BIOMETRY 371 



system and to establish certain principles as a result of statistical 

 study. He was the real founder of the scientific study of inheritance; 

 he studied characters singly and he introduced quantitative measures. 

 Galton's researches, which were published in several volumes, con- 

 sisted chiefly in a study of certain families with regard to several 

 selected traits, viz., genius or marked intellectual capacity, artistic 

 faculty, stature, eye color and disease. As a result of his very exten- 

 sive studies two main principles appeared to be established: 



i. The Law of Ancestral Inheritance which he stated as follows: 



The two parents contribute between them on the average one-half 

 of each inherited faculty, each of them contributing one-quarter of 

 it. The four grandparents contribute between them one-quarter, or 

 each of them one-sixteenth; and so on,thesumof the series 1+1+1+^ 

 being equal to i, as it should be. It is a property of this infinite series 

 that each term is equal to the sum of all those that follow: thus 

 i = lH-HiV , l = l+iV+ , and so on. The pre- 

 potencies of particular ancestors in any given pedigree are eliminated 

 by a law which deals only with average contributions, and the various 

 prepotencies of sex with respect to different qualities are also presum- 

 ably eliminated. 



The average contribution of each ancestor was thus stated defi- 

 nitely, the contribution diminishing with the remoteness of the ances- 

 tor. This Law of Ancestral Inheritance is represented graphically in 

 Figure 65. Pearson has somewhat modified the figures given by 

 Galton, holding that in horses and dogs the parents contribute f , the 

 grandparents f , the great-grandparents f , etc. 



Number of ancestors. Theoretically the number of ancestors 

 doubles in 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 about 57 generations since the beginning of the Chris- 

 tian 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 repre- 

 sented by (2)" or about 120 quadrillions a number far greater than 

 the entire human population of the globe since 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 late Emperor of Germany 

 had only 162 ancestors in the zoth ascending generation, instead of 



