MATHEMATICATi CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
287 
The intensity or duration of fecundity in the liusband must, one or other, be less 
than that of the wife,—and this will hardly be so in the great run of cases—if his 
family is to be in any way a measure of his fertility, or, as it might be better 
to call it in this case, his sterility. We are seeking to find a correlation between 
two characters, one in father and one in the son, neither of which we can measure 
unless they fall short of a certain limit. The result is that our correlated material is 
weakened down by the admixture of a mass of uncorrelated material in the manner 
indicated in Proposition V. of the theoretical part of this investigation. Within the 
family we cannot hope to get a correlation which will approach that indicated by the 
law of ancestral heredity. We may still, however, hope to ascertain whether 
fertility, respectively sterility, is an inherited character in man as well as woman. 
(ii.) Our first attempt was to collect as much material as ])ossible, so that our 
limitations were few. The Peerage, Baronetage, Landed Gentry, Family Histories, 
private pedigrees, and collected data provided the 6,070 cases arranged in Table V. 
Here large famdies were weighted because several, Ayhere available, were taken from 
one family. The son’s marriage must either have lasted till the death of one partner 
or at least 15 years; there was no condition as to the duration of the father’s 
marriao’e. 
o 
We have spoken of the correlation between fertility of father and son, but since 
only a single marriage of the father is taken, it may be equally well termed a 
correlation between the fertility of the mother and son, which may, perhaps, to some 
extent explain the relatively high values reached. 
Let Mj, o-j be the mean and standard-deviation of the son, o-^, of the parent, 
and the correlation ; then we found ; 
M, = 3-871, M^, = 5-831, 
0-, = 3-003, o-^, = 3-190, 
* jy = -0514. 
The probable error of = -0087. Thus the correlation is nearly six times the 
probable error, or fertility in man is certainly inherited. 
(Hi.) Table VI. contains the result of extracting 1,000 cases from the Peerage, only 
one son being taken from each family, and his marriage having lasted at least 15 
years. No attention was paid to the length of parents’ marriage. 
We found : 
M, = 5-070, Mp = 5-827, 
(T, = 2-910, 0-, = 3-142, 
~ ’ 0656 . 
The probable error of = -0212. This case closely confirms the previous case; 
Mp and o-^ remain sensibly the same, M, has risen owing to the longer period of 
