The theory of Debye and Bueche for the scattering of light by an amorphous solid is extended to the case where fluctuations in anisotropy as well as density are considered. A generalized correlation function is defined, which gives the probability of a simultaneous occurrence of fluctuations in polarizability in two volume elements a distancerapart. The fluctuations are specified by the magnitudes of the polarizabilities and the directions of the optic axes. The correlation function is assumed to depend onr, on the angle between the axes of the fluctuations, and on the angle giving the position of the second element with respect to the optic axis of the first. The intensities of the horizontal and vertical components of the scattered light are expressed as integrals over the correlation function of explicit functions ofrand the two angles. From the initial slopes and intercepts of the intensities plotted against sin2(&thgr;/2) where &thgr; is the scattering angle, one can obtain average values and average dimensions of the fluctuations, and a measure of the extent to which fluctuations in density and anisotropy are correlated. The theory is applicable to glasses, gels, and liquid crystals.