EVOLUTION 469 



the array be S. What are //^ and % ? These are the 

 questions of bi-parental heredity. Now we can proceed 

 exactly as we have indicated before and correlate the 

 three organs in father, mother, and son, pair and pair. 

 This is not a tJieoretical suggestion, but it has been fre- 

 quently done, and we already know the values of such 

 correlations for a variety of organs in several races. Let 

 /'i be the correlation between the father's and the son's 

 organs, this is the coefficient of paternal heredity ; let i\ 

 be the correlation between the mother's and the son's 

 organs, this is the coefficient of maternal heredity ; let r^ 

 be the correlation between the father's and mother's organs, 

 this is the intensity of assortative mating, which we have 

 considered on p. 429. 



Now if the deviations from the type are small as 

 compared with the organ or character measured, the type 

 of the son's array A, must consist of two terms, one pro- 

 portional to Ji and one to /^.,. In other words, we shall 

 have 



where c^ and c^ are numerical constants to be determined 

 in terms of the correlations and variabilities r^, /'^j ^'3. o"!* 

 cr.^, o-,,. Now the algebraical discussion of this problem 

 cannot be entered on here, but it may be stated that it 

 involves no further assumptions than those already made 

 for uni-parental inheritance. We obtain the following 

 results, which are cited to show the important conse- 

 quences that flow from them : — 



r^ — r^r,, o-^ ^ o", 



iSj— , say, 



^1 = 



1 "1 



f 2 = -^ S = P-2 ' say, 



while %, the variability of the array, is given by 



Here c^ and r., are termed partial regression coefficients, 

 ySj and /3., are convenient expressions involving the 



