UNITS IN THE ELECTROMAGNETIC UNIT OF ELECTRICITY. 
713 
Since the greatest difference in temperature does not affect the result by one part 
in a thousand, the correction for temperature is neglected. 
We find from these numbers that the distance between the cylinders is ‘941 centim. 
When the distance between the cylinders was measured by hair dividers, the least 
distance was found to be '826 centim., the greatest '984 centim., giving 79 centim. 
as the distance between the axes of the cylinders. 
Since the axes of the cylinders are not quite coincident, we cannot calculate the 
capacity by the ordinary formula. We proceed to investigate a formula which will 
hold in this case. 
Fig. 4. 
Let the figure represent a section of the cylinders by a plane perpendicular to their 
axes. Let 0 be the centre of the section of the cylinder O A, O' the centre of the 
section of O' B. Let 0 A= a, O' B =b. 
Let P and Q be inverse points with respect to both circles, so that 
OP.OQ=« 2 
OT.O'Q=6 3 
Then if (f >=A — B log rjr^, when r 1? r 3 are the distances of a point T from P, Q 
respectively, </> will satisfy Laplace’s equation and will be constant over both 
cylinders. Thus <j> will be the potential of the electrical distribution, and by com¬ 
parison with the ordinary form for the potential of an electrified cylinder we see that 
\ B will be the quantity of electricity per unit length upon either cylinder. Let the 
outer cylinder be connected with the earth so that its potential is 2 'ero, and let the 
potential of the inner cylinder be V. 
Then we have 
* ^ i PA 
0=A-Blog— 
V=A-B 
V=B 
--Blog 
PA.QB 
QA.PB 
V 
PA.QB 
QA.1T> 
therefore 
