164 Miss M. Beeton, Mr. <:. U. \ 'ulc. ami Prof. K. Pearson. 



fertility even up to 90 years of age. With English mothers it is less 

 marked, hut appears to be quite true up to 75 years. Beyond 75 

 there appears to be a slight decrease. Turning to the two series for 

 fathers we see that we might possibly have better taken 60 than 50 as 

 a dividing age, for the general trend of the observations is much the 

 same up to 60 years. After this there is still a sensible trend in the 

 American results, so that aged fathers are again the most fertile. 

 With the English fathers this relation is, as in the case of English 

 mothers, far less marked, although it is sensible if we take fathers 

 above 50 years. 



Thus I think we might sum up : That the peculiar physique in both 

 men and women which leads to longevity is also associated with 

 greater fecundity. Of two women who both live beyond 50 years, 

 the longer lived is likely to have had l>efore 50 the larger family. 

 The association is, however, much greater for American than 

 English parents, although the American parents dealt with are, in 

 the great majority of cases, of Anglo-Saxon race. Climate, mode 

 of life, generally selection and environment, seem to be differentiating 

 in this respect the English and the Anglo-American. The English 

 Friends, we should suppose, would be a class very comparable with 

 the American Friends, yet their average life is longer, their fertility 

 greater, and there is less association between longevity and fecun- 

 dity. In lx)th cases our algebraical formulae show that American 

 men and women are more alike, and English men and women are 

 more alike than the women to the women or the men to the men of 

 the two races. This is the more remarkable, as the English Friends 

 as a class are by no means identical with the Landed Gentry. 



(ii.) In order to represent the continuous change in the regression, 

 which cannot be done by two straight lines, which only enable us to 

 distinguish the fecund and non-fecund periods of life, the statistics 

 were fitted with cubical parabolas. The regression line at any age in 

 life may then be looked upon as the tangent to the cubical parabola at 

 that age. An inspection of Diagrams 3, 4, 7, 8 shows what an excel- 

 lent expression such parabolas are for these statistics. 



For American mothers and fathers we see dijjdx consistently positive 

 throughout life, and we have a most excellent graphical demonstration 

 of the physical characters which tend to longevity being also associated 

 with fecundity. In the English fathers the same feature appears in a 

 much less marked degree ; there is a point of inflexion in the curve, 

 although dy/dx remains positive. Up to about 75, however, the 

 number of offspring continues to increase with duration of life, and 

 when we break off at 95, the curve has got a renewed outward trend. 

 With English mothers, however, the curve has a small but sen-iUe 

 trend inwards in old age. For fifteen years after the climacteric 

 increased life connotes larger family, i.e., shows fecundity associated 



