ON ELECTRICAL THEORIES. 149 
of the moving conductor. This equals Qaw, the same value as that 
given by Ampere’s theory, so that in this case the two theories lead to 
identical results, which are in agreement with the result of Helmholtz’s 
experiments. 
Rontgen has recently published! a preliminary account of some 
experiments which seem to prove directly that the variations in the 
dielectric polarisation produce effects analogous to those due to a 
current. 
This completes the account of the experiments which have been made 
to test the various theories. As the result of them we may say that they 
show that it is necessary to take into account the action of the dielectric, 
but they tell us nothing as to whether any special form of the dielectric 
theory, such as Maxwell’s or Helmholtz’s, is true or not. 
I have described two experiments which would decide whether 
Maxwell’s theory that all circuits are closed is true or not. It seems to 
me, however, that even if Maxwell’s theory be wrong, Helmholtz’s is not 
the only alternative. I have givena sketch of a theory in which I have 
tried to make as few assumptions as possible; al] that I have assumed is 
that when a dielectric is acted on by a changing electromotive force, 
it behaves like a conductor conveying a current whose intensity is pro- 
portional to the rate of change of the electromotive force. We know 
from experiment that it produces effects of the same character, and I 
have assumed as the simplest assumption I could make that for the same 
dielectric the equivalent current is proportional to the rate of change of 
the electromotive force, so that equivalent current = 7 (rate of change 
of electromotive force). 
Both Maxwell and Helmholtz assume that » depends only on the 
specific inductive capacity of the dielectric, but I think it is preferable, 
until we have more experiments on this point, to look on » as the measure 
of a new property of a dielectric, and not to assume that it is merely a 
function of the specific inductive capacity, the only experimental evi- 
dence for this being the by no means perfect agreement between the refrac- 
tive index and the reciprocal of the square root of the specific inductive 
capacity. To prove Maxwell’s theory of closed circuits it would not be 
sufficient to prove that for one medium, say air, 7 = K/4z, for it is quite 
conceivable that electrical phenomena may be simpler in a dielectric like 
air, Where the electrical behaviour of the ether seems to be but little 
affected by the presence of the dielectric, than in such a one as glass or 
other substance possessing a comparatively large specific inductive 
capacity, when the effect of the ether is seriously modified by the 
presence of the medium. 
Since in the theory I have sketched the values of 
du dv, dw 
de dy dz : 
and 1 (uy — Uy) + m (v) — vo) + 1 (wW, — We) 
are not zero, but arbitrary, inasmuch as they involve y, in order to find 
the value of the force between two circuits where there is any dis- 
continuity in the currents we shall require to know the value of the 
quantity # which occurs in vy. Helmholtz’s theory. 
The most pressing need in the theory of electrodynamics seems to 
1 Phil. Mag., May. 1885. 
