Faraday's "Magnetic Lines" as Quanta. 525 



momentum of such a system about its axis of symmetry is 

 N 7n N e /27r, where N e is the number of tubes of electric in- 

 duction terminating on the surface, and N m is the number 

 of tubes of magnetic induction passing through the aper- 

 ture *. Assuming that this amount of angular momentum 

 is an integral number of times the quanlum, Ji/27r, we find 

 N m ~N e = nh, where n is an integer. If we identify the mag- 

 neton with the electron, and put N e =<?, where e is the charge 

 of the electron, we obtain 



N m = n (h/e) (1) 



2. The same result is reached by considering a point 

 charge, e, travelling in a circular orbit with large velocity. 

 Such a charge, making v revolutions round the orbit per 

 second, may be regarded as equivalent to a current i = ev. 

 If L denote the self-inductance of the equivalent circuit, the 

 electrokinetic energy, T = JLi 2 . Putting Li = N m and i = ev, 

 this gives 



T=±K m ev (2) 



According to the quantum theory the steady motion must 

 be such that the kinetic energy is given by 



2§Tdt = nh, (3) 



where the integration is to be extended over the complete 

 period of the motion. The quantum theory has been 

 expressed in different ways by Planck f , W. Wilson J, 

 Sommerfeld §, Ishiwara ||, and others, but in this simple 

 case, where the energy can be expressed by a single term,, 

 all forms of the Quantum theory lead to. the same condition 

 for determining steady motion. This has been pointed out 

 by W. Wilson. 



We assume that the kinetic energy of the moving charge 

 may be identified with electrokinetic energy. Substituting 

 the value for T given by (2) in the integral in (3), and 

 noticing that during the steady motion the kinetic energy is 

 assumed constant (Maxwellian principles being suspended) 

 so that N. H „ e, v, are all constant, we find 



~N m ev ^dt = nh. 



* H. S. Allen, Phil. Mag-, vol. xii. p. 113 (1921). 



1 Planck's " Heat Radiation " (trans. Masius). 



% W. Wilson, Phil. Mag. vol. xxix. p. 795 (1915) : vol. xxxi. p. 156 

 (1916). 



§ A. Sommerfeld, Ann. d. Thydk, vol. li. p. 1 (1916). 



|| J. Ishiwara, Tdkyd Sugaki-Buturigakfaoai, 2nd ser. vol. viii. no. 4. 

 p. 106. 



