476 SECTIONAL COMMUNICATIONS. 
where we have supposed the mass of the nucleus large compared with that of the 
electron and where further the charge on the nucleus is numerically that of the electron. 
A hydrogen atom, according to Rutherford and Bohr, is a system of this latter 
kind. 
An important additional hypothesis is employed in connection with radiation. 
Tf, in a transition from one stationary state to another, a system emits radiation, the 
frequency v of this radiation is given by equating the emitted energy to hy. This 
hypothesis is due to Bohr, who succeeded in deducing Balmer’s and similar series 
emitted by hydrogen by applying this hypothesis in connection with (3) given 
above. 
This gives for the Rydberg constant 
2m?me* 
4 Sos : 
Equation (3) requires a simple modification in consequence of the fact that mass | 
of the nucleus is finite, and a further modification due to Sommerfeld takes account — 
of the relativistic dependence of the mass of the electron on its velocity, the kinetic 
energy being equated to 
(5) pe?(y—1), 
where #is the mass of the electron for small velocities, and y=(1 —?2/.9)—4, v being 
the velocity of the electron. Sommerfeld has shown that the modification of 
(3) which is thus introduced is just what is required to account for the fine structure 
of the lines in Balmer’s series. 
[The hydrogen atom, without the relativistic modification of its motion, furnishes 
an example of what is called a degenerate system in which the number of fundamental 
frequencies is smaller than the number of co-ordinates i. ] 
Epstein, by employing the classical dynamics of Hamilton and Jacobi for the 
stationary states of a hydrogen atom in the presence of a uniform external electro- 
static field, and the principles of the quantum theory as given above, has succeeded 
in explaining the resolution of the hydrogen lines observed by Stark. 
For transitions between stationary states for which the changes in the integers T 
are small by comparison with their initial and final values, the quantum theory 
approaches asymptotically to the ordinary theory and in particular the frequencies 
of the emitted radiation are, in such a case, what would be given by ordinary electro- 
dynamics. Bohr and his pupil Kramers have recently made use of this feature of 
the quantum theory, by a sort of process of extrapolation, to get information about 
the intensity and polarisation of spectral lines. Notwithstanding their success in 
this direction, this process of extrapolation (Bohr’s correspondence principle) can 
only be regarded as provisional in character. 
The evidence for the existence of stationary states is not confined to spectro- — 
scopic observations. Such experimental investigations as those of Franck and Hertz, — 
Richardson and Bazzoni and Davis and Goucher furnish additional evidence of the 
most striking kind. 
These states then have to be reckoned with as physical facts, and when, as in the 
case of atoms, they involve the revolution of electrons round charged centres, we are 
confronted with what is doubtless the chief of the difficulties besetting the quantum 
theory—namely, that the electromagnetic theory requires continuous radiation of © 
energy from such a system. Probably this and some other difficulties will be sur- } 
mounted by a suitable alternative for the four Maxwell-Lorentz equations ’ 
(6) Hern =—J™, 
These, I think, can only be true in a macroscopic sense. The remaining field 
equations are not in any obvious way inconsistent with the features of the stationary 
states of the quantum theory. , 
Prof. J. ©. McLunnay, F.R.S.—In applying to hydrogen his theory of the 
fine structure of spectral lines, developed by extending Bohr’s ideas of the 
origin of radiations founded on the quantum theory and incorporating with 
them the principle of relativity, Sommerfeld has shown that each member 
of the doublet H, should consist of a close triplet, each member of Hg of a 
