﻿570 Dr. S. R. Milner on the 



By this relation each term may be obtained in succession. 

 As an example the following numbers are abstracted from 

 the tables : — 



/.(8)=/s(7) + /i(7)x*(8) 

 or 38-182 = 26-1216 + 13*4489 x -89676. 



Tabulation of the values of /«(m) is equivalent to deter- 

 mining the absolute probability of a specified arrangement 

 of the ions under a certain restriction, namely, that the m 

 nearest ions contain n — ions. This last restriction might 

 obviously be removed by an additional summation, but it 

 will be more convenient for the calculation of the arithmetical 

 value of the virial to work out the results in terms oi f n {m). 



When we confine our attention to those views of the m 

 nearest ions in which n — ions are contained, the absolute 

 probability of an arrangement in which the positions of the 

 n — ions are unspecified may evidently be taken as 1, the 

 relative probability is as we have seen/ n (?rt), therefore, since 

 the relative probability o£ an arrangement specified by the 

 positions p l ...p n of the — ions is given by ei(pi) ... e«(p n ), 

 it follows that the absolute probability of this arrangement is 



p (ffl) ^i(P,) r ^(^) . . . . (3?) 

 (37) may now be used in place of the expression (27) 



m 

 -AS a-pup 



r(m)=k m e p=i , 

 for the same probability ; it differs from (27) in that all the 

 quantities in it are numerically determinate, whereas (27) 

 contains the unknown k m . We have thus solved the first 

 part^ of our problem, since we can now by (37) and (27) 

 eliminate k m from our expressions whenever we please. 



We can now return to the original problem of determining 

 the average virial on A of the m nearest ions. We have 

 first to integrate expression UP(E), or by (10) and (16) its 

 equivalent 



; *=}m P 4 3 

 2 ^k m e » =1 *=» * 3 d^ sin e.dd^dn 



v— 1 1 v 



. . .depm sin m d0 m rm 2 dr m , 



over all possible values of $, 0, and r. The integrations are 

 carried out exactly as on pp. 558 to 564, and give 



m 



j UP(E) = £ ± w7iu v . hn e l ^ apVP . . (38) 



