Notes towards a theory of concentration of solids in natural sands

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Abstract
SUMMARY: Theory based on the sphere as the ideal particle, fails to account satisfactorily for the concentration of solids observed in unconsolidated natural sands, which at the same time display a substantial degree of dimensional ordering of the particles. However, when the prolate spheroid of moderate axial ratio is substituted for the sphere, a theory which is satisfied by observation becomes possible, for the reason that equal spheroids can be regularly packed in both close and open ways. A spheroid assemblage of mixed open and close packings can retain a high degree of dimensional ordering of the constituent solids, yet have a relatively low particle concentration. Observations made on sandstones carefully selected for evidence of rapid cementation seem to bear out the theory as applied to natural sands. Clusters of grains resembling the open packings of equal spheroids are found in these sandstones to be uncommon but not rare, in accordance with the theory as thus far developed.