and d(mm) is the grain diameter in millimeters. This transformation 

 uses the logarithm to the base 2, which is equal to the power of the 

 geometric series, and produces a dimensionless, arithmetic- size scale 

 that can be easily divided into smaller units with limits of integer 

 value. Differences in the shapes of the gsds using the phi-size scale 

 can be seen by comparing a and b in Figure 1 in which the range of 

 finer grain sizes has been significantly expanded. Also, the plots of 

 weight percent for each size class tends to be fairly symmetric about 

 the most frequently occurring sizes when phi is used (Fig. 2, a versus 

 b). 



I 0.5 



Grain Size (mm] 



-30 



Sample 2 



2 I 0.5 



Grain Size (LofJiodTim) 



Figure 2. Size- frequency plots comparing (a) millimeter 

 versus (b) phi-size scales. 



11 



