﻿576 



Dr. S. R. Milner on th 



curve ; the limit is then obtained by extrapolation to m = co . 

 A practical difficulty comes in due to the fact that the rate 

 at which the curves converge to the limit is extremely slow, 

 but by considering the curves corresponding to two specially 

 chosen arrangements, it is nevertheless possible to obtain a 

 fair approximation to the limit at m = cc. If we plot the 

 curves of \J n (in), taking cases in which m is always equal to 

 2n, we are confining our attention to arrangements in which 

 the numbers of + and — ions surrounding the central ion 

 A are always equal. The virial for any finite number of 

 nearest ions will then always be less than the limiting value 

 for an infinite number, since the ??i + lth ion, which is not 

 included, always tends to be a — one. Again, if we extra- 

 polate from cases in which m=2w — 1, we confine our atten- 

 tion to arrangements in which there are equal numbers of 4- 

 and — ions when A is included, i. e., to arrangements which 

 possess no total charge. In this case it follows from (27) 

 that the ions external to the arrangement will be distributed 

 at random with respect to A , and will on the average have 

 no virial on it. The virial of these arrangements will always 

 be in excess of the limit. 



The following table shows the values of U»(??2)/Wi for 

 7i = -3, in these two sets of cases. The values of f n (m) and 

 g n {m), which correspond to them, are printed in Tables III. 

 &, IV. in thicker type. The first set of values shows a 

 continual increase, and the second a continual decrease with 

 m. In the diagram the values are plotted against m~i as 

 abscissse. 



Table V. 



11. 



m. 



S(m). 



gn{m) _ 

 fn(m) ' 





JJ)i(vi)/wh. 



2 '.'.'".. 



3 



4 



5 



6 



7 



8 



1 



2 



3 



4 



5 



6 



7 



8 



o 



4 

 6 

 8 

 10 

 12 

 14 

 16 



1 



3 



5 



7 



9 



11 



13 



15 



- -45137 

 -•53496 

 — •57583 

 -•60156 

 - -61982 

 -•63373 

 -•64483 

 -•65398 



-1-35412 

 -1-20366 

 -1-14794 

 -1-11615 

 -1-09471 

 -1-07888 

 -1-06652 

 -1-0564S 



•39061 

 •42677 

 •43182 

 •42879 

 •42326 

 •41699 

 •41057 

 •40432 





 •14031 

 •19155 

 •21666 

 •23120 

 •24023 

 •24611 

 •24996 



-•06076 

 -'10819 

 -•14401 

 -•17277 

 -•19656 

 -■21674 

 -•23426 

 -•24966 



-1-35412 



-1-06336 

 -0-95639 



- -89949 



- -86351 



- -83865 



- -82041 



- -80652 



