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David Layzer and Donald H. Menzel proposed a microscopic theory of ionospheric cross modulation in 1965, as an alternative to the Bailey-Martyn theory. The Bailey-Martyn theory, proposed in 1937, suggests that radiation from a disturbing transmitter is absorbed in the ionosphere, raising the temperature and affecting the attenuation of a wanted wave. The theory predicts the dependence of transferred modulation on the power of the disturbing radiation and its modulation frequency. However, the theory is limited to modulation frequencies much less than 150 c/s, and experimental ranges extend to nearly 1500 c/s. The new microscopic theory takes into account the velocity-distribution function of electrons and calculates the absorption coefficient and transferred modulation as functions of modulation frequency. The results show significant effects from departures from a Maxwellian velocity distribution and are sensitive to the assumed form of the electron-molecule collision law. The theory suggests that further refinements could lead to an experimental determination of the electron-molecule interaction law in the D region.