Faraday's "Magnetic Lines " as Quanta. 537 



is obtained, we are really concerned with the time-average 

 of a certain quantity. In fact, the process of taking a time- 

 average occurs twice over, first in evaluating the integral 

 ^Tdt on one side of the equation, and, secondly, in the 

 assumption that i = ev in connexion with the other side of 

 the equation. It is difficult to understand how an integer n 

 could arise in the process of taking an average, unless the 

 integer correspond to some physical entities which are 

 present at each instant of time. At any rate, it may be said 

 that the simplest explanation that can be given of the results 

 is based on the assumption that discrete magnetic tubes 

 exist determined by the fundamental unit (Ji/e). 



Summary and Conclusion. 



The results may be summarized briefly as follows. The 

 stationary states of a dynamical system may be determined 

 by Hamiltonian dynamics as applied to conservative systems. 

 The restrictions imposed by the Quantum Theory require 

 that when " separation of the variables " * can be effected, 

 the mean value of the kinetic energy corresponding to a 

 particular degree of freedom is equal to \ri\iv> where the 

 mean value is taken over the period, l/i/, corresponding to 

 the co-ordinate under consideration. Let this mean energy 

 be identified with the mean electrokinetic energy i^&ev, 

 arising from the periodic motion of an electric charge e with 

 frequency v. Then N, the number of magnetic tubes as- 

 sociated with the moving charge, is given by ?i(h/e). As 

 n is an integer, and e may be identified with the charge of 

 an electron, the simplest interpretation to be given to this 

 result is to assume with Faraday the existence of discrete 

 tubes of magnetic induction, the fundamental or " quantum " 

 tube being determined by h/e, the ratio of Planck's constant 

 h to the electron charge e. This unit tube is equal to 

 1-374 x lO" 17 E.8.U. or 4420 x JO" 7 E.M.U. Consequently 

 one C.G.S. magnetic tube (one maxwell) contains nearly two 

 and a half million (2*43 x 10 6 ) quantum tubes. The applica- 

 tion of this view to the case of circular and elliptic orbits 

 has been discussed at some length in the foregoing pages, 

 and in a subsequent communication I hope to bring forward 

 certain other developments of the hypothesis. 



Physical Laboratory, 

 The University, Edinburgh. 



* See N. Bohr, "On the Quantum Theory of Line Spectra." Pari I. 

 § 3, Dansk Acad. Sc. 1918. 



Phil Mag. S. 6. Vol. 42. No. 250. Oct. 1921. 2 



