ON ELECTRICAL THEORIES. 127 
on by electromotive forces which polarise it. This statement is one as 
to whose truth nobody seems to entertain any doubt, whilst the state- 
ment that changes in the dielectric polarisation produce effects analogous 
to those produced by ordinary conduction currents is by no means so 
universally received, and yet the one seems the necessary consequence of 
the other. If we regard the whole electric field as a dynamical system, 
and to fix our ideas consider an element a of the dielectric, and the cur- 
rent, which is supposed to vary, then, since a variation in the current 
polarises a, 7.e., produces a change in its structure, there must be 
mechanism connecting the current with the element a; but if this is so 
then it follows from dynamical principles that a non-uniform variation 
in the structure of a must produce a change in the current—in other 
words, that a change in the rate of change of the polarisation of a pro- 
duces an electromotive force on the current, i.e. that the change of polarisa- 
tion produces an effect analogous to that of an ordinary conduction 
current. We may illustrate this by a purely dynamical example. Sup- 
pose we have a dynamical system defined by two co-ordinates p and q, 
and let T be the kinetic energy of the system and V the potential energy ; 
then by Lagrange’s equation the force tending to increase q 
Mind Mair eet dh. 
agay Weeds 
Now if there is a force tending to alter g which depends upon the 
acceleration of p, there must be a term in the kinetic energy of the 
form 
Apd; 
but if we apply Lagrange’s equations to the p co-ordinates we see that 
this term implies the existence of a force tending to increase p equal to 
ad 
cw Aq, 
sso that an acceleration of gq will produce a force tending to alter p. 
To make this applicable to the case of the current and the dielectric, we 
have only to suppose that p represents the current, g the polarisation of 
the dielectric. That a change in # produces a change in q is shown by 
the fact that the dielectric is polarised when the current is changing, and 
this shows that there must be a term of the form Aj@, in expression for 
the kinetic energy ; from this it follows that a change in 4, 7.e., in the rate 
of change of the polarisation, will produce an E.M.F. on the circuit. As 
the variation of the dielectric polarisation produces the same effect as a 
conduction current, we must in the case, when both conduction current 
and alteration in the polarisation are present, look upon the true or effec- 
tive current as the sum of the conduction current and the change in the 
polarisation. 
The components f, g, h of the dielectric polarisation are defined by the 
equation 
K K K 
inde gee ge 
where K is the specific inductive capacity of the medium, X, Y, Z the 
components of the electromotive force. If u,v, w are the components 
of the effective current, p, g, r the components of the conduction 
