256 
MR. J. LARMOR OX A DYXAMK’AL THEORY OF 
x,= 
Itt 
/' ^ + ^/' 1 + ^' ^)/' + i (/" + i/" + - 1 /' ^ ^ 
. \ .V 
d 
dx 
dj! 
dz 
dx 
A f 1 "-H- 
\ d.x dy 
dll' 
*’^1* M - + !7 ' + i + & ) - 'J [ai 
dy j \ dz do: 
with similar expressions for and Zj^; while the torque vanishes in the limit. 
43. In these formulse the aim has been simply to represent as they are the regular 
local forcives acting on the molecules, as a distribution of force throughout the 
volume and, if need be, of traction over the surfaces of the material, thus avoiding 
the use of any hypothetical stress-system which might be a geometrical equivalent. 
It will presently be shown that an extension of the ideas underlying the Young- 
PoissoN principle of the mutual coinj^ensation of molecular forcives, employed in the 
theory of capillary action, recjuires that this local forcive shall set up a purely local 
physical disturbance of the molecular configuration in the material, until it is thereby 
balanced ; in the case of an isotropic medium in a steady state it must thus neces¬ 
sarily be expressible as an imposed stress symmetrical with respect to the direction 
of polarization. 
Let us, therefore, with a view to the verification of this proposition, analyze the 
eftects of an internal stress symmetrical with respect to the lines of some kind of 
polarization denoted generally by i or (/, y, li). Such a stress must be of the type 
of a tension (p -f q) along these lines combined with a tension qi^ in all directions 
at right angles to them ; for the stresses we are examining clearly vary as the square 
of the polarization. Thus the stress must be made up of a hydrostatic pressure 
— qv^ combined with a tension pr along the lines of the polarization. The tractions 
exerted by the latter part on elements of interface parallel to the coordinate planes 
yz,zx, xij^VQ, per unit area, Ujf\ qfg, qfh), {qgfy qg~, qgh) and {qhf, qlig, qh~). Hence 
the total force exerted by the stress on the element of volume Sx By Bz is, per unit 
volume, (X, Y, Z) where 
X = ^ (pP) + (</Y) + {'!<//) + f (</¥) 
U' + hi) P + if (f; + + 
% 
d.i 
df dh\ 
do: ' dx ’ ' dy 
L I'M' 
dy • 
and, the stress being self-conjugate, there is no torque. On comparison ot this force 
with the local molecular, or cohesive, force on the element ol volume, of electric 
origin, expressed above, it appears that they are of the same type provided 
f dxg dyh dz is an exact differential, which is the case with the equilibrium 
electric polarization i' or {f, g, h') induced in an isotropic medium, the electric force 
being always under conditions of equilibrium circuital. The material stress which 
represents the regular electrostatic part of the molecidar forcive by Avhich the 
molecules hang together, is therefore a tension l .-f Trf' along the lines of the polarization 
i' combined with an equal pressure in all directions at right angles to 
