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The electromagnetic surface wave that can propagate over a square mesh of intersecting parallel wires is considered. A combined analytical and numerical method developed earlier is employed to deal with the interacting wire currents. For small mesh spacings, the propagation constant is found to be almost independent of the azimuthal direction of propagation. This is in agreement with previous results obtained by Soviet investigators who utilize averaged boundary conditions for analyzing such bonded wire meshes. However, for larger wire spacings, greater than about one tenth of a wavelength, there is a significant dependence on the direction of propagation over the mesh. The validity of describing the wire mesh in terms of an effective transfer inductance and related questions are discussed briefly in the Appendix.