An R-mode factor analysis based on twenty petrographic variables observed in thin sections of sixty Cincinnatian biomicrosparrudites was performed to illustrate the geologic use of this statistical procedure. Five significant factors were extracted from a 20x20 correlation matrix, which account for 82 percent of the total variance. The geologic interpretations of the factors in order of decreasing statistical significance are (1) mechanical energy gradient at the depositional site, (2) substrate firmness, (3) degree of lithification, (4) relative contributions of carbonate mud and skeletal grains to the sediment, and (5) Eh at or slightly below the depositional interface. Three limestone classes were compared with each factor, and the following genetic relationships were obtained. Classes 1-2, 1L, and 3 formed in environments typified by high to low mechanical energy respectively. Field relationships suggest that the differences in mechanical energy among these classes were probably small. The substrates associated with class 1L were softer than those of classes 1-2 and 3. Breakage of skeletal grains was greatest in class 1-2 and progressively lower in classes 1L and 3. Sparite was apparently not introduced until a fair degree of substrate stability had been attained. Burrowing gastropods associated with class 1L tended to maintain oxidizing conditions a limited distance below the depositional interface by consuming some of the available organic matter and reworking the substrate.

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