The problem of the calculation of the electric field distribution of a system of infinite parallel cylindrical conductors in the presence of a grounded plane is reexamined. The exact solution of a class of two‐dimensional harmonic problems in multiply connected domains proposed by Burnside in 1893 is reviewed. This is shown to agree with recent generalizations of the method of images. An improved version of the exact solution which is more convergent than the conventional methods when the conductors are very close to one another is presented. The potential usefulness of the theoretical ideas and the mathematical apparatus used here for technological applications is emphasized.