Before sorting can be interpreted, it must be measured quantitatively. Unfortunately, sorting can be measured in many different ways, as recently discussed by McCammon (1962). Probably the most common, but most inefficient, method is Trask's sorting coefficient (So) determined by (P₂₅/P₇₅)^1/2 where P₂₅ is the millimeter diameter at the 25^th percentile of the cumulative distribution, etc. The fault of this is that it measures sorting only in the central 50 percent of the distribution, thus mediumgrained sand with 20 percent boulders and 20 percent clay might have just as good numerical sorting as a pure medium sand. Krumbein (1934) developed the phi scale as a logarithmic transformation of the millimeter scale, realizing that the grain size distribution of most natural normal sediments was nearly lognormal, and this allowed simpler measures to be used. His QDf, (P₇₅-P₂₅)/2 (Krumbein, 1936) was the phi analogue to Trask's sorting measure, and suffered from the same limitations. Griffiths (1951) improved matters by using PDf, (P₉₀-P₁₀)/2 taking in more (80 percent) of the curve. Recently, most workers have used phi standard deviation (sf) as the measure of sorting, thus coming into harmony with statisticians in other sciences. The standard deviation may be computed mathematically by the moment method (Krumbein and Pettijohn, 1938), or much shorter graphic approximations to s can be made. Otto (1939) and Inman (1952) both used (P₈₄-P₁₆) /2 Folk and Ward (1957) introduced the "inclusive graphic standard deviation,"sI =(P₈₄ -P₁₆) /4 + (P₉₅-P₅) /6.6 which is more accurate than the method of Otto (1939) and Inman (1952) because it takes in 90 per cent instead of 68 per cent of the distribution, and gives a closer approximation to s as computed by the method of moments. McCammon (1962) demonstrates that the inclusive graphic standard deviation is the most efficient graphic approximation now in use. The geologic significance of sorting has remained obscure. Inman (1949) and Griffiths (1951) showed that sorting was a function of mean grain size; in both of their studies, the best sorted sediments were those with a mean grain size of about 2.5 phi (.18 mm.) and sorting progressively worsened into the coarse sand or silt sizes. Inman attributed this to fluid mechanics, i.e., that grains of about 2.5 phi were easiest to move because of a combination effect of surface roughness and flow characteristics. Folk and Ward (1957) continued this study by extending the size sorting relation into the gravel sizes, and found surprisingly enough that sorting in a river bar improved from coarse sands into the gravel range, so that gravels of a mean size of 3 phi (8 mm.) were about as well sorted as medium or fine sands. They proposed a source of supply explanation, leading to a sinusoidal size sorting relationship, in contrast to the fluid mechanics hypothesis of Inman, which would have predicted continually worsening sorting in the coarser gravels. Blatt (1958) confirmed the sinusoidal relation by finding it in the Atlantic beach sands and gravels of New Jersey, where common quartz sand and vein quartz pebbles where the main constituents. Again best sorted sediments occurred at mean sizes of 1-3 phi and -3 phi; sediments of intermediate sizes were more poorly sorted. Later Elliott (1958) and Nienaber (1958) traced the size vs. sorting relations from sand into clay sizes for some marine and bay samples. Sorting was worst for samples with mean sizes of 7.0 phi, then improved into the pure clay range.

The explanation for the sinusoidal trend when sorting is plotted against mean size is obvious; it is simply a matter of two, or more, different populations of materials being supplied to the environment. Consider a hypothetical series of samples made up of peas and potatoes in different proportions. Obviously, a sample consisting entirely of peas will be relatively finegrained and of rather uniform size, i.e., it will have a low standard deviation. A sample of potatoes alone will also be fairly uniform in size even though it is much coarser than the peas. But if we analyze the grain size of a sample consisting of half peas and half potatoes, we will get a mean particle size somewhere in between, and the sample will be much more poorly sorted. The same principle operated in terrigenous sediments, Brazos River bar samples (Folk and ard, 1957) consisted of (a) limestone and chert pebbles, and (b) quartz sand, with little material of intermediate size. Either material by itself is well sorted; a mixture of half quartz sand and half chert-plus-limestone is obviously going to be more poorly sorted than either one alone, so the size-sorting curve is going to be an inverted V (more precisely, a segment of sinusoidal curve).

The writer for the past several years has been studying the geological significance of sorting of recent carbonate sands. Why are some calcarenites poorly sorted, others well-sorted? Is it a function of mean grain size, as it is in terrigenous sediments; and if so, are the two properties related by a similarly sinusoidal curve? How do sorting values of terrigenous beaches compare with those of carbonate beaches, with their great range of constituents? Is there any difference in sorting between calm coasts and those with vigorous waves? Finally, can a consistent sorting boundary be established quantitatively between beach and submerged carbonate sands?