A method is described for the calculation of the time dependence of the component of the macroscopic nuclear magnetic moment of a solid in the direction of a steady magnetic field H0 following the application of a strong, transverse radiofrequency field. Observation of the time variation of the magnetization corresponds to a free induction decay experiment performed in a frame of reference rotating at the frequency of the transverse field, and the decay function is proportional to the Fourier transform of the rotary saturation line shape. A marked lengthening of the decay is expected when the static field effective in the rotating frame is inclined at 54.7° to H0 and the method is potentially useful as a line-narrowing technique. The theory is applied to the fluorine resonance in calcium fluoride and good agreement is found with the experimental results of Goldburg and Lee. The theory makes use of a unitary transformation method described in an earlier paper. A close correspondence is found with certain of the results already established for the related problem of motional narrowing by rapid rotation.