We apply the Rayleigh method to solve the problem where a uniform electrost
atic held is imposed upon a rectangular array of elliptical cylinders embed
ded in a matrix of unit dielectric constant. This new formulation overcomes
geometric restrictions inherent in previous methods and is shown in princi
ple and in various examples to converge far all possible geometries of the
array and inclusion. Also presented are forms of both the interior and exte
rior addition formulas for harmonic functions in elliptical coordinates tha
t possess optimal regions of convergence. [S1063-651X(99)03609-0].