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Methods for synthesizing the optimum patterns for arrays of isotropie sources have been given by Dolph and Riblet, using Tchebyscheff polynomials, except for arrays containing an even number of elements spaced less than a half-wavelength. The conditions which the optimum polynomial must satisfy in the latter case will be considered. For arrays of nonisotropic sources, it is possible to establish the mathematical conditions which the optimum polynomial must satisfy. Approximate methods for devising the polynomial which satisfies these conditions are discussed, and an example shown. The nature of the optimum pattern of an array of nonisotropic sources spaced more than a half wavelength is considered, and shown to be slightly different.