﻿5G6 



Dr. S. R. Milner on the 



refer to these two ions in the expression (27) for the 

 probability of the arrangement, as is done in the following 

 table : — 





Before interchange. 



After. 





JLp(=Bi) 



Ap+i. 



p+1 



+ 



p+1 



i 



p-i + 1 



+(p-2i+l) 



A,. 



A p +i(=Bi). 



Position of ions 



V 



V 



i-l 



p-i+1 



-(P-21+2) 



V 



+ 



P 



i-l 

 p-i+J 



+ [p~2i+2) 



P + l 



P+l 



i-l 



p-i+2 



-(p-2i+3)\ 



Sign 



Number of ions " inside " 

 (including Ao^ 



Number of — ions " inside " 



+ » 



"Excess" of like ions "in- 

 side " = coef. a p or ap+i. 



Now interchange the two ions B t and A p+i , and we get 

 the values for a p and a p+1 , shown in the last two columns. 

 It is easily seen that this interchange will not affect any of 

 the coefficients a other than these two in the expression for 

 the probabilitj T , so that w r e can include them all in a single 

 constant 0, for the purposes of the present argument, and 

 write before the interchange 



and after it 



V( Pl ...^+l...^) = C*"^ + ^" a ' f ^" ( ^" a+ ^"' + - l] . 



The relative probability of these two arrangements is given 



by 



P(p! ...p+l .../>„) _-2k(p-2i+2)(u P -tt P+ i) (m 



Since 



r<» P T( P ) 



equation (30) may be written 



'p+\ 



Y(p l ...p...p n ) 



If pi is greater than 2i — 1. put down the values which this 



