162 THE FIRST PRINCIPLES OF HEREDITY 



father, regression tells us by how much the son is nearer 

 to the mean of the population than his father, both values 

 being the same. 



As there is regression from father to son, so there is, on 

 the other hand, regression from son to father i.e., the 

 father will on an average be more mediocre than a given 

 son. (We only need to compare the figures for the different 

 classes of sons given on the top line of Fig. 71 with those 

 at the bottom line indicating the mean heights of the corre- 

 sponding arrays of fathers.) Further, there is regression 

 from grandfather to grandson, and vice versa. 



Galton has given in his classic work on Natural Inheritance 

 " the coefficients of correlation " for stature as follows : 



Uncle and nephew . . 



Grandson and grandparent 

 Cousin and cousin . . 



Mid -parent and son . . 



Father and son . . . . 



Son and father . . . . \ 



Brother and brother . . f 



NOTE. This would mean that if the stature of the mid -parent is 

 PD, that of the coresponding son would be PD, while if the 

 stature of the father is given as the same, PD, that of the son 

 would only be P + \ D, and so on for the other cases. 



Karl Pearson's coefficients of correlation have somewhat 

 different values. We must here shortly explain the term 

 " mid-parent " as introduced by Galton. As a son inherits 

 from both his parents, father and mother, the peculiarities 

 of stature from both parents will be added in the filial 

 inheritance, and the coefficient of correlation, instead of 

 being \, is f . For the purpose of calculation Galton intro- 

 duced the term " mid-parent " that is, according to his 

 own explanation, " an ideal person of composite sex, whose 

 stature is halfway between the stature of father and the 

 transmuted stature of the mother." In order to transmute 

 the stature of the mother into that of the father, the 

 stature of the mother is reckoned of that height which it 

 would be if the mother were of the male sex. Galton 

 found that for this purpose i inch has to be added to each 



