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Kapteyn's Transformation of Grain Size Distribution
A method proposed by Kapteyn (1903, 1916) and Kapteyn and van Uven (1916) enables one to transform into normal distributions not only the lognormal type, which is realized in grain size distribution, as for example, by means of the phi transformation, but also, if a proper transforming function is known, any other type of distribution. In the present paper, Kapteyn's transformation is carried out graphically--by means of a proposed log hydrodynamic probability chart which utilizes logarithms of settling velocity. The resulting distributions are characterized, depending upon mean grain size and sorting, by a definite negative phi skewness; from this it is concluded that some occurrences of negative phi skewness result from hydrodynamic processes, and not from the mixing o certain modes or from winnowing as described by Folk and Ward (1957), Folk (1961, p. 5-6) and Friedman (1961). The ideal log hydrodynamic probability chart would remove from the cumulative grain size distribution curves the negative phi skewness and other hydrodynamically caused features common to all sediments deposited by water. Deviations of the transformed distributions could then be interpreted in terms of effects of local geologic or hydrodynamic environments. Existing grain size distribution measures are not effective in dealing with all types of grain size distributions.
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