﻿1074 Mr. R. Hargreaves on Atomic Systems 



On introducing the ratio x equations (1) become 



. . . (6 a) 



lnWhich /^-V 1 l-^cos(2r + lWn m 



yW r to{H-^ 2 ~2^cos(2^4-l)7r/n} 3 / 2 - * ■' 



If there is a positive charge at the centre, formulae (6 a) 

 are replaced by 



m 1 &) 2 a 1 3 = e2 {/(~) — i c »— 1|> m 2 a) 2 a 2 3 = € 2 {f(x) — ±c,l + l}. 



'. . . (6/,) 

 When the value of # satisfying f(x) = ^c n is substituted 

 in /l - > J — ic n we have the tabulated number N, while N^ is 



used for the corrected value when m 2 : m x is not neglected. 

 The kinetic energy of orbital motion is given by 



2T = n (m^ 2 + m 2 a 2 2 ) to 2 - ^^ ( 1 + ^ V . (8 a) 



for which it is generally sufficient to write 



2T = nNe 2 /a 1 . (8 6) 



The potential energy U, total energy of orbital motion T, 

 and total angular momentum H are then given by 



E = T + U, 2T + U = 0, 2T = Ha>; . (9a) 

 while 



2TH 2 = miNVe 4 (9 6) 



is a relation into which neither a> nor a enters, written in 

 the form suited to the approximation (8 6). A symmetrical 

 form can be given to (8 a) and (9 6) by using 



M = m L ■+ m 2 , Ma s 2 = m x a 2 + m 2 a 2 



and N s : N^ = Ma/ : m Y a{. 



§ 9. As the numerical work of solution only appears in 

 the tabulated results, it may be of service to show the work 

 for the simplest case n = 2. With a 2 = l, a^ — x the equa- 

 tions are 



m 2 <o 2 = - * c - c - , ?7z 1 o> 2 < r = 



^1 + 0-8)3/2 4' "** w ~ (1 + A' 2 ) 3 ' 2 4/y 2 ' 



