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Notes: Abstract The interpretation of diagnostic parameters in the spectral reflectance data for asteroids provides a means of characterizing the mineralogy and petrology of asteroid surface materials. An interpretive technique based on a quantitative understanding of the functional relationship between the optical properties of a mineral assemblage and its mineralogy, petrology and chemistry can provide a considerably more sophisticated characterization of a surface material than any matching or classification technique for those objects bright enough to allow spectral reflectance measurements. Albedos derived from radiometry and polarization data for individual asteroids can be used with spectral data to establish the spectral albedo, to define the optical density of the surface material and, in general, to constrain mineralogical interpretations. Mineral assemblages analogous to most meteorite types, with the exception of ordinary chondritic assemblages, have been found as surface materials of Main Belt asteroids. C1- and C2-like assemblages (unleached, oxidized meteoritic clay minerals plus opaques such as carbon) dominate the population (∼80%) throughout the Belt, especially in the outer Belt. A smaller population of asteroids exhibit surface materials similar to C3 (CO, CV) meteoritic assemblages (olivine plus opaque, probably carbon) and are also distributed throughout the Belt. The relative size (diameter) distributions for these two populations of objects are consistent with an origin by sequential accretion from a cooling nebula (‘C2’ as surface layers, ‘C3’ as interior layers or cores). Based on information from meteoritic analogues and on qualitative models for the behavior of these materials during a heating episode, it seems unlikely that these ‘C2’- and ‘C3’-like asteroidal bodies have experienced any significant post-accretionary heating event either near surface or in the deep interior. The majority of remaining studied asteroids (20) of 65 asteroids exhibit spectral reflectance curves dominated by the presence of metallic nickel-iron in their surface materials. These objects are most probably the several end products of an intense thermal event leading to the melting and differentiating of their protobodies. These thermalized bodies are concentrated toward the inner part of the Asteroid Belt but exist throughout the Belt. The size of the proto-asteroid has apparently exercised control over the post-accretionary thermal history of these bodies. The available evidence indicates that all asteroids larger than about 450 km in (present) diameter have undergone a significant heating episode since their formation. The post-accretionary thermal history of the asteroidal parent bodies was apparently affected by both distance from the Sun and body size. The C2-like materials which dominate the main asteroid belt population appear to be relatively rare on earth-approaching asteroids. This suggests that most of these Apollo-Amor objects are not randomly derived from the main belt, but (a) may derive from a single event in recent time (∼107 yr), (b) may derive from a favorably situated source body, (c) may derive from a particular, compositionally anomalous region of the belt, or (d) may derive from an alternate source (e.g. comets).