THE ELECTRIC AND LUMINIFEROUS MEDIU^M, 
251 
sufficiently satisfied even if the intermediate layer is only one or two molecules 
in thickness ; for as these molecules are arranged slightly in and out, and not in 
exact rows along the interface, their polarity can still be averaged into a continuous 
density as above. The aggregate tractions over a thin layer of transition thus 
do not depend sensibly on the nature of tlie transition, but only on the circumstances 
on the two sides of the layer. 
37, In the case of a fluid medium, the bodily part of the forcive produces and is 
compensated by a fluid pressure jfT7F, where i', being the polarization induced by the 
electric force F, is for a fluid in the same direction as F and a function of its 
magnitude. This pressure will be transmitted statically in the fluid to the inter¬ 
faces combining it there with the surftice traction proper, it appears that the 
material equilibrium of fluid media is secured as regards forces of electric origin 
if extraneous force is provided to compensate a total normal traction towards each 
side of each interface, of intensity — 277)).'^ — In the case usually treated, 
in which a linear law of induction is assumed so that the relation between i ana F is 
% = (K — 1) F/Itt, the mechanical result of the electric excitation of the fluid medium 
is easily shown to be the same+ as if each interface were pulled towards each side by 
a Faraday-Maxwell stress, made up of a pull KF^/Stt along the lines of force and 
an equal pressure in all directions at right angles to them. But this imposed 
geometrical self-equilibrating stress-system would not be an adequate representation 
of the mechanical forcive in a solid medium ; for then the bodily forcive, instead of 
being wholly transmitted, is in part balanced on the spot by reactions depending on 
the solidity of the material. The forcire acting on isotropic material may hoAvever 
in every case, whether the induction follows a linear law or not, be expressed as an 
extraneous or imposed sj'stem, made up of bodily hydrostatic pressure dh (which 
in the case of a fluid only relieves the ordinary fluid pressure and so diminishes the 
compression, § 79 infrct) together with noroial tractions on the interfaces between 
dielectric media, of intensity — — \idY acting towards each side, and tractions 
— JfdF on the surfaces of conductors acting towards the dielectric, 
38. A similar analysis applies to the electromagnetic forcive acting on a magnetically 
polarized medium. Excluding as before the part arising wholly from the interaction 
of neighbouring molecules, which (§ 44 infra) is not transmitted by material stress, 
but is compensated on the spot by molecular action due to change of physical state 
induced by it, the electromagnetic forcive proper is made up of a bodily force (X, Y, Z) 
and torque (L, M, N), where, (yf, v , w') representing the true current, 
X = v'y — iv'^ -j- A dajdx B da/c7y + C dajdz 
= VC — ivb -{- A-diy-ldx fl- ^dftldx -h Cdyjdx — ydgjdt + (Bdhldt, 
* That is, a reacting pressure ftVZP exerted by the interface will keep the medium in internal 
equilibrium ; no constant term is added because the pressure must vanish along with the polarization. 
t It is a normal traction equal to — (K — I) (KN® -F T^)/87r towards each medium, or in all a single 
traction (K^ — Kj) (27r>r''2/K^K2 — T'/Stt) towards the medium 1. 
O T- o 
