495 
of Edinburgh, Session 1881-82. 
outwards. The most natural assumption in the first instance would 
he that so long as the curvature of the surface is finite, K is a 
function simply of the distance from the surface, and independent 
of its curvature, that it starts with a value K 0 just at the surface, 
and very rapidly reaches a value K v which it retains until the 
immediate neighbourhood of another solid is reached. The equation 
of the potential now becomes 
d ( i 
K^?] = 0 
ax \ ax 
(i), 
x being measured perpendicular to the two parallel plates, from the 
one at higher potential to the one at lower. We thus get 
xW 
K~ = A 
ax 
( 2 ), 
where A is a constant. 
Whence 
U 
= A / 
x dx 
. K’ 
and if V denotes the difference of potential between the plates, and 
6* the distance between them, 
V 
= -A/ 
s dx 
o K 
The resultant force at the surface is 
H _ a_ 
R- - K — 
V 
o Tr f s 
Yo K 
(3). 
(4). 
If s be less than a certain distance (comparable with a millimetre, 
/s clffi 
r? may be 
s 
dx /* 2 dx 
— - and / each of 
s K s Q K 
which is the same function of — t the whole is therefore some 
/•s g 
function of s , so that we may write / — = ■ - , where K 0 /(s) 
So Av 0 J\ s ) 
has a value intermediate between K 0 and K x , we thus get 
E=-/W 
b 
( 5 ). 
