714 
MR, j. J. THOMSON ON THE NUMBER OF ELECTROSTATIC) 
but \ T> is the quantity of electricity per unit length upon either cylinder, and since 
the capacity is the quantity of electricity divided by the difference of potential, the 
capacity of the two cylinders 
2 PA.QB 
log 
QA.PB 
where l is the length of either cylinder. 
Let 
0 P =x 00' —e 
0Q = 
then 
therefore 
similarly 
Since 0T.0'Q=6’ we have 
PA=a-r. QA= — a. 
x 
PA_ x 
QA a 
QB 
PB x — c 
therefore 
( X ~ C \x- c ) = h ^ 
(a 3 +c 3 -6 3 )-c--caj=0 
»— 
' x 
O I 0\ 
or 
, , J> 2 -(a 2 + c 2 ) , „ 
x ■' fi- x ci~ — 0 
Solving we find that 
ca- 
x— 
ct-V 
1 + 
(« 2 -& 2 ) £ 
approximately, supposing that as in our condenser _^ is small. 
c5 2 
therefore 
x—c — 
O TO 
a~—b“ 
\a*-by 
a(l-\- 
7 -7 9 . 
{ct?-by 
. PA.QB . x.b 
° g QA.PB - Og ’«0-Q _ ° g a * c * 
(a?-by 
so that the capacity of the condenser 
— 2 
[J 1 
5 V \-] 
log d 
V-z> 2 )7 
h ( 1 
a-c - \ r 
IV 
r (a*-byJ J 
l 
1_ 
2- « 
log 7- i -77i 
° 0 Cl" — b~ 
qy— approximately. 
