68 



Life and Letters of Francis Galton 



But let us return to less exciting questions. Galton does not, it is sad to 

 record, classify his data in four fundamental parental tables, and till the 

 material is reworked we must be content with the following arrangement. 



Midparent and Child, Artistic Faculty. 





Unfortunately there is no distinction of sex in the offspring. Working 

 out the correlation of this table in three different ways* I find the mean 

 correlation coefficient to be '4405 with a probable error of the order of "024. 

 There appears little doubt accordingly of the resemblance of offspring in 

 artistic faculty to their parents, but the problem which Galton was investi- 

 gating was not the existence of this resemblance, but whether its intensity 

 might be taken as practically identical with those he had found for eye- 

 colour and stature. The reader for whom the following remarks may be too 

 technical is recommended to pass to the conclusions at the end of this para- 

 graph. Galton assumes (i) equal inheritance from both parents, we will 

 represent this by the correlation coefficient r ; (ii) he does not correct by 

 reducing female to male measure, we will suppose this done ; (iii) he neglects 

 the assortative mating, we will represent this by the correlation coefficient e, 

 in the present case this being equal to "2418. The following results can be 

 easily demonstrated : 



(a) 



Variability of Midparent 



v r 



+ e 



2 ' 



Variability of Offspring 

 (b) Correlation of Offspring and Midparent = 



_rv/2 



= •4405, 



+ e 



2r 



1+6 



v/2x-4405 



J\ +> 



(c) Regression of Offspring on Midparent 



or substituting the value of e : 



Regression on Midparent = , 559 = fx0 - 84, 



Parental Correlation, r= '3471 =£ x T04. 



Now Galton deduced for regression of offspring on midparent for both 

 stature and eye-colour the value f , and for parental correlation £. For the 



* Treating the degrees of artistic faculty in the midparents as 1, 0-5, and 0, a biserial corre- 

 lation coefficient after correction for class index gives 4523+ -0138. The two possible divisions 

 giving fourfold tables provide -4655 + -0240 and -4039 + -0298. The three results are thus in 

 reasonable accord. 



