Data for the Problem of Evolution in Man. 



295 



only to look at our regression diagrams, in particular at that for 

 brethren, to assure himself that no curve will serve for practical pur- 

 poses substantially better than a straight line. Now, if <t x be the 

 standard deviation of the relative whose mean age at death is taken ? 

 and o-y of the relative of a given age at death, and r be the correlation 

 defined by 



r = S{.z(x-m x )(ij-m y )}l(N(r x o- y ), 



where z is the frequency of deviations x-m x and y-m y from the 

 means m x and m y in the total observations N, then the line of closest 

 fit, the regression line, passes through m x and m y , and has rcr x /o- y for 

 its slope. All this is independent of any theory of frequency distribu- 

 tion, and the vanishing of r with the correlation simply flows from the 

 fundamental problem that the chance of a combined event is the 

 product of two independent probabilities. Our conclusions in this paper 

 are deduced from the above value of r and from the slope of the regres- 

 sion line, and they involve no further assumption than the approximate 

 linearity of the regression curves. Our appeal to the memoir, "On 

 the Law of Ancestral Heredity " makes also no greater demands. 



5. We now turn to the material itself. Our data consist of three 

 series, from which all deaths recorded as accidents, an exceedingly small 

 proportion of the whole, were excluded. In excluding these we of 

 course slightly, but very slightly, reduced the non-selective death-rate. 

 In the first series, 1000 cases of the ages of fathers and sons at death, 

 the latter being over 22*5 years of age, were taken from 'Foster's 

 Peerage'; in the second series a 1000 pairs of fathers and sons, the 

 latter dying beyond the age of 20, were taken from ' Burke's Landed 

 Gentry'; and in the third series the ages at death of 1000 pairs of 

 brothers dying beyond the age of 20 were taken from the Peerage. 



The first series was obtained by grouping all fathers dying between 

 22-5 and 27*5, 27'5 and 32*5, &c. We started at 22*5 because this 

 was the earliest recorded death of a father among those extracted from 

 the Peerage, and to have sons dying in the same range they were also 

 .started at 22*5 years. In extracting the ages at death, they were 

 taken to the nearest whole year, and consequently in the subsequent 

 grouping we were spared decimals. In the second and. third series we 

 •originally took all deaths from birth onwards also to the nearest 

 whole year, and then grouped in five-year periods ; thus fractions were 

 introduced when a death fell on a five-year division. Subsequently we 

 eliminated the few deaths occurring before 20 years of age. 



The aggregate material for the three series is given in Tables I, II, 

 and III ; and the means of the arrays of fathers' ages at death for sons 

 dying at a given age, i.e., the regression polygons of fathers' on sons' 

 age at death in figs. 1 and 2 ; the regression polygon for brethren is 

 given in fig. 3. 



In the case of brothers, we have rendered the original distribution, 



