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Using perturbation theory, a Boundary Element Method is developed for solving a class of three dimensional electrostatic problems. This class includes problems for which an axially symmetric object is weakly coupled to other objects without symmetry so that the total geometry is three dimensional. A problem which falls into this class is that of a surge arrester located near one or more other arresters. The time required for set up and solution using this method is not significantly greater than that required for solving the axially symmetric problem by itself. A simple empirical formula for error is developed by comparing exact solutions with solutions developed using the method described here.