THE QUANTUM THEORY. 477 
close quartette, each member of H, of a close quintette, etc. He has shown, 
moreover, that his theory lends itself to the precise calculation of the intensities of 
these constituents of the members of the doublets. Sommerfeld has found, too, that, 
theoretically, the magnitude of the doublet separation should be constant for all members 
of the Balmer series, and equal to 0.365 cm.~!. In the case of H, and Hg and of H,, 
the calculated distribution and intensities of the fine structural components is such 
that in actual determinations of the doublet separations values less than 0.365 cm.~! 
should be obtained. For Hz, and the higher members of the series, effects connected 
with the fine structure of the components of the doublets should be less in evidence. 
It follows, therefore, that in proceeding from H, to the higher members of the 
Balmer series we should expect on the basis of Sommerfeld’s theory to obtain for the 
doublet separations values that rapidly increased up to 0.365 em.~! for Hs and then 
remain constant for the remainder of the series. A direct test of Sommerfeld’s theory 
through an examination of the structure of the doublets of the Balmer series of 
hydrogen is necessarily attended with considerable difficulty. With atoms so light as 
those of hydrogen the Doppler effect arising from molecular thermal agitation is 
considerable at ordinary temperatures. As a result the members of the doublets cannot 
ordinarily be obtained as sharp lines, but as broad and more or less diffuse bands. 
This diffuseness is, however, enhanced by the Stark effect which always exists to a 
greater or less extent when the emission of radiation is brought about by electrical 
stimulation. What has been taken to be a remarkable confirmation of the validity 
of Sommerfeld’s theory has been obtained by Paschen through a study of the structure 
of spectral lines belonging to serie: originating in the Helium univalent ion. With 
this element the Doppler effect is less marked than with hydrogen, and although the 
nuclear electric charge for Helium atoms is twice as great as that for atoms of hydrogen 
the lines of the spectrum of Helium are less influenced than those of hydrogen by the 
Stark effect, and on that account are sharper. 
In summing up the results of Paschen’s observations, Sommerfeld has reached the 
conclusion that, qualitatively and quantitatively, they constitute a definite and strong 
confirmation of his theory. A further confirmation is found in the fact that the 
series of the Rontgen spectra of the elements consists of doublets with a constant 
separation between the components of approximately 0.365 cm,—!. 
In discussing Sommerfeld’s theory and its supposed confirmation by Paschen, 
Stark has pointed out that a vital characteristic of the theory lies in its quantitative 
features. He has drawn attention in particular to Paschen’s observations on the 
Helium line A = 4686 A. U., and has emphasised the latter’s failure to find three 
components whose presence was demanded by the theory, and to his observation of a 
component whose presence was not predicted by it. Stark also makes a point of the 
fact that the observed relative intensities of the components of A = 4686 A. U. do not 
agree with the values calculated by Sommerfeld. Moreover, he lays particular stress 
on the fact that while Sommerfeld’s theory indicates that the doublet separations in the 
Balmer series of the hydrogen spectrum should gradually increase in passing from 
H, to Hy, the results of Gehrcke and Lau taken as they stand show doublet separations 
gradually decreasing in magnitude as we pass from the first to the fourth member of 
the series. 
From the above it will be seen that while strong confirmation of Sommerfeld’s 
theory has been obtained from Paschen’s investigation of the structure of a number 
of wave-lengths in the spectrum of Helium, and from an important characteristic of 
the L. series in the Réntgen spectra of the elements it is highly desirable to have the 
validity of the theory tested directly by making accurate determinations of the doublet 
separations of as many as possible of the members of the Balmer series of hydrogen. 
In some experiments made at Toronto, measurements were made of the separations 
of the doublets H., Hg, H,, and Hs. 
In determining the separation of the components of the different wave-lengths 
the plates were measured up with a Hilger photo measuring micrometer, and readings 
were taken with it at the edges as well as at the centres of the interference bands. 
The mean values of the separation of the components of the four doublets Ha, Hg, 
H,, and Hz, taken from centre to centre are given in the Table below. The results 
of Merton and of Gehrcke and Lau are also given in the table. It will be seen that the 
separation gradually decreased from 0.154 A.U. for H,, to 0.049 A.U. for Hy, while 
the corresponding frequency differences dropped from 0.36 cm.~! to 0.29 em.—!. 
