OF AN ENSEMBLE OF SYSTEMS. 43 



We always suppose these external coordinates to have the 

 same values for all systems of any ensemble. In the case of 

 a canonical distribution, i. e., when the index of probability 

 of phase is a linear function of the energy, it is evident that 

 the values of the external coordinates will affect the distribu- 

 tion, since they affect the energy. In the equation 



(105) 



by which ty may be determined, the external coordinates, a x , 

 2 , etc., contained implicitly in e, as well as ,^are to be re- 

 garded as constant in the integrations indicated. The equa- 

 tion indicates that -fy is a function of these constants. If we 

 imagine their values varied, and the ensemble distributed 

 canonically according to their new values, we have by 

 differentiation of the equation ^ 



/ v aii 



f i ./. \ 1 / 







, \ 



(- I ^ + I ) = p 



all 



phases 



all Jf 



-/^ e ~ d Pi d v- ~ ete -> ( 106 ) 



phases 

 t 



or, multiplying by e, and setting 



-^ = ^ - = ^ etc -> 



all 



|d = ^ f. . .f 



ee 



phases 







i e dp l . . . dq n 



phases 



r r 



i I . . . 



phases 



r * ( fcf 



2 J ...JA 2 e & dp l ...dq n + etc. (107) 



