L. Page — Relativity and the Ether. 169 



Art. XVII. — Relativity and the Ether; by Leigh Page. 



The object of this paper is to discuss the properties of a 

 type of ether which is consistent with the Principle of Rela- 

 tivity, and to show that all the phenomena of electrodynamics, 

 — those relating to accelerated charges as well as those involv- 

 ing charges moving with constant velocity, — are an exact con- 

 sequence of the postulate of the relativity of all systems which 

 are moving with constant velocities. Also an expression will 

 be derived for the electromagnetic mass of an electron whose 

 Held is not quasi-stationary, as in the case of Abraham's, 

 Bucherer's and Lorentz's electrons. 



Let K and K' denote two systems moving with constant 

 velocities, the velocity of the second relative to the first being 

 v. Let XYZbe a set of orthogonal right handed axes fixed 

 in K and so oriented that K' is moving relative to _iTin the 

 direction of the Z axis. Let X' Y ' Z r be a set of axes fixed in 

 K' and mutually parallel to XYZ. Unprimed letters denote 

 quantities as measured in K and primed letters the same quan- 

 tities as measured in K '. The Principle of Relativity demands 

 that the velocity of a light wave proceeding in any direction 

 shall be the same whether measured by an observer in K or 

 by one in K '. The mathematical expression of this condition 

 is contained in the familiar Lorentz-Einstein group of homo- 

 geneous linear transformations.* 



(1) 



V1-/3 2 V1-/3 2 



where c = velocity of light, and /3= -. By differentiation the 



usual transformations for velocity and acceleration can, be 

 obtained. 



t'— 



t- 



'IL 





■-/»* 



x'= 



-X 





y'-- 



=y 





?;= 



z- 



-m 







f — 









vr 



-F 



X = 



-X 





V = 



--y' 





Z — 



z' 



+ vt' 



/ V' 2 V 



K- _, v; _r l — ,^;.v^ 



v, r 



V 1 e » H c (9) 



y- V -~ v V - V '' + " 



z — y z — y 



l-pf i+fiT 



* Einstein, Annalen der Phvsik, xvii, 891, 1905. 



