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: in point of fact, he might get one-tenth or nine-tenths, none or all of a given trait. But, when dealing with a large population, the errors on one side balance the errors on the other, and the law is found, in the cases to which it has been applied, to express the facts.[51] While, therefore, this Galton-Pearson law gives no advice in regard to individual marriages, it is yet of great value to applied eugenics. In the first place, it crystallizes the vague realization that remote ancestry is of much less importance than immediate ancestry, to an individual, while showing that every generation has a part in making a man what he is. In the second place, it is found, by mathematical reasoning which need not here be repeated, that the type of a population may be quickly changed by the mating of like with like; and that this newly established type may be maintained when not capable of further progress. Regression is not inevitable, for it may be overcome by selection.