Mathematical Contributions to the Theory of Evolution. 279 



selection, but why should this be expected to influence only the 

 mother ? The father of many children remains equally influential, 

 but the mother's relation is weakened when we give weight to the 

 quantity not the relative ages of her children. This is not a steady 

 telegonic influence, but a correlation between fertility and heredi- 

 tary influence in mothers, which if it could be verified by further 

 observation, would undoubtedly be of high significance. I would 

 accordingly suggest as a possible law of heredity, deserving careful 

 investigation, that : Hereditary influence in the female varies inversely 

 as fertility. 



In my paper on " Reproductive Selection," (' Roy. Soc. Proc.,' vol. 

 59, p. 301), I have pointed out the important evolutionary results 

 which flow from a correlation between fertility and any inheritable 

 characteristic. If a law of the above character should be established 

 after further investigation, it is conceivable that it may act as an 

 automatic check on the extreme effects of reproductive selection. 



(iii) The above results give us for practicable purposes a quite 

 sufficiently close value of the correlation between parents and sons, 

 when the influence of reproductive selection is excluded. Judging 

 from stature the correlation between sons and parents is very closely 

 given by 



0-41 0-03. 



The J, adopted by Mr. Galton, may, I think, safely be increased by 

 25 per cent., and further, the assumption that collateral heredity is 

 twice as strong as direct heredity must, I hold, be finally discarded, 

 for no determination of the former has given such a high value 

 as 0-82. 



(5) Hitherto we have regarded only the coefficients of correlation, 

 and considered them to measure the strength of the hereditary in- 

 fluence, but it must be remembered that the means of elder and 

 younger sons are not the same, and that there is another way of 

 looking at the problem. We may ask : Do younger or elder sons 

 differ most from the stature of their father, and is the order altered 

 in the case of the mother ? 



If we neglect the influence of sexual selection (see " Contributions to 

 Math. Theory of Evolution," 111, pp. 287 8) we have, if hf and h m 

 be deviations of father and mother from their means, and M, and 

 M y be mean heights of corresponding fraternities of elder and younger 

 sons in inches : 



M, = 69-1494 + 0-4281fc/+0-4374/i, B . 

 My = 691948 + 0-4427 V+0-4488fc. 



Now the ratio of the mean heights of parents is 68'5740 : 63'3078 = 



