EFFECT OF VARIOUS PROCESSES. 153 



represented by the notations of that chapter, especially by the 

 index of probability of phase (??). There are therefore 2 n 

 independent variations in the phases which constitute the 

 ensembles considered. This excludes ensembles like the 

 microcanonical, in which, as energy is constant, there are 

 only 2 n 1 independent variations of phase. This seems 

 necessary for the purposes of a general discussion. For 

 although we may imagine a microcanonical ensemble to have 

 a permanent existence when isolated from external influences, 

 the effect of such influences would generally be to destroy the 

 uniformity of energy in the ensemble. Moreover, since the 

 microcanonical ensemble may be regarded as a limiting case of 

 such ensembles as are described in Chapter I, (and that in 

 more than one way, as shown in Chapter X,) the exclusion is 

 rather formal than real, since any properties which belong to 

 the microcanonical ensemble could easily be derived from those 

 of the ensembles of Chapter I, which in a certain sense may 

 be regarded as representing the general case. 



Let us first consider the effect of variation of the external 

 coordinates. We have already had occasion to regard these 

 quantities as variable in the differentiation of certain equations 

 relating to ensembles distributed according to certain laws 

 called canonical or microcanonical. That variation of the 

 external coordinates was, however, only carrying the atten- 

 tion of the mind from an ensemble with certain values of the 

 external coordinates, and distributed in phase according to 

 some general law depending upon those values, to another 

 ensemble with different values of the external coordinates, and 

 with the distribution changed to conform to these new values. 



What we have now to consider is the effect which would 

 actually result in the course of time in an ensemble of systems 

 in which the external coordinates should be varied in any 

 arbitrary manner. Let us suppose, in the first place, that 

 these coordinates are varied abruptly at a given instant, being 

 constant both before and after that instant. By the definition 

 of the external coordinates it appears that this variation does 

 not affect the phase of any system of the ensemble at the time 



