Electromagnetic Mass of a Moving Electron. 539 



o£ light. The present paper reconsiders Abraham's discussion 

 and conies to the conclusion that the objection is not valid. 

 The discussion was suggested by the fact that it has been 

 proved that Maxwell's equations represent equally well the 

 sequence o£ electromagnetic phenomena relative to a set of 

 axes moving relative to the aether, as relative to a set of axes 

 fixed in the aether. More explicitly this is stated as follows : — 

 If there are two sets of rectangular axes (A, A') coinciding 

 at a certain instant, of which A' is moving relative to A with 

 velocity v in the direction of the axis of a?, which is conceived 

 as at rest, and if a\ y, ~, t be space and time variables 

 associated with A, and x\ y' c', t' similar variables associated 

 with A', then the equations 



1 dE , -TT- 1 ^H , -^ 



- -^— =curl H, — =— = —curl E, 

 c d f c Qt 



transform identically into the equations 



1 BE' , .p., 1 dH' 



- -^7 =curl ri, - -^zy = —curl ±j , 



c of c o? 



the accented and unaccented magnitudes being connected bv 

 the relations 



/3 = (l-^r)- 



<>-?)■ 



E 



H 



' = /3(^p H,+ rE„ H,-,E,). 



Further, if p=-r~ div E. and p' = — divE' the volume 



integrals taken through corresponding regions t, t', \ T pdr and 

 \ T <p'dT' are identically equal, giving an exact correspondence 

 as regards distribution of electric charge. 



Thus the above transformation renders the electromagnetic 

 equations of a system independent of a uniform translation of 

 the whole system through the aether *. 



* The transformation in question is given by Einstein in a paper in 

 the Annalen der Phi/sik, xvii. (q. v.). It is in substance the same as that 

 given by Larmor in • ./Ether and Matter,' chap. xi.. though the correlation 

 is only proved to hold as far as the second power of r c. Prof. Larmor 

 tells me he has known for some time that it was exact. Vide also 

 Lorentz. Amsterdam Proceedings, 1903-4. 



