ATOMIC STRUCTURE 
81 
v. 4] 
to the papers already mentioned. It is necessary to consider 
the resultant action of all the electrons in uncompleted shells 
for the atom in question, and this may involve the consideration 
of numerous possibilities ; but the process is for the most part 
arithmetical and it may be said that the completion of the shells 
in the atom is decided " not by classical mechanics but by 
quantum arithmetic ” (Sommerfeld). 
These methods have met with brilliant success in the 
classification of spectra, even when the atom has more than two 
outer electrons. Hund * * * § himself has investigated the iron 
group, and has predicted the electronic orbits in the rare earths. 
Bechert and Catalan f have examined the palladium group. 
R. H. Fowler and D. R. Hartree J have applied the theory to 
the spectrum of ionized oxygen (O II) and have found most 
satisfactory agreement between the terms deduced from the 
theory and those derived by A. Fowler from the analysis of the 
observed spectrum. McLennan § and his fellow-workers in 
Toronto have investigated the structure of the spectrum of gold 
and of palladium. 
Considerable importance attaches both in theory and in 
experiment to the so-called “ raies ultimes ” of de Gramont. 
Although not necessarily the strongest lines in the ordinary 
spectrum, these are lines which persist when the quantity of 
the element responsible for them is extraordinarily minute. 
Generally, these are supposed to be the resonance lines and the 
first members of principal series. This means that they 
correspond to transitions from the nearest possible orbit of 
higher energy to the lowest level or to the normal state of the 
atom. As a result of the Heisenberg-Hund theory it is now 
possible to predict the spectroscopic ground term associated with 
the normal state of each neutral atom, and also to specify with 
considerable confidence the actual electronic arrangement of all 
the elements. Tables exhibiting results of this kind have been 
given by Paul Foote, || by McLennan McLay and Smith and by 
Fowler, in papers already cited. Fowler’s Table is reproduced, 
by permission, in Appendix V, the values of the ground term 
directly determined from spectra being marked with an asterisk. 
We may sum up the results of the more recent theories of 
atomic structure by saying that the character of a spectral term 
is determined by a set of quantum numbers which depend on 
* Hund, Zeits. f. Physik, vol. 33, p. 345, 855, 1925. 
f Bechert and Catalan, Zeits. f. Physik, vol. 35, p. 449, 1926. 
% Fowler and Hartree, Proc. Roy. Soc., vol. in, p. 83, 1926. 
§ McLennan, Proc. Roy. Soc., vol. 112, pp. 76, 95, no, 1926. 
|| Paul Foote, Trans. Amer. Inst. Mining and Metal Eng., No. 1547 D 
(1926).