Observations of the distribution of linearly polarized lunar thermal emission were made at a wavelength of 3.1 mm with The University of Texas 4.88 m parabolic reflector (0.042° HPBW). A shadow corrected, rough surface, thermal emission model for a homogeneous Moon was leastsquares-fitted to the polarization data. Results indicate an effective lunar dielectric constant of 1.34 ±0.04 with surface roughness characterized by a standard deviation of 17° ± 5° for surface slopes with a normal probability density, independent of lunar phase. A comparison of these results with published values at other wavelengths suggests that the effective lunar dielectric constant, as obtained by lunar emission measurements, decreases with decreasing wavelength of observation. This wavelength dependence may be interpreted in terms of an inhomogeneous surface and/or a surface that possesses intermediate scale surface roughness.