162 EFFECT OF VARIOUS PROCESSES 



Let us now suppose that we have a certain number of 

 ensembles, E Q , E l , E% , etc., distributed canonically with the 

 respective moduli , O x , @ 2 , etc. By variation of the exter- 

 nal coordinates of the ensemble E Q , let it be brought into 

 connection with E^ , and then let the connection be broken. 

 Let it then be brought into connection with U 2 , and then let 

 that connection be broken. Let this process be continued 

 with respect to the remaining ensembles. We do not make 

 the assumption, as in some cases before, that the work connected 

 with the variation of the external coordinates is a negligible 

 quantity. On the contrary, we wish especially to consider 

 the case in which it is large. In the final state of the ensem- 

 ble EQ , let us suppose that the external coordinates have been 

 brought back to their original values, and that the average 

 energy (e ) is the same as at first. 



In our usual notations, using one and two accents to dis- 

 tinguish original and final values, we get by repeated applica- 

 tions of the principle expressed in (463) 



V + n' + V + etc. > ^ " + i" + ^ 2 " + etc. (474) 

 But by Theorem III of Chapter XI, 



ft" + Z ft 1 + ' (476) 



*" + g > .7 + { (477) 



etc. 



or, since </ = </', 



(479) 



If we write IF for the average work done on the bodies repre- 

 sented by the external coordinates, we have 



