s otherwise; he has two grandfathers, four
great-grandfathers, etc. With collaterals and descendants the average
number of _fertile_ relatives in each specified degree must be
stationary in a stationary population, and calculation shows that
number is approximately _one_. The calculation takes no cognizance of
infertile relatives, and so its results are unaffected by the detail
whether the population is kept stationary by an increased birth-rate
of children or other infertiles, accompanied by an increased
death-rate among them, or contrariwise.

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,