Correlation between arrays in a table of correlations

Two recent papers in these Proceedings have dealt with certain problems of probability which are of very great importance for psychology in particular, but in themselves are quite general. As both papers made reference to some of my own, the following considerations may not only be a further positive contribution to the topic, but incidentally serve to clear up some misunderstandings. Suppose that the product moment coefficients of correlation have been determined between any set of variables a, b, c, d , ... z , and have been set forth in a square Table thus:—