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A new numerical method is described for the solution of two-dimensional electrostatic field problems with multiple dielectrics. The method is particularly suited to unbounded fields, for which conventional finite-difference or finite-element methods are difficult to apply. The method is based upon a set of functions derived from Sander's basic dipole function, which are precomputed. This permits rapid assembly of the matrices involved without the need for numerical integrations for each individual problem. The method, which may be termed an equivalent-source method, is described for simplicity throughout in terms of the resistance network analogue.