Structure of the Atom. 245 







an—l Qk sar 1 
Tr= > cos—— a 
1 7 3 sw 
on 
Zé 
Sw 
+ Se Qhsar ase db 
a > 
1 | eS 2 
sin” —= 
n 
for we have 
Dy) 
o e 
fg =(G:;+T1,)— NeSG@ie—se) 
( t) Su”? ( : ) oa 
9 
a am 
Case of two ber b 
When n=2 we have 
2 e” e 
1 2s? Nat =: oe 
1, = Sa?’ M,=0, di Sq®? 0 8a?’ 
2¢e? e e 
a = OM =O 2 NS ey Pee Se 
1 8 ae 1 3 1 8 a? 1 Sa? 
Hence for vibrations in the plane of the orbit we have, 
when k=0, 
: G = — mq) (— mq?) =4m’e’@? : 
the roots of this equation are 
3 Gras 4 ey aaa ae 
g—0; : 4 ma? 
When k=1, the frequency equation is 
oS —s ng?) =4in*w"¢7’; 
the roots of this equation are 


2 
Lo es z ve" 
4 ma? 7 mb? 

g= @o+ 
and 
1 a Jz 
j= =—-W + ——s —_— —_s 
a 4 ma? ne rea mb® 
the second set of values only differing in sign trom the first. 
