Energy in the Electrodynamic Field. 393 



in the media of the field, temporarily classified as magnetic, 

 less that part of it which is associated with the mechanical 

 forces on the polarized media, and which is available only 

 in so far as the presence of the media increases the available 

 energy in the field. This difficulty seems to place the last 

 form of the theory beyond the range of physical possibility; 

 further, the actual form of the theory adopted by Macdonald, 

 which is the mean of this theory and the simpler and more 

 general one first obtained, is open to a similar criticism 

 and must therefore itself be regarded as inadmissible as a 

 physical theory. 



The point involved in these remarks is further emphasized 

 by the fact that the term in the magnetization which is 

 properly expressed as available energy does not, on Mac- 

 donald's theory or the one alternative, fit in with the 

 remaining terms in the expression for the kinetic energy, 

 as it does in the simpler theory ; and it may be illustrated 

 by an appeal to the fundamental physical basis of the 

 theory. In this theory the vector 



~ Adv 

 c 



is taken as measuring the electrokinetic momentum in the 

 small element dv of the field : the force assisting the rate of 

 change of this momentum is in consequence 



■di ldA J 

 F = --jr-dv. 



c at 



On the other hand, the velocity of displacement of the 

 affected medium is assumed to be measured by the total 

 current C, so that the rate of working of the forces on the 

 small element is 



!(«tf)* 



which must represent the rate of gain of available kinetic 

 energy in the element, in agreement with the one form of 

 the theory. 



6. Of course, if we rely on these physical ideas and agree 

 to retain only the simplest and most general form of the 

 new theory, we must expect to encounter difficulties of 

 a fundamental kind. In fact, we cannot in general assume 

 that 



j dv f (CdA) = \dv i (AdC) ; 

 so that, even if there is no magnetism, the intrinsic energy 



