740 THE AMERICAN JOURNAL OF SOCIOLOGY
that we may measure its sub-homogeneity by (i) multiplying each successive numerical mark on a marking-scale of resem- blance 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 ex- penditure of educational and reformatory effort, it can stand- ardize 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 con- ceiving 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, o, i, 2, 3, 4, . . . . n.
Designate frequencies by Ko, Ki, K2, Kz, Ki, .... Kn Designate total individuals, or population by P. Designate per-capita degree of sub-homogeneity by 5". Then :
„ Ki + 2K^ + T,Ki+ . . . +NKn b .
Applying this formula to the data presented in the tables of ethnic distribution by resemblance positions, we obtain for 1890 the coefficient .01579 ^s our expression for the per-capita degree of sub-homogeneity, and for 1900 the coefficient .01552. Apply- ing the formula to the data presented in the tables of religious distribution by resemblance positions, we obtain for 1890 the coefficient 1.833, ^^^ ^^^ igo6 the coefficient 1.953. These co- efficients indicate that in ethnic composition the people of the United States are now becoming, contrary to the prevailing im- pression, slightly more homogeneous, but that in religious per- suasion they are still becoming slightly more heterogeneous.
