﻿based on Free Electrons. 1081 



groups, viz. 



S 

 for type a 3 , 2S 3 — - 



„ „ 'da% — 2 - 2 (logn + 7-log|j, 



„ „ 6abc, — -^Uogw + 7-log|j, 

 AVe have then 



2 cosec 3 stt/k = 3 < n 3 S 3 + 3«S 2 ( log n + 7 — log - — ) I . . 



. . . (19 a) 



The difference between this formula as written with n and 

 2w is 



2 3 = J{2n 3 T 3 + nT 2 (logn + 7 + log|-|j}, (19 6) 



where T 3 = 2 (2r + l)" 3 , and so 7S 8 = 8T 8 ; 



while 3S 2 = 4T 2 = tt 2 /2. 



In the case of 2 5 it will be enough to write the main term 

 64>i 5 T 5 /7r 5 . This gives for (14 6) the form 



^ 2 |2T 3 + 3n- 2 T 2 ^log e n-^ 7 -log e |-^ [ 



and in numbers u j, (20) 



^ 2 = 3'2521-13-1749n- 2 log 10 n + 5-0738n- 2 ..., 

 N/h = '44127 + -4242b*- 2 - l'45342>2- 4 log 10 n 



+ -86256n" 4 ....^ 



Table III. has been calculated from these formulae. 



§ 14. The formula? of § 11 may be applied when n is not 

 small to find the changes in x and N which result from small 

 additions to the central forces. If we describe these extra 

 forces as a central repulsion on my of amount eV^ai 2 , and a 



Phil. Mag. S. 6. Vol. 44. No. 264. Dec. 1922. 4 A 



