example, the 1S term is defined by n=1, the 2P term by n=2, the 3d 
term by n=3, and the 4F term by n=4, &c. The azimuthal quantum 
number k indicates the type to which a term belongs. For k=1 an 
8,9 or S term is signified, for k=2 a p, m or P term, for k=3.ad,8 D 
term, and for k=4 anf, @ or F term. A 3, term, for example, would 
. signify a 3s, a 3, or a 3S term, and a 4, term would be one which 
_ in spectroscopy is usually designated as a 4p, 4% or 4P term. We 
_ have then in the symbol n, a means of defining a particular spectral 
_ term as well as a particular electronic orbit. 
A.—_MATHEMATICS AND PHYSICS. 31 
4 
Principles of Selection—The Correspondence Principle. 
In the early development of Bohr’s theory it was found that the 
censorship imposed by the quantum conditions referred to above were 
not sufficiently drastic to account completely either for the observed 
complexity of the fine structure of spectral lines originating in the 
: variation of the mass of an electron with its velocity or for the 
observed complexity and state of polarisation of the components of 
_ spectral lines that had their origin in the application of an external 
electric or magnetic field. 
To make up for this deficiency arbitrary Principles of Selection, 
involving such factors as intensity and polarisation, were brought 
forward by Rubinowicz and by Sommerfeld, that found immediate and 
remarkable verifications in the relativity fine structure of the Balmer 
lines, in the Stark effect, in the Zeeman effect, and in the spectra of 
rotation, 1.e. the band spectra of Deslandres. 
Although these principles of selection furnished rulés that have 
served as useful guides in unravelling the intricacies of various types 
of spectral resolution, it has all along been recognised by the proposers, 
as well as by others, that the principles as formulated rested upon a 
dynamical basis that was rather limited and scarcely adequate. 
The whole matter, however, was given an entirely new orientation 
and an enhanced significance by Bohr’s enunciation of the Correspond- 
ence Principle. 
To elucidate this principle we may revert for a moment to the 
properties of the stationary orbits of the atom of hydrogen. It can 
be easily shown that the frequency with which the electron revolves 
in the nth orbit is given by 
2)! 4nm Me" ; 
(m+ M)n*h® 
nd the frequency of the light emitted when a transition occurs of the 
electron from the nth to nth orbit is given by 
_ Or'mMe! 1/1 4 
VRS  8\ irl) al}e 
mt+M h\n n 
From these two relations it follows that 
¥ =i af a) 2 
oO \n? w/t nn} 
1923 E 
