PREFACE

ferhales 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 is 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," Septem

ber 29, 1904, P. 529), that if 2d 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, 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