Doppler effect in light-scattering

It is a problem of great interest to consider the changes in spectral character of monochromatic radiation resulting from the thermal agitation of a medium in which it is scattered. If we regard the subject classically, the result to be expected is obvious: there should be a Doppler broadening of the incident spectral line, varying with the angle of observation, and determined by the Maxwellian distribution of velocities of the molecules which scatter the light. It can readily be shown that, except in respect of the total intensity of scattered light, it would make no difference to the argument by which this result is deduced whether the molecules are loosely distributed as in a gas or are closely packed together as in a dense vapour or liquid