LV. Kinetics of a System of Particles illustrating the Line and the Band Spectrum and the Phenomena of Radioactivity.

By H. NAGAOKA, Professor of Physics, Imperial University, Tokyo
Philosophical Magazine
Series 6, Volume 7
May 1904, p. 445-455


SINCE the discovery of the reularity 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 formulae 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 observed in spectral lines, inasmuch as the empirical formulae 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 dynamicalanalogy 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 mathematical 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 satellites by negative electrons and the attracting centre by a

* Read before the Physico-Mathematical Society, Tokyo Dec. 5th. 1903. Communicated by the Author.


positively charged particle. The investigations on cathode rays and radioactivity have shown that such a system is conceivable as an ideal atom. In his lecture on electrons, Sir Oliver Lodge calls attention to a Saturnian system which probably will be of the same arrangement as that above spoken of. The objection to such a system of electrons is that the system must ultimately come to rest, in consequence of the exhaustion of energy by radiation, if the loss be not properly compensated.

To begn with, it is necessary to show that the system is stable.

[The remainder of page 446 and through to p. 452 will be done at a future time.]


The refined apparatus recently introduced by Michelson and Lummer in spectrum analysis have revealed a complex crowding of lines where formerly a single line was supposed to exist. In the present system, we have supposed that v-particles are arranged in a circle, but in the actual case the particles may be at slightly different distances from the attracting centre, which, was identified with a geometrical point. The hypothesis of a point centre would only be a rough approximation, and we have reason to believe that the complexity of the structure of spectral lines is a consequence most likely to be expected.

Where there are many series of spectra, we have to consider the same number of rings of particles, all of which may or may not lie in the same plane. The occurrence of doublets in elements of the alkaline group may be attributed to the separation due to magnetic force by other rings, but it is extremely improbable that the field is so great as to cause the observed separation. The mutual disturbances of the rings will again result in intricacy in the structure of the spectra. The two neighbouring rings will be so influenced as to give rise to forced waves, so that they perform oscillations which are participated in by other rings. Cases may occur where the resonance due to the oscillation of other atoms makes the amplitude extremely large and ultimately tears the ring. The most noteworthy is the influence of the amplitude of oscillation of one ring on others. It affects the period of the neighbouring ring to a slight extent and may cause the flutings of the spectrum-lines. Of course this may be looked upon as one cause of the broadening of lines, while various other causes tending towards the same effect will exist.

[The last portion of p. 453 is deleted.]


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 production of [alpha] and [beta] 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 remarkably exhibited in elements with high atomic weights. When h is small, [equations deleted] after a certain time t, showing that the more massive the, ring, the greater the disturbance, .... 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 [nu] 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 simpler 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


which contribute to the instability of the system are those associated with the higher harmonics. This evidently lies in the region of small wave-length, and the destruction of the system will be easier for ultra-violet light to bring into effect, if the system will resonate to these oscillations. The actinoelectric action may be the result of the destruction of atoms under the combined action of electric force, which places the electrons in a constrained state, and the resonance to ultraviolet rays of the period participated in by the rings. The dismemberment of the rings will result in the ionization of gas in the neighbourhood of the illuminated surface.

The same course of reasoning with regard to resonance seems to apply to the change of resistance often observed in semi-insulators. Apply electromotive force to a semi-insulator and pass the electromagnetic wave whose period coincides with that of the constituent atoms, then it will set the electrons in resonating vibration, break them from the revolving system, and thereby cause the flow of electrons and reduce the resistance of the circuit. This perhaps explains in a simple manner the change of resistance in selenium by exposure to light; that the green light is less effective than red or violet seems to give strong evidence to the resonating action.

The metals have usually a large number spectral lines, extending from ultra-violet to the infra-red region. The exposure of metallic filings to electric waves has the same action as that of light in the case of selenium. Perhaps the same reasoning as above applies to this case, as the Hertz waves are more penetrating, and there will be a greater number of resonating atoms than when illuminated with visible light. The theory of the coherer is probably to be based on the footing that electric current consists in the stream of electrons set free by the incident electromanetic wave.

As another example of forced oscillation I may mention the fluorescence or phosphorescence of certain substances, the vibrations of particles being excited either by light or by electromagnetic pulses. In the former phenomenon the action is apparently temporary, but remanent in the latter. In fact, the theory of luminiscence will be capable of further development on the line of reasoning here expounded.

There are various problems which will possibly be capable of being attacked on the hypothesis of a Saturnian system, and many such as chemical affinity and valency, electrolysis other subjects connected with atoms and molecules. The rough calculation and rather unpolished exposition of' various phenomena above sketched may serve is a hint to a more complete solution of atomic structure.