498 THE GRAMMAR OF SCIENCE 



pp. 394-99, and the correlation between fraternal durations 

 of life was found to be : — 



.2602 + .0216. 



In the accompanying diagram the regression line is actu- 

 ally drawn to bring the matter closely home to the reader. 

 The broken line gives by its circles the observations, 

 that is the mean age of death of the array of brothers corre- 

 sponding to a man who dies at a given age. The mean 

 age at death of men not dying as minors is 60.97 years. 

 But if a man have a brother, dying, for example, at 77.5 

 years, his probable age at death will be 65 years, or he 

 will be likely to live four years longer than the general 

 population mean. The line hk corresponds to the re- 

 gression line with a slope of .2602 ; the line /;// is the 

 regression line with the theoretical slope of .4. The non- 

 selective death-rate has swung lin round to the position hk. 

 This reduction in correlation will give us an appreciation 

 of the magnitude of the non-selective death-rate. 



To determine this we proceed as follows : Let N be 



the number of pairs of brothers, and let - of N be the 



number of men out of N, whose death is not a function 



of their characters and organs. Then in the record -N 



of one set of N brothers will have a duration of life 



which is no function of their constitution, while - — N 



will have a duration recorded, which is a function of 

 their constitution. The same holds for the second set 



of brothers. Hence in the record "^^ x '^—^ X N pairs of 



brothers will exhibit correlation in their ages at death, 



and the remainder N — —^ X -^ X N will not. Thus we 



have a mixture of correlated and uncorrelated material in 

 the above proportions, and accordingly the correlation .4 



will be reduced in the ratio of — — x —-' N to N ; but this 



reduction is to be .2602. Hence ~ 



n - ly .2602 



71 ) ~ .d, '' 



