FTTXDAMEXTAI. FOR>rrLATTOX,S OF ELECTRODYXAMICS. 
225 
This last remark points to the possibility of obtaiiimg an elementary deduction of 
the expression 
E+ - B] 
c 
for the complete electromotive forcive simply by calculating the rate of cliange of 
intrinsic energy of a moving bi-pole, and the calculation has in fact been carried out 
by Larmor,^ taking however a parallel plate condenser with equal and oppositely 
charged plates, moving in a uniform magnetic field. 
An analogous argument in the magnetic case will give a deduction of the magneto¬ 
motive forcive 
B- - [.V, E], 
9. We have stated that the magnetic energy expressions just obtained are 
effectively equivalent to those usually derived, whereas as a matter of fact this is true 
only of the final result; the various formulm employed in the derivation of this result 
are not in their usual form but it has been shown elsewheret that they are consistent 
with the complete dynamical theory, the more usual formulge and the various 
modifications of them which have from time to time been suggested being all 
inadmissible on this score. ,A complete discussion of the justification for this last 
statement is necessarily beyond the scope of the present paper, but it may perhaps 
serve a useful purpose if a brief outline of some of the more important reasons is 
given, especially as they have some bearing on points raised elsewhere in the jiresent 
discussion. 
In the first place there is probably little or no difhculty in seeing the fallacy in the 
usual and simplest form of the theory wherein the expression //HYStt for the magnetic 
energy density is derived in the statical theory as potential energy and in the 
dynamical theory as kinetic energy : we need only enquire as to the type of energy 
represented by the same expression when the field is due in part to rigid magnets 
and in part to steady currents. The more consistent result is obtained by taking 
47r 
as the expression for the density in the statical case as this agrees with the opposite 
sign in the dynamical case and yet gives the same total. 
There is however another form of the results first tentatively suggested by Hertz 
and Heaviside and subsequently developed in great detail by other writers, more 
particularly by K. Gaxs| and H. Weber, wherein the difficulty presents itself in 
* ‘ Proc. bond. Math. Soc.’ (1915). 
t Cy. my ‘ Theory of Electricity,’ p. 417, or ‘ Roy. Soc. Proc.,’ vol. 93, A, p. 20 (1916). 
+ ‘ Ann. der Physik,’ vol. 13 (1904), p. 634, and ‘ Encyklopadie der Math, Wissensch.,’ vol. v., art. 15, 
where references to other authors will be found. 
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