64 Life and Letters of Francis Galton 



It was by the help of these propositions that Galton discussed the action of 

 inheritance in stable populations. Assuming normal distribution of characters, 

 as he did, then the above relations really involve the fundamental properties 

 of bivariate regression, stated with a truly amazing minimum of algebra. 



In Chapter VI Galton describes his data. After referring to the moth- 

 breeding experiments then in progress, and to his much earlier experiments 

 on the characters of sweet-peas, he passes to his Records of Family Faculties 

 obtained by the offer of £500 in prizes. He obtained the records of 150 

 families, 70 by male and 80 by female recorders. The records contained data 

 as to Stature, Eye-Colour, Temper, the Artistic Faculty, and some forms of 

 Disease. As a measure of the amount of material thus obtained, we find 205 

 couples of parents and 930 adult children of both sexes. A further set of 

 Special Data was obtained by circulars requesting measurements of the 

 stature of pairs of brothers. The constants for this material differ consider- 

 ably from those for the Family Records. I think Galton thought the former 

 material more reliable, but in working through his data in 1895* I came 

 to the conclusion that the Special Data, owing to the heterogeneity of their 

 origin, were scarcely to be fully trusted. 



The chapter on Data concludes with some account of Galton's work on 

 the weight of sweet-pea seeds. He states that : 



"The results were most satisfactory. They gave me two data, which were all that I wanted 

 in order to understand, in its simplest form, the way in which one generation of a people is 

 descended from a previous one; and thus I got at the heart of the problem at once." (p. 82.) 



Galton had thus first learnt of the nature of regression in 1875 from his 

 sweet-pea experiments. He gives in Appendix C, pp. 225-6, of the Natural 

 Inheritance, the first correlation table for inheritance, that of the diameters 

 of parental and filial plants. The regression is about ^. I have drawn the 

 regression line (see our p. 4). Galton also states that he had made con- 

 firmatory measurements on foliage and length of pod, but he does not enter 

 into details. 



Chapter VII contains the Discussion of the Data of Stature. This 

 chapter covers the same ground as the papers dealt with in our pp. 11-20, 

 but there is some amplification and some attempt to simplify the mathematical 

 reasoningf. The table on p. 133 is, as I have indicated on our pp. 23-4, 

 very doubtful as far as the numerical values are concerned. In particular 

 Galton terms the mean regressio n w, an d then says that the probable devia- 

 tion of the regressed array is p V 1 — w 2 , where p is the probable deviation of 



* See Phil. Trans. Vol. 187, A, pp. 283-4. 



t Certain corrections should be made. On p. 127, formula (2), there should be no radical 



c 2 

 before c 2 /(£> 2 + <?). This is a relic of an error on p. 70, where - — — a should be read for 



C T 



r c } 



„J -- — — , see p. 224. The numerical value for b deduced from (2) is correct. On p. 128, the 



numerical value for b should be -96 not -98, and this value, - 96, should be inserted in the table 

 on p. 129 instead of the 110 given under the (3) heading. The mean is then 1*03 instead of 

 1-06. 



