298 
]\IR. .T, L71B:\I0R ox a DYXA^illCAL THEORY OF 
which must be wliollj normal and depend only on the intensity of the field of force 
at the 2 )la( 3 e. That this is the case for fluids, but not for solids, has already been 
sliown. And this law of dependence of vapour tension on electric state only applies 
to fluids, not to solids like ice ; for a flow of the medium is required to com^flete the 
cycle on which the argument is based. In the case oi a solid with finite vapour- 
tension, electric excitation—as also gravity, strains, and other physical agencies— 
will jDi’omote evaporation, excessively slow of course, from some parts of its surface, 
and condensation on others, until a form suitable to equilibrium of vajDOur tension is 
attained. 
In expressing conditions of equilibrium for fluid media, the above total electric 
normal traction over each interface is simply to be added to such other forces as 
would exist in the material system if there were no electric field. Thus if we take 
for example the case of a number of dielectric fluids siqDerposed on each other in a 
tall jar under the action ot gravity, the form of the U 2 :>per surface is obtained by 
equating the electric traction to the pressure difference produced by difference of 
level alone; and for anv interior interface the same statement holds P’ood. the form 
o ' 
Oi each interface depending only on the electric field at the jfiace and the inductive 
capacities of the two fluids which it sejiarates. And this 2 ^ 1 'ocedure is quite general 
whatever extraneous forcives there may be ; the form of each interface is always 
determined by equating the difference of electric tractions on its two sides to the 
difference of pressures due to other than electric causes. 
82. Tractions on the Interfaces of a divided Magnetic Circuit .—An important 
jiractical deduction is that when a bar or ring, longitudinally magnetized temporarily 
or permanently, is divided by an air-gap, the force drawing together the two halves 
of it consists of the attractions of the uncomjjensated polarities which would remain 
if there were no air-gaj), together with a traction on each face of the gap, at right 
angles to its plane, and of intensity wflrere v is the normal component of the 
magnetization. This traction is in other respects quite indejiendent of the character 
of the magnetic field that may exist at the gap ; when the gap is narrow it is 
simply the attraction between the free polarities on its two faces. When the gap is 
transverse, the total amount of the traction is 27 rJ'F dS, that is ( 87 r)“\|’(B — H)-dS, 
where B and H are the longitudinal components of the magnetic induction and 
force ; when it is oblique the longitudinal pull between the halves of the bar varies 
as the square of the cosine of the obliquity. When the substance is magnetized b}^ 
an electric coil, there may in addition be the attraction between the two halves of 
the coil. For the case of iron H is very small compared with B, unless the field is 
far greater than is required to saturate the iron ; so that the part of the mechanical 
traction across a transverse ga^) which is due to the jioffu'ities on its faces is 
practically ( 877 )~^JB^ dS. 
83. Interciction of Mechamced Stress and rfagnetization .—Consider a wire, 
magnetized to intensity I by a longitudinal magnetic field IT, and subject to an 
