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Propagation on a. helix as a function of frequency is characterized by ranges in which there is a slow wave which can be explained as very nearly a transverse electromagnetic wave traveling along the wire, and ranges in which the helix does not propagate; these are associated with "forbidden regions" of propagation constant pointed out by Sensiper. Each mode of propagation consists of an infinite number of spatial Fourier components called spatial harmonics. The complicated behavior with frequency of the modes of a helix is explained as an effect of the coupling through spatial harmonics of the slow wave which travels with about the velocity of light along the wire to fast free-space or waveguide waves which travel with about the velocity of light along the axis. The qualitative effects of such coupling agree with a tape-helix analysis of helixes in free space and helixes surrounded by a conducting tube. The case of the bifflar helix is also treated.