214 
THE QUANTUM 
[xv. 4 
Many attempts were made before 1926 to give a physical 
interpretation to this formula, and for these reference may be 
made to Stoner’s book, Magnetism and Atomic Structure (pp. 
237-8). It was possible to obtain on theoretical grounds an 
expression of the form: 
. 15 :12 
This formula bears considerable resemblance to the empirical 
formula, but if we adopt the older quantum theories we can 
not get exact agreement. The newer quantum theories associ 
ated with the names of Heisenberg and Schròdinger introduce 
modifications which are equivalent to writing J 2 in the form 
j{j + I )- ... 
In order to obtain this formula it was necessary to assume 
that the contribution of the core to the magnetic moment of 
the atom is twice as great as would be expected from its angular 
momentum. As we shall see in the next chapter, the hypothesis 
of the spinning electron removes this difficulty. 
Stoner concluded that electron orbits and cores are charac 
terized by integral magnetic moments (in terms of the Bohr 
unit). The magnetic moment of an electron orbit is assumed 
to be given by the azimuthal quantum number k. The maxi 
mum magnetic moment of the cores was then found equal to 
the number of electrons it contains in uncompleted groups, i.e. 
to the number of “ outer ” electrons in the core, if we define 
“ outer ” electrons as those the core possesses in addition to 
those forming a completed configuration. The maximum term 
multiplicity is greater by two than the magnetic moment of the 
core, [x cy that is r — ¡a c + 2. Magnetic balancing in pairs of core 
electrons gives rise to lower multiplicities, all odd or all even 
for odd or even numbers of core electrons. 
Intensities of the Components.—-Much important work on the 
intensities of multiplet lines has been done at Utrecht by Pro 
fessor Ornstein and his fellow-workers Burger and Dorgelo. By 
means of certain “ summation rules ” which have been put for 
ward, it is possible to obtain results which agree closely with the 
experimental determinations. Employing the inner quantum 
numbers of Sommerfeld, each n, k, j term splits up in a magnetic 
field into 2j + 1 equidistant components. Then P, which is 
equal to 2j + 1, determines the number of possible and equally 
probable ways in which the nkj state can be realized, and is 
consequently called the statistical weight of the term. The 
“ summations rules ” provide a relation between the sum of the 
intensities of the line components produced by certain transitions 
and the corresponding statistical weights.