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Reciprocity theorems are developed for the average field specularly reflected, and the average power randomly scattered, to a point by a statistically described array of objects. A reciprocal quasivariational expression for the average power is developed for use when the self-consistent method applies to calculating currents in the individual objects. This formula is applied to calculate differential scattering cross sections for two idealized arrays bounded by plane "rough surfaces." General conclusions, relating to reciprocity, power conservation, grazing behavior, etc., for rough surface scattering, are made and applied heuristically to show that grazing reflection and backscatter from the rough ocean should be independent of polarization.