_—— 
OE 
A.—_MATHEMATICS AND PHYSICS. 4) 
The diagram shown in Fig. 1 represents an instantaneous aspect of 
the orbits of the different stationary states, and the designations n, give 
the values of the quantum numbers characterising the different orbits. 
According to this treatment each of the numbers of the Balmer series 
eo i a) 
ee KF m 
should consist of a doublet, and each of the components of these 
doublets should possess a fine structure. Calculations made by 
Sommerfeld showed that the frequency difference for these doublets 
should be constant over the whole of the Balmer series, and should be 
equal to 0.36cm.-". 
FIG. 5.—Rosette. 
As the theory applies equally well to the corresponding series in the 
spectrum of positively charged helium, the doublets of this series were 
investigated by Paschen, and were found to have separations that led 
to a value of 0.3645+0.0045 for the frequency difference of the doublets 
of the hydrogen Balmer series. 
Since the publication of Paschen’s work on the helium doublets a 
number of investigators” have attempted, from measurements on the 
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