230 
ME. C4. 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 l)e applied also to the expression for F,‘ l>ut 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 detinite assumption 
that no work is done by the magnetic forces during the motion of electric charges. 
()f course the usual expression for such force as proportional to the vector product of 
the velocity and magnetic force confirms this assumption, hut tlie derivation of this 
expression by dynamical methods from residts 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 tliat 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 
T = — 1 dr f (H rZB), 
Att J j 
but this special form will subsequently be proved to he 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., 
C J 
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 
Curl H = — 
c 
