f. a5- J 
LV. Avnetics of a System of Particles illustrating the Line 
andthe Band Spectrum and the Phenomena of Radioactivity. 
By H. Nacaoxwa, Professor of Physics, Imperial University, 
Tokyo*. 
INCE the discovery of the regularity of spectral lines, the 
kinetics of a material system giving rise to spectral 
vibrations has been a favourite subject of discussion among 
physicists. The method of enquiry has been generally to find 
a system which will give rise to vibrations conformable to 
the formule given by Balmer, by Kayser and Runge, and by 
Rydberg. The characteristic difference between the line- 
and the band-spectrum in the magnetic field has scarcely 
been touched upon in these theoretical investigations. Instead 
of seeking to find a system whose modes of vibration are 
brought into complete harmony with the regularity ebserved 
in spectral lines, inasmuch as the empirical formule are still 
a matter of dispute, I propose to discuss a system’ whose 
small oscillations accord qualitatively with the regularity 
observed in the spectra of different elements and by which 
the influence of the magnetic field on band- and line-spectra 
is easily explicable. The system here considered is quasi- 
stable, and will at the same time serve to illustrate a dynamical 
analogy of radioactivity, showing that the singular property 
is markedly inherent in elements with high atomic weights. 
It must, however, be borne in mind that out of the manifold 
structure of systems that may exist enjoying the said properties, 
the one here presented is perhaps the most easily conceivable, 
although the actual arrangement in a chemical atom may 
present complexities which are far beyond the reach of mathe- 
matical treatment. 
The system, which I am going to discuss, consists of a 
large number of particles of equal mass arranged in a circle 
at equal angular intervals and repelling each other with forces 
inversely proportional to the square of distance; at the 
centre of the circle, place a particle of large mass attracting the 
other particles according to the same law of force. If these 
repelling particles be revolving with nearly the same velocity 
about the attracting centre, the system will generally remain 
stable, for small disturbances, provided the attracting force 
be sufficiently great. The system differs from the Saturnian 
system considered by Maxwell in having repelling particles 
instead of attracting satellites. The present case will 
evidently be approximately realized if we replace these satel - 
lites by negative electrons and the attracting centre by a 
* Read before the Physico-Mathematical Society, Tokyo, Dec. 5th, 
1903. Communicated by the Author. . - . biel 
