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.
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