Page:Popular Science Monthly Volume 85.djvu/327

Rh The average contribution of each ancestor was thus stated definitely, the contribution diminishing with the remoteness of the ancestor. This Law of Ancestral Inheritance is represented graphically in the accompanying diagram (Fig. 48). Pearson has somewhat modified the figures given by Galton, holding that in horses and dogs the parents contribute 1/2%, the grandparents 1/3%, the great grandparents 2/9%, etc.

Theoretically the number of ancestors doubles in each ascending generation; there are two parents, four grandparents, eight great-grand-parents, etc. If this continued to be true indefinitely the number of ancestors in any ascending generation would be (2)$n$, in which n represents the number of generations. There have been about 57 generations since the beginning of the Christian Era, and if this rule held true indefinitely each of us would have had at the time of the birth of Christ a number of ancestors represented by (2)$57$ or about 120 quadrillions—a number far greater than the entire human population of the globe at that time. As a matter of fact, owing to the intermarriage of cousins of various degrees the actual number of ancestors is much smaller than the theoretical number. For example, Plate says that the present Emperor of Germany had only 162 ancestors in the 10th ascending generation, instead of 512, the theoretical number. Nevertheless this calculation will serve to show how widespread our ancestral lines are, and how nearly related are all people of the same race.

Davenport concludes that no people of English descent are more distantly related than 30th cousins, while most people are much more closely related than that. If we allow three generations to a century, and calculate that the degree of cousinship is determined by the number of generations less two, since first cousins appear only in the third generation, the first being that of the parents and the second that of the sons and daughters, we find that 30th cousins at the present time would have had a common ancestor about one thousand years ago or approximately at the time of William the Conqueror. As a matter of fact most persons of the same race are much more closely related than this, and certainly we need not go back to Adam nor even to Shem, Ham and Japhet, to find our common ancestor.

2. The second principle which Galton deduced from his statistical studies is known as the Law of Filial Regression, or what might be called the tendency to mediocrity. He found that on the average extreme peculiarities of parents were less extreme in children. "The stature of adult offspring must, on the whole, be more mediocre than the stature of their parents, that is to say more near to the mean or mid of the general population"; and again, "the more bountifully a 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." This so-called law of filial regression is represented graphically in Fig. 49 in which the actual