CHAPTER V

for only one family. Further, we can afford to reëmphasize the fact that it in no way prevents the improvement of a race by selection and assortative mating.

Stature is the character which Dr. Galton used to get an exact measurement of the amount of regression. More recent studies have changed the value he found, without invalidating his method. When 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: