and some Related Properties of the Ring Electron. 115 



of the cross-section, or the size of the cross-section or of the 

 ring. Further, it would seem that the same result would 

 hold not only for a surface distribution of electrification, but 

 also for a volume distribution . as in the case of the ring- 

 electron, which is usually looked upon as a circular anchor- 

 ring of negative electricity rotating about its axis with large 

 velocity *. 



Sir Joseph Larmor f has pointed out that one or more 

 classical electrons constrained to move round a channel 

 would be like an amperean current. The same method of 

 proof might be applied in such a case, leading to the above 

 expression for the angular momentum. 



Angular Momentum and Planch's Constant. 



In his paper on the constitution of the solar corona, 

 Prof. J. W. Nicholson % first introduced the concept of a 

 natural unit of angular momentum, finding such a unit in 

 the quantity A/27T, where h is Planck's constant. This 

 is the quantity which appears in Bohr's theory as the 

 angular momentum of a " bound " electron. If we identify 

 this unit of angular momentum with the* angular momentum 

 of the magneton, we find 



Unit angular momentum = 7i/27r=N m Nr e /277V 



This identification gives the remarkable result 



or Planck's constant is equal to the product of the number of 

 tubes of magnetic induction and the number of tubes of electric 

 induction associated with the magneton. 



Assuming NT e = e, the natural unit of electric charge, 

 which is equivalent to identifying the magneton with the 

 electron, we find 



Taking 6 = 4-771 X 10" 10 E.S.U. and fc-6'558 x 10" 27 , this 

 gives N,„ = l-374xl0- 17 E.S.U. or 4120 xlO" 7 E.M.U., 

 assuming c = 2*999 x 10 10 cm. per sec. 



* Parson, " A Magneton Theory of the Structure of the Atom," 

 Smithsonian Misc. Coll. vol. lxv. No. 11 (1915). 

 t Proc. Phvs. Soc. vol. xxxi. p. 68 (1919). 

 X Monthly Notices, P.A.S., June 1912. 



12 



