(8).
Whereas if it is an ellipsoid of revolution round the minor axis b (oblate), we have
| 1 | = | sin−1ae |
| C² | ae |
(9).
In each case we have C = a when e = 0, and the ellipsoid thus becomes a sphere.
In the extreme case when e = 1, the prolate ellipsoid becomes a long thin rod, and then the capacity is given by
C1 = a / logε 2a/b
(10),
which is identical with the formula (2) already obtained. In the other extreme case the oblate spheroid becomes a circular disk when e = 1, and then the capacity C2 = 2a/π. This last result shows that the capacity of a thin disk is 2/π = 1/1.571 of that of a sphere of the same radius. Cavendish (Elec. Res. pp. 137 and 347) determined in 1773 experimentally that the capacity of a sphere was 1.541 times that of a disk of the same radius, a truly remarkable result for that date.
Three other cases of practical interest present themselves, viz. the capacity of two concentric spheres, of two coaxial cylinders and of two parallel planes.