40 SECTIONAL ADDRESSES. 
These and other features of the classification that might be referred 
to are illustrated by the arrangement of the elements shown in Fig. 4. 
In this representation, it will be noted, those elements that belong to 
the same period are given in vertical columns, and those that from their 
chemical and optical properties can be considered homologous are 
connected with one another by straight lines. Groups of elements 
that possess analogous physical properties, and that differ from one 
another by variations in the number of electrons belonging to inner 
groups, are enclosed, as the diagram shows, by rectangular spacings. 
Peculiar interest attaches to the newly discovered element of atomic 
number 72, to which the name ‘ Hafnium ’* has been given. Condi- 
tions imposed by the quantum theory, in Bohr’s view, make it impera- 
tive to assign this element to the platinum group instead of to the rare- 
earth group, as Dauvillier * and others have suggested. Theoretically, 
this element would appear to be a homologue of zirconium, and it is 
interesting to note that Coster and Henesy, who have been chiefly 
concerned with its discovery, have been able to obtain from zircon- 
bearing minerals considerable quantities of a substance whose chemical 
properties are similar to those of zirconium, and whose X-ray spectrum 
is that of an element with atomic number 72. 
In the remainder of my address I propose, with your permission, 
to deal with a number of matters that are closely associated with 
developments of the quantum theory of the origin of spectra and that 
appear to merit some special attention and consideration at the present 
time. 
The Fine Structure of the Balmer Lines of Hydrogen. 
In the simplest treatment by the quantum theory of the origin of the 
spectrum of atomic hydrogen no allowance is made for a variation 
in the mass of the electron with its speed. If this factor be taken into 
account, as it has been by Sommerfeld, it is found that the motion 
of the electron is reducible to a motion in an elliptic orbit upon which 
is imposed a slow rotation in its own plane about the nucleus as focus. 
The resulting orbit has the form of a rosette, and is similar to that 
shown in Fig. 5. 
In this treatment the chief factor in determining the stationary 
states is the principal quantum number n, but the subordinate quantum 
number k is also contributory. The former practically determines the 
major axis and the period of the elliptical orbit, while the latter defines 
the parameter of the ellipse—i.e. the shortest chord through its focus. 
The subordinate quantum number k also determines the period of rota- 
tion of the elliptic orbit in its plane. The energy corresponding to 
each stationary state is in the main determined by the value of the 
quantum number n, but stationary states determined by the same value 
of n are characterised by energy values that vary slightly with different 
values of the quantum number k. 
° Coster and Henesy, Nature, Jan. 20, Feb. 10, 24, and April 7, 1923. 
* Dauvillier, C.#., t. 174, p. 1347, May 1922; Urbain, C.R., t. 174, p. 1349, 
May 1922, and t. 152, p. 141, 1911. 
