FUNDAMENTAL FOEMULATIONS OF ELECTRODYNAMICS. 
245 
and the magnetic polarisations give rise to the analogous terms 
\Yith 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 mdiation phenomena, to the 
energetic relations of the magnetic media and, finally, to the fundamental problem of 
the representation of the forces in the field, 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 emphasi.se the fact that the theory in its complete form is entirely independent of 
the.se 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. 
PRESENTBlu 
2 0 Ilf AR 13^0 
