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The traveling-wave modes associated with an infinite, periodic structure are considered. An approximate equation for the propagation constants of these modes is derived through the use of Fourier analysis and an approximate application of the reaction concept. In the homogeneous case considered, it is found that two dominant modes may exist: an attenuated fundamental mode representing a perturbation of the dominant mode of a closed rectangular waveguide, and an unattenuated surface wave, which is similar to the wave associated with a corrugated surface waveguide. By means of the appropriate variation of physical parameters, including the slot length and spacing, essentially independent control of the attenuation constant and phase velocity of the fundamental mode is possible over a wide range. Typical curves of the propagation constant in terms of these parameters are given, and the results of experimental measurements are shown to be in close agreement with the theory.