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The observed interstellar extinction over the wavelength range 0.11 μm < λ < 1 μm was fitted with a very general particle size distribution of uncoated graphite, enstatite, olivine, silicon carbide, iron, and magnetite. Combinations of these materials, up to three at a time, were considered. The cosmic abundances ofthe various constituents were taken into account as constraints on the possible distributions of particle sizes. <P />Excellent fits to the interstellar extinction, including the narrowness of the λ2160 feature, proved possible. Graphite was a necessary component of any good mixture, but it could be used with any of the other materials. The particle size distributions are roughly power law in nature, with an exponent of about -3.3 to -3.6. The size range for graphite is about 0.005 μm to about 1 μm. The size distribution for the other materials is also approximately power law in nature, with the same exponent, but there is a narrower range of sizes: about 0.025-0.25 μm, depending on the material. The number of large particles is not well determined, because they are gray. Similarly, the number of small particles is not well determined because they are in the Rayleigh limit. This power-law distribution is drastically different from an Oort-van de Hulst distribution, which is much more slowly varying for small particles but drops much faster for particles larger than average. <P />The extinction was also fitted with spherical graphite particles plus cylinders of each of the other materials. Linear and circular polarizations were then determined for the cylinders on the assumption of Davis-Greenstein alignment. The extinction was quite satisfactory, but the linear polarization reached a maximum in the ultraviolet (about 1600 Å). This is because the mixture contains many small particles. Ifthe small particles are not elongated or aligned, the wavelength dependence of the polarization can be fitted, but the larger particles which are aligned do not provide enough polarization per magnitude of extinction. However, a fit to polarization and extinction can be achieved if the material responsible for the polarization contributes only a small part of the extinction but consists of fairly large particles and is very well aligned. Dielectric particles with coatings could also provide the polarization. Subject headings: interstellar : matter «— polarization —