In the sample given, the coefficient of correlation obtained is .081, which not being reliably greater than zero (because of possible error due to the smallness of the group and other conditions) tells us that the two functions are in this case related to each other only very slightly, if at all. The child who stands above the average of the group in mental age, may or may not stand above the group average in spelling. With a relationship so far from unity as is expressed by a coefficient of .081, we may expect to find in this group comparatively intelligent children who are very poor spellers, and good spellers who stand low in mental age. Among children taken at random, however, a different relationship exists between spelling ability and general intelligence, as represented by mental age. The positive correlation is much higher among children not selected, as these were, for an observed discrepancy. At the present time the more elaborate methods of partial correlation and multiple correlation are being applied to the study of relationships, where more than two functions are involved. Into the intricacies of these we shall not enter, except as concerns their results. II. GENERAL INTELLIGENCE _vs._ SPECIAL APTITUDES The original attempts to apply mathematical formulæ to the study of relationship among mental traits eventuated in divergent hypotheses. In England, Spearman, with his students and collaborators, interpreted his researches to mean that there is in mental constitution a “general factor,” which shows itself in all the performances of a given individual. This would render relatively predictable the quality of performance in all functions, from knowledge of performance in one function. “All branches of intellectual activity have in common one fundamental function (or group of functions), whereas the remaining or specific elements of the activity seem in every case to be wholly different from that in all others.... The function almost entirely controls the relative position of children at school (after making due allowance for differences of age), and is nine parts out of ten responsible for success in such a simple act as Discrimination of Pitch.... Its relation to the intellectual activity does not appear to be of any loosely connected or auxiliary character (such as willingness to make an effort, readiness in adaption to unfamiliar tests, or dexterity in the fashion of executing them), but rather to be intimately bound up in the very essence of the process.”