and some Related Properties of the Ring Electron. 117 



The left-hand side of this equation gives the magnetic flux 

 through the aperture of the magneton in maxwells, and we 

 see that the flux in maxwells is equal to the electron charge 

 (in E.S.U.) multiplied by a numerical factor. 



Let L' denote the self -inductance of the ring in electro- 

 static units, and n the number of revolutions per second of 

 the electricity in circulation. Then N m = li'ne, and 



2tt 

 or 



Q 



. LW =\/(S 5 )x lfe2 

 Or, if L denote the self-inductance in electromagnetic units, 



L "/'-=\/(i?) x16 - 



2tt 

 9. 



It would be interesting to know whether a toroidal surface 

 could be found which would require a factor of the form 



</m* 



in the formula for its self-inductance. 



It is usual to assume that the ring electron is of the form 

 of an anchor-ring of circular cross-section. Webster * has 

 pointed out that, in order to account for the observed mass 

 of the electron, it is necessary to suppose that /?, the radius 

 of the section, is very small compared with a, the radius of 

 the circular axis. The self-induction of electric currents 

 in a thin anchor-ring of this type has been investigated by 

 the late Lord Rayleigh f. When terms involving the square 

 of p/a are neglected, the formula for the self-inductance is 



L = iira log k L 



P 



where k has the value 2 when the current is limited to the 

 circumference of the anchor-ring, and the value 7/1 when 

 the current is uniformly distributed over the cross- section. 

 In the present problem the term log 8a/ p is so large that the 

 difference between the values of k is inappreciable. 



Substituting this value for L in the previous equation, 

 we find 



[>°*T-']-^lfH- 



4:7rna r\ 8a 



or 



P 



* Webster, Phys. Rev. vol. ix. p. 484 (1917). 



f Rayleigh, Roy. Soc. i'roc. vol. lxxxvi. p. 562 (1912); 



