LI. On the Constitution of the Atom. To the Editors of the Philosophical Magazine. Gentlemen, — May I put forward a suggestion in connexion with a question discussed by Lord Rayleigh in his paper " On Electrical Vibrations and the Constitution of the Atom " [citation redacted] ? Lord Rayleigh states an objection against regarding the atom as a system in steady orbital motion, rather than as one performing small oscillations about a position of statical equilibrium, — namely, that the sharpness of spectral lines indicates a definiteness of structure such as it is difficult to imagine associated with a system of electrons in orbital motion. He goes on to say : " It is possible, however, that [header] 605 the conditions o£ stability or o£ exemption from radiation may after all really demand this definiteness. . . . The frequencies observed in the spectrum may . . . form an essential part of the original constitution of the atom as determined by conditions of stability." If this were so, these frequencies would depend only on the constituents of the atom and not on the actual type of motion taking place in the atom. Thus if we regard the atom as made up of point-charges influencing one another according to the usual electrodynamical laws, the frequencies could depend only on the number, masses, and charges of the point-charges and on the æther-constant V. What I wish to point out first is that it is impossible, by combining these quantities in any way, to obtain a quantity of the physical dimensions of a frequency. If to the quantities already mentioned we add another, for instance the energy of motion o£ the atom, it may be possible to obtain frequencies. Here, however, the frequencies will be functions of the energy. And, as Lord Rayleigh says, the energy must change in the course of time, whereas the frequencies, so far as we know, do not. Or, instead of combining the original quantities with the energy, we may combine them with a length, in such a way as to obtain frequencies. Thus Lord Rayleigh obtains frequencies in his analysis, but only in virtue of having introduced the radius of the imaginary sphere of positive electrification. If this positive electrification, instead of being limited to an invariable sphere, were supposed free to expand under its self-repulsion, Lord Rayleigh's p would be indefinite, as would consequently be the frequencies also. The situation with regard to linear dimensions is precisely the same as that with regard to frequencies. It is impossible to derive a scale of linear dimensions from the quantities permanently associated with point-charges and aether. Thus the atom would have no definite size, but would expand and contract indefinitely under external influences. It seems, then, that we must somehow introduce new quantities — electrons must be regarded as something more complex than point-charges. And when we have once been driven to surrendering the simplicity of the point-charge view of the electron, is there any longer any objection to putting the most obvious interpretation on the line-spectrum, and regarding its frequencies as those of isochronous vibrations about a position of statical equilibrium ? The main objection felt, as I understand, against this interpretation, lies in its being inconsistent with the point-charge view of an 606 [header] electron. I suggest that the objection applies equally to the " orbital motion " interpretation. Lord Rayleigh's objection to the statical interpretation, that the theoretically calculated spectrum series would be for p 2 and not for p, and that they would apparently be too complex to agree with the observed facts, remains, and seems, it is true, to be almost insuperable; but is the case any worse than that which mig lit have been made out against the atomic theory a century ago from the fact of the ratios of specific heats of gases forming the simple series [formula redacted] , in spite of the enormous complexity of the atomic conception of matter ? Evidence, which seems to me to have great weight, can be derived from considerations of the partition of energy. The value of Dulong and Petit' s constant shows that those parts of the energy which vary with the temperature are fully accounted for by the potential and kinetic energies of the atom regarded as a point; and the same is shown by the fact that [gamma] for monatomic gases has the value 12/3. Thus the energies of the degrees of freedom which represent rotation or internal motions of the atom, are either infinitesimal or are incapable of variation under the ordinary interatomic forces. Thus if electrons are describing orbits, the planes of these orbits must remain almost or completely fixed in space. If we rotate a body in the hand the atoms must maintain their directions in space, as indeed, on this view of the atom, would be shown also by the fact of our not experiencing any gyrostatic couple. But if the body is a crystal, its optical constants and axes do not change by rotation — as they surely would if all the atoms rotated their planes relatively to the body as a whole — and if the body is a permanent magnet, its magnetic properties and constants do not change. A similar dilemma is soon reached with reference to the velocity of rotation. The Zeeman effect shows that this can be altered even by the fields available in the laboratory, while the value of y would show that it is not altered by the much more effective magnetic fields which ought (on the " orbital motion " theory) to be found at collisions of molecules. Finally, may I mention that in the Phil. Mag. for Nov. 1901, I attacked a problem similar in many respects to that which forms the main substance of Lord Rayleigh's paper ? The actual premises upon which I worked were different from those of Lord Rayleigh — his positive sphere being represented, in my work, by a crowd of positive electrons, and the definiteness of structure, which he obtains by regarding [header] 607 "this sphere as rigidly fixed, being obtained in my work by using a law more general than [formula redacted]. Both papers, however, deal with a spherical atom executing small vibrations : in both the principal vibrations are found to correspond to spherical harmonics., the order of the harmonic being the n of the spectrum series. Lord Rayleigh obtains only a single series, falling off from the head according to the law 1/n, and also a single spectral line. Nothing corresponding to this series appears in my work; but corresponding to the single line I obtained a number of series falling off according to the observed law 1/n 2 . Given the value of e/m for electrons (or electric fluid) the same relation can be obtained, in either case, between the frequencies and the radius of the atom. Unfortunately the numerical calculation given in § 23 of my paper was inaccurate : corresponding to frequencies of the order of those of light the radius must be about 3 x 10 -7 , which is not good as regards agreement with facts, but is perhaps as near to the true value as can be expected in a vague calculation of this kind. My picture of the atom led to a Zeeman effect, consisting of a splitting into three or more sharp and fully polarized lines. Lord Rayleigh's model would, I believe, do the same. If, however, the atom consisted of electrons in orbital motion, the planes of these orbits making all directions with the lines of magnetic force, it appears as if the Zeeman effect could at best consist of a widening into a continuous band, a point which has, I think, already been made by Lord Kelvin. J. H. JEANS. Princeton, N. J., Jan. 24th, 1906.