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The control and direction of electromagnetic waves is accomplished, in general, by the use of boundary materials and structures which produce desired effects on such waves when irradiated by them. An important class of boundary structure for this purpose is a surface having alternate areas of conducting and nonconducting material. Grids formed of a large number of parallel cylindrical conductors of circular cross section, uniformly spaced and lying in a common surface, are among the most generally useful of this class of boundary structure. Single layer parallel wire grids have received considerable study in the past. However, little information is available concerning the characteristics of multiple layers of such grids An analytical solution is obtained for the power transmission coefficient of a double grid system. Power transmission coefficients for various combinations of system parameters are computed from the analytical solution and tested experimentally. The solution is found to yield excellent correlation with experiment until the interwire spacing approaches the wavelength.