environments and analyze the response of sediments to varied flow con- 

 ditions. These comparisons can be quite effective, especially when the 

 parameter is used within some multivariate analysis scheme. However, 

 the skewness parameter is not as stable statistically as the mean and 

 sorting parameters and small deviations from normality can result in 

 fairly large skewness variations. 



3. Terminology and Use . 



The phi scale is less familiar to engineers than to geologists and 

 its use has traditionally created some problems. Many of these problems 

 arise from improper use of terminology and from incorrect conversions 

 between phi and geometric grade scales. Although millimeter equivalents 

 can be assigned to individual phi values, the phi notation is dimension- 

 less. The symbol "<})" represents a ratio of lengths (eq. 1) and 

 identifies the or-igin of the value it follows. It does not have the 

 same significance as the dimensional abbreviation "mm" which indicates 

 in what units the measurements were made. McManus (1963) suggested that 

 one way to keep the meaning of these symbols straight is to place cj) 

 only after values that indicate a single particle size (e.g.. Ma = 3.0(j), 

 or diameter = 2.0(|)), and to use the notation "phi unit" following an 

 interval value such as sorting (e.g., Sj, = 2.5 phi units). Thus, sorting 

 as defined by equation (2) is the interval on a graph representing the 

 number of Vi/entworth grades occurring on either side of M^j, as defined by 

 the concept of standard deviation (e.g., 1 phi unit = 1 Wentworth grade). 

 Finally, since sorting values are the number of phi units, they cannot be 

 converted directly into millimeter value. Sorting values in millimeters 

 can b4 calculated directly using appropriate formulas or, if desired, the 

 phi values at M(j, ±1 Sa can be converted to millimeters. 



Although no single grade scale will best serve all uses for describ- 

 ing texture, the phi scale does have the following advantages as summa- 

 rized by the Inter-Society Grain Size Committee of the Society of 

 Economic Paleontologists and Mineralogists (from Tanner, 1969) : 



(a) Evenly spaced division points, facilitating plotting; 



(b) geometric basis allowing equally close inspection of 

 all parts of the size spectrum; 



(c) simplicity of subdivision of classes to any precision 

 desired, with no awkward numbers; 



(d) wide range of values, extending automatically to any 

 extreme; 



(e) widespread acceptance; 



(f) coincidence of major dividing points with natural 

 class boundaries (approximately) ; 



15 



