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