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The penetration of an incident wave through an aperture in a perfectly conducting screen is considered. The dimensions of the aperture are small with respect to the wavelength λ. The fields are expanded in a power series in jk, where k = 2π/λ. The zero-order terms are well-known: they require the solution of electrostatic or magnetostatic problems. The article is concerned with the first-order terms. The integro-differential equations for these terms are derived, and the diffracted field in the far-field region of the aperture is investigated. The relevant multipole-moments are evaluated.