CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE 

 MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE. 

 E. L. MARK, DIRECTOR. — No. 146. 



THE LAWS OF HEREDITY OF GALTON AND MENDEL, 

 AND SOME LAWS GOVERNING RACE IMPROVEMENT 

 BY SELECTION. 



By W. E. Castle. 



Presented October 14, 1903. Received September 26, 1903. 



Contents. 



Page 



I. The "Law of Ancestral Heredity" 223 



II. Mendel's Law of Heredity 227 



III. Yule on Galton's Law and Mendel's Law 232 



IV. Race Improvement by Selection of Desirable or by Elimination of Unde- 



sirable Individuals 234 



Bibliography 240 



I. The " Law of Ancestral Heredity." 



In the year 1889, the eminent English statistician, Francis Galton, 

 attempted to give precise mathematical expression to the well-known 

 fact that the child resembles in varying degree its ancestors near and 

 remote. From a study of family statistics of stature, he found that 

 children resemble their parents, on the average, more closely than their 

 grandparents, and the latter more closely than their great-grandparents, 

 and so on to ancestors still more remote. He tentatively advanced the 

 hypothesis that the resemblance to each earlier generation of ancestors 

 is just half that to the next later. 



Galton subsequently tested this hypothesis in the case of a domesti- 

 cated animal, by applying it to an extensive series of records of the 

 inheritance of black spots in Basset hounds. Satisfied with the result; 

 Galton ('97, p. 502) then formulated as follows the general " Law of 

 Ancestral Heredity": — "The two parents contribute between them, on 

 the average one-half, or (0.5) of the total heritage of the offspring ; the 

 four grandparents, one-quarter, or (0.5) 2 ; the eight great-grandparents, 

 one-eighth, or (0.5) 3 , and so on. Thus the sum of the ancestral contri- 



