This paper develops the theory of transformation of arithmetic to phi-moments and vice versa for any method of size analysis and where the frequency is recorded as weight (in percentage) or as number (in percentage). These transformations are most essential for size distributions obtained from thin-section analysis where a correction is needed to eliminate the effect of random sectioning. The correction procedures for such observed arithmetic moments for number and weight frequency moments have been developed by Krumbein and Sahu respectively.

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