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[1] Each Mars Exploration Rover carries a Rock Abrasion Tool (RAT) whose intended use was to abrade the outer surfaces of rocks to expose more pristine material. Motor currents drawn by the RAT motors are related to the strength and hardness of rock surfaces undergoing abrasion, and these data can be used to infer more about a target rock's physical properties. However, no calibration of the RAT exists. Here, we attempt to derive an empirical correlation using an assemblage of terrestrial rocks and apply this correlation to data returned by the rover Spirit. The results demonstrate a positive correlation between rock strength and RAT grind energy for rocks with compressive strengths less than about 150 MPa, a category that includes all but the strongest intact rocks. Applying this correlation to rocks abraded by Spirit's RAT, the results indicate a large divide in strength between more competent basaltic rocks encountered in the plains of Gusev crater (Adirondack-class rocks) and the weaker variety of rock types measured in the Columbia Hills. Adirondack-class rocks have estimated compressive strengths in the range of 70-130 MPa and are significantly less strong than fresh terrestrial basalts; this may be indicative of a degree of weathering-induced weakening. Rock types in the Columbia Hills (Wishstone, Watchtower, Clovis, and Peace class) all have compressive strengths <50 MPa and are consistent with impactites or volcanoclastic materials. In general, when considered alongside chemical, spectral, and rock textural data, these inferred compressive strength results help inform our understanding of rock origins and modification history.