FUNDAMENTAL FORMULATIONS OF ELECTRODYNAMICS. 245 



and the magnetic polarisations give rise to the analogous terms 



With the exception of the magnetic terms these results are in general agreement with 

 those usually derived on the basis of the electronic theory, and the discrepancy in the 

 magnetic terms is proved to arise from the inadequacy of the treatment of the 

 magnetic relations in that theory, no allowance being made in it for the convection of 

 the magnetic polarisations. 



The results derived from the dynamical theory are then examined in connexion 

 with the usual developments of the theory in regard to radiation phenomena, to the 

 energetic relations of the magnetic media and, finally, to the fundamental problem of 

 the representation of the forces in the Held, as an applied stress system and the 

 subsidiary question of electromagnetic momentum. In regard to each of these results 

 are derived which do not differ materially from those usually given, but the slight 

 discrepancies in each case, although probably of little or no practical significance, 

 prove ultimately to be of theoretical importance as helping to justify the fundamental 

 equations on which they are based. The auxiliary conception of electromagnetic 

 momentum is not however completely attained under the most general conditions, 

 although it will still remain to enable us to obtain an effective mode of expressing 

 certain results of the simpler theory ; it is probably present in no other capacity in 

 former interpretations of the theory so that this is hardly a disadvantage of the present 

 formulation. 



The present theoretical relations require, of course, to be supplemented by the usual 

 empirical laws for the induction of the two polarisations and the conduction current. 

 We have however specially refrained from introducing these relations as it was desired 

 to emphasise the fact that the theory in its complete form is entirely independent of 

 these laws, so that for example it necessarily covers the most complex fields. 

 involving ferromagnetic inductions and polarisations. If we interpret the theory as 

 determining the electrodynamic changes in the system during its transition from one 

 configuration to another even the presence of hysteritic qualities in the inductions 

 will not vitiate its validity. This is, of course, no special advantage attaching 

 to the present form of the theory as it is in reality fundamentally inherent 

 in every interpretation, although it may be hidden by the particular form of 

 expression adopted. 



