Page:SearleEllipsoid.djvu/5

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

Now I have shown {§21} that if there is a surface A carrying a charge $$q$$, and any surface B is found for which $$\mathbf{\Psi}$$ is constant, then a charge $$q$$ 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.



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

If we make $$a=b=c=0$$, the surfaces of equal "convection potential" are the ellipsoids given by

$\frac{x^{2}}{\alpha}+y^{2}+z^{2}=\lambda$.|undefined

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 $$\sqrt{\alpha}:1:1$$ I have called a Heaviside Ellipsoid, since Mr. Heaviside was the first to draw attention to its importance in the theory of moving charges. Whatever be the ratios $$a:b:c$$, the equipotential surfaces