HEREDITY 531 



Where h^ and // 2 are the deviations of parents from the mean 

 of parents for the character in question, ^ 3 f is the deviation of 

 the offspring of these parents from offspring in general, v l is 

 the standard deviation of fathers from the mean of their gener- 

 ation, cr 2 is the standard deviation of mothers from the mean 

 of their generation, er 3 is the standard deviation of offspring in 

 general as to the character in question, r is the coefficient of 

 heredity between offspring and parents (parents being taken 

 as equipotent, that is, making r 2 = r^ y r s is the coefficient of 

 assortative mating. 



Now formula (i) may be written as follows : 



+-*, 



0-2 



or, again, it may be written 

 i 



(3) 



2 \ 0-2 



In this form the formula is made up of four factors. Of these 

 the first represents the mid-parental deviation ; the second, the 

 variability of mid-parents ; the third, the correlation coefficient 

 between mid-parent and offspring ; and the fourth, the standard 

 deviation for this particular character. If, now, each of these 

 factors (except cr 3 ) be represented by a single letter, we have 

 the following : 



H = - ( AI + ^ 2 1 = the mid-parental deviation, 



2 \ 0-2 / 



S I = - = - = the variability of mid-parents, 



V2 

 T "v 2 



R = = correlation coefficient between mid-parent 



v i 



* For derivation of this formula, see Appendix. 



t The offspring will, of course, form an array, and the h$ is the deviation of its 

 mean from the mean of offspring in general. 



J This last expression is inverted because we desire to use S in the denominator. 



