PHENOMENA RELATING TO THE SPECTRA OF HYDROGEN AND HELIUM. 263 
very nearly coincident with the Balmer series, and this leads to separations in wave 
number which are not constant. The values for H a and are respectively 
= 0'248, Sn 2 = 0'218, and the corresponding separations in wave-length become 
<W = 0T05, S\ 2 = 0-054 A.U. 
These are nearer to Michelson’s estimate. It is just possible, therefore, that the 
presence of these two series with different intensities under different conditions may 
be the cause of the discrepancies which have been found in the separation of H a . 
We do not at present pursue the subject beyond this conclusion, but it may be stated 
that such a view could give an account of the spectrum of Hydrogen, as at present 
known, which is in accord with the series relations known among other elements. 
The possibility of this new interpretation, in addition to such interpretations as that 
given by Fowler, only serves to emphasise the need for an examination of the 
structure of the Balmer lines, which alone can be decisive. Another fundamental 
question with an intimate relation to the preceding remarks is the value of the 
Rydberg constant N for Hydrogen. The careful reduction of this value by Curtis* 
depends ultimately on an accurate determination of the optical “centre of gravity” 
of the leading Balmer lines, and his formula is not applicable to the individual 
components. If the separations of H a and H^ were very different, this formula and 
its contained value of N would cease to represent the series for any individual 
components, or even to give a series lying uniformly between two component series, 
and the value of N would need revision. In view of the theoretical importance 
which the exact value of N for Hydrogen and for Helium has recently assumed, it 
is necessary that the true value should not remain a matter of doubt, and only a 
precise determination of the separations can decide the question. If for example, 
the separation in H^ were found to be of the same order as that of a Principal series, 
a very important correction would be necessary in the observed wave-length of the 
optical centre of H^ which might change N very appreciably. This, in fact, as is 
shown by the experiments to be described later, actually occurs. 
(XIII.) Theoretical Considerations on the Basis of the Quantum Theory. 
Sommerfeld* has recently published a remarkable investigation on the fine 
structure of the lines of the Balmer series. This is based on Bohr’s theory of the 
origin of this series, and it represents the only manner in which this theory at present 
can be applied in order to account for the existence of structure. On the view that 
the Hydrogen atom consists of one electron in orbital motion—its path being circular 
or elliptical—about a positively charged nucleus, with steady states characterised by 
discrete values of the angular momentum, the quantum theory requires the emission 
* Luc. at. 
t ‘Sitz. der K. Bayr. Akad., Miinchen,’ Jahrgang, 1916. 
2 O 2 
