| | |
|First cousins, | _fa bro son_ | 265 | _fa bro da_ | 302 |
| male and | _fa si son_ | 184 | _fa si da_ | 208 |
| female | _me bro son_ | 236 | _me bro da_ | 266 |
| | _me si son_ | 237 | _me si da_ | 246 |
|_______________|_______________|___________|______________|___________|

It may seem at first sight surprising that a brother and a sister
should each have the same average number of brothers. It puzzled me
until I had thought the matter out, and when the results were
published in "Nature," it also seems to have puzzled an able
mathematician, and gave rise to some newspaper controversy, which
need not be recapitulated. The essence of the problem is that the sex
of one child is supposed to give no clue of any practical importance
to that of any other child in the same family. Therefore, if one
child be selected out of a family of brothers and sisters, the
proportion of males to females in those that remain will be, _on the
average_, identical with that of males to females in the population
at large. It makes no difference whether the selected child be a boy
or a girl. Of course, if the conditions were "given a family of three
boys and three girls," each boy would have only two brothers and
three sisters, and each girl would have three brothers and two
sisters, but that is not the problem.

Subject to this explanation, the general accuracy of the observed
figures which attest the truth of the above conclusion cannot be
gainsaid on theoretical grounds, nor can the conclusions be ignored
to which they lead. They enable us to make calculations concerning
the average number of kinsfolk in each and every specified degree in
a stationary population, or, if desired, in one that increases or
decreases at a specified rate. It will here be supposed for
convenience that the average number of males and females are equal,
but any other proportion may be substituted. The calculations only
regard its fertile members; they show that every person has, on the
average, about one male fertile relative in each and every form of
specific kinship.

Kinsfolk may be divided into direct ancestry, collaterals of all
kinds, and direct descendants. As regards the direct ancestry, each
person has one and only one ancestor in each specific degree, one
_fa_, one _fa fa_, one _me fa_, and so on, although in each _generic_
degree it i