Directional distributions of thermal radiation emitted from a succession of smooth to roughened surfaces of an electric nonconductor have been measured monochromatically. The test material was an aluminum oxide ceramic, while the ranges of surface roughness and wavelength respectively extended from 0·26 to 3·8 μ and from 4 to 12 μ. The directional emittance distributions, normalized by the corresponding normal emittances, exhibit a strong dependence on wavelength. Moreover, the normalized emittance distributions are not monotonically ordered with wavelength. At a given wavelength, the emittance distribution tends to approach toward the diffuse limit as the surface roughness increases. However, the rate of approach is not rapid, and if the diffuse limit is to be achieved at all, surfaces of very substantial roughness will be required. Comparisons were made between the experimental results and the predictions of electromagnetic theory in those wavelength ranges in which the optical constants are available. Good agreement was found both in the general trend with wavelength as well as for the detailed directional distributions for the highly polished test surface.