Some roll-type uranium deposits are marginal to an altered tongue in sandstone beds that originally contained more-or-less uniformly distributed pyrite. Mineralizing solutions percolated through the sandstone, oxidized nearly all the pre-existing pyrite, and then redeposited part of the pyrite downstream in an embryonic ore zone. The pyrite and the entire ore zone continued to migrate downstream in the sandstone, much as a sand dune migrates. The amount of pyrite in mature deposits varies systematically with the position in the ore body. It is postulated that the rate at which the pyrite was redeposited controlled the systematic variation in distribution of pyrite.Biogenic and chemical models which are described in the literature provide alternate explanations for the genesis of roll-type uranium deposits in sandstone. The different theoretical rates for the precipitation of pyrite in the two genetic models provide a distinctive distribution of pyrite that characterizes each process. The theoretical difference between the biogenic and chemical models provides a mathematical technique for identifying the origin of a deposit. Mathematical analysis of the pyrite content of a uranium deposit in the Shirley Basin, Wyoming, illustrates a practical application of the theory. Although a definite conclusion about the origin of roll-type deposits would require considerably more data than are now available, the pyrite content of this deposit does correspond to the theoretical pyrite content of the chemical model, suggesting that a disproportionation reaction was involved in its formation.