24 



Life and Letters of Francis Galton 



Galton, by means of seeking the slope of the regression line, found the 

 regression of brother on brother to be § and this accordingly would be the 

 fraternal correlation ; he then said : a nephew is the son of a brother, therefore 

 his regression on his uncle = -j x f = f- Again I do not believe that regressions 

 can be built up in this manner. It appears to be multiplying together 

 probabilities that are not independent, but correlated; for all a regression 

 provides is a probable deviation, and we cannot apply independent probabilities 

 to a correlated triplet. Why may not a brother be considered as the son of a 

 midparent and so have regression § x § = $ instead of Galton's observed value 

 |^? Why might we not equally well argue that a nephew is the grandson of 

 a midparentage, which gave rise to his uncle and thus the nephew-uncle 

 regression be-jxfx§ = ^- instead of § % Why should cousins* be considered 

 the offspring of two brothers |x|x| rather than as the grandsons of one 

 midparentage -jXfxfx^? Even if we are always to take the "shortest way 

 round," no argument is given in favour of it, and it could only be satisfactorily 

 demonstrated by actual data. 



:iGHTj 



ines MEAN STATURE OF 

 7S ~ CHILDREN Or MID- PARENTS , 

 OF VARIOUS HEIGHTS / 



70 " from, R.F.F data /K* 



w- p r t 



MEAN STA TURE OF 

 BRO THERS OF MEN OF 

 ' VARIOUS HEICHTS 



n-'A 



from.' Special data 



MEAN STATURE 8^! 



>jf Pitfi".'t*H'>rt)^ 



Fig. 6. Galton's Filial and Fraternal Regression Lines. 



I do not think Galton's method of deducing the degrees of resemblance 

 between kinsmen of various degrees of blood relationship from the single 

 datum of the regression of a filial array on its midparent will pass muster; 

 it is extraordinarily suggestive — no one had thought before of giving 

 a quantitative measurement to the various types of kinship. Galton indicated 

 how it could be done by aid of correlation tables and gave at this time two 

 such tables t, those for midparent with offspring and for brother with brother. 

 These are both from his R. F. F. [Records of Family Faculties), but he also 

 provided another correlation table giving the distribution for a special series 

 of pairs of brothers. In Fig. 6 will be found his regression lines for offspring 

 on midparents, and for brother on brother. His method of reduction was, 

 however, very different from any we should adopt to-day. When he wanted 

 a mean he determined a median, and he did this by roughly proportioning 

 (graphically) the total in the cell in which it lies, he worked not with the 



* The value J x § x ^ = ^ T is given by Galton : Natural Inheritance, p. 133. 



t If we include the earlier one for the seed-weights in mother and daughter plants for the 

 case of sweet-peas (see our p. 4) we have here the four earliest correlation tables and regression 

 lines ever published. 



