302 Journal of the Asiatic Society of Bengai. {N.5., XVIII, 

Therefore 
°. See 1 
pe gee of Antes 
1 ze enh? 
27 et 67*e8 t 
= nth? = cinth* ire 
H,,—H,, mc ( Drees DAnret Grte® Gate’ : 
oot.) +s ——_ - 7 Ct Oe: 
h ee: en eh? c'n,*h® ctnht cin,th' 
=e (4-5 1-25 2(— +23) rete. f 
hs Ne ny) ¢ eAt in, «aS 
7 tee | orev. t 
pee | Tce ak aa eractc\ Kebect 
Re (as aap} oh witaz)te ms 
where N is the Rydberg number. 
The corrected Rydberg number N’ therefore 
c 374 1 l 
mt rT, (stax)? 
for the hydrogen lines. 
According to Sommerfeld 
a dt ee aes | 
nd =¥)1 tala i 
It will thus appear that the order of the correction pro- 
posed agrees with that of Sommerfeld’s formula. : There is 
however a difference in sign. If we observe however Paschen’s 
experimental values! for H,, Hg, H. 


y? Hs 
H H 
H H 3 
a B y 
Nn’ | 109678:205 | 109678-164 | 109678°167 | 109678198 | 
it will be noticed that apart from H, the successive numbers 
show an increase and not a decrease and this fact is more 10 
harmony with the negative sign than with the positive sig of 
Sommerfeld’s form which by making AN positive would 
necessitate N decreasing down the series. 
ConcLUSION. 
The extension of the theory of the present paper to a casé 
of f degrees of freedom may be made provided we are able to 
find the f first integrals of the motion of which one is neces 
sarily the integral of energy. If the corresponding positional 
a ee See ee ee hee = Pet saat Ee aan 

1 Ann, d, Phys. vol. 50, 1916, p. 935. 

