O that in the absence of accurate D-region electron-density tion, differential phase, propagation time and Faraday rotation. data, estimates are liable to appreciable error. Atl.f. propagation is Theory shows that signals propagated via the ionosphere can more conveniently described by wave-hop theory in terms of com- become cross-modulated by high-power interfering signals which ponent waves with different numbers of hops. As at v.l.f. reflection heat the plasma electrons through which the wanted signals pass. occurs at the base of the ionosphere and the accuracy of the field- This heating causes the electron-collision frequency, and therefore strength prediction is largely determined by uncertainties in ionos- the amplitude of the wanted signal to fluctuate at the modulation pheric models and reflection coefficients. Medium-frequency frequency of the interfering transmitter. Investigations of this phe- signals penetrate the lower ionosphere and are usually reflected nomenon (known as the Luxembourg effect after the first identified from heights of 85-100km, except over distances of less than 500km interfering transmitter) usually employ vertically transmitted and by night when reflection may be from the F-region. Large absorp- received wanted pulses, modulated by a distant disturbing transmit- tions occur near the height of reflection and daytime signals are very ter radiating synchronised pulses at half the repetition rate. Changes weak. It is now realised that because of the uncertainties in ionos- in signal amplitude and phase between successive pulses are pheric models, signal-strength predictions are best based on empiri- measured, and by altering the relative phase of the two transmitters, cal equations fitted to measured signal-strength data for other the height at which the cross-modulation occurs can be varied. Such oblique paths. data enable the height distributions of electron density in the D-re- Prediction schemes for h.f. tend to be complicated because they gion to be determined (Fejer, 1955). mus