take place in the course of time in an ensemble 

 of isolated systems. Let us now proceed to consider the 

 changes which will take place in an ensemble of systems under 

 external influences. These external influences will be of two 

 kinds, the variation of the coordinates which we have called 

 external, and the action of other ensembles of systems. The 

 essential difference of the two kinds of influence consists in 

 this, that the bodies to which the external coordinates relate 

 are not distributed in phase, while in the case of interaction 

 of the systems of two ensembles, we have to regard the fact 

 that both are distributed in phase. To find the effect pro- 

 duced on the ensemble with which we are principally con- 

 cerned, we have therefore to consider single values of what 

 we have called external coordinates, but an infinity of values 

 of the internal coordinates of any other ensemble with which 

 there is interaction. 



Or, to regard the subject from another point of view, 

 the action between an unspecified system of an ensemble and 

 the bodies represented by the external coordinates, is the 

 action between a system imperfectly determined with respect 

 to phase and one which is perfectly determined ; while the 

 interaction between two unspecified systems belonging to 

 different ensembles is the action between two systems both of 

 which are imperfectly determined with respect to phase.* 



We shall suppose the ensembles which we consider to be 

 distributed in phase in the manner described in Chapter I, and 



* In the development of the subject, we shall find that this distinction 

 corresponds to the distinction in thermodynamics between mechanical and 

 thermal action. 



