748 
SW 
MR. LARMOR ON A DYNAMICAL THEORY OF 
f - nSr,) + h^g («8j - ISi) + c^h {tSg - mSf)} dS 
'■ f 2’')++ o’- s, - Pi 
[ _ mcVi) + (IcVi - na\f) Srj + {maY - Ihh/) 
) 
(!("-f')»+(?-f)*'+ 
dh^ _ day 
dx dy 
H \dT, 
where (/, m,, n) represents the direction of tlie normal to the element c/S. 
The vanishino- of the volume integral in this expression for all possible types of 
variation of (f, rj, {) requires that 
cdf dx + hV/ d.y -{- cVi dz = — r/Y, 
where V is some function of position, in other words that 
if, fJ, /o 
(J-dL _L A _1 1\ V 
\ cd dx ’ h~ dy ’ cr dz ) 
The vanishing of the surface integral requires that the vector {cdf, hh/, c%) shall 
he at each point at right angles to the surface. 
It is hardly necessary to observe that in this solution Y is the electric potential, 
from which the electric displacement {/, g, h) is here derived by the ordinary electro¬ 
static formulae for the general type of crystalline medium, and that the surface 
condition is that the electric force is at right angles to the surface, or in other words 
that the electric potential is constant all over it. 
In deducing these conditions it has been assumed that the electrostatic energy is 
null inside a conductor; thus in statical questions the conductors may be considered 
to be regions in the mediiim devoid of elasticity, over the surfaces of which there is 
no extraneous constraint or forcive applied. 
41. In this analysis it has not been explicitly assumed that the electric displace¬ 
ment is circuital, i.e. that 
^ -4- ^ 4- — = 0 
dx dy dz 
If we were to introduce explicitly this equation of constraint, we must by Lagrange’s 
method add a term 
df , dg , dhp 
