Energy in ihe Electrodynamic Field. 391 



In his theory, however, Macdonald neglects the presence 

 of magnetism, or at least he includes it as effectively repre- 

 sented in the total current o£ the theory, so that in his case 

 the integral in I does not appear. This procedure is not, 

 however, completely satisfactory as it fails to take into 

 account the fact that a part of the total magnetic energy of 

 the system corresponding to the magnetic polarization of the 

 media of the field, and which represents intrinsic energy 

 of those media temporarily classified as magnetic, is not 

 effectively available mechanically. Further, the magnetic 

 distribution in any arbitrary finite volume of space cannot 

 be completely represented as a continuous current dis- 

 tribution throughout that volume, but must at least be 

 supplemented by a distribution of surface currents over the 

 bounding surface of the space. 



For the purposes of a mathematical theory it may, how- 

 ever, be desirable under some circumstances to replace 

 the magnetism by its effectively equivalent current dis- 

 tribution. This can be done bv transforming the integral 

 iu I. In fact we can write 



j;(4>-£(-4> 



so that we can now use 



T = i ( (AG')dv-(dv f (Curll.dA) 

 and 



B =^H] + ^[AB]-[§.I], 



and in the former expression c Curl I represents the current 

 density of the electric flux replacing the magnetism. 



4. The transformation adopted by Macdonald is not, how- 

 ever, a unique one. Starting again from the relation 



jy - 1 i^ dv 'i{ i §)^ + 4# EH ^ 



we can write 



£ij>*-ii(-f)*-iX(«^f)* 



