MATHEMATICAL CONTRIBUTIONS TO THE THEORY OP EVOLUTION. 285 
the mothers’ fertility is far too low. This again emphasises the point we have 
already referred to. The peculiar character of the selection, which leads to the 
female record in the Landed Gentry, is not one such as we have considered in our 
theory,* where the record of any family is likely to appear in pro23ortion to its size. 
Such a distribution is a chance distribution, but a selection of women inheriting land 
has not this character, and a woman who is the mother of co-heiresses is hardly 
doubly as likely to appear as the woman who is mother of one. A marriage in either 
case is likely to be arranged, and if we take only one daughter from each family the 
record will not already have weighted—at any rate to the full extent—every mother 
with her fertility. If the reader will compare the variation columns for both daughters 
and mothers in Table III. with the corresponding columns in Table II. or Table IV., 
he will at once see how anomalous is the selection of women given in the Lauded 
Gentry. 
(iv.) Table IV. gives the results for 1000 cases taken from the Peerage and 
Baronetage under the following limitations : one daughter only was taken for each 
mother, and in the case of both mother and daughter the marriage must have lasted 
at least 15 years. We found : 
= 4-335, = 5-898, 
(T, = 2-967, o-„: = 2-830, 
'>'md — '2130. 
The probable error of = -0204. Thus, as it is now hardly necessary to repeat, 
fertility is certainly and markedly inherited. The regression coefficient is now as 
high as -2233, the closest limit we have yet reached to the theoretical -3 of the law 
of ancestral heredity. 
Owing to the limitation to marriages of 15 or more years, the means of tlie 
fertilities of both mothers and daughters have risen, in the latter case more, how¬ 
ever, than the former. It might have been expected that the fertility of mothers 
would have risen more, but it must be remembered that M,„ is the apparent and not 
the real fertility of mothers ; and further, since the record largely weights the more 
fertile women, the bulk of the mothers are already those with large families, i.c., 
those whose marriages have lasted at least 15 years. 
Assuming that there is no sensible secular change in unweighted fertility, i.e., 
(Ti — (Tn, we have from the formula on p. 284 : 
(Ti = 2-973. 
Prom (v.) with Mi = M2 we find : 
Ml = 3-845 
for the real fertility of mothers. This is a sensible increase on the value 3-463 given 
ill Case (ii.), in which there was no minimum duration to the length of the mother’s 
marriage. 
