CORRELATED VARIABILITY. 37 



When assortative mating occurs, as is usually case, the 

 abmodality of a fraternity is given by 



p 3 pip* cr, Pi Pips 



711 = ' A * + 



where pi = 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 - P i 9 ' oV 



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 of the whole ; from the 4 grand- 

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



from the ?ith ancestral generation of the whole ; the total 



/w 



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

 Pearson ('98) as follows : 



1 <T O 1 <TO 1 cr 1 CT O 



ill = n --- i -f -# a +5 --- *a + rn &4 + 



2 <T! 4 o- 2 8o- 3 Ib cr 4 



where /i! = average abmodality of fraternity. 

 cr = standard deviation of fraternity. 

 (T! , (Ji . . . cr s = standard deviation of mid-parent of 



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

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



tion. 







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



. . . sth 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. 



