﻿22 Mr. G. A. Schott on tli 



ie 



from Maxwell's equations of the electromagnetic field by 

 direct integration. They are identical with those obtained 

 by Abraham * by an indirect process. 



The mass m is of electromagnetic origin, at any rate in 

 part. It can be shown by the method o£ dimensions that the 



electromagnetic part of the mass is of the form p^K/^), 



where a is a length, which we shall take to be the mean 

 radius of the electron, and yfr(0) depends on j3 and on the 

 shape of the electron. If a be supposed invariable, as is 

 usually done, m is constant when ft is so; but this restriction 

 is unnecessary. The variation allowable in a is very small ; 



for — = , and m cannot possibly vary at a greater rate 



than, let us say, J per cent, per annum ; that is, - is certainly 



less, and probably very much less, than 10 -10 . 

 § 3. The force (T, P) consists of two parts : 



(1) (T 1? Pi) due to electrons outside the ring ; 



(2) (T 2 , P 2 ) due to the remaining electrons of the ring. 

 In the first place, T 1 vanishes for a system of electrons in 



steady motion. 



For Ti is due partly to a steady electric force, partly to a 

 steady magnetic force. The electric part vanishes, because 

 the lines of force of a steady electric field cannot form closed 

 curves. The magnetic part vanishes, because the mechanical 

 action of a magnetic field on a moving electron is always 

 perpendicular to its velocity. 



Secondly, I find for (T 2 , P 2 ) the expressions 



2 3p 2 (l-/3 2 ) 2 p 2WU ' 



where 



„ ^-n mi 



K = 2, t cosec — , 

 »=i 4 n 



P,=-^(l+/9")K+JV, 



U = 2V[OT/3 2 J' 2OT (2sn/3)-sV(l-/3 2 ) i J (Zmx)dx\ t 



s=l J 2sn 



V=lVi) ^-^±^[,3(1-/3^ {(2,+ l)/8} 



+ (l + /3 2 ) J {(2* + l)x}dx\ 



\ 2s+l 

 * Theorie der ElektrizitMt, vol. ii. p. 123 (85). 



