Whatever group be selected, both ability and environment must be rated according to the requirements of that group.  It then becomes possible, and it is not difficult, to roughly array individuals under each of these two heads successively, and to label every person with letters signifying his place in either class.  For purposes of the following explanation, each quality will be distributed into three grades, determined not by value, but by class place—­namely, the highest third, the medium third, and the lowest third.  In respect to ability, these classes will be called A, B, and C. In respect to environment, the grades will refer to its helpfulness towards the particular success achieved, and the classes will be called E, F, G. It must be clearly understood that the differences between the grades do not profess to be equal, merely that A is higher than B, and B than C; similarly as to E, F, and G. The A, B, C may be quite independent of E, F, G, or they may be correlated.  Both cases will be considered.

Ability and Environment being mutually helpful towards success, the successes statistically associated with AE will be reckoned higher than those associated with AF.  Again, for simplicity of explanation only, it will here be assumed that Ability and Environment are equally potent in securing success.  Any other reasonable relation between their influences may be substituted for the purpose of experiment, but the ultimate conclusion will be much the same.

Table I.—­Combinations of ability and environment.

+-------------+-------------+-------------+
|  AE.    I.   |  AF.    I.   |  AG.   II.   |
+-------------+-------------+-------------+
|  Be.    I.   |  BF.   II.   |  BG.  III.   |
+-------------+-------------+-------------+
|  CE.   II.   |  Cf.  III.   |  CG.  III.   |
+-------------+-------------+-------------+

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.