On a Dynamical System illustrating the Spectrum Lines and the Phenomena of Radio-activity

Abstract

BY the study of a system of particles, which is similar to a Saturnian system, I was led to the discussion of disturbances which propagate in the system, having close analogy with the band and line spectra while illustrating the phenomena of radio-activity. The system 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 between the particles; at the centre of the circle is placed a large particle attracting the other particles forming the ring according to the same law of force. If the repelling particles be revolving about the attracting centre, the system will generally remain stable for small oscillations, which consist of the transversal vibration perpendicular to the plane of the orbit, together with the radial and angular disturbances representing the rarefaction and condensation in the distribution of the particles. Small oscillations of this kind have already been treated by Maxwell in his essays on the stability of Saturn's rings; the system will be the same if the repelling particles of the present system be substituted by the attracting satellites. Evidently the system here considered will be approximately realised if we place negative electrons in the ring and a positive charge at the centre. Such an ideal atom will not be contradictory to the results of recent experiments on kathode rays, radioactivity, and other allied phenomena.