590 PROF. J. J. THOMSON AND MR. G. F. C. SEARLE ON THE RATIO OF THE 
The quantity of electricity on the conductor FGP when P is a point on GH 
= 4^ 
Jj , t — a 
= S ’ 
where t is the value of t at P. If we represent the increase in the quantity of 
electricity, due to the irregularity of the distribution, by supposing a strip of breadth 
d to be added to the conductor GH, and the distribution of electricity to be regular, 
and the same as if the air space were not present; the equation to find d is, if x is 
the value of a? at P and V, the difference of potential between AB and GH. 
IttA '■ 
— C +(/]= — 
t — a 
substituting for x and t their values in terms of 0, and remembering that 
V = ttB, 
we get 
C =■ 
h = 2 Att cot a 
or 
Ain 1 X 1 (0 ~~ «) 
A [0 — h cot a log ^ 
* Sin (sc + 0) 
d = c \ I — " 0 
TV 
— c d = — AA cot a lot 
(sin 6 — sin sc) 
A 
- lo.c»- 
” (sin sc + sin 6) ’ 
(sin ^ — sin sc) sin (u + 0) 
TV ^ (sin sc + sin 0) sin (0 — sc) 
Now if P be some distance from G we may put 0 = a and we get 
d = c 
- log cos^ a 
from equations (4) and (5) we see that tan a = c/h, so that 
t™"’ /,} + b log 11 + )7,}. 
To deduce the corresponding solution for the cylinders from this we must multiply 
by the correction for curvature 1 + ^h/a, where a is here the radius of the inner 
cylinder, so that we have finally, if D be the whole breadth to be added for the two 
air spaces. 
I - b tan ' y !> + log (l + 
TV 
Now in our condenser I was about 60, 2c = ‘3, and h = 1, so that if we put 
I) = 2c the value of the capacity will be correct to I part in 2000. 
