388 Mr. G. H. Livens on the Fluoc of 



theory depending on the motion o£ the electrons : it includes 

 a part due to the changing polarization in the dielectric 

 medium, the work corresponding to which is stored up as 

 potential energy in that medium ; also a part due to moving 

 electrons constituting true conduction currents, the work in 

 which is converted into heat in Joule's manner ; and finally 

 a part due to the convection of electric charges and polarized 

 media, the work corresponding to which is stored up as 

 potential energy in the mechanical configuration of the 

 system or as kinetic energy of its organized motions. 

 Thus we have 



dt ~ dt 

 C -° 1 + Sr"^ 



f(EC)dt>, 



is the total current of Maxwell's theory. 

 It follows that 



§ + JV/= -jaw)*, 



which is the relation between S and T that must in every 

 case be satisfied. It is a consequence solelyof the energy 

 principle and approved ideas in electrodynamic theory. In 

 proceeding from this relation various possibilities are.!' now 



open to us. 



Poynting's form of the theory is immediately obtained by 

 transforming the integral on the right by the substitution 



G = 4- Curl H 

 given by Ampere's circuital relation. We have then 

 T^(EC) = ^ f (B Curl K)dv 



= _4£ [ EH]^ /+ / 7r |(HCurlE)^ 



since by Faraday's relation 



c dt 



