Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/222

 or the potential at any point outside the body is

and if $$\sigma$$ is the surface-density at any point

or

Hence, if the surface differs from that of a sphere by a thin stratum whose depth varies according to the values of a spherical harmonic of degree $$k$$, the ratio of the difference of the superficial densities at any two points to their sum will be $$k-1$$ times the ratio of the difference of the radii of the same two points to their sum.