118 Dr. H. Stanley Allen on the Angular Momentum 



Now 2ir?ia = v, the velocity of the electricity as it travels 

 round the ring. Hence 



, 7©- 



, ba 

 loo- A- 



or 



[VM 



Since the peripheral velocity, r, must be less than c, the 

 velocity of light, log k must be greater than 



</<$)*>*■ 



which gives log — greater than 433, showing that p is 



r 



excessively minute compared with a. 



The Mass of the Parson Magneton, and the Radius of 

 the Ring. 



The electromagnetic mass of the Parson magneton has 



been investigated by Webster, who found an expression of 



the form 



e 2 . 8a 

 m = — =- lop - — , 

 irc-a 6 p 



in which the small term k has been omitted. This leads as 

 before to a very small value for the radius of the cross- 

 section of the ring, and it follows that most of the energy 

 and momentum of the field are concentrated very closely 

 around the ring. 



To obtain further quantitative information as to the 

 properties of the ring electron, one further quantity must be 

 known, and we shall assume for this purpose the value 

 of the radius a given b}^ A. H. Compton *, He finds 

 a= (l'85 + *05) x 10~ 10 cm. on the basis of an investigation 

 of the scattering of X-rays or 7-rays by the ring. Taking 



m = 8-999xlO- 2S gm., we find log(— -k\ =2064, which 



satisfies the condition that log— should be greater than 433. 



The value of vje is 433/2064, so that the peripheral velocity 

 is about one-fifth of the velocitv of liodit. 



* Bhys. Bev. vol. sir. pp. 20, 247 (1919). It is well to keep in mind 

 the possibility that the radius. of the ring may assume various values, as 

 in the case of the radius of an electron orbit in Bohr's theorv. 



