A formula is provided by mathematicians which enables us to compute the degree of resemblance between these two orders. There are, in fact, several formulae for such purposes, all of which yield substantially the same results. The one used in this case was r = 1.00-(6 Sigma d^{ 2})/(n(n^{ 2}-1)). In this formula _r_ stands for the coefficient of correlation for which we are working; _d_ is the difference between the positions which each of the photographs receives in the two traits; Sigma means the sum of these differences when each has been squared or multiplied by itself; _n_ means the number of cases, which is in this case 20, since there are that number of photographs. When these substitutions are made and the equation solved, the result will be the measure of resemblance, which will lie somewhere between +1.00 and -1.00, as explained in the text. This calculation is carried out here for the two sample traits, for the convenience of readers who may not be familiar with statistical methods.
[5] These experiments were conducted by Lucy G. Cogan, M. A., to whom I am indebted for permission to use the results in advance of their more detailed publication in her forthcoming paper on "Judgments of Character on the Basis of Photographs."
Barren as phrenology and physiognomics were of formulable and useful results, they nevertheless served the purpose of directing attention toward the study of individual differences in mental characteristics as a distinct branch of inquiry. The next step consisted in the semi-experimental plan of observing the individual's _behavior_ under a variety of uncontrolled circumstances or on more carefully planned occasions, in the endeavor to secure more or less exact quantitative expressions of the degree to which he displayed certain types of ability. Underlying the various abilities and involved in them there were assumed to lie a limited number of faculties or powers of the mind. Each individual was conceived to possess much the same faculties, but in varying degrees or amounts or forms. Attention, memory, apperception, reasoning, will, feeling, etc., were the fundamental "faculties"; and differences in character were thought of as depending upon the varying amounts and interrelations of these fundamental faculties. In the endeavor to discover types of experiment which would measure these "faculties" it was found, in time, that a given "faculty" did not appear, on close examination, to be as unitary as it was formerly supposed to be. It was seen that to have a good memory for one kind of material did not at once signify a good memory for every sort of thing. Determination in one direction did not imply the general quality of resoluteness. It began to be realized that attention, memory, discrimination, and the other "faculties" are very much more highly specialized than these general names indicate. The unitary soul had early been split up into the list of "faculties" or categories, and now these in turn came each to be split up into finer and finer aptitudes and tendencies, until, in the radical reaction of recent years, we find the human mind described as made up of an infinite number of independent connections or bonds between more or less specific stimulus and more or less definite response. The old "faculties" came now to be looked on as descriptive terms for certain rather general and abstracted characteristics of these multitudinous and detailed reaction tendencies, rather than as in themselves agents or powers or forces, as they were formerly conceived.