Mathematical Contributions to the Theory of Evolution. 



Thus, it does not differ very widely from the value suggested (0'41) 

 for sons, but is even further removed from the value (0'33) at first 

 determined by Mr. Gralton. 



The greater correlation between sons and both parents noticed in 

 my first memoir is not borne out by the present statistics ; the 

 advantage is now it is true to a much less extent with daughters. 



On the whole, I am not well satisfied with these results for 

 daughters. I can see no persistent source of error in the method of 

 collecting the observations, nor can I find any mistake in the calcu- 

 lations. I can only trust that more elaborate returns and measure- 

 ments of other characteristics may some day throw light on what 

 now appear to be anomalies. 



(7) Finally, I may just notice what conclusions are to be drawn, 

 if we pay attention to the absolute difference in stature between 

 parents and daughters. Let S em and d ym be the differences in stature 

 between elder daughters and mothers, and younger daughters and 

 mothers respectively, then in inches we have for the corresponding 

 arrays : 



c em = 0-7450-0-5707^. 



fy* = 1-0406-0'5237A. 



Thus, arrays of younger daughters differ more from their mothers 

 in stature than arrays of elder daughters, if the mothers be more than 

 6'29 in. below the mean or more than 1*63 in. above the mean, or if 

 their deviations are not within the limits of about 2'64 and 0'68 

 times the standard deviation of mothers. This gives us about 74 to 

 to 75 per cent, of elder sisters nearer in stature to their mothers than 

 younger sisters. 



If fy e , Sfy be the stature differences for fathers and daughters, we 

 have ; 



ty = 4-4100-^0-5472/y. 



fo = 4-1144-0-6039/i/. 



Here, so long as the father lies between 5'21 in. less and 7'41 in. 

 more than the average, the array of younger daughters will more 

 nearly approach him in stature than the array of elder daughters. 

 These limits correspond to 1'89 and 2'68 times the standard devia- 

 tion of fathers. Accordingly, about 90 to 97 per cenfc. of younger 

 sisters are closer in stature to their fathers than elder sisters. Thus, 

 if we had started the discussion of the problem from a consideration 

 of the relative nearness in stature of daughter to father and mother, 

 we should have found that a great majority of younger sisters were 

 nearer to their fathers than their elder sisters, and a considerable 

 majority of elder sisters nearer to their mother than their younger 

 sisters. We might then have concluded that there were substantial 



