53 2 



TRANSMISSION 



We are now able to put formula ( i ) in the form of a regression 

 equation, giving the value h z as follows : 



h z = R ^ H, (4) 



which is the deviation of this special population from the mean 

 of the race. 1 



This form of expression of formula (i) has the advantage of 

 simplicity. Instead of the deviations (h^ and. 7z 2 ) of two parents 

 with variabilities cr l and cr 2 , we now have the deviation (H) of a 

 single artificial mid-parent made by first transmuting female 

 deviations into male values by multiplying by the ratio of male 

 to female variabilities for the character in question and then 

 taking the mean of the male and the transmuted female values. 2 

 This is Pearson's mid-parental deviation (H). 



S is the portion of this formula which involves the variability 

 of parents, for it depends upon cr 1 and upon the coefficient of 

 assortative mating (r 3 ), and when associated with H as it is in 

 the formula it may be looked upon as expressing the variability 

 of the mid-parent. 



Likewise R is the portion of the formula which involves the 

 correlation between parent and offspring, and from the form of 

 equation (4) it may be looked upon as the coefficient of correla- 

 tion between offspring and mid-parent. 



If we neglect the coefficient of assortative mating, making 

 r% = o, the following conclusions may be drawn from formulas 

 (3) and (4), and the values of R and S: 



i. The variability of the mid-parent (S) is equal to that of 

 fathers divided by V2.* 



1 Experimental determinations show that for most characters thus far investi- 

 gated the regression coefficient of offspring as compared with mid-parents is 

 about 0.6, so that we may write, in general, h% 0.6 H ; or, in other words, if a 

 mid-parent deviates a certain amount the offspring may be expected in general 

 to deviate 0.6 of that amount from the mean of the race. 



2 This is the - ( h + h% } Hoi the formula. 



2 \ cr 2 / 



* That is, in S = ^ 8 , if assortative mating be disregarded, r & becomes 



"V/2 f 



zero and the formula becomes * l _ ; but Vi = i, and we have -~< 



V 2 V2 



