hen large
numbers are taken it is now abundantly proved that if parents exceed the
average stature of their race by a certain amount their offspring will,
in general, exceed the racial average by only one-half as much as their
parents did. This is due, as Galton said, to the "drag" of the more
remote ancestry, which when considered as a whole must represent very
nearly mediocrity, statistically speaking.

The general amount of regression in heredity, then, is one-half. If it
be expressed as a decimal, .5, the reader will at once note its identity
with the coefficient of correlation which we have so often cited in this
book as a measure of heredity. In fact, the coefficient of correlation
is nothing more than a measure of the regression, and it is probably
simpler to think of it as correlation than it is to speak of a Law of
Regression, as Sir Francis did.

This correlation or regression can, of course, be measured for other
ancestors as well as for the immediate parents. From studies of
eye-color in man and coat-color in horses, Karl Pearson worked out the
necessary correlations, which are usually referred to as the law of
Ancestral Inheritance. Dr. Galton had pointed out, years before, that
the contributions of the several generations of individuals probably
formed a geometrical series, and Professor Pearson calculated this
series, for the two cases mentioned, as:

Parents Grandparents G-Grandparents G-G-Grandparents

.6244 .1988 .0630 .0202 ... etc.

In other words, the two parents, together, will on the average of a
great many cases be found to have contributed a little more than
three-fifths of the hereditary peculiarities of any given individual;
the four grandparents will be found responsible for a little less than
one-fifth, and the eight great-grandparents for about six hundredths,
and so on, the contribution of each generation becoming smaller with
ascent, but each one having, in the average of many cases, a certain
definite though small influence, until infinity.

It can not be too strongly emphasized that this is a statistical law,
not a biological law. It must not be applied to predict the character of
the offspring of any one particular mating, for it might be highly
misleading. It would be wholly unjustified, for example, to suppose that
a certain man got three-tenths of his nature from his father, because
the Law of Ancestral Heredity required it