The spectrographic imagers on the MSX satellite have made the first observations of the middle ultraviolet spectra (200--315 nm) of polar mesospheric clouds (PMCs). Dividing the PMC spectra by the solar spectrum yields a scattering spectrum expressible as a matrix-vector formalism of Mie scattering functions and the particle distribution. Using this formalism, PMC particle distributions are related to the observed scattering spectrum. The scattering spectrum always exhibits a peculiar hump at ~260 nm that cannot be explained by any effect other than the particle distribution. A lognormal distribution of small particles (mode ~ 50 nm) produces the overall shape of the spectrum but not the hump. Although not unique, a simple bimodal distribution of small particles (r ~ 50 nm) and large particles (r ~ 200 nm) describes the scattering spectrum and its hump very well. The clouds may therefore consist of two different populations, as suggested by some models of the clouds. Numerically, smaller particles dominate by about 10:1, but the larger particles strongly influence the scattering spectrum.