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A doubly infinite set of linear equations is derived for the currents excited on a rectangular wire mesh that is located over a conducting half space. The mesh consists of two parallel grids whose wires are perpendicular to each other. In the formulation, the spacing between the grids is arbitrary but the numerical method, involving direct matrix inversion of the truncated set, is only feasible if the intergrid spacing is nonzero. The numerical results show that the reflection properties of the grid are a strong function of the azimuthal direction of incidence. This characteristic is consistent with earlier results for unbonded meshes in free space. An important conclusion is that wire mesh ground systems used, for example, in high frequency antenna installations should employ unbonded (i.e., unsoldered) wire junctions.