CHAPTER VII.--NUMBER OF KINSFOLK IN EACH DEGREE._Noteworthy families (modern science)

The population may be likened to counters spread upon a table, each

corresponding to a different individual. The counters are linked

together by bands of various widths, down to mere threads, the widths

being proportional to the closeness of the several kinships. Those in

the first degree (_father_, _mother_, _brother_, _sister_, _son_,

_daughter_) are comparatively broad; those in the second degree

(_grandparent_, _uncle_, _aunt_, _nephew_, _niece_, _grandchild_) are

considerably narrower; those in the third degree are very narrow

indeed. Proceeding outwards, the connections soon become thinner than

gossamer. The person represented by any one of these counters may be

taken as the subject of a pedigree, and all the counters connected

with it may be noted up to any specified width of band. In this book

one of the counters is supposed to represent a Fellow of the Royal

Society, whose name appears in the "Year-Book" of that Society for

1904, and the linkage proceeds outwards from him to the third degree

inclusive. Usually it stops there, but a few distant kinships have

been occasionally inserted chiefly to testify to a prolonged

heritage of family traits.

The intensity with which any specified quality occurs in each or any

degree of kinship is measured by the proportion between the numbers

of those who possess the quality in question and the total number of

persons in that same degree. Particular inquiries were made on the

latter point, but, as already stated, the answers were incomplete.

There is, however, enough information to justify three conclusions of

primary importance to the present inquiry--namely, the _average_

number (1) of brothers of the subject, (2) of brothers of his father,

and (3) of brothers of his mother.

The number of Fellows to whom circulars were addressed was 467. The

number of those who gave useful replies was 207, a little more than

one-half of whom sent complete returns of the numbers of their

brothers and uncles; some few of these had, however, placed a query

here or there, or other sign of hesitation. As the number of

completely available returns scarcely exceeded 100, I have confined

the following tables to that number exactly, taking the best of the

slightly doubtful cases. It would have been possible, by utilizing

partial returns and making due allowances, to have obtained nearly

half as many again, but the gain in numbers did not seem likely to be

compensated by the somewhat inferior quality of the additional data.

The first three lines of Table V. show 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.

______________________________________________________________________

| | | | | |

|_______________|_______________|___________|______________|___________|

| | | | | |

|Brothers and | _bro_ | 206 | _si_ | 207 |

|_______________|_______________|___________|______________|___________|

| | | | | |

|_______________|_______________|___________|______________|___________|

| | | | | |

| | Mean | 224 | Mean | 223 |

|_______________|_______________|___________|______________|___________|

| | | | | |

| | _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 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_-½, 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.