474 EVOLUTION, GENETICS, AND EUGENICS 



an individual was worked out by statistical methods, and the result 

 was Galton's Law of Ancestral Shares in Inheritance (Fig. 89). 



According to this law, the two parents contribute between them 

 on the average about one-half of each inherited character, each parent 

 contributing a quarter of the whole. The four grandparents combined 

 contribute one-half of the remainder, or one-fourth of the whole, each 

 of them one-sixteenth. The eight great-grandparents contribute half 

 of the remaining one-quarter, or one-eighth of the whole, each con- 

 tributing one-sixty-fourth. The remaining ancestors contribute the 

 remaining eighth. The total heritage would be 1. This is an infinite 

 mathematical series whose principal property is that each term is 

 equal to the sum of all those which follow: thus, \ = |+|+tV+ 3V+^¥> 

 etc. No account is taken of the prepotencies of particular ancestors — 

 and there is no question that such prepotencies exist — but all individ- 

 ual peculiarities are averaged up. The results are mass results, in- 

 applicable to any particular individual or pedigree. 



The exact shares of various grades of ancestors, as stated by 

 Galton, have been questioned by Pearson, who, after careful study, 

 has revised Galton's figures to read: parents |, grandparents |, great- 

 grandparents I, etc. 



Criticism of Galton's work. — The scheme used by Galton assumes 

 that the number of ancestors is far greater than is actually the case. 

 "Theoretically," says- Conklin, "the number of ancestors doubles with 

 each ascending generation; there are two parents, four grandparents, 

 eight great grandparents, etc. If this continued to be true indefinitely 

 the number of ancestors in any ascending generation would be (2)", 

 in which n represents the number of generations. There have been 

 5 7 generations since the beginning of the Christian Era ; and if this rule 

 held true indefinitely, each of us would have had since the time of the 

 birth of Christ a number of ancestors represented by (2)", or about 

 120 quadrillions — a number far greater than the entire human popula- 

 tion of the globe since that time. As a matter of fact, owing to inter- 

 marriage of cousins of various degrees, the actual number of ancestors 

 is much smaller than the theoretical number. For example, Plate 

 says that the late emperor of Germany had only 162 ancestors in the 

 tenth ascending generation, instead of 512, the theoretical number. 



"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 the century, 

 and calculate that the degree of cousinship is determined by the num- 



