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 mothbreeding 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 considerably 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 3. I have drawn the regression line (see our p. 4). Galton also states that he had made confirmatory 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 reasoning'. 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 regression w, and then says that the probable devia
tion of the regressed array is p %/ 1 - w2, 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
before c2/(b2 + c2). This is a relic of an error on p. 70, where c2 + b'z a should be read for V c2 + b2' 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 1.10 given under the (3) heading. The mean is then 1.03 instead of