be subdivided into five grades by the geometric series 1,000, 100, 10, 1, 

 0.1, and 0.01 millimeters where each grade limit in the series is one- 

 tenth as large as the preceding one, or 10 times larger than the suc- 

 ceeding one. 



2. Common Classification Schemes . 



Udden (1898) introduced the first true geometric grade scale. He 

 chose 1 millimeter as the starting point for his scale and used the ratio 

 1/2 (or 2) to create size classes with limits of 1/2, 1/4, 1/8 millimeter 

 etc. (2, 4, 8 millimeters, etc.). Wentworth (1922) adopted and expanded 

 Udden 's geometric grade series, adding descriptive terms for the grades 

 such as "sand" and "silt." He selected size limits for the grades that 

 employed common usage of the terms by geologists and that reflected 

 transport characteristics of different sediment sizes (e.g., clay sizes 

 are commonly transported in suspension, whereas sand is usually rolled 

 or saltated along the bed) . The resulting Udden-Wentworth grade scale 

 (called the Wentworth Classification, Table 1) is generally preferred by 

 geologists. It is geometric with fixed ratio 2, and consists of 24 

 classes that systematically span the range from 1/4096 to 4,096 milli- 

 meters. The width of each class relates directly to the diameters of 

 grains within it so that coarse grains are described in terms of classes 

 with relatively wide ranges of size, and fine particles by classes of 

 fairly narrow width. 



The Unified Soils Classification (Table 1) is the most common grade 

 scale used by soil scientists and engineers. This scale was developed 

 by Casagrande (1948), adopted by the Corps of Engineers (U.S. Army 

 Engineer Waterways Experiment Station, 1953) and the American Society 

 for Testing Materials (ASTM) , and is based on the mesh size of sieves 

 used for the mechanical analysis of sediments. The Unified scale is 

 also geometric because sieve openings are graduated at the fixed ratio 

 /2 (or 1.1892) and, starting at 4 millimeters, every fourth value in 

 the scale agrees with the Wentworth class limits. 



Table 1 has been constructed to show how grade limits and descriptive 

 terms compare for the Unified Soils and Wentworth classification schemes, 

 Although generally similar, the two schemes do assign somewhat different 

 size ranges (in millimeters) to each sediment category. For example, 

 the total range of sand sizes in the Unified Soils scheme is 0.074 to 

 4.76 millimeters as opposed to 0.062 to 2 millimeters for the Wentworth. 

 Because of these differences, communication problems with terms can be 

 encountered and care must be taken to identify the classification scheme 

 being used. 



III. PHI NOTATION 



1. Background . 



Geometric grade scales are not necessarily best for all types of 

 sediment-size analysis. Although the property of fixed-size ratio among 



