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Artificial dielectrics utilizing three-dimensional arrays of spherical and cylindrical holes in base materialsof polystyrene, Plexiglas, Teflon, and others have been investigated. A theoretical expression relating the dielectric constant to the number and size of the spheres, and to the dielectric constants of the sphere and base materials, is derived. The analysis is restricted to spherical voids small with respect to the wavelength. The theoretical expression (in terms of the fractional volume of the cylinders) applies also to cylindrical-void media, if the length-to-diameter ratio of the cylinders is not far removed from unity. However, for large length-to-diameter ratios, the dielectric constant depends appreciably on the orientation of the cylinder axes with respect to the electric field. Measured dielectric constants obtained by the shorted wave-guide method at 5,000 mc are shown. Values of dielectric constant in the range of 1.1 to 2.6 have been obtained. By using high-dielectric-constant base materials this range could be raised.