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The current excited on a horizontal thin-wire structure above the surface of a finitely conducting earth is derived, and is shown to be the sum of discrete modal contributions as well as a number of continuous spectrum (radiation) components for any source of finite extent. The wire structure need only be characterizable approximately by an axial surface impedance, and so particular cases previously treated in the literature can be recovered. In particular, an expression for the current excited by a transverse aperture of finite extent is given, and using orthogonality properties between different parts of the mode spectrum, it is concluded that any of the discrete modes can, in principle, be excited with arbitrarily high efficiency by an appropriately chosen aperture field of finite extent.