The early generations include too few individuals to be of much statistical value, but where the number of offspring rises to 500 or over, the statistical constants acquire undoubted value. The data have been given in the form of correlation tables which will repay careful study. In the tables a single entry has been made for each individual offspring in that row which corresponds with the _mean grade_ of its two parents. Thus, if one parent were of grade 2 and the other of grade 2½, the offspring would be entered in the row 2¼ along with the offspring of parents both of grade 2¼. Offspring of parents whose mean grade fell between the rows given in the tables were divided equally between the adjacent rows, alternate litters being assigned to each. Thus, if the mean grade of the parents were 2⅟₁₆, alternate litters of offspring would be entered in row 2 and in row 2⅛. PLUS SELECTION SERIES. This series begins with pairs ranging in average grade from +1.87 to +3. From these parents were obtained 150 young, which range in grade from +1 to +3, as is shown in Table 1. It will be observed that the lower-grade parents have on the average lower-grade offspring than the higher-grade parents. But in no case is the average grade of the offspring as great as that of their parents. Thus 1.87 parents had 1.82 offspring (average grade); 2.00 parents had 1.76 offspring; 2.25 parents had 1.87 offspring; and so on to 3.00 parents, which had 2.35 offspring. There is a falling back in grade or “regression” of the offspring as compared with their parents, which increases in amount as the grade of the parents becomes higher. (See column “Regression” in Table 1.) The parents of this first generation were chosen because of their high grade. They were all probably in grade above the general average of the population from which they were selected. In the case of those which deviate most from the general average the regression is greatest, as we should expect. This phenomenon of regression, which is a very general one in cases of selection, was first observed by Galton in selecting sweet-peas of varying size from a mixed population. Later Johannsen, who repeated the experiment with beans, found that by pedigree culture he was able to break the mixed population up into pure lines within which, considered singly, no regression occurred. We shall need later to return to this subject and consider whether pure lines free from regression exist or can be produced as regards the hooded pattern of rats.