126 A PERMANENT DISTRIBUTION IN WHICH 



Jr=o 



(*-O, 



j . v ' - "j~Q> 



F=0 ^ / 



Differentiating (405), we get 



=00 (f-O 2 (*~O 2 



de-* rdcj> rf+* _ / - ~~rf~ +<t> de a \ 



T = I -- e de[e } 



^ da^ J dc^ \ ddij 



where e a denotes the least value of e consistent with the exter- 

 nal coordinates. The last term in this equation represents the 

 part of de~ c jda^ which is due to the variation of the lower 

 limit of the integral. It is evident that the expression in the 

 brackets will vanish at the upper limit. At the lower limit, 

 at which e p = 0, and e q has the least value consistent with the 

 external coordinates, the average sign on ^] 6 is superfluous, 

 as there is but one value of A 1 which is represented by 

 de a /da r Exceptions may indeed occur for particular values 

 of the external coordinates, at which dejda^ receive a finite 

 increment, and the formula becomes illusory. Such particular 

 values we may for the moment leave out of account. The 

 last term of (408) is therefore equal to the first term of the 

 second member of (407). (We may observe that both vanish 

 when n > 2 on account of the factor e$.) 

 We have therefore from these equations 



F=0 



or 



That is : the average value in the ensemble of the quantity 

 represented by the principal parenthesis is zero. This must 



