251 
1921-22.] Quantum Theory of Secondary Spectra. 
Reverting to the case of two centres of force, we shall simplify 
work by considering the case in which 
/^i = /X 2 = ft and K = 0 , 
Equations (3) become 
I h = ^mna? f ^ ^ t ^ dcf) , 
1 Jo (l-eV) 
= 4=77i7ia^{l - e2) / v ^ d<^ , 
JO (1-eV) 
where s — sin (p and c — cos <p. 
Let 
— - r-/2 s^l - ifW , ^ 
^ Jo 1-e^ + e‘^s- 
= ^ud?l‘ 
Jo 
W2 c2(l _ 
1 _ e‘2 + e%2 
where 
( 4 ) 
I + (l 
1 (l-/cV)* 
+ e"S‘ 
{s2 + (l_e2)c2}rf,^, 
, I + ( 1 - )J = IP' ( 1 _ &V) V?,^ = 1 E (y A;). 
(5) . 
since 
I + J 
1 
=-[ 
// L 
k'Jo (1 — e^) + eV 
1 /V2 (l_/,2g2)i 
7V1 ^ ■> kWv --- 
A; ( 1 — e^)Jo 1 — ld&7i'‘v s- 1 
k‘^c7dv mhi 
JO 1 — k‘^c7i^v siihi, 
1 
//(I - eh 
1 
E + 
T7' V tt/7^ \ 
K — : — I4(L5 
I + J = 
7d(l — e^)L S7ivdnv 
j CTl 'D 
/d(l — e2)[ S7ivdnv 
n(K, v) = KE(Q - t;E = KZQ) . 
Equations (4) and (5) give 
( 6 ) . 
( 7 ) . 
A;2 
E-K+— ^^KZ(v) 
S7l V d7l V 
{ 71 ^ + 7i^)h = 4?72?7a2[j + (1 - e^)J] 
r 
I (n-^ + 772 )/i ^ 47?777a2 — , from (4) 
i 77j^/7 = i77ina^ I . 
our 
