286 
PROFESSOR KARL PE ARSON AND MISS ALICE LEE, 
incj formula (i.) we find : 
M'l = 6-144, 
which is somewhat more than the observed value 5-898. The reason for this lies, 
w^e think, in the difficulty already referred to on p. 263. If we start extracting 
mothers, it is often difficult to follow the daughter’s history ; starting with the 
daughter it is much easier, although still laborious, to trace back her ancestry, and 
find the number of her brothers and sisters. Even in this case the search may be 
lengthy. But as daughters when married change their name, it requires great care 
in extracting large quantities to be sure that a mother is not repeated, i.e., some 
approach made to weighting her with her fertility. Everj^ care was made in 
extracting the records, but we cannot hope to have always avoided weighting to 
some extent a mother, and if this be done we shall have a transition from formulae 
(xi.), (v.), and (i.) towards formuhe (xv.), (vii.), and (viii,), which would well account 
for the difference found between theory and observation. 
If we sum up for inheritance of fertility in the female line on the basis of these 
four cases, we draw from each one of them the uncjuestionable result that fertility in 
woman is an inherited character. Further, the more we remove causes of fictitious 
values for the fertility in either generation, the closer does the value approach that 
I’equired by the law of ancestral heredit}^. The two chief disturbing factors vliich 
we have not been able to eliminate are («.) the age at which marriage is entered 
upon, [h.) restraint giving a fictitious value to the fertility. Both these causes must 
o-ive a lessened value to the correlation of fertilitv between mother and daufiliter, 
and the first, judging from the great influence of age at marriage on fertility, cannot 
fail to yive a serious diminution. Hence if we find the regression coefficient as high 
as *2233, when we neglect these factors, it is no stretching of facts to conclude that 
it would in all probability rise to -3 could we take them into account. 
Our conclusion, therefore, is that fertility in woman is certainly iidierited through 
the female line, and most probably according to the law of ancestral heredity. 
Beproductive selection is actually a vera causa of progressive change, but its 
influence is largely, if not entmely screened by the numerous factors tending to make 
the apparent fertility of women differ from their real or potential fertility. 
(10.) On the Inheritance of Fertility in Man. 
(i.) While many of the difficulties involved in the extraction of data for women 
still exist for mau, a new and important feature tending to screen the full influence 
of the law of ancestral heredity arises in his case. The full fertility of the husband 
is not in the average case at all approached in tlie case of monogamic marriage. 
Hence, in considering the size of a man’s fainilv as a measure of his fertilitv we 
are measuring a character which differs largely from the character of fertility in 
woman. It is only in the case of sterile or even very sterile men that there is 
likely to be a correlation shown between the sizes of the families of fathers and sons. 
