﻿Virial of a Mixture of Ions. 555 



So far no account has been taken of the sign of the ions 

 in the configuration, but since any ion, say the pth nearest 

 ion, is just as likely to be + as — , the probability of any 

 one order of succession in the signs of the m nearest ions 

 counting outwards from A is the same as that of any other 

 order, and is 1/2 W . 



In order to allow of the introduction of the sign of the 

 charge into the statement of the configuration, we shall 

 write the charge on A as q , on A 1 as q x , &c. q p can be 

 afterwards put + q or — q, according as the pth ion is 

 positive or negative. Also let ri p be the distance between 

 A; the ith nearest ion, and A p the pth nearest ion to A . 



The potential energy of the assumed configuration is given 

 by the following scheme : — 



+ yo&A'a + ?i^ r i2j 



+ qo f h/>' d + qiqs/r n + q 2 q z lr 2 to 



+ , 



+ <]oip' r P+Mp/ r ip+ q P -iqpl r P-hp, 



+ qoqm/r m + qiq m jr lm + q 2 q m Jr ftm + + q m -\qmjr m _ lf m . 



which may be written shortly 



E = X X q -^ (9) 



p — l i=0 I'ip 



The virial of the central ion A vuth respect to these m 



ions is 



U = Mi/ r i + M2/ f 2 + MsM+ +< ?oW r 



or 



U= X ^ (10) 



v~\ 'I'v 



Introducing the values of P and E from (8) and (9) into 

 (3) we get for the probability of the given configuration 

 when the inter-ionic forces are taken into account, and the 

 signs of the ions are specified 



] m p-1 q,q. p 2N 4 



P(E)=;- ) „.r»4i»^-v-^.2N. i ,.f rf ,, »*.(U) 



where /• . is written for Ix , . 



