Electrodynamics for Moving Ponderable Media. 51 



It is of interest to note in passing that Minkowski's 

 equations of the electromagnetic field are identical with 

 those obtained by Walker from the hypothesis of " con- 

 tinuous polarization " both in the aether and in the material 

 medium. 



We have thus shown that Minkowski's method of applying 

 the principle of relativity cannot lead to a unique system of 

 electrodynamical equations for matter in motion, for we 

 have no means of determining from the three axioms alone 

 the functions/!, f 2 , . . . .f G . 



§4. _ 

 If we remove the second restriction (/>) on the functions 

 fu fit • • - f% in (7), we can include in (8) the equations of 

 the electromagnetic field for moving media as given by 

 Hertz. These are, in our notation, 



curlH=|2 + J + curl[D, «;], 



ot 



curl E = — ~ — curl [B, w~\ , 

 Ot 



divD = />, divB = 0. 



On comparison with equations (8), these make f 2 =/ 4 =0, 



/ 1= -[D, w], / S =[B,.«7], 



so that the corresponding constitutive relations from (6) and 

 (7) should be 



D+[w,H] + [>, [w, D]] = K E, 



B-|>,E]+j>, [w,B]]= A * H, 



J— pw = k {e~ l , e, e}E. 



These are of course different from the constitutive re- 

 lations given by Hertz, but it is clear from the way in 

 which they have been obtained that they satisfy the principle 

 of relativity, and from this point of view complete a scheme 

 of electrodynamical equations by adding on to Hertz's 

 equations of the field the correct constitutive relations. 



The above equations differ from those in § 3 (A) (B) (C) 

 in that in Hertz's equations the free sether is not defined by 



D-E = B-H = J-^ = 0, 

 and consequently not by 



K = /i =l, *o=-0j 



the aether in his theory being always in motion with the 

 moving medium. 



E 2 



