Electrodynamics for Moving Ponderable Media. 47 

 given by the Maxwellian equations o£ the field 



curl! Hl!= ^— + Ji, div T> l =p 1 

 oh 



curliE^-^-, 



> 



div B 1= =0 



(2) 



J 



together with the constitutive relations in the form 



Di=KoEi, B 1 =/i H 1 , Ji^^Ej, ... (3) 

 where the symbols have their usual meanings, J 1 beino- the 

 true electric current and equal to the conduction current G L 

 for matter at rest, and k the conductivity of the medium. 

 Now transform back again to the original x, y, z s t space 

 by the transformation 



a! 1 = e(a—wt), yi=y, z^ — z, t x = e (t—wx), 

 obtained by solving equations (1), and by the third axiom 

 we shall obtain the electrodynamical equations for matter in 

 motion with a constant velocity w in the form 



curl Q= ~ -+-K, div R = t 



oG 



h 



(4) 



curl F=-~ divG = 

 dt J 



(5) 



where the vectors F, G, Q, R, K are connected with 

 F 1? Di, Hj, Bj, J x by the relations 



F={1,6,€}{E 1 -KB 1 ]} 1 



a={l,e,e}{B 1 +[«7,E l ]} 



R={1,6,6}{D 1 -KH 1 ]} 



Q={l,e,e}{H 1 4[^D 1 ]} 



K={e, 1,1} {Ji + wpi} 

 and 



T = e{/?i + (iu, JO}. 



Further, the constitutive relations (3) in the %, y x , j x , t t 

 space transform into 



G-[w,F]=^o{Q-[w,R]} L • (6) 



K_ Z(;T = £ {e- 1 ,e,e}{F + [>, G] } J 



which give the constitutive relations in the a?, y, z, t space in 

 which the matter is in motion with a constant velocity w *. 



* C/. Einstein and Laub, Annalen der Physik, vol. xxvi. (190S), where 

 a derivation of Minkowski's equations is given. 



