Faraday' s "Magnetic Lines " as Quanta. 535 



average of the kinetic "energy be identified with the electro- 

 kinetic energy associated with the co-ordinate in question. 

 In the simple case of a charge e moving in an orbit of any 

 shape whatever with high frequency v u the electrokinetic 

 energy may be written in the form ^N"^, where N x is the 

 magnetic flux through the orbit and i i = ev 1 is the equivalent 

 current. 



Hence 2 n i^i — i^Vi 



= iN lWl (19) 



Thus we obtain a series of relations 



N 1 e = n 1 h') 



N 2 e = n 2 Ji i '. (20) 



Hence^ when the charge e is the fundamental electronic 

 charge 





(21) 



J 



showing that, associated with each canonical co-ordinate 

 there is a magnetic flux of an integral number of quantum 

 tubes, the unit tube being defined by the ratio hje. 



14. The argument is made clearer by considering the 

 particular ease of the Keplerian elliptic orbit. 

 The kinetic energy is now given by 



T=f(r> 2 + r 2 ), 



which is of the required form. 



Corresponding to the angular motion, </), there is an 

 amount of angular momentum, mr 2 cj), which in this case is 

 constant and ==p. The quantum relation is 



i/)c?g = ;?l d$ = 2irp = nl\, . . . (S. 1) 



This may be written in the equivalent form 

 j mr 2 <p dcf> = \ mr 2 <fi 2 dt = nh. 



It is instructive to compare these 'expressions with the 

 corresponding results in equations (18). 



If we regard the angular momentum of the revolving 



