SPECIFIC INDUCTIVE CAPACITY OF DIELECTRICS. 
577 
the charge, this can only arise from the action of the two sides of the platymeter being 
equal to that of the one charged side, say p, before the connexion was made. But the 
surface of action is now equal to p, and the potential ot the system, therefore, 
is now /— where v is the original potential of A and p. But the quantity ot 
1 H — 
71 / 
electricity taken from A and p is such as to raise B and p' to the same potential as that 
to which A and p, with which they are now connected, are reduced. But in conden- 
sers at equal potentials the capacities are proportional to the amounts of the charges. 
Suppose the original charge of A and p to be unity. Then their charge after distri- 
bution is 
i+i 
n 
and that of B and p' is 
Then 
but 
and therefore 
A+p:B+p' :: + : ( B + 1 ) : : “ : 1 
p:p ' : : n : 1, 
A : B ::p:p’. 
That is, generally, when there is no deflection, the condensers compared are to one 
another as the sides of the platymeter with which they are connected. But the reading 
obtained with the platymeter connexions arranged normally was greater than that ob- 
tained when they were reversed. The side p' is therefore greater than the side p. 
Now let a be the greater and b the less reading with the value of the sliding con- 
denser when its index is at zero added to them, and let x be the true value to be deduced 
from them. Then we have the ratios 
therefore 
p : p' : : x : a and p 1 : p : : x : b , 
x : a : : b : a, and x—\/ ah. 
That is, the true value of a condenser measured by an imperfect platymeter is the geo- 
metric mean of the two values obtained by the different arrangements of the connexions. 
In practice, when the error of the platymeter is so small as it is in the present case, 
the arithmetic mean may be taken instead of the geometric. For let M be the arithmetic 
mean of a and b, and D the difference between it and either of these values. Then 
j?=v 7 M 2 — D 3 =MI 1 — )• in present case, where is about 
M does not differ sensibly from x. If a be the greater and (3 the less reading, 
then z, the value (in scale-divisions) of the sliding condenser with its index at zero, is 
x When z has been determined, the true value of any condenser may be got by 
adding to it the mean of the two readings obtained ; and when the error of the platy- 
