Calculations of the Conductivity of a Medium Containing Cylindrical Inclusions

Abstract
Finite difference calculations of the conductivity of an infinite medium containing a square array of perfectly conducting cylindrical inclusions are reported. For dense packing the results agree with and yield an estimate of the next term in an expansion derived by J. B. Keller. For sparse and intermediate packing the calculations are in excellent agreement with a formula derived by Rayleigh and improved by Runge.