The concept that with continued current transport all sand-grain distributions, when logarithmically transformed, become symmetrical (normal) has been taken to indicate a progressive approach toward ideal textural maturity. Whereas residual soil appears to display a distribution of sizes that obeys Rosin’s law of crushing, streams that carry such debris are considered to modify the distribution until it becomes log normal. Rosin’s law appears to be well founded on crushing theory, but there is no established basis for the development of a log-normal size distribution as currents shift sediment from one locality to another. Although Rosin’s and log-normal distributions do not stem from the same general equation and are not mathematically related, they yield graphic similarities for certain special sand populations. For such examples, the distributions appear to have the same degree of symmetry. Sand transported by long streams, for example, develops a steady-state size distribution, apparently related to the crushing law.
A steady-state, log-normal size distribution of pronounced symmetry is produced along shorelines where "winnowing" is the current process. Ideal cratonic shoreline sands (pure quartz and laminated quartz-glauconite sandstones) illustrate that symmetric, log-normal size distributions are developed when laminar flow dominates the current regime. Conversely, turbulent flow introduces asymmetry to size distributions.
A series of special cases characterizes sand-size distributions in streams and along shorelines; hence, individual distributions should be compared with known standards of reference. The standard for streams should be taken from a very long stream such as the Mississippi, and for shorelines from ideal, stable-cratonic sandstones such as those in western Wisconsin.