in each descending kinship d. If 2d = 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.

Only 207 persons out of the 467 who were addressed sent serviceable replies, and these cannot be considered a fair sample of the whole. Abstention might have been due to dislike of publicity, to inertia, or to pure ignorance, none of which would have much affected the values as a sample; but an unquestionably common motive does so seriously—namely, when the person addressed had no noteworthy kinsfolk to write about. On the latter ground the 260 who did not reply would, as a whole, be poorer in noteworthy kinsmen than the 207 who did. The true percentages for the 467 lie between two limits: the upper limit supposes the richness of the 207 to be shared by the 260; the lower limit supposes it to be concentrated in the 207, the remaining 260 being utterly barren of it. Consequently, the upper limit is found by multiplying the number of observations by 100 and dividing by 207, the lower by multiplying by 100 and dividing by 467. These limits are unreasonably wide; I cannot guess which is the more remote from the truth, but it cannot be far removed from their mean values, and this may be accepted as roughly approximate. The observations and conclusions from them are given in Table VII., p. xl.

Chapter IX.—Marked and Unmarked Degrees of Noteworthiness.

Persons who are technically “noteworthy” are by no means of equal eminence, some being of the highest distinction, while others barely deserve the title. It is therefore important to ascertain the amount of error to which a statistical discussion is liable that treats everyone who ranks as noteworthy at all on equal terms. The problem resembles a familiar one that relates to methods for electing Parliamentary representatives, such as have been proposed at various times, whether it should be by the coarse method of one man one vote, or through some elaborate arrangement which seems highly preferable at first sight, but may be found on further consideration to lead to much the same results.

In order to test the question, I marked each noteworthy person whose name occurs in the list of sixty-six families at the end of this book with 3, 2, or 1, according to what I considered his deserts, and soon found that it was easy to mark them with fair consistency. It is not necessary to give the rules which guided me, as they were very often modified by considerations, each obvious enough in itself, but difficult to summarize as a whole. Various provisional trials were made; I then began afresh by rejecting a few names as undeserving any mark at all, and, having marked the remainder individually, found that a total of 657 marks had been awarded to 332 persons; 117 of them had received 3 marks; 101, 2 marks; 104, 1 mark; so the three subdivisions were approximately equal in number. The marks being too few to justify detailed treatment, I have grouped the kinsmen into first, second, and third degrees, and into first cousins, the latter requiring a group to themselves. The first degree contains father and brothers; the second, grandfathers and uncles; the third, great-grandparents and great-uncles. The results are shown in Table VI. The marks assigned to each of the groups are given in the first line (total 657), and the number of the noteworthy persons in each group who received any mark at all is shown in the third line (total 329). In order to compare the first and third lines of entries on equal terms, those in the first were multiplied by 329 and divided by 657, and then entered in the second line. The closeness of resemblance between the second and third lines emphatically answers the question to be solved. There is no significant difference between the results of the marked and the unmarked observations. The reason probably is that the distribution of triple, double, and single marks separately is much the same in each of the groups, and therefore remains alike when the three sets of marks are in use at the same time. It is thus made clear that trouble taken in carefully marking names for different degrees of noteworthiness would be wasted in such a rough inquiry as this.