Page:SearleEllipsoid.djvu/5

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Thus, as Prof. Morton has also shown by the same method,

. (12)

Now I have shown {§21} that if there is a surface A carrying a charge , and any surface B is found for which is constant, then a charge placed upon B and allowed to acquire an equilibrium distribution will produce at all points not inside B the same effect as the charged surface A.

Searle1.png

Hence the ellipsoid (11) when carrying a charge produces at all points not inside itself exactly the same disturbance as the ellipsoid with the same charge.

If we make , the surfaces of equal "convection potential" are the ellipsoids given by

.

They are therefore all similar to each other. Thus the ellipsoid of this form produces exactly the same effect as a point-charge at its centre, and thus an ellipsoid of this form takes the place of the sphere in electrostatics. An ellipsoid with its axes in the ratios I have called a Heaviside Ellipsoid, since Mr. Heaviside[1] was the first to draw attention to its importance in the theory of moving charges. Whatever be the ratios , the equipotential surfaces

  1. 'Electrical Papers,' vol. ii. p. 514.