First, suppose Ability and Environment to be entirely independent, A being as frequently associated with E as it is with F or with G; similarly as regards B and C, then the nine combinations shown in Table I. will be equally frequent. These tabular entries fall into three equal groups. The three that lie in and about the upper left-hand corner contain the highest constituents--namely, either _high_ combined with _high_, or one _high_ with one _medium_. They produce Successes of Grade I. The three in the middle diagonal band running between the lower left and the upper right corners are either one _high_ and one _low_, or both are _medium_; they will produce Successes of Grade II. The three in and about the right-hand corner are either one _medium_ with one _low_, or both are _low_; they will produce Successes of Grade III. This is still more clearly seen by sorting the results into Table II., from which it is clear that a high grade of Success is statistically associated with a high, but less, grade of Ability, a medium with a medium, and a low grade of Success with a low, but less low, grade of Ability. TABLE II.--ABILITY INDEPENDENT OF ENVIRONMENT. _____________________________________________________________________ | | | | | Grades of | | | | Success. | Contributory Combinations. | Corresponding Abilities. | |___________|_____________________________|___________________________| | | | | | | | | | I. | AE | AF | BE | 2 of A | 1 of B | -- | | II. | AG | BF | CE | 1 of A | 1 of B | 1 of C | | III. | CG | BG | CF | -- | 1 of B | 2 of C | |___________|_________|_________|_________|_________|________|________| Secondly, suppose A, B, C to be correlated with E, F, G, so that A is more likely to be associated with E than it is with F, and much more likely than with G. Similarly, C is most likely to be associated with G, less likely with F, and least likely with E. The general effect of these preferences will be well represented by divorcing the couples which differ by two grades--namely, AG and CE, by re-mating their constituents as AE and CG, and by re-sorting them, as in Table III. The couples that differ by no more than one grade are left undisturbed. The results now fall into five grades of Success, in four of which each grade contains two-ninths of the whole number, and one, the medium Grade 3, contains only one-ninth. As remarked previously, the grades are not supposed to be separated by equal steps. They are numbered in ordinary numerals to distinguish them from those in Table II.