Correlation and Application of Statistics to Problems of Heredity 77 



on the presence of the ancestral mediocrity. He does not state what experi- 

 mental evidence there is for this other type of regression, and my impression 

 is that it arose in his mind from a belief that regression was always in action 

 and so evolution impossible by mere selection of continuous variations. 



Under the same heading of Pure Breed Galton also considers the vari- 

 ation within a sibship or group of brethren. If, as he defines a pure breed, it 

 be merely a line in which the ancestors have been given the same selection 

 value for a large number of generations, then on Galton's theory of normal 

 distribution of variates, the theory of multiple regression shows us that the 

 variability will be the same within the sibship, whether the ancestry have 

 been selected or not. Galton, to whom that theory was not familiar, deduces 

 by a rough approximative method that the ratio of variability in the pure 

 breed is to that in the mixed breed as - 98 to TOO; but actually on his 

 hypothesis they are equal ; the variability of the sibship is independent of 

 whether the characteristics of the progenitors are alike or unlike. Of course 

 the reader must understand that by pure breed and mixed breed Galton is 

 only referring to sibships which have their progenitors alike and their pro- 

 genitors unlike in character respectively. All these progenitors are supposed 

 of the same race, and he was not dealing with cross-breds, or mixture of 

 races, in his "mixed" breeds. 



In the final paragraph of this chapter Galton gives the results of his 

 experience. He considers that for practical prediction you need to know not 

 only the obvious somatic characters of the two parents, but the latent 

 characters of their germ-plasms. These latter he considers can be respec- 

 tively determined with a fair degree of approximation from the paternal and 

 maternal uncles and aunts, if they exist in considerable numbers. Also what 

 may be ascertainable of grandparents and their sibships will be of value. 

 But he considers that if he were to start collecting family records again, he 

 would limit himself to families having at least six adult children, and with as 

 many members in both paternal and maternal sibships. There is much that 

 is true in this view, yet at the same time, where a stirp occasionally throws 

 a noteworthy individual, it may be doubted whether a sample of 12 in the 

 first generation and six in the second is large enough to bring out all the 

 latent possibilities which may be of importance. The desire of the Eugenist 

 must always be for as complete a family pedigree as possible. It would not 

 be feasible on a sample of 18 to say whether a single occurrence showed 

 insanity to be a latent character of the stock or not. 



Galton's final chapter contains a brief summary of the work, of which 

 our present section is a more complete one. Only two points may be referred 

 to. On p. 196 he writes: 



" There are no means of deducing the measure of fraternal variability [i.e. variability in the 

 sibship from the same pair of parents] solely from that of the co-fraternal [i.e. the array of 

 individuals who all have one parent of the same character value]. They differ by an element of 

 which the value is thus far unknown." 



We need no longer admit this ignorance. If R be the multiple correlation 

 of an individual on all his ancestry, or on his "generant," then <r J\—R? is 



