Numerical Correlation and Petrographic Variation

Percentage data occur in every natural science but are possibly of more central importance to the petrographer than to most other naturalists. Whether he is attempting to describe the lithosphere, to classify the rock species of which it is formed, to determine the chemical or mineralogical relations between species, or to speculate about the processes which control these relations, his basic data are percentages-of weight, volume, norm, mole-and often they are percentages of the same whole. This latter restriction, which is implicit in all the variation diagrams and projections so popular in petrology, imposes severe limitations on both the amount and kind of variation which are possible under any circumstances, and on the variation which is likely to occur in the absence of departures from randomness. Most petrographers are aware that the percentage form of statement does create a problem of this sort. The questions we attempt to answer by means of variation diagrams and projections seem of such importance, however, that we are divided into two camps: those who are willing to publish variation diagrams despite fears about their propriety, and those who are glad that others are willing to do so. From innumerable conversations with fellow petrologists I gather that most of us suspect a strong element of circularity in arguments based on variation diagrams. In some types of diagrams the key variable, against which each of the others is in turn plotted, itself contains some or most of the others. These common elements naturally impose considerable correlation on the ar-