Page:Proceedings of the Royal Society of London Vol 60.djvu/308

282 Thus, it does not differ very widely from the value suggested (0'41) for sous, b u t is even fu rth er removed from the value (0"33) at first determ ined by Mr. Galton.

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 m istake in the calculations. I can only tru s t th at more elaborate returns and measurements of other characteristics m ay some day throw lig h t on what now appear to be anomalies.

(7) Finally, I may ju st notice w hat conclusions are to be drawn, if we pay attention to the absolute difference in stature between parents and daughters. Let hemand c,jm be the differences in stature between elder daughters and mothers, and younger daughters and m others respectively, then in inches we have for the corresponding a rra y s : bem = 0-7450 - 0 5707^. bym = 1-0406—0-5237/iW!.

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 th an 1*63 in. above the mean, or if their deviations are not w ithin the lim its 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 th eir mothers than younger sisters.

If Sfe, cfy be the stature differences for fathers and daughters, we h a v e : bfe = 4-4100-0-5472/?/. Sjy = 4-1144 - 0-60397/

Here, so long as the father lies between 5"21 in. less and 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 lim its correspond to 1’89 and 2-68 times the standard deviation of fathers. Accordingly, about 96 to 97 per cent, 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 th at a great majority of younger sisters were nearer to th eir fathers than their elder sisters, and a considerable majority of elder sisters nearer to their m other than their younger sisters. W e m ight then have concluded th at there were substantial