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Radio-wave transmission from above the maximum-intensity ionospheric layer to ground surface locations beyond the direct line-of-sight distance is examined in this paper. Transmission involving penetration of the F-layer, and subsequent ground-to-F-layer reflections, is found to be more reliable than transmission, depending upon ducting either along the F-layer or between the E- and F-layers. At a frequency approximately three times the maximum plasma frequency (measured with respect to the transmitter location) transmission must take place in a direction along which the maximum plasma frequency increases. The transmission path is reciprocal. At a frequency approximately 20 per cent higher than the plasma frequency, transmission may take place along a constant or even slightly decreasing plasma frequency contour, but the transmission is severely attenuated.