tion, and the make-up of its social mind, they would be serviceable enough to repay the labor involved in applying them. They have, however, a further and more important use, which must now be indicated. 5 40 30 FIG. 7.-Religions: Frequency Curve of Resemblance Positions, 1890. The question has been raised whether the American population is becoming more or less heterogeneous in ethnic composition. Not less interesting are the questions: Are we becoming more heterogeneous or less heterogeneous in religious belief? FIG. 8.-Religions: Frequency Curve of Resemblance Positions, 1906. Are we becoming more unlike or less unlike in conduct? Are we becoming more unequal or less unequal in educational attainments? But to ask these questions is to raise yet another which is preliminary to them all, namely: Is it in any case possible to measure relative heterogeneity? Given two compounds, is it possible to determine how much more compounded one is than the other? I do not know what attempts may have been made to answer this question in its generalized form, but I believe that no method has hitherto been suggested, or at any rate used, for measuring the sub-homogeneity of mixed populations, or of the social mind. I venture therefore to suggest that the problem admits of solution and to offer a formula for finding a numerical measure or coefficient of heterogeneity, or, as I think we may more accurately say, of sub-homogeneity. When we plot the surface of magnitude (the polygon of distribution as defined by Galton), we measure magnitudes, or we determine successive positions, by vertical distances from a baseline. Since equal magnitudes must be measured, and positions that indicate equal degrees of relationship must be determined, by equal vertical distances, the plotted points indicating such equal measures must lie in a horizontal straight line. Therefore, the horizontal straight line is the graphic expression of equality or of homogeneity. Departures from equality, or degrees of sub-homogeneity, are best plotted as minus or negative magnitudes, graphically expressed by points placed at proper distances below a horizontal line, which itself expresses the ideal homogeneity from which departures are supposed to be made. Let us then suppose that we have to describe a group of human beings, twelve in number, of whom three are unobjectionable in conduct; three are vicious persons, or minor misdemeanants; two are petty criminals or major misdemeanants; two are felons, not capital; and two are felons, capital. The group as a whole is sub-homogeneous. Plotting the data, we get the arrangement shown in Fig 9. Imagine now, that by expending one unit of some kind of effort, we could lift any one vicious person up to the level of the men whose conduct is unobjectionable; that by expending two units of the same kind of effort we could lift any one major misdemeanant to the same standard level; that by expending three units of the same kind of effort, we could lift any one of the minor felons, and by expending four units of the same kind of effort we could lift any one of the major felons, to our standard level. Then, by expending 1 unit X3+2 units X2+3 units X2+4 units X2, or 21 units in all, or 1.75 units per capita, for the whole group of twelve persons, we should convert the entire sub-homogeneous group of twelve persons into a group perfectly homogeneous in respect of a standardized conduct. Students of the physical sciences who are accustomed to measure physical phenomena of every description by the number of units of effort, or of energy, necessary to transform them from one state into another, will assent to the proposition that if we could thus actually transform any heterogeneous group of human beings into a homogeneous group, the number of units of effort necessarily expended in the process could be taken as an accurate measure of the total sub-homogeneity of the original group, and that the total number of units of effort so expended, divided by the total number of individuals in the transformed group, could be taken as a measure of the per-capita degree of sub-homogeneity of the original group. Is it legitimate to conceive of any heterogeneous group as ideally transformable by such a procedure, and then to assume that we may measure its sub-homogeneity by (1) multiplying each successive numerical mark on a marking-scale of resemblance positions by the "frequency" or number of individuals assigned to that position, (2) obtaining the sum of the products, and (3) dividing it by the whole number of individuals in the group or population? It is, I think, an adequate and satisfactory answer to this question to observe that the conception and the assumption are legitimate, if mankind is waranted in believing that by an expenditure of educational and reformatory effort, it can standardize knowledge and conduct, and can assimilate alien habits and ideals to prevailing or national types. If the validity of this pragmatic belief be conceded, there can be no objection to conceiving of an average and abstract unit of standardizing effort, practically unchanging throughout the same group or population, living under practically constant conditions. If so much be granted, we may write the formula for measuring sub-homogeneity as follows: Designate positions on the marking-scale by the numerals, 0, 1, 2, 3, 4, ท. Kn Designate frequencies by Ko, K1, K2, K3, K1, Applying this formula to the data presented in the tables of ethnic distribution by resemblance positions, we obtain for 1890 the coefficient .01579 as our expression for the per-capita degree of sub-homogeneity, and for 1900 the coefficient .01552. Applying the formula to the data presented in the tables of religious distribution by resemblance positions, we obtain for 1890 the coefficient 1.833, and for 1906 the coefficient 1.953. These coefficients indicate that in ethnic composition the people of the United States are now becoming, contrary to the prevailing impression, slightly more homogeneous, but that in religious persuasion they are still becoming slightly more heterogeneous. THE PSYCHOLOGICAL VIEW OF SOCIETY CHARLES A. ELLWOOD Auguste Comte suggested, in the later years of his life, that all sciences might be reduced to two great general sciences, physics and sociology, the former dealing with all the phenomena of the physical universe, the latter dealing with all the phenomena of human society. The sociologist of today, however, would acknowledge that it is more reasonable to suggest that the two master sciences are, not physics and sociology, but physics and psychology. He would not claim for his science the proud position which Comte claimed for it, but would rather subordinate it to psychology. This is due to the fact that the modern view of the world recognizes the clear distinction between the objective and the subjective, between the physical and the psychical; and this recognition has led inevitably to the recognition of psychology as the master science of the subjective, or psychical; just as physics has been elevated to the central position among the physical sciences, so modern thought has elevated psychology to the central position among all those sciences which deal in any way with the psychical or its products. Comte did not deny the existence of psychology, but he subordinated it partly to biology (organic physics), and partly to sociology. This was due, in part, to his materialistic world-view, but even more to the fact that psychology in his time had not developed sufficiently to have even an independent position among the sciences. Comte, in other words, could not have subordinated sociology to psychology without being misunderstood. At present, however, conditions are reversed; the development of psychology, and of modern science generally, has made it evident that sociology must be subordinated partly to biology (organic physics) on the one hand, and partly to psychology on the other. It needs no extended argument to show that sociology is much |