COERELATED VARIABILITY. 55 



The precise method of using r in modifying any determi- 

 nation of r is uncertain. Pearson recommends using r r 

 as the true measure of "organic correlation" in the case of 

 indices. 



HEREDITY. 



Heredity is a certain degree of correlation between the 

 abmodality of parent and offspring. The statistical laws of 

 heredity deal not with relations between one descendant and 

 its parent or parents, but only with mean progeny of 

 parents. Any group of selected parents is called a parentage, 

 the progeny of a parentage is called a fraternity. 



Three categories of inheritance have long been recognized 

 (Galton, 1888, p. 12). These are: (1) blending heritage illus- 

 trated by stature in man; (2) alternative heritage, illustrated 

 by human eye-color; and (3) mixed heritage, illustrated by 

 the piebald condition of the progeny of mice of different 

 colors. The immediately following statistical laws of inherit- 

 ance hold especially for blending heritage. 



In u 11 i parental inheritance, as in budding or asexual 

 generation, heredity of any character is measured by the coef- 

 ficient of correlation between the abmodality in a parentage 

 and the abmodality of the corresponding fraternity. More 

 strictly, since the variability of the character in the second 

 generation, a 2 , may (as a result of selection or of environ- 

 mental change) be different from the variability of the char- 

 acter in the first generation, <7 1? the index should be taken as 



r , called the coefficient of regression. 



The probable error of this determination is 



.6745^. /I -r 12 2 . 



I/ , in which r 12 means the correlation coem- 



cient between the filial character and that of the single parent 

 under consideration. 



The variability of the fraternity is to variability of offspring 

 in general as\/lr 2 is to 1. 



In bipareiital inheritance, if there is no evidence of 

 assortative mating, or correlation between the two parents in 

 the character in question, the mean abmodality of any f rater- 



