﻿564 



Dr. S. R. Milner on. the 

 Table I. 



p- 



Up. 



p. 



Up. 



1 



1-345120 



9 



0-493155 



2, 



0-902746 



10 



•474890 



3 



•752289 



11. 



•459060 



4 



•668701 



12 



•445150 



5 



•612976 



13 



•432784 



6 



•572111 



14 



•421687 



7 



•540327 



15 



•411647 



8 



•514597 



16 



•402500 







17 



•394114 



We have now reduced the problem to such a form that 

 the probability of a given order of succession of the signs 

 of the m nearest ions, an order which may be specified by 

 showing a particular arrangement of the symbols -f and — 

 in a row, is given by (27). Thus an arrangement of the 

 nearest ions in which the sign of the ^>th nearest ion is given 

 bv the following scheme will have its probability given by 

 (28). 



A, A s 



■A-4 A 5 A 6 A 7 A 8 A 9 A 10 A u 



■^13 -A-14 A 15 



+■' ■ I +-4----H-4-++ - + - -- 



p/^W^ e — *(%-2m 2 +w 3 -2«« 4 -«« 5 -0-« 7 +0+m 9 +2m 10 -3«« u 4-2w 12 ~3« 1 3--2w 14 --m 1s ). # , gg) 



The coefficient of u p in (28), being the excess of like ions 

 inside the pth, is easily written down for each ion by 

 inspection. 



The probability P(S) of the arrangement S, which 

 is characterized by the ions being arranged + and — in 

 regular order, is given by (29). 



A 

 + 



Arrangement S. 



A 1 A 2 A 3 A 4 A 5 A G A 7 A a A 9 A 10 A u A ]2 A 13 A 14 A, 

 -+- + - + -+- + -+ -+- 



P^gw^+^+wi+o+ws+o+^+o+^+o+ttB+o+^+e+^a+o+w^). t / 29 x 



We shall call this the " standard " arrangement. It is 

 also the most probable one, since each term of the exponential 

 is positive, and it is easy to see by trial that any alteration 

 of the order of succession of the signs will diminish its 

 value, or at the most leave it unchanged. 



Now a given arrangement may be specified completely by 



