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. 512 families of 4; | m^4 m^3 f m^2 f^2 mf^3 f^4 yielding | 81 + 148 + 161 + 98 + 24 (observed.) 1188 M. : 860 F. | 57 + 168 + 184 + 88 + 15 (calculated.) 512 families of 5; | m^5 m^4 f m^3 f^2 m^2 f^3 mf^4 f^5 yielding | 50 + 82 + 161 + 143 + 61 + 15 (obs.) 1402 M. : 1158 F. | 25 + 103 + 172 + 143 + 59 + 10 (calc.) 512 families of 6; | m^6 m^5 f m^4 f^2 m^3 f^3 m^2 f^4 mf^5 f^6 yielding | 30 + 48 + 115 + 146 + 126 + 40 + 7 (obs.) 1612 M. : 1460 F. | 10 + 56 + 133 + 159 + 108 + 41 + 5 (calc.) The numbers for the larger families are as yet too small to be worth giving, but they show the same tendency. It will be seen that in every case the observed central values are less than the calculated; and that the observed extreme values are much greater than the calculated. The results seem to suggest (so far) that a family cannot be likened to a chance drawing of the requisite number from _one_ bag. A better analogy would be to suppose two bags, one with M.s in excess and the other with F.s in less excess, and that some persons draw from one and some from the other. But fuller statistics are needed. It will be observed that the total excess of male births is large. This _may_ arise from undue omission of females; but I have carefully confined myself to the two or three last generations, in each pedigree, for greater security. 1. _Essay on Probabilities_, p. 114.