Page:Electricity (1912) Kapp.djvu/81

and a parallel plane is also easily treated, but it would exceed the limits of this book to enter into such details, which have more immediate interest for the cable engineer or the telegraphist. The case of two parallel plates may, however, be here given, because the derivation of a mathematical expression for the capacity is exceedingly simple. We found that the capacity of concentric spheres is given by the expression

$C={\frac {R^{2}}{\delta }}$

If we multiply nominator and denominator with $4\pi$ we do not alter the equation, so that we also may write

$C={\frac {4\pi R^{2}}{4\pi \delta }}$

$4\pi R^{2}$ is nothing else than the surface of the sphere, so that we also have

$C={\frac {S}{4\pi \delta }}$

The capacity is therefore given by the surface divided by $4\pi \delta$. The radius does no longer appear in our formula. If we assume the radius to be infinitely large, any part $S$ of the surface becomes a plane, and we thus have for the capacity of two parallel plane surfaces