The exact conclusions were ("Nature," September 29, 1904, p. 529), that if 2_d_ be the number of children in a family, half of them _on the average_ being male, and if the population be stationary, the number of fertile males in each specific ancestral kinship would be _one_, in each collateral it would be _d_-1/2, in each descending kinship _d_. If 2_d_ = 5 (which is a common size of family), one of these on the average would be a fertile son, one a fertile daughter, and the three that remained would leave no issue. They would either die as boys or girls or they would remain unmarried, or, if married, would have no children. The reasonable and approximate assumption I now propose to make is that the number of fertile individuals is not grossly different to that of those who live long enough to have an opportunity of distinguishing themselves. Consequently, the calculations that apply to fertile persons will be held to apply very roughly to those who were in a position, so far as age is concerned, to achieve noteworthiness, whether they did so or not. Thus, if a group of 100 men had between them 20 noteworthy paternal uncles, it will be assumed that the total number of their paternal uncles who reached mature age was about 100, making the intensity of success as 20 to 100, or as 1 to 5. This method of roughly evading the serious difficulty arising from ignorance of the true values in the individual cases is quite legitimate, and close enough for present purposes. CHAPTER VIII.--NUMBER OF NOTEWORTHY KINSMEN IN EACH DEGREE. The materials with which I am dealing do not admit of adequately discussing noteworthiness in women, whose opportunities of achieving distinction are far fewer than those of men, and whose energies are more severely taxed by domestic and social duties. Women have sometimes been accredited in these returns by a member of their own family circle, as being gifted with powers at least equal to those of their distinguished brothers, but definite facts in corroboration of such estimates were rarely supplied. The same absence of solid evidence is more or less true of gifted youths whose scholastic successes, unless of the highest order, are a doubtful indication of future power and performance, these depending much on the length of time during which their minds will continue to develop. Only a few of the Subjects of the pedigrees in the following pages have sons in the full maturity of their powers, so it seemed safer to exclude all relatives who were of a lower generation than themselves from the statistical inquiry. This will therefore be confined to the successes of fathers, brothers, grandfathers, uncles, great-uncles, great-grandfathers, and male first cousins.