42 
Proceedings of the Royal Society of Edinburgh. [Sess. 
that constraint of this kind will have to be introduced into molecular 
models to give an account of paramagnetism and ferromagnetism — namely, 
structure in space or atom involving channels more or less definite for the 
electrons to circulate in.” It would seem that such a view is consistent 
with Bohr’s theory of stationary orbits and with the later developments of 
that theory by Sommerfeld and others in connection with the fine structure 
of spectral lines. In these applications of the quantum theory it is not 
merely the size of the orbit, but also its shape and its position in space 
which must be determined by the quantum principle, and can assume 
certain prescribed values only. Consequently, as Sommerfeld puts it, the 
stationary paths of the electrons in the atom, and also in the molecule, 
form not a continuum but a network. The “ phase-space ” is interwoven 
by the curves of the stationary paths as by the meshes of a net. The size 
of the mesh is determined by Planck’s h. 
On the present hypothesis the network is formed by the magnetic 
tubes, between and around which the electrons are able to circulate. It 
may prove necessary to proceed a step further and suppose that the tubes 
can be divided up in the direction of their length so as to form “ aether 
cells,” but such a subdivision need not at present be discussed, beyond 
pointing out that in considering how the theory of molecular vortices 
could be applied to statical electricity Maxwell * assumed the rotating 
matter to be the substance of certain cells, such substance possessing 
elasticity of figure. On this hypothesis he was able to explain electrostatic 
phenomena, and showed that the velocity of transverse undulations in a 
medium so constituted was in almost exact agreement with the velocity of 
light, so that “ we can scarcely avoid the inference that light consists in 
the transverse undulations of the same medium which is the cause of 
electric and magnetic phenomena.” 
§ 10. It is commonly assumed that an explanation of magnetic 
phenomena can be obtained from the theory of the classical electron on 
the basis of ordinary mechanical laws. That this supposition is incorrect 
was shown by W. Voigt, f who proved that, assuming the electronic motions 
are undamped, changes in the velocities of the electrons in consequence of 
the formation of magnetic fields will not give rise to magnetic phenomena. 
This result, recognised by Bohr J in his application of the quantum theory 
to an atomic model, received confirmation in the work of M‘Laren,§ who 
* Maxwell, Phil. Mag., vol. xxiii, p. 12 (1862). It should be noted that this paper is 
two years earlier than that which gives “ A Dynamical Theory of the Electromagnetic Field.” 
f Voigt, Annalen d. Physik , vol. ix, p. 115 (1902). 
I Bohr, Studier over Metallernes Elektrontheori , p. 106. 
§ M‘Laren, Phil. Mag., vol. xxv, p. 43 (1913). 
