FUNDAMENTAL FORMULATIONS OF ELECTRODYNAMICS. 

 and then we get POYNTING'S theory in which 



231 



T = 



and 



where 



' = H-47r[P IV ] 



is equivalent to the vector H' introduced in paragraph 8. 



This theory has the advantage, in addition to that already discussed at length, that 

 it involves no further dynamical assumption other than those expressed in the special 

 forms chosen for W and F. The Amperean equation used to effect the separation 

 being more in the nature of a kinematical definition of the electric current or magnetic 

 force than of a dynamical relation between the field vectors. 



Another form can be obtained by using the equations 



with 



we then get 



J dA. 

 ~rt--8 



div C = 

 ' 



with 



T = - \dr ' (i'dA)- ' dv ( 1-UPI) 



C J ~ c * J 



-c I* (Curl [PvJ, d\.) 



S = (C-c Curl [Pi/J). 



The special form of this result when the media are at rest has been shown* to be 

 inconsistent with our usual conception of such things as radiation phenomena. 

 Yet another form of the theory can be obtained by taking 



T = - dt 



\ [(EC+ i ( k,B], ^]-c (E Curl [P, J)] dv 



and then 



S = 0. 



In such a theory there would be no such thing as radiation. 



We can go on multiplying the different forms of this theory indefinitely and each 

 form obtained would in itself be perfectly consistent with the Maxwellian 

 electrodynainic theory. The expressions for S and T in them are of course dependent 



VOL. COXX. A, 



* 'Phil, Mag-,' vol. 34 (1917), p. 385, 

 2 K 



