292 
MR. J. LARMOR OX A DrXAMICAL THEORY OF 
equal to KF^Stt, act on the element across the faces SS, and another pressure — Q 
act on it, which is the same across all perpendicular faces. For, resols’hig' the forces 
along Bn, we must have for equilibrium 
- f (P 8S) - Q 8S ( Y + A) + 5^1 F f SS = 0. 
Now, by the constancy of the induction, we have d/dn (F 8S) = 0, leading to 
(j)i ^ dn ~ 8^ ^ on substitution, we 
obtain - Q = (K — 2) F^/Stt. The constancy of Q all round the edge of a flat element 
of volume SS Bn secures the balancing of the tangential components of the forces. 
Hence the mechanical stress in any condenser sheet of uniform thickness is the same 
as has been found above for the spherical case. If e and / denote the elongations of 
the material in the normal and tangential directions, X(e + 2/) + 2/re = — KF^/'S??, 
^ + 2/) + 2fxfz=z — (K — 2) F^Stt ; hence /= (2 + X//r - K)/(3X + 2/x) . F 7877 , 
e = (2X//r — K)/(3X H- 2/r). F^Stt; so that the extension of the volume of the shell 
and the change in its thickness are the same as were found above for the spherical 
case. If the shell is an open one, the presence of its free edge will disturb these 
lelatioris . but that influence will be mainly local, as the forces introduced by the 
edge will be almost wholly of the nature of local action and reaction.] 
Various Practical Illustrations and Applications of the Stress Theory. 
77. Refroxtion of a Uniform Field of Electric Force. —An arrangement by which 
these principles may be precisely verified is that of the refraction, at°a plane interface 
AB, of a sheaf of parallel lines of electric force F, according to the Faeaday-Maxwell 
law of tangents, tan tj/tan t, = Kj/K,, Fj/Fg = cosec ij/cosec tg. This configuration 
of lines of force may be obtained and fixed by means of a condensing system having 
its plates P^Qi and PgQg normal to the incident and refi’acted lines. Each plate may 
be protected from convective discharge into the fluid dielectric by a covering plate of 
glass 01 mica, vdiich will itseif produce no refraction. In such a case, when both the 
dielectric media are fluid, the total mechanical result of the electric excitation will be 
the same as that of normal tractions on the interface between them, of intensity 
- 27tiU - liV towards each side, that is, in all (K. -Kj) ( 27 r;f'pKiK, -TbSir) towards 
the side 1. As the field of force in this condensing system is uniform except near its 
edge, the interface will simply be lifted up between the plates by the amount which 
corresponds to this traction, without ceasing to be horizontal. Thus the common 
surf ice will be elevated when tan q is less than (Kj/Kg)", while at greater incidences 
it will be depressed. 
This piinciple supplies in fact a method of obtaining the inductive capacities of 
fluid media by angular measurement only, without the aid of an electrometer. When 
the condenser P^Q^, P^Qo is charged, the interface between the fluids will usually 
