PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
485 
Electric Elasticity. 
(66) When an electromotive force acts on a dielectric, it puts every part of the 
dielectric into a polarized condition, in which its opposite sides are oppositely electri- 
fied. The amount of this electrification depends on the electromotive force and on the 
nature of the substance, and, in solids having a structure defined by axes, on the direc- 
tion of the electromotive force with respect to these axes. In isotropic substances, if Jc 
is the ratio of the electromotive force to the electric displacement, we may write the 
Equations of Electric Elasticity , 
Y=lf 
Q =kg, 
R =kh. 
Electric Resistance . 
(67) When an electromotive force acts on a conductor it produces a current of elec- 
tricity through it. This effect is additional to the electric displacement already con- 
sidered. In solids of complex structure, the relation between the electromotive force 
and the current depends on their direction through the solid. In isotropic substances, 
which alone we shall here consider, if g is the specific resistance referred to unit of 
volume, we may write the 
Equations of Electric Resistance , 
<*=-&[ (F) 
R = - f r.J 
Electric Quantity. 
(68) Let e represent the quantity of free positive electricity contained in unit of 
volume at any part of the field, then, since this arises from the electrification of the 
different parts of the field not neutralizing each other, we may write the 
Equation of Free Electricity , 
6 + dx^dy^dz 
0. 
(G) 
(69) If the medium conducts electricity, then we shall have another condition, which 
may be called, as in hydrodynamics, the 
Equation of Continuity, 
de .dp .dq .dr q 
dt dx dy dz 
(H) 
(70) In these equations of the electromagnetic field we have assumed twenty variable 
