﻿798 Dr. W. Wilson on the Quantum- Theory 



constant, and also to equation (4). We easily obtain, by the 

 usual variational method, 



l+l0g/p<rr,_. + PEpor... +7 = 



or f P ar... =Ae~ f3E P°r... .... (9) 



The value of A is determined by equation (4). The 



quantity j3 can be shown to be equal to ps, where T is the 



absolute temperature of the collection of systems. From 

 (8) and (9) we find 



A=-J&Nt!t. . . Ae~P Ep(XT -'- (log A-/3E p<rr ) 







or rf>=-£Nloff A + ££Nitt. . .AE p<rr . r^ r - 

 r ooo r ■ 



and therefore by (5) and (9) 



0=-J&NlogA+Jfe/8E (10) 



On differentiating with respect to /S we get 



d$ 7Vr «71offA 7T . 7 _rfE /11N 



J =s -*N-^- + ftB + ^, . . ( 11) 



and since 



OO OO 00, OT -, 



i=Ans... e -^v... 



ooo 

 we have 



= ^4_Attt...E,„...^V... 



# A ooo p 



</ log A E 

 or ~aW = N' 



Substituting this in equation (11) we see that 



dp- 1 " 1 * dp 



or -^ = *£. 



d4 

 dE 



Therefore k& = rp . The law of distribution of the systems 



