454 Prof. H. Nagaoka: Kunetics of a System of 
The motion of the ring will not be oscillating, but in course 
of time, if the. disturbance be persistent, will acquire such an 
amplitude as to break the ring. In this case, the particles 
will fly away with enormous velocities, and the central 
particle will participate in the same motion, owing to the law 
of conservation of the centre of mass. If the particles be 
supposed to be negative electrons, they will disperse in 
various directions with great velocities, and the positively 
charged particle at the centre will also fly off. Here we have 
arrived at a mechanical analogy, which explains the pro- 
duction of a and # rays by the disintegration of the ideal 
atom. ‘The results of calculation above expounded lead us to 
the conclusion that the phenomenon of radioactivity is remark- 
ably exhibited in elements with high atomic weights. When 
: espe 4 J f 
h is small, N= he , consequently the disturbance of the ring 
T 
with v particles will be given by 
p— Ae Cos a. - 
; 17 
o = Be*sin up, | (it) 
after a certain time ¢, showing that the more massive the ring, 
the greater the disturbance, which is proportional to e”. As 
most of the elements exhibit regular spectral lines, it appears 
that such rings as above described are generally to be found. 
It is more probable that massive rings will be found in 
elements with high atomic weights, and if the high atomic 
weight is accompanied by simple spectral lines, it needs no 
proving that v in the rings must be greater than in elements 
with complex spectral series. In that case, the instability of 
the ring will immediately set in, and result in the expulsion 
of the particles. Radium enjoys the said property, the high 
atomic weight being accompanied by spectral lines which 
are far simpier than in iron or mercury. 
If the spectra of the elements be due to the motion of 
electrons revolving in circular orbits, as above supposed, 
several rings of electrons must exist where there are different 
series of spectra, as in most of the elements. The resonance 
due to forces, whose periods coincide with those of the rings, 
will be most efficacious in causing the disturbance and also 
in placing it in an unstable state. The destruction of the 
rings will be easier if the innermost ring be torn asunder 
than if the outside one is, and, moreover, if these electrons 
are subject to electric forces, the dismembered electrons will 
fly away with accelerated velocity. The modes of vibration 
