220 MR. G. H. LIVENS ON THE 



for the motion of the matter and of type 



d /3L n \ 3L . /ui . I r m 



for the electrical elements. In the first of these equations p = 2e is the density of 

 the free charge, and C t = 2er e is the density of the true conduction current ; in the 

 second equation r = r m + r e is the absolute position co-ordinate of the electrical 

 element and v = r is its resultant velocity. 



In addition we have the variational equation for the internal energy which can be 

 left as it stands in the form 



' *- l -[t m , E + E ], 



G 



Interpreted in terms of the language of ordinary dynamics these equations imply 

 that 



(PV)E I+ (IV)B I+ if[PU|?)-7 



-Ti +C - B l [ E+E 1 



c L dt Jz c Lai J x 



is the force per unit volume at each place tending to accelerate the motion of the 

 matter, whilst 



is the force tending to accelerate the motion of the element of electricity e. 



The electrical terms in the first of these results are consistent with those obtained 

 by LAKMOR* and others, but the magnetic terms, which are in fact analogous with 

 the electrical terms depending on the dielectric polarisation, are fundamentally 

 different from those obtained by these authors. Further, since 



c dt 

 it follows that 



Curl E - - - 4 Curl A I 

 c dt 



_ 



c dt ' 



so that our equations are in complete agreement with the most general form of 

 MAXWELL'S theory. 



* ' -(Ether aud Matter,' Chap. VI. 



