CORRELATED VARIABILITY. 37 



When assortative mating occurs, as is usually case, the 

 abmodality of a fraternity is given by 



7 



7 " = 



where p\ = correlation between male and female parents. 

 The other letters have the same signification as before. 



The strength of heredity in assortative mating is measured 

 by the formula 



1 - /V ' crV 



Galton ('97) has shown that an individual inherits not only 

 from his parents, but also from his grandparents, great-grand- 

 parents, and so on. The heritage from his 2 parents together 

 is, on the average, 50$ or J of the whole ; from the 4 grand- 

 parents 25$ or J ; from the 8 great-grandparents 12.5$ or J ; 



from the Tith ancestral generation of the whole ; the total 



heritage adding up 100$. This law has been generalized by 

 Pearson ('98) as follows : 



1 O*O T . 1 CT O . 1 (TO. 1 CT O 



li\ = ~ -- ki + i -- &a + ~ -- &3 H --- #4 + 



2 <r l ^ 4 o- a ^ 8 cr 3 ^ 16 <7 4 



where A! = average abmodality of fraternity. 

 <T = standard deviation of fraternity. 

 (7i, cr a . . . <r s = standard deviation of mid-parent of 

 1st, 2d ... 5th ancestral generation. 

 ki = abmodality of mid-parent of 1st ancestral genera- 



tion. 

 & 3 , & 3 . . . k s = abmodality of mid-parent of 2d, 3d 



. . . 5th ancestral generation. 



The abmodality of the mid-parent of any degree of ancestry 

 may be taken as the average abmodality of all the contributory 

 ancestors of that generation. 



