Data for the Problem of Evolution in Man. 



165 



with the physique peculiar to longevity, but beyond 65, as judged by 

 the parabola, longevity is slightly unfavourable to fecundity.* 



The following are the values of the regression coefficients obtained 

 by differentiating the cubical parabola and referring to birth as origin 

 and a year as unit : 



Table III. Regression Coefficients showing their Change with 

 Duration of Life. 



By simply substituting the number of years of life , we can find the 

 value of the regression at any age. 



5. Illustrations of these Results. (i.) What is the probable family of 

 an English mother dying at 40 ? 



(a) gives 4'93, (b) 5'00, and ((/) 5-24, all of which might equally well 

 have been read off on the diagrams. The actually observed 

 number is considerably in excess of all these, i.e., 6'23. In 

 fact, if an English mother lives to 40 years, she will, on the 

 average, have very nearly completed her family. For an 

 American woman (a) gives 4' 16, (b) 4*54, and (d) 4*64. But if 

 she lives another ten or twenty years she will probably have 

 a family of 5 or even 6. 



(ii.) Compare the strength of the relationship between duration of 

 life and size of family for American fathers dying at 40 and 70 

 respectively. 



We find the slope of the cubical parabola at the points corresponding 

 to 40 and 70 years to be 0-1459 and 0-0249 respectively. The mean 

 regression for the whole of life is 0-1056 ; for the first fifty years 

 0-1683, and for the last fifty 0-0437 (see Table I, and reduce to year as 

 unit). It thus appears that the influence of mere number of years as 



* It has been suggested that this is due to the nature of the record, there being 

 a tendency to enter only the children who survive their parents. Thus the longer 

 the latter live the fewer would be the offspring entered. In other words, we 

 should be under-estimating the correlation between fertility and longevity. But 

 the Quaker birth -records include all children, and their system is uniform. There 

 does not appear any reason on this ground for English and American returns 

 differing so sensibly. 



