# Page:SearleEllipsoid.djvu/9

line marked ${\displaystyle \lambda =0}$ is the "image". The semi-length of the line and the radius of the disk are each taken as unity.
I will now write down the values of ${\displaystyle \mathbf {E} }$ and ${\displaystyle \mathbf {H} }$ at any point near the ellipsoid of revolution with axes ${\displaystyle a,b,b}$. Instead of ${\displaystyle \lambda }$ it will be convenient to take as the parameter of any one of the equilibrium surfaces its ${\displaystyle x}$ axis and to denote this by ${\displaystyle h}$. Thus
${\displaystyle h^{2}=a^{2}+\alpha \lambda }$ ;
and consequently if we put ${\displaystyle l^{2}}$ for ${\displaystyle a^{2}-\alpha b^{2}}$, so that ${\displaystyle l}$ is the semi-length of the line which is the "image" of the ellipsoid, we have
${\displaystyle b^{2}+\lambda ={\frac {h^{2}-l^{2}}{\alpha }}}$.