Page:SearleEllipsoid.djvu/13

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that as far as terms in the electric part of the energy is unaltered by the motion.

(C) Energy of a very slender Ellipsoid. When the ellipsoid is so slender that may be neglected in comparison with unity we have

. (26)

When is small, this becomes

.

(D) Energy of a Disk.

When the ellipsoid is more oblate than Heaviside's, and becomes negative. In this case let us write

,

so that is the radius of the disk which is the "image" of the ellipsoid . Then writing we have from (23)

.

But

,

so that (23) becomes

. (27)

When we find for the energy of a disk of radius moving along its axis

. (28)

In all these cases it will be found that when the energy becomes infinite, so that it would seem to be impossible to make a charged body move at a greater speed than that of light.