224 
Proceedings of the Royal Society of Edinburgh. [Sess. 
We shall determine the nature of the functions <p v (p 2 , <p 12 and <p 21 later, 
but in order to allow of the solution of our equations, we shall make the 
assumptions implicit in the equations 
2-07 
am r-i 
2 (fr - » 2 )02I Pd = X 
2-08 
X £ r r) — (£ r ^1)5 
where and \fr 2 are functions of the distance between the centres of the 
two atoms. 
Let p be the frequency of the electro-magnetic field of force. 
Our equations now become 
2-09 
2-10 
211 
242 
2-13 
2:14 
2*15 
— XE x h 2 /(^i ~ ^’) 0 i( a i ^2)3 
] 
— M^p 2 ^ = XL 2 — (*^2 £ »') — 0 2(^2 ^1)3 
1 
Mi Mi Mi 
= — X/x 1 e — ^ (£ r — aq) + \f / 1 (£?• — a? 2 ) 
- i - x /x 2 e - (£V “ *2) + 02^ (& “ *1) 
where - 
Let 
, 4 
h = 3^^ 
, 4 
*2 = 3 7r P2 e * 
4 #*1 
4 
% = 3 7r f ) 2 e 2^ 
?-?* 
1! ^ 
ir=2r... 
Equations 2’09, 2*10, 2*11, and 2*12 now become 
2-16 
2-17 
248 
(<£i + h/h “ M iP 2 K - cf > lX 2 - ^ = XE r 
(02 "h ^2^2 — 02*^1 ~ Vi ~ XE2* 
O_0i_ 
V ^ ^ / 
2/i h/^l^l "h — /i]X^6 
