The following remarks were rather too long for convenient insertion on [p. 259], and are therefore appended here.
The ‘random’ character of male and female births has generally been rested almost entirely on statistics of place and time. But what is more wanted, surely, is the proportion displayed when we compare a number of families. This seems so obvious that I cannot but suppose that the investigation must have been already made somewhere, though I have not found any trace of it in the most likely quarters. Thus Prof.
Lexis (Massenerscheinungen) when supporting his view that the proportion between the sexes at birth is almost the only instance known to him, in natural phenomena, of true normal dispersion about a mean, rests his conclusions on the ordinary statistics of the registers of different countries.
It certainly needs proof that the same characteristics will hold good when the family is taken as the unit, especially as some theories (e.g.
that of Sadler) would imply that ‘runs’ of boys or girls would be proportionally commoner than pure chance would assign. Lexis has shown that this is most markedly the case with twins: i.e., to use an obviously intelligible notation, (M for male, F for female), that M.M. and F.F. are very much commoner in proportion than M.F.
I have collected statistics including over 13,000 male and female births, arranged in families of four and upwards. They were taken from the pedigrees in the Herald's Visitations, and therefore represent as a rule a somewhat select class, viz.
the families of the eldest sons of English country gentlemen in the sixteenth century. They are not sufficiently extensive yet for publication, but I give a summary of the results to indicate their tendency so far. The upper line of figures in each case gives the observed results: i.e.
in the case of a family of four, the numbers which had four male, three male and one female, two male and two female, and so on. The lower line gives the calculated results; i.e.
the corresponding numbers which would have been obtained had batches of M.s and F.s been drawn from a bag in which they were mixed in the ratio assigned by the total observed numbers for those families.
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