226 Proceedings of the Koyal Society of Edinburgh. [Sess. 
Substituting these values in 2 ‘20 we obtain 
2*38 
x -t' k 
+ (E,- w+ .to>, + xg 
= i-wN 
^2«/2 ' ^1^2 a i a 2 
[(«,- 
\ h/i ' h\h<i ~ a i a s 
a 2 .. 0 2 ~ 
Vi + *2/2- 
x. 
2*39 
2-40 
Let 
X' = PX, then 
P = -^-7rN ^Ej - /q e + e 
l x 2 { l / 2 \ j 1^2 ■?2 a l _j_ /^l^ 2 
^ 2/2 1^2 — a l a 2 bjh 
+ ( E 2 - ft,e + +W? 
h/l ' ^1^2 _ a i a 2 
In the same way as in I (6) we can show that 
H' \ _ p 
^ + 2 
molecule ' 
(b) From the form of equation 2 '40 it is seen that the additive law does 
not hold exactly when the contribution due to interaction between the 
atoms is considered. In order to examine the contribution due to electrical 
interaction, let 
P(molecule) = P x + P 2 + P 12 , 
where P x = contribution to P due to atom 1 alone. 
P 2 = contribution to P due to atom 2 alone. 
P 12 = contribution to P due to electrical action between atoms 1 and 2. 
Then we find 
2-41 
12 
= f p _ .7 2^1 . e Vi 
V 1 h/i ^ 2 / 2 ^ 1^2 ~ a i a 2 h/i 
. f p _ e l x 2 , —Jjh 2 e 2 /x 2 
' 2 ^ 2/2 h/i ^ l i^2 ~ a i a 2 ^ 2/2 
p _ fyh V 1 _ e2 /h 
/ 1^1 h / 1 
- E 
e f x 2 s y 2 _ e2 / x 2 
J 2 ^ 2 y 2 
where f\=f v g\=g v h\ = h v etc., when ^ = 0. 
(c) Sir J. J. Thomson in his paper, PM. Mag., 1906, assuming the 
interaction between the atoms to be that which comes into play between 
the two spheres of positive electricity, concluded that the contribution to 
