SPINNING ELECTRONS 
221 
XVI. 2] 
The result obtained has great physical interest for it shows that 
the assumptions of Uhlenbeck and Goudsmit really lead to the 
correct doublet separation and at the same time to an explanation 
of the anomalous Zeeman effect, when the problem is treated 
by the new quantum mechanics. Thus the theory of the spinning 
electron connects the anomalous Zeeman effect with the optical 
and relativity doublets, and accounts for them as manifestations 
of the magnetic properties of the electron. It must be supposed 
that the axis of the electron precesses about a magnetic field 
with an angular velocity differing from that of the Larmor 
rotation. In fact an angular velocity (e/m 0 c) H, twice the Larmor 
precession, must be assumed. Starting from this idea, values 
of the Land6 factor, g, can be obtained differing from unity. 
The procedure may be outlined as follows : Assuming that the 
electron has the above-mentioned precession about the magnetic 
field in a system of axes in which its centre is instantaneously at 
rest, the secular rate of change of direction of its axis when it 
revolves in an orbit can be found. “ Assuming that there is 
some total angular momentum which is secularly conserved, 
that which the electron itself adds to that of the orbit having 
magnitude h/Agcc, the secular motion of the system can be found. 
An approximate formula for the doublet and Zeeman effect 
separations follows. The new quantum mechanics of Heisenberg 
transforms this into a formula which fits the observed doublet 
separations and Zeeman effect exactly, as far as first order terms 
in the relativity correlation are sufficient.” 
(4) Paschen-Back Effect.—The gradual transformation of the 
multiplet structure as the magnetic field increases, known as 
the Paschen-Back effect (p. 211), can be explained by supposing 
that the influence of the field on the precession of the spin axis 
becomes comparable with the effect due to the orbital motion in 
the atom. 
(5) Statistical Weight.—Another paradox which has been 
resolved by means of this spinning electron is that in connection 
with the statistical weight of a term. By this we mean the total 
number of states which must be associated with a particular 
spectral term. The weight to be assigned to the core is R, where 
R denotes the maximum multiplicity. If the electron be a 
point charge the total number of states of total quantum number 
n must be asymptotically equal to n 2 for large values of n, and 
the total number of states of core and orbital electron must be 
R n 2 . Actually it is found to be 2R W 2 for all values of n in all 
cases. The only way out of this difficulty is to suppose that the 
electron has a structure. 
(6) Atomic Models.—The capabilites of the spinning electron 
in the construction of models of atoms and also of molecules