﻿Virial of a Mixture of Ions. 

 Table IV. gjm) [/i=-3]. 



5 < ;> 



w. 



#i(™)- 



ffzM- 



ffs( m )- 



ffd m ): 



ffsfa)' 



9l m )> 



g : (m). 



M m )- 



... 



1 ... 



2 



•o 



+'34428 



— -15046 















3 !" 



4- -72749 



4- 19382 



- -27560 













4 ... 



1-10297 



+1*07649 



- -23572 



- -37267 











5 ... 



14589 



2-4229 



+ '84078 



- -80737 



- -42358 









... 



1-7904 



4-1390 



+3*5107 



- -30557 



- 1-5800 



- -43797 







7 ... 



2 0981 



6-1352 



8-1149 



+ 3*2051 



- 2-5000 



- 22796 



- -42305 





8 ... 



2-3830 



8-3352 



14803 



+11*8576 



4- '0045 



- 50713 



- 2-8553 



- -3^8729 



9 ... 



2 6466 



10-6760 



23-581 



27-793 



+ 11*922 



- 7-2200 



- 9-4998 



- 3-2521 



10 ... 





13-1065 



34-355 



52863 



41*073 



+ 30094 



-19-404 



-13540 



11 ... 







46-906 



88-508 



97-022 



+44*142 



-20-879 



-30-382 



12 .. 









135-71 



189-93 



144*916 



+18718 



-05-580 



13 ... 











329-82 



343-80 



+163*64 



—00-309 



14 ... 













087-39 



518*48 



4-89 981 



15 ... 















1233-45 



+608*46 



10 ... 

















1875*50 



Now from equation (43), when tables of f n (rn) and g n {m) 

 have been calculated for a given value of h, we can deter- 

 mine for that value of h the average virial on A for all the 

 possible arrangements of any finite number m of nearest 

 ions which contain among them a given number n of negative 

 ions. The result is of course a function of m, n, and h. The 

 complete average virial of all the ions on A would be theo- 

 retically obtained by proceeding to the limits in which 

 m = co , and n is unspecified. (43) would then become a 

 function of h only, of the form 



\J = wh(f)(Ji), 



where <j)(li) is the value of the expression in the brackets 

 of (43) when m = », and n is unspecified. To satisfy the 

 conditions with regard to n theoretically requires an addi- 

 tional summation over all the possible values of n, but 

 practically the necessity for this is removed by observing 

 that as m becomes infinite, n must tend indefinitely towards 

 the value ra/2, for the probability of arrangements in which 

 this condition does not hold becomes indefinitely small. I 

 have not been able to find an accurate algebraical expression* 

 for the limit of (43) when m=o© , but an approximate arith- 

 metical value can be obtained if we take n differing from 

 mj2 by any finite number, and determine the virial for 

 successively increasing values of m and plot the results on a 



* It may be shown that, as an approximation, and when h is very small, 



