296 
]\[R. J. LARMOR OX A DYNAMICAL THEORY OF 
the gradual rise of the charge of the condenser and its residual discharge. With 
such a “glass thread electrometer” it appears that the curvature takes place 
gradually on excitation, occupying for small charges sometimes as long as 30 seconds: 
and on discharge it is annulled with corresponding slowness. As part of this 
deformation is intrinsic, that is, due to molecular forces and not to the mechanical 
stress, it is a direct indication of gradual shaking down of the material into modified 
molecular groupings under the influence of the electric field. 
80. Influence of Polarization of a Fluid on Surface Ripples.— TIiq last illustra¬ 
tions helon^ to cases in which the field of force is uniform, so that the bodily 
mechanical forcive vanishes. A problem amenable to experimental examination, in 
which this is not the case, is the influence of electric polarization on ripple motion in 
fluids. The fluid, in a glass dish, might for example form part of the dielectric of a 
horizontal condenser, of which the upper coating is a wire grating separated from the 
fluid by a plate of glass or mica so as to prevent communication of electrification to 
its surface. 
Taking the axis of y downwards into the fluid whose dielectric constant is K.., and 
the axis of a: along the interface, the electric potentials in the two fluids, of which 
the uppei will usually be air, are — A^y -}- BjC'^'^cos iiix, = A.,ycos wiai. 
subject to the condition that at the interface y = 0 cos nix we must have 
and dV fdn =■ Kn dYfdn. riius A^C -f- = A.3C + B.,, and (A^^ -j- inB^ cos nix) 
= Ko (A. — niB, cos mx) which latter involves both KjA^ = K3A0 and K^B^ = — K.B^. 
The velocity potentials of the wave-motions in the two fluids are 
(f)^ = m 1 dCldt e’“’J cos nix, dCjdt e~”^'J cos nix. 
In addition to the h 3 ^drodynamical pressure-difference acting from the ipiper to the 
loAver side of the interface, equal to - p (p^ - pi) y + (p^ d<pfdt - d^fdt), that is 
~ {9 {Pi ~ Pi) C -T ni~^ [p., -j- pf d-Qflt-] cos nix, there will act on it a downward 
capillary traction T chyldx^, or — ?n~TC cos nix, and a downward electric normal 
traction'"' (K^ — KA — Tp), 87 r, in which N;^ = A^ + mBi cos mx while 
1 is of the second order. This electric traction is therefore equal to (K^ —K..)/ 87 rIv.,. 
2 »iA^B^ cos nix), where B^ = (K^ — Ko)/(K^ + K 3 )-CAj; while the intensity 
of the total displacement, material and aethereal, in the electric field is 
Ihe balancing of these tractions at the interface y—O cos mx requires that, in addition 
to the mean statical elevation, we should have 
(pi + /’i) ^ ~ Pi) '71 + 
m 
IvjKo (1^3 1 ^ 1 ) 
in which njin is the velocity of wave-propagation. The effect of the electric polariza¬ 
tion is thus for ripples of length ^ (= 27r/?n) the same as would be that of a diminu¬ 
tion of the surface tension by (K. — Kj)2/KiK3(Ko f - Kf.\i'~. 
This is the statical cquivaleut as above (§3/) of both the actual electric traction on the surface, 
and the electr’ic pressure transmitted from the interior of the fluid to the surface. 
