452 Prof. H. Nagaoka: Kinetics of a System of 
present system. The frequency x for the line-spectrum is 
approximately given by 
n? =o? + p(L+4N+4+2K),. 
For tolerably large values of h, 2L=N=2J ; consequently 
n=. + 9p. 
For the frequency of the band-spectrum due to the same 
particles 
ju? 
=O, fb 
Thus the successive difference of frequency for the same 
ring of particles is about nine times greater in the line than 
in the band-spectrum. The proximity of lines in the hand- 
spectrum is well borne out by observation. 
Observation shows that the Zeeman effect is only peculiar 
to the line-spectrum, while the band-spectrum is not affected 
by the magnetic force. If we suppose that the moving 
particles are electrons, then the force acting on any one of 
them, when the magnetic field is perpendicular to the plane 
of the orbit, would be radial and equal to Hae —=eHao. 
The equation of motion is therefore modified by the introduc- 
tion of the new term vcHaw; consequently 
H 
wo =S+uK+ wo, 
The waves travel round the ring with different velocities 
SES Ge e(2) 8 \ 
i (15) 
ae SS eee 
@.= —,/S+yK+ 5; | 
All the line-spectra belonging to the same series appear 
as doublets, which are circularly polarized in opposite sense. 
The magnetic force perpendicular to the plane of the orbit 
does not affect the transverse vibrations, but when the field H 
is parallel to the plane, the force 
bal’ 
eH cos ha a 
normal to the plane of the orbit will be operative. This 
force is however oscillating, and its mean value is zero ; it 
will therefore produce no sensible effect on the period of 
transversal oscillation which gives rise to band-spectrum of 
the present system. 
