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The general formulas for electromagnetic transmission through an infinitely long slot in a perfectly conducting screen of finite thickness are specialized to the case of a narrow slot. The slot may be filled with a homogeneous isotropic material. A simple equivalent circuit for the narrow slot is developed. It is found that for certain screen thicknesses the slot becomes resonant, and exceptionally large transmission of energy may occur. In fact, as the slot width approaches zero, the transmission width at resonance becomes wavelengths regardless of the actual slot width. The effect of loading the slot with a lossy dielectric is also considered. Computations are given to illustrate the validity of the equivalent circuit model and the accuracy of transmission characteristics computed from it.