FUNDAMENTAL FORMULATIONS OF ELECTRODYNAMICS. 
229 
polarisation are to a certain extent similar to those connecting the electric force, total 
electric displacement and dielectric displacement, the similarity ends with these 
relations, and the dynamical characteristics of the two types of field are essentially 
different; and the analogy itself, so far as it exists, seems to be based on eri'oneons and 
confused conception of the nature of the magnetic energy as determined by the usual 
expression of the theory, so that it finds no place in a consistent formulation of the 
subject, notwithstanding even Heaviside’s spirited defence in criticism of Larmor. 
In his treatise Abraham adopts the analogy as a sufficient basis for the discussion 
of the magnetic theory, but decides that the procedure is not without its difficulties, 
particularly as regards the ferro-magnetic phenomena ; not being able to overcome 
these he condemns the whole procedure as being inadequate to include a proper 
account of these matters. 
10. We now turn from these discussions to a brief review of the general energy 
relations of the electromagnetic field. A concise account of these relations so far, 
that is, as they have been dealt with in existing accounts of the subject, has been 
given with full references in my treatise (Ch. XIV.), and it will suffice for the present 
to give the barest ’outlines of the discussion so far as they may be required. 
The fundamental equation expressing in its most concise form the energy principle 
for the electromagnetic field can be written in the form 
dW dT 
dt dt 
+ F+js.rf/ 
= 0 , 
wherein W and T are respectively the potential and kinetic energies inside any 
volume bounded by the closed surface f in the field, F is the rate of dissipation of 
electromagnetic energy into energy of other types such, for instance, as results 
mainly from the inertia of the electric charges constituting the conduction and 
convection currents ; and S is the vector determining the flow of electromagnetic 
energy outwards over the bounding surface. 
In this equation it is generally assumed that our knowledge of the forms of F and 
W is precise and accurate, and that in fact in agreement with the results of 
paragraph 8. 
VV = -l|E^dc4-|dcr(E'^T) 
8 7T J V 
where P is the polarisation intensity of the dielectric media produced by the electro¬ 
motive force 
E' = E + 1[V,.B] 
0 
whilst 
F = j(EC0du 
