328 STATISTICAL STUDY OF INHERITANCE 



character of the individual offspring, we ask : What is the correct 

 method of deahng, with the problem of heredity in such cases ? 

 The causes A, B, C, D, E, . . , which we have as yet succeeded 

 in isolating and defining are not always followed by the effect 

 X, but by any one of the effects U, V, W, X, Y. We are, there- 

 fore, not dealing with causation but correlation, and there is, 

 therefore, only one method of procedure possible ; we must 

 collect statistics of the frequency with which U, V, W, X, Y, Z, 

 respectively follow on A, B, C, D, E. . . . From these statistics 

 we know the most probable result of the causes A, B, C, D, E 

 and the frequency of each deviation from this most probable 

 result. The recognition that in the existing state of our know- 

 ledge the true method of approaching the problem of heredity 

 is from the statistical side, and that the most that we can hope 

 at present to do is to give the probable character of the offspring 

 of a given ancestry, is one of the great services of Francis Galton 

 to biometry." 



Summary. — Galton formulated his Law of Ancestral In- 

 heritance as follows : " The two parents contribute between 

 them on the average one-half or (o'5) of the total heritage of 

 the offspring ; the four grandparents, one-quarter, or [o'^)"- ; 

 the eight great-grandparents, one-eighth, or (o"5)^ and so on. 

 Thus the sum of the ancestral contributions is expressed by the 

 series [(o"5) -I- {o'^Y -f (o'5)^ etc.], which, being equal to i, 

 accounts for the whole heritage" (1897, p. 402). 



But it is quite legitimate to accept the general idea of this 

 Law without accepting the fixity of the fractions of partial 

 inheritance which it expresses. 



Mr. G. Udny Yule states the law of ancestral heredity in the 

 most general way possible when he says : " This law, that the 

 mean character of the offspring can be calculated with the more 

 exactness, the more extensive our knowledge of the corresponding 

 characters of the ancestry, may be termed the Law of Ancestral 

 Heredity" (1902, p. 202). 



