The cases of greatest practical importance are those of a sphere (which is an ellipsoid with three equal axes) and an ovoid or prolate ellipsoid of revolution.
An experiment was devised by Lord Kelvin for demonstrating this, in which the difference of steadiness was shown of a copper shell filled with liquid and spun gyroscopically, according as the shell was slightly oblate or prolate.
In the extreme case when e=1, the prolate ellipsoid becomes a long thin rod, and then the capacity is given by C 1 = a/log e 2a/b (io), which is identical with the formula (2) already obtained.
The name cycloid is now restricted to the curve described when the tracing-point is on the circumference of the circle; if the point is either within or without the circle the curves are generally termed trochoids, but they are also known as the prolate and curtate cycloids respectively.
Another group are prolate, having the major axis horizontal, usually.