2l8 
THE QUANTUM [xvi. 2 
a correlation with a more familiar structure, viz., that of an 
electron at rest. The correlating velocity has no more physical 
existence than has the factor V — 1 used to correlate the structure 
of the four-dimensional world to the more familiar structure of a 
four-dimensional Euclidian space.” 
Independently, a tentative suggestion that the electron is a 
charged magnetic doublet was made in America by Bichowsky 
and Urey.* They claimed that on their hypothesis it seemed 
possible to explain relativity doublets and also anomalous 
Zeeman effects. 
The way in which this magnetic electron influences stationary 
states is not difficult to understand. Since the electron possesses 
a magnetic moment and is moving in the electric field of the 
nucleus, it will be acted on by a couple, and this couple will cause 
a slow precession of the spin axis. To ensure the conservation 
of the angular momentum of the atom there would be a com 
pensating precession of the orbital plane of the electron. 
Corresponding to each stationary state of a Bohr atom in which 
the electron has no spin, there will, in general, be a set of states 
which differ in the orientation of the spin axis relative to the 
orbital plane. For a one-quantum spin there will be in general 
two such states. Further, it can be shown that the energy 
difference of these states will be proportional to the fourth 
power of the nuclear charge. 
For the interpretation of complicated spectra it is necessary 
to assign to every electron two quantum numbers. The first of 
these must correspond to the azimuthal quantum number which 
determines the moment of momentum of the electron about the 
nucleus. According to Uhlenbeck and Goudsmit the second 
quantum number may be regarded as specifying the moment of 
momentum of the electron itself. This may be illustrated by 
some applications to the finer structure of spectra. 
(1) Sommerfeld’s explanation of the fine structure of 
hydrogen-like spectra is now modified, and the Dutch authors 
consider as an illustration the energy levels corresponding to 
electronic orbits for which the principal quantum number is 
equal to three. In the diagram (Fig. 29) are given on the left 
the results to be expected from the older theory, the levels being 
fixed by the azimuthal quantum number k (where k = 1, 2, 3), 
and on the right the levels given by the new theory. 
The moment of momentum of the electron about the nucleus 
is now given by ~Kh/27c, where K = f, f, f. The total angular 
momentum or the atom is }h/2n where J = 1, 2, 3. In the ab 
sence of electron spin the dotted lines show the position of the 
* Bichowsky and Urey, Nat. Acad. Sci. Pvoc., vol. 12, p. 80, February, 
1926. 
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