Quite a number of investigations have been made in relation to the intensity of heredity of parents and of grandparents; and, notwithstanding the uncertainty of the quantitative result, it seems reasonably certain that the intensity of heredity for each parent may be expressed by the value of about one-third (Pearson, Boas). It is somewhat difficult to explain clearly the significance of this value. I may, however, briefly indicate it in the following manner. Provided the mother differs in her stature by an amount of 9 cm. from the racial norm,—for instance, if she is 9 cm. taller than the average individual,—then we may expect the child to be one-third of 9 cm., or 3 cm., above the average. It will thus be seen that if both parents differ in the same direction from the average, the effect of both will be cumulative; and if both differ from the average of their people by the same amount, the joint effect of the two parents may be expressed by the coefficient of about two-thirds. In case, for instance, both father and mother should be 9 cm. above the type average, we should expect the child to be about two-thirds of 9 cm., or 6 cm., above the average. Although definite information on the amount of heredity of previous generations is not yet available, the probability seems to be that the grandparents have jointly an influence of about two-ninths, the great-grandparents jointly of about two twenty-sevenths, etc., upon the offspring. When we study these problems according to statistical theories, and take into consideration the observations on the resemblance of brothers and sisters, it can be shown that the theory of alternating inheritance cannot be taken too literally; for, if there were an absolute reversion of any one trait to pure ancestral types, we might say that the probability would be very small that two brothers should happen to repeat the bodily form of the same ancestor, because the number of ancestors in remote generations is very large. In other words, there must be an additional cause of resemblance between brothers and sisters. It is possible to show, that in case the inheritance has the strength denoted before, and if bodily form of a certain generation were due only to alternating inheritance acting from parents, grandparents, great-grandparents, and so on, and directly upon the generation in question, and without an occurrence of the same individuals in various places in the line of ancestors, then the resemblance between brothers and sisters, or, as we say, between the members of a fraternity, would result in a degree of resemblance which is much lower than the one actually observed. When the total number of ancestors is small, the recurrence of the same forms would become more probable, and the similarity of the series would increase. On the whole, the data seem to be best explained if we assume that there is not only alternating inheritance, but also a direct dependence upon the combination of the two parental types.