122 A PERMANENT DISTRIBUTION IN WHICH 



average value of u in an ensemble in which the whole system 

 is microcanonically distributed in phase, viz., 



(387) 



where fa and V 2 are connected by the equation 



i + 2 = constant = e, (388) 



and u, if given as function of ei , or of ei and e 2 , becomes in 



virtue of the same equation a function of e 2 alone.* 



Thus 



Je = e+ J F! rf F 2 , (389) 



(390) 



This requires a similar relation for canonical averages 



= e ~+ V\ e = e^rje = e~+*V\* . (391) 



Again 



e 2 =e 



SB =e-*f ^V'rfF,. (392) 



de l |e J de l 



F^O 



But if w : > 2, *i vanishes for Fj = 0,f and 



. (393) 



de 



Hence, if n^ > 2, and w 2 > 2, 



d<f> _ dfal _ dfa\ /qq .. 



^e ~ ^ | f ~ de z \f 



* In the applications of the equation (387), we cannot obtain all the results 

 corresponding to those which we have obtained from equation (374), because 

 <t> p is a known function of e p , while fa must be treated as an arbitrary func- 

 tion of j , or nearly so. 



t See Chapter VIII, equations (306) and (316). 



