A.—MATHEMATICS AND PHYSICS. 57 
to involve not only the core of the atom but the two outer valency 
electrons as well. It is shown when the theory is extended to take 
account of an external magnetic field in addition to the internal one, 
that the Zeeman separations of the magnetic components of doublet 
and triplet lines are in exact agreement with the laws formulated by 
Preston and Runge. 
When the external magnetic field is high compared with the internal 
one, the theory shows that for doublets and triplets the final result is 
a normal Zeeman triplet in complete accordance with the observations 
of Paschen and Back.*® 
To illustrate the validity of the theory Heisenberg used his formule 
to evaluate the magnitude of the internal magnetic field of the atoms 
of lithium, and found that it led to a value of 0.32cm-" for the frequency 
difference characterising the doublets of the second subordinate series 
in the spectrum of this element. As the experimental value found by 
Kent °° is 0.34cm~’, it will be seen that the agreement is good. 
Again, in connection with the matter of triplet series the theory 
shows that in the case of the p terms the ratio of the triplet frequency 
differences should be as 2:1, for the d terms it should be as 3:2, and 
for the f terms as 4:3. These deductions find ample verification in the 
measurements made on the frequency differences of triplet series in the 
spectra of such elements as magnesium, calcium, strontium, barium, 
zine and cadmium. 
To say the least, the theory outlined above is extremely suggestive. 
It leads, however, to rather surprising results. If we are to account 
for doublet separations generally as being due to Zeeman separations 
produced by intra-atomic magnetic fields, it follows that with some 
atoms these must be exceedingly high. Taking the doublet separations 
of the second subordinate series in the spectra’of the alkali elements, we 
find the following values for the internal magnetic fields of the different 
atoms :— 
Element . : : ‘ : f = «AY, H; 
Lithium . A : : ; ; é 0:34 em 7,173 Gauss 
Sodium : , : ‘ ; é 3 718s, 366,744 ,, 
Potassium . F ; : : ‘ - 57-71 ,, 1,231,945, 
Rubidium . " : : é 3 coat Otek « 5,072,090 _ 
Cesium 5 ; é 5540 ,, 1E826:330° ~;,; 
If it should turn out that magnetic fields so high as those given 
above are present in atoms of elements such as those in the alkali 
group, the results obtained by Wood and Ellett would be easily explained. 
Whether the existence of a magnetic coupling between the valency 
electron and the atomic core justifies Heisenberg in adopting the artifice 
of partitioning the quanta of rotation between the electron and the 
atomic core is a debatable point. 
It does not appear to be permissible to adopt the value 4 for the 
azimuthal quantum number in defining the stationary orbits of a heavy 
atom such as that of uranium. In a recent paper by Rosseland,** in 
49 Paschen and Back, Ann. der Phys., vol. 39, p. 897, 1912; vol. 40, p. 960, 
1913. 
50 Kent, Ast. Phys. Jl., vol. 40, p. 343, 1914. 
5 Rosseland, Nature, March 17, p. 357, 1923. 
