As to the application of this law, let Galton himself speak: "The Law of Regression tells heavily against the full hereditary transmission of any gift. Only a few out of many children would be likely to differ from mediocrity so widely as their Mid-Parent [i. e., the average of their two parents], allowing for sexual differences, and still fewer would differ as widely as the more exceptional of the two parents. The more bountifully the parent is gifted by nature, the more rare will be his good fortune if he begets a son who is as richly endowed as himself, and still more so if he has a son who is endowed yet more largely. But the law is evenhanded; it levies an equal succession-tax on the transmission of badness as of goodness. If it discourages the extravagant hopes of a gifted parent that his children on the average will inherit all his powers, it not less discountenances extravagant fears that they will inherit all his weakness and disease. "It must be clearly understood that there is nothing in these statements to invalidate the general doctrine that the children of a gifted pair are much more likely to be gifted than the children of a mediocre pair." To this it should be added that progeny of very great ability will arise more frequently in proportion to the quality of their parents. It must be reiterated that this is a statistical, not a biological, law; and that even Galton probably goes a little too far in applying it to individuals. It will hold good for a whole population, but not necessarily for only one family. Further, we can afford to reemphasize 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.