Correlation and Application of Statistics to Problems of Heredity 17 



nor short, short. Galton discusses* the absence of assortative mating for 

 stature and forms the following table, where the medium group embraces 

 individuals of 67" and up to 70 stature for males or transmuted females: 



Husband 



He notes that there are 27 like marriages short with short and tall with 

 tall, and 26 contrasted marriages^ short with tall, and argues that there is 

 no assortative mating in stature. In a fuller treatment of the same data 

 by the present writer the coefficient of resemblance between husband and 

 wife was found to be "093 + "047 J, which might just be significant. Later 

 work has shown that there is sensible assortative mating not only in stature 

 (•280), but in span ( - 199) and cubit ("198)§; in other words big men do tend to 

 marry big women and small men small women. Galton's data show, however, 

 so little assortative mating that his results were not sensibly influenced by 

 disregarding it. 



Galton now turns to another point, namely : Does the difference in stature 

 of parents influence the stature of the offspring? He was clearly conscious 

 that this was an important point, for on it depends whether his value for the 

 midparental stature is or is not to be considered correct. As we should now 

 express it, he was really asking whether the stature in the offspring was 

 equally correlated with the statures of the two parents, or rather, that is the 

 question he would have been asking had he transmuted his female deviations 

 to male deviations by aid of the ratio of the two variabilities and not of the 

 two means 1 1. If the two correlations be not equal, then Galton's " Forecaster," 

 based on his conception of midparent, would give incorrect results. Galton 

 indicates in a table (Journ. Anihrop. Instit. Vol. xv, p. 250) that the differential 

 influence of the parents should not be very great, but he does not really 



* Joum. Anthrop. Instit. Vol. xv, p. 251. 



f Printed in loc. cit. 32 instead of 26. 



\ Phil. Trans. Vol. 187 A, p. 270, 1896. 



§ Biometrika, Vol. II, p. 373. 



|| If r M be the paternal, r 23 the maternal coefficient of correlation and r 12 that of assortative 

 mating, the bivariate formula shows us that to give equal weight to father and mother we must 

 have equality of the two expressions 



!-»■„■ 



and 



1 — r * 



(Roy. Soc. Proc. Vol. VIII, p. 240, 1895), and this involves r n = r„ 3 , i.e. the equality of the parental 

 influences. 



p G III 



