48 Mr. H. R. Hasse on the Equations oj 



§2. 



We have now to decide what physical interpretation is to 

 be attached to the symbols occurring in the equations of the 

 electromagnetic field (4) and in the constitutive relations (6), 

 for the final form of the electrodynamical equations for 

 moving ponderable media depends entirely on the meanings 

 given to the various quantities. The equations (4) have to 

 satisfy two conditions, (a) for w = Q they must reduce to the 

 Maxwellian equations for matter at rest in which the physical 

 interpretation of the symbols involved is definitely known, 

 and (b) they must for the free sether reduce to the known 

 equations for electromagnetic disturbance in that medium. 

 The constitutive relations (6) must also be consistent for the 

 ease of the free a?ther, where K =//- =l, and £ = 0. 



These conditions are all satisfied if we put 



F = E +f x (w, D-E, B-H, J-pw) 1 

 G = B + f 2 (w, D-E, B-H, J-pw) | 

 Q=H-f/ 3 0, D-E, B-H, J-pw) ' 

 R = D + / 4 (w, D-E, B-H, J-pw) 

 K=J + f 5 (w, D-E, B-H, J-pw) 

 r = p +f 6 (w, D-E, B-H, J- ptv ) 



where E, H denote the electric and magnetic forces B D 

 the magnetic induction and electric displacement respectively 

 p the true electric density, and J the true electric current! 

 This latter is equal to the sum of the conduction current C 

 and the convection current pw, so that 



J=Ch- pw. 



The vector functions /„ / 2 , . . . are to be so chosen that 

 they vanish when w = 0, and also when 



D-E=B-H=J-p«;=0, 



h • • 0) 



i. e. vanish for media at rest and for the free sether, but are 

 otherwise arbitrary. If the resulting electrodynamical 

 equations are to be linear in the electric vectors involved 

 the functions f\, /„.... must further be limited so 

 as to be linear functions of their nine electromao-netic 

 variables. 



The final equations of the electromagnetic field for media 



