Mathematical Contributions to the Theory of Evolution. 277 



words, to judge from stature, the exceptional parent tends to have 

 offspring of the opposite sex. 



(ii) Younger sons are taller and more variable than elder sons, 

 and elder sons are taller and more variable than fathers. 



This conclusion, although less markedly, appears in the results on 

 pp. 270 and 281, of my former paper. It might be accounted 

 for by : 



(a) A secular change going on in the stature of the population, 



and even noticeable in the difference between the stature of 



younger and elder sons. 

 (6) A further growth of sons, and an ultimate shrinkage, which 



will leave them at the age of their fathers with the same 



mean height and variation. 



(c) Conditions of nurture on the average less favourable, and on 



the whole less varied in the case of elder than in that of 

 younger children.* 



(d) Natural selection. The difference between younger and elder 



sons and between elder sons and fathers represents the 

 selective death rate in man due to causes correlated with 

 stature in the years between youth and manhood, and man- 

 hood and age. The difference is thus to be accounted for 

 by a periodic and not a secular change. 



Possibly (a), (6), (c), and (d), may all contribute to the observed' 

 results. It cannot be denied that (d) has a special fascination of its 

 own for the student of evolution, but prolonged study of the laws of 

 growth must precede the assertion that we have here, or in any 

 similar case, real evidence of an actual case of natural selection. 



(iii) Younger daughters are taller than elder daughters and elder 

 daughters than mothers. 



This is in complete agreement with the result for fathers and sons. 

 Further : 



Daughters, as a class are far more variable than mothers, but 

 while in the earlier memoir younger daughters were sensibly more 

 variable than elder daughters and thus exactly corresponded with 

 sons elder daughters are in this case more variable than younger. I 

 have been unable to find any slip in the tables or calculations, which 

 might account for this divergence. It exceeds considerably the 

 probable error of the observations, and is not in accordance with 

 the general law connecting the variation of parent and offspring evi- 

 denced for both sexes in the earlier, and for sons in the present 

 memoir e.g., the variation whether it be due to growth- change, 



* Mr. Francis Galton suggests this as a possible cause. It has, I think, to be 

 taken in conjunction with a greater amount of parental experiment, not only in the 

 birth, but in the nurture of the elder children. 



y 2 



