Dispersion curves for a periodic slot array, of narrow slots, cut in an infinite conducting sheet and placed at the interface between two homogeneous, isotropic, and lossfree dielectrics, are obtained. The results are accomplished through the development of a determinantal equation which is stationary with respect to the longitudinal phase constant of the structure. This stationary determinantal equation is derived through the generalization of similar stationary relations for the propagation constant along a uniform continuous slot cut in a rectangular or a circular waveguide. The stationary property of this relation holds both for real and complex longitudinal phase constant. A somewhat lengthy Fourier transform approach has been employed to put the equation into a fast converging form, suitable for numerical analysis. The final determinantal equation is quite suitable for calculation by a high-speed digital computer. It is shown that not only a periodic slot array located at the interface between two dielectric media, but also a periodic slot array or its electro magnetic dual, an infinite yagi antenna in a uniform medium, can support a radiating or leaky mode.