36 Proceedings of the Koyal Society of Edinburgh. [Sess. 
that this result may be proved in a very general way, and that in ordinary 
units we have 
Angular momentum = — N e N w . 
Ji7T 
It is to be noted that this expression is quite independent of the 
quantum hypothesis. If we now apply the quantum theory to this case 
we have 
r2ir 
rz* 
i pd<f> = nh , 
J o 
or as p, the angular momentum, is constant 
2 irp = nh. 
Identifying these two expressions for the angular momentum, we obtain 
If we regard the charge of the magneton as equal to e, the electron charge, 
the relation may be written 
or the number of magnetic tubes passing through the aperture of the 
magneton is directly proportional to an integer n. 
§ 4. It seems probable that this result may be applied not only to 
M'Laren’s magneton, but also to the case of a classical electron circulating 
in a closed orbit. Such an extension has in fact been suggested in an 
interesting, but not altogether convincing, paper by A. L. Bernoulli.* This 
author has given an electrodynamic interpretation of Planck’s constant by 
introducing a principle which he terms the “ Principle of the Universal Flux 
of Induction,” defined as follows : — “ If electrons are moving in identical 
closed trajectories in a molecular magnetic field, the number of lines of 
force cut by the radii vectores at each revolution is. one and the same 
universal constant.” In other words, all the electron-resonators are 
traversed by a like tube of magnetic force. The product of the induction 
flux and the charge is equal to Planck’s constant. 
In the paragraph immediately following I have attempted to give a 
more general proof of this principle, with the object of avoiding as far 
as possible particular assumptions as to the character of the electrical 
distribution. 
§ 5. Consider a system composed of any number of point charges e v e 2 , 
. . . rotating with angular velocity <*> about a common axis. These will be 
the starting-points of electrostatic tubes rotating about the same axis. 
* Bernoulli, Archives des Sciences , vol. xlii, p. 24 (1916). 
