50 Mr. H. R. Hasse on the Equations of 



the field in the form given by Larmor and Lorentz, viz., 



curl H = ^- + J + curl [P, iv] , div B = 0, 



curlE== ^-, divD = / o, 



(jt 



(ii) 



where we define a new vector P = D— E, and call it electric- 

 polarization. 



The corresponding constitutive relations deduced from (6) 

 and (7) are given by 



D + [«., H] + [to, [w, D-E]] = K {E + [w, B] }, 

 B-[ lr ,E]=MH-[»,E]}, 

 3-wp = h{e-\ e, e}{E+[w, B]}. 



(12) 



If we write out these equations in full, remembering that 

 they are only true for a vector whose components are 

 w, 0, 0, we should obtain them in the form given by the 

 author *. 



(C) If we make 



/ 3 =-[D-E,H 



/is + EB-H,**], 



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

 electromagnetic field in the form given by Walker f , which 

 correspond to his hypothesis of " continuous polarization ** 

 in the pettier and " molecular polarization " in the material 

 medium. The corresponding constitutive relations differ 

 from those used by Walker by terms of the second order 

 in w, so that his system does not completely satisfy the 

 principle of relativity. 



* Proc. Lond. Math. Soc. ser. 2, vol. viii. (1910) p. 190. Equations (10). 

 and (11). 



t G. T. Walker, " Aberration and the Electromagnetic Field," § 14. 

 Walker refers his equations to axes moving with the matter, and intro- 

 duces new vectors E' =E + [w, H], H'^zH— [?y, E] ; he also assumes 

 symmetry as regards all electric and magnetic quantities. A system of 

 electrodynamical equations of this type has been given by J. Ishiwara, 

 ''Bericht iiber die Relativitatstheorie," p. 621, Jahrbuch der Radioak- 

 tivitat, vol. ix. 1912, in which the general question of the equations of 

 electrodynamics for ponderable media is discussed. It is clear, however, 

 that a great number of systems of equations could be obtained and that 

 no one system is, from the standpoint of the principle of relativity,, 

 better than any other; it is only when we take account of some theory 

 of the constitution of matter that we can attempt to decide between the 

 various systems of equations. 



