THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
297 
If the lower medium were conducting, we should have had 4.iC + = 0, and the 
electi-ic downward traction would be — K^NiYStt, that is — K^A^VStt + ?n/ 47 r. 
cos mx. Thus in the equation giving as above the velocity of propagation, the 
electric term would be - Ai747rm, or — where a is the density of the 
electrification on the interface. The effect of this electrification is thus the same as 
that of a diminution of the surface tension by 2cr^X/K,^, where X is the wave-leno’th.'"' 
_ 1 . / i • 
81. Relations of Electrijication to Vapour Tension and Fluid Equilihrium. _It 
has already been shown 52) that the possibility of mechanical equilibrium between 
fluid dielectrics which do not mix requires tliat the electric tractions on the interface 
shall be in the direction of the normal. There are also other dynamical relations 
ceducible fioin the fact that such forcives, when integrated round a closed circuit in 
fluid media, must give a null result, in order to avoid the establishment of cyclic 
perpetual motions. The earliest example which led the way to relations of this kind 
was Lord Kelvin’s establishment of a connexion between the vapour tension of a 
liquid and the curvature of its free surface ; and similar balances must independently 
hold good between vapour tension and other causes of surface traction. 
Consider in the first place a volume of conducting fluid with a large horizontal free 
surface. Let an electric field be established over a portion of this surface ; there 
will be a surface density a- of electrification induced over that portion, which will 
vary from point to point ; while the electric forces will elevate the surface bv an 
«/ 
amount h, — 2TTCT~lgp where p is the density of the fluid, above the level at a 
distance where there is no electrification. The vapour tension over the electrified 
part must thus be smaller by gpf than over the unelectrified part, where p^ is the 
density of the vapour. This difference of tension must be the natural steady 
difference produced by the electrification of the surface ; for otherwise a process of 
distillation will set in and there could not be equilibrium, though there could 
theoietically be perpetual generation of work while the temperature remains uniform, 
as the electric charge does not evaporate with the fluid. It follows that an 
electiification of surface density cr must depress the equihbrium vapour tension 
by an amount 27ra-7o/p-'*' 
Suppose again that the fluid is a dielectric of inductive capacity K, and has no 
free charge. A similar train of reasoning shows, by the formula of § 87, that when 
the polarization of the material dielectric, at the surface, is made up of a normal 
component n' and a tangential component t', its vapour tension is thereby diminished 
by an amount 27r (Kn'^ + t'^)l(K — f). pfp. Conversely, we can argue that, as the 
change of vapour tension can depend only on the state of polarization or electrification 
at the part of the surface which is under consideration, the effect of the electric 
excitation must be completely expressible l)y a mechanical traction over the surface 
* T]ai.s result was given twice too large in ‘ Proc. Camb. Phil. Soc.,’ April, 1890. 
t This agrees with a result given by Prof. J. . 1 . Thomson, “ Applications of Dynamics to Physics and 
Chemistry,” 1888, § 86. 
VOL. CXC.—A. 2 q 
