220 
ME. G. H. LIVENS ON THE 
for the motion of the matter and of type 
/8Lo\ 
(it \'dxj 
for the electrical elements. In the first of these equations p = 2e is the density of 
the free charge, and Cj = is the density of the true conduction current; in the 
second equation r = + is the absolute position co-ordinate of the electrical 
element and v = f 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 
Wi = (E+i[f..B], JP) + (B-i[r„ E + EJ 
Interpreted in terms of the language of ordinary dynamics these equations imply 
that 
(PV)E, + (IV)B,+ i([PrJ, |S) 
1 
+ - 
c 
. dt 
+ C„ B 
_ 1 
X G 
dt' 
E + E„ 
+ ( Ej -t - [f’mB]; 
G 
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 fii’st of these results are consistent with those obtained 
by Larmoe* and others, but the magnetic terms, which are in fact analogous with 
the electrical terms depending on the dielectric polarisation, are fundamentally 
difierent from those obtained by these authors. Further, since 
it follows that 
E = - 
1 dK, 
c dt 
-V0, 
Curl E = - - 4 Curl 
c dt 
1 ^ 
c dt 
so that our equations are in complete agreement with the most general form ol 
Maxwell’s theory. 
* ‘aEther and Matter,’ Chap. VI. 
