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

From Wikisource
Jump to: navigation, search
This page has been proofread, but needs to be validated.


or the potential at any point outside the body is

(80)

and if is the surface-density at any point

or

(81)

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 , the ratio of the difference of the superficial densities at any two points to their sum will be times the ratio of the difference of the radii of the same two points to their sum.