Electrodynamics for Moving Ponderable Media. 49 

 moving with a constant velocity are therefore 



curl{H+/ 3 }=<g + |f +J+/ 5) 



curl{E+/ 1 } = - 3< -^, 



div {D+/ 4 }=p+/ 6 , div{B+/ 2 }==0.j 



(8) 



The corresponding constitutive relations are obtained by 

 substituting in equations (6) the expressions for F, G, Q, R, 

 K, and r given in equations (7). It is clear that we have 

 satisfied all the conditions given in Minkowski's three 

 axioms, and that equations (8) are true in the two limiting- 

 cases of media at rest and free sether, regard being had 

 to the conditions limiting- the form of the functions 



Jljj2i • • • • /6- 



§3. 



We have now to show that by suitable choice of these 

 functions the equations of the electromagnetic field (8) can 

 be made to agree with those given by various physicists. 



(A) Minkowski obtains his equations by interpreting 

 F, R 5 Q, G, K, and t as electric force, electric displacement, 

 magnetic force, magnetic induction, true electric current, 

 and density of true electricity respectively. This is equi- 

 valent to assuming that all the functions f\, / 2 , .... / 6 are 

 .zero, and the equations of the field are then 



curlH=^+J, divB = o") 



% B \. ' 0» 



curlE=— -^- , divD=/oJ 



The corresponding constitutive relations obtained from 

 (6) and (7) are 



D+[^H]=K {E+[^B]}, 

 B-[w, E]=^{H-KD]j, 

 J-wp = k {e-i,e,e}{V + [w,BY 



(B) If we make 



/jE£-[D-E,£l>] 



and all the other functions zero, we obtain the equations of 

 PJiiL Mag. S. 6. Vol. 27. No. 157. Jan. 1914. E 



