Capacitance coefficients of two spheres

Compact and exact expressions are obtained for the capacitance coefficients C_aa, C_bb and C_ab of two conducting spheres of radii a and b, for any distance c between the sphere centres. The results are equivalent to those of Maxwell, Russell and Jeffery, but enable rapid calculation of the coefficients in the limit of close approach, which is otherwise computationally difficult. Erroneous results published by several authors are corrected.