53 



TRANSMISSION 



As Pearson says, what now are h% and 2 ; that is, what 

 deviation from the mean of offspring in general (// 3 ) is to 

 be expected in the offspring of these particular parents, and 

 what is their variability or standard deviation (2) with respect 

 to their own mean ? Cast in still more general terms, the 

 questions are these : How will the offspring from selected parents 

 differ from offspring in general, and how will they differ among 

 themselves ? 



Now these are fundamental questions in breeding, and their 

 answer involves the following additional conceptions, all with 

 reference to the character in question : 



1. The standard deviation for fathers in general (o-j). 



2. The standard deviation for mothers in general (<r 2 ). 



3. The standard deviation for offspring in general (<r 8 ). 



4. The coefficient of heredity between fathers and offspring 

 reckoned as sons (r^. 



5. The coefficient of heredity between mothers and offspring, 

 also reckoned as sons (r a ). 



6. The coefficient of correlation (cross heredity) between 

 fathers and mothers, due to assortative mating (r a ). 



Galton considered that inheritance from two parents is sub- 

 stantially equivalent to inheritance from a " mid-parent," which 

 should be the mean of the two after transmuting the female 

 values (measurements, for example) into male equivalents by 

 multiplying those values by the ratio of the male to the female 

 mean, for the character in question. 



Pearson, on the other hand, deals first with deviations, and 

 by the deviations of the parents from parents in general he 

 attempts to predict the deviation of their particular offspring 

 from the mean of offspring in general, which is the same as say- 

 ing "from the mean of the race." 



While Galton thus artificially built up a mid-parent to take 

 the place of the two parents, Pearson developed first the theory 

 of " biparental inheritance," taking into account the means 

 and variabilities of the parents, the coefficient of assortative 

 mating, and the coefficient of correlation between offspring and 

 parents, thus leading to the following formula for biparental 

 inheritance : 



