230 MR. G. H. LIVENS ON THE 



where C, represents the part of the total current depending on the motion of the 

 electrons constituting the conduction current and the current due to the convection 

 of electric charges, but excluding the part due to the convection of the polarised media. 



It seems difficult to dispute the form of the expression for W, but careful 

 consideration will also convince one that it is probably just as difficult to support it in 

 the most general case, except it be by the results which are derived from it, which 

 certainly seem to be in satisfactory agreement with our knowledge of these things. 

 A similar reservation must be applied also to the expression for F, but there is here 

 an additional point worth noticing. It is not often remarked that the form given 

 tacitly involves an assumption which is derived as an independent result from 

 discussions based on this special form. In fact it involves the definite assumption 

 that no work is done by the magnetic forces during the motion of electric charges. 

 Of course the usual expression for such force as proportional to the vector product of 

 the velocity and magnetic force confirms this assumption, but the derivation of this 

 expression by dynamical methods from results derived from the present discussion is 

 by so much deprived of interest. In fact, if to the assumption that these forces do 

 no work we add the further conditions that they are linear in the magnetic and 

 velocity vectors, it would appear that their form is completely determined, at least to 

 a constant factor, without further considerations either of a dynamical or any other 

 nature; 



The form for the expression T is not usually regarded as being sufficiently definite 

 to be used in the present connexion, mainly because it is the more readily convertible 

 into equally simple alternative forms. We have in our previous discussions made 

 certain assumptions which have proved to be equivalent to taking 



but this special form will subsequently be proved to be irrelevant to the discussion. 

 It is usually regarded as being most advisable to consider the expression for T as 

 bound up with that for S, the equation connecting the two being that derived from 

 the energy principle by the insertion of the forms chosen for W and F, viz., 



dv 



C being now the total current of MAXWELL'S theory. This is all we can derive from 

 the energy principle. The various possibilities open to us have been examined in 

 detail before. We may take 



Ourl H = C 

 c 



^ 4- JS. df = _ j (EC) cto- j|( 0,,,B], *) dr 4 1 J (E, Curl [P..] ) 



