FUNDAMENTAL FORMULATIONS OF ELECTRODYNAMICS. 223 



This result is consistent with that generally obtained in these theories. The last 

 term arising on account of the current due to the convection of the polarisations is 

 however probably of kinetic origin. 



Of course, in the general case, all the potential energy put into the field cannot be 

 got out of it again in the form of useful mechanical work, or, in other words, it is not 

 all available. The effectively available energy in the present case consists in the main 

 of the part 



For the magnetic polarisations the results are somewhat different. Tn this case the 

 kinetic energy of the field is assumed to be 



to which we must add the intrinsic kinetic energy involved in the induced magnetic 

 polarisations to obtain the total energy in the field ; reckoned as potential energy the 

 intrinsic energy is 



\dv\(B'dl), 

 and therefore as kinetic energy it is 



-JdvJ(B'dl), 

 giving a total for the field equal to 



OTT 



= _L I'd,, [(BdH) + - \dv f (E + Eo, [dl, rj), 



47T J J C J J 



a result which is again practically equivalent to that usually given in this theory. 



If we treat the convection of the dielectric polarisation as effectively equivalent to 

 a magnetic polarisation of intensity 



T' - I [PU 



C- 



and the convection of the magnetic polarisation as effectively equivalent to a dielectric 

 polarisation of intensity 



P' = -l 



VOL. CCXX. A. 2 I 



