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Approximate formulas for the complex propagation constant and characteristic field configuration for dielectric-filled traveling wave slot antennas are obtained by a variational procedure. To set up the variational method, the generalized reciprocity theorem for traveling wave line sources is deduced; it differs considerably from the reciprocity theorem for point sources. A perturbation technique for solving the variational equations is given. Formulas are worked out for rectangular wave guides and good agreement with available measurements is obtained.
V. Rumsey (Sun,) studied this question.