Noteworthy Families (Modern Science) | Page 8

that there is no significant difference between the average numbers of brothers and sisters, nor between those of fathers' brothers and fathers' sisters, nor again between those of mothers' brothers and mothers' sisters; nor is there any large difference between those of male and female cousins, but it is apparently a fact that the group of "brothers" is a trifle smaller than that of uncles on either side. It seems, therefore, that the generation of the Subjects contains a somewhat smaller number of individuals than that of either of their Parents, being to that extent significant of a lessening population so far as their class is concerned.
TABLE V.--NUMBER OF KINSFOLK IN ONE HUNDRED FAMILIES WHO SURVIVED CHILDHOOD. ______________________________________________________________________ | | | | | | | Generic | Specific | Number of | Specific | Number of | | Kinships. | Kinships. | Persons. | Kinships. | Persons. | |_______________|_______________|___________|______________|___________| | | | | | | |Brothers and | bro | 206 | si | 207 | | sisters | | | | | |_______________|_______________|___________|______________|___________| | | | | | | |Uncles and | fa bro | 228 | fa si | 207 | | aunts | me bro | 219 | me si | 238 | |_______________|_______________|___________|______________|___________| | | | | | | | | Mean | 224 | Mean | 223 | |_______________|_______________|___________|______________|___________| | | | | | | |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 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," September 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_-?, in each descending kinship d. If 2d = 5 (which is a common size of family), one of these