284 PROFESSOR KARL PEARSON AND MISS ALICE LEE, 
least 15 years. No limitation was placed on the duration of the parents’ marriage. 
We found : 
M,, = 4-232, M,, = 5-403, 
(T, = 3-292, cr„ = 3-241, 
= -1045. 
The probable error of = -0211, and again we see that fertility is certainly 
inherited. The correlation has, however, sunk ; probably, as the great increase of 
variation indicates, because we are dealing with much more heterogeneous material than 
in the case of the Peerage. While the selection of “ heiresses ” has largely reduced 
the number of brothers and sisters, /.e., the fertility of mothers, the limitation to 
marriages of at least 15 years has increased the apparent fertility of daughters; nor 
is this increase at all balanced by the fact that heiresses come from small families, and 
may, therefore, be supposed to be the children of rather sterile mothers. The average 
number of children of heiresses is sensibly as large as the average number of children 
of women who are not in the bulk heiresses, and who have, as in the following case, 
been selected with the same condition as to duration of marriage. The fact is that 
heiresses are not on the whole the children of sterile mothers; their high fertility and 
their small correlation ivith their mothers shows us that heiresses in the bulk are 
rather the daughters of mothers whose apparent fertility is fictitious. They have, 
owing to the sterility or early death of their husband, to their own marriage late in 
life, or to some physical disability, or other restraint, never reached their true fertility. 
If this conclusion be correct, and a comparison of the values of and in this and 
the following cases thrusts it almost irresistibly upon us, then Ave see that the 
argument against the inheritance of fertility based upon the fertility of heiresses and 
non-heiresses is of no validity.^ It could not be valid as against the values of the 
correlation Ave have found, but the present investigation shoAvs by the value of 
exactly Avherein the error lies : the heiress is not infertile, but is the daughter of a 
fictitiously infertile mother. 
Applying our theory to this case, Ave find from formula (xi.), ])utting {T, = cto : 
Avhence we find o-j = 3-293, a result sensibly identical Avith 0 -^. Solvmg the quadratic 
(ax) Avith Ml = M, to find Mi Ave find ; 
Ml = 3-952. 
Hence by (i.) we have : 
M\ = 6-838, 
the actually observed value being 5-403. Thus the theory completely fails to give 
the fertility of the heiresses’ mothers ; for such a fertility as Ave find in the daughters, 
* See, for example, a recent letter of Mr. Howard CoLLiXb in ‘ Nature,’ NoA'cmber 3) 1898. 
