592 PROF. J. J. THOMSON AND MR. G. F. C. SEARLE ON THE RATIO OF THE 
corrections the effect of increasing the thickness of the ebonite would be to add a 
breadth '218 cm. to the cylinder in consequence of the increased air space, and '06 in 
consequence of the difference of potential, thus the two would add ‘28 to the length of 
the cylinder, and would increase the capacity by ^ X 2760, or 12 parts in 2760. 
Thus the observed and calculated results agree well together. 
Correction for ellipticity of the cross section .—Let us consider the case of a 
cylinder whose cross section is represented by the equation 
r =1) [I e cos 26], 
placed inside one whose cross section is represented by 
r — a [1 a cos 2^ + sin 26], 
where, since the measurements of the cylinder show that e, a, /3 are less than 
we can neglect the squares of these quantities. 
Let the potential between the cylindea’S be given by 
TT A 1 . C cos 20 . ^ , E sin 20 , _ „ . 
V = A log r H- 3 -b cos 26 -\ -^— + Fr'- sm 26. 
Then, neglecting the squares of e, a, (B, the difference of potential between the 
cylinders is 
A log , 
h 
and to the same approximation the charge per rmit length is -^A, thus the capacity 
per unit length is ^ log a/b. Here a and h are the means of any two radii of the 
cylinders at right angles to one another. If we take these values as the radii of the 
cylinders the only correction required will be one of the order of one part in (2000)^ 
which may be neglected. 
Cori'ection of Conicality .—We may see how to get rid of this correction by 
considering the electrical distribution on two infinite conductors, the one a plane 
pei'pendicular to the axis of y, the other a corrugated plane represented by the 
2/ = /i + ^sm—, 
the other plane being taken as the plane of xz. Let V the potential between the 
planes be given by 
V^Ay+Csin-'"'* 
putting y — li f (B sin 2iTxjI, and rraking the potential constant and equal to Vq 
