Data for the Problem of EvolvMon in Man. 



297 



6. First Series. — The means of the arrays of fathers for a given age 

 at death of the son, are shown by the broken line abcdefg in tig. 1. 

 The point a for the group of sons dying between 17*5 and 22*5 years 

 was put in from a few observations not afterwards included in the 

 table. Beyond the group 82*5 to 87*5 years, there were not sufficient 

 observations to form a reliable mean at all : yy gives the mean age of 

 all the 1000 fathers observed, and represents 65*835 years, xx. gives 

 the mean age of the 1000 sons, and represents 58*775 years. The 

 former may be taken as the mean age at death of all fathers, the 

 latter was only the mean age at the death of so as who live more than 

 22*5 years. The regression curve is a somewhat broken polygon, but 

 one or two points may be deduced at once from it. 



(a) It is entirely to the left of yy above xx and entirely to the right 

 of yy below xx. Thus there is certainly correlation between the ages 

 at death of father and son. A son dying below the mean age will 

 have on the average a father dying below the mean age, and a son 

 dying above the mean age will have on the average a father dying- 

 above the mean age. Graphically we see that correlation must exist. 

 The straight line which best fits the regression polygon is given on the 

 diagram by Id. The Law of Ancestral Heredity would give hn with a 

 slope of 0*3. It is clear that with a quite sensible regression there is 

 a quite sensible divergence from the law of inheritance, in other words, 

 the death-rate is only in part selective. 



Quite similar results are to be observed in fig. 2 ; there is again a 

 very sensible correlation, but it is sensibly less than that required by 

 the Law of Ancestral Heredity. The lines are lettered the same. 

 Numerically, if Ms, Mf be the mean ages at death of sons and fathers, 

 o- s , o-f their standard deviations, *»*sf their correlation, R S f = ?"sf o*s/SF, 

 R FS = rsF o"f/o"s the regression coefficients of son on father and father 

 on son, we have — 



i 



First Series. 



Second Series. 



1 Peerage.' Fathers and sons, . 



25 years 



' Landed Gentry,' Fathers and sons, 



and on. 





20 years and on. 



65 "835 years 



Mf 



65 '9625 years 



58 775 „ 



Ms 



60 -9150 ., 



14-6382 „ 



<7 F 



14 -4308 „ 



17 "0872 „ 



c-s 



17 -0986 ., 



0-1149 ±0-0210 



'/"ST 



0-1418 ± 0-0209 



0-0985 ±0*0182 



Rfs 



0-1 196 ±0-0178 



0-1341 ±0-0367 



Ksf 



0-1682 ±0-0371 



Now these results extracted from very different records are in good 

 accordance. The values of the correlation and regressions are 5 to 7 



VOL. LXV. Z 



