292 Miss M. Beeton and Prof. Karl Pearson. 



the issue of data cards. We were thus compelled to limit this first 

 • study to the case when both relatives die at a greater age than 20. 

 In the case of fathers, when we are dealing with the correlation 

 between father's and son's ages at death, this is practically no limita- 

 tion at all, as no father dying under 20 years of age was met with. 

 In the case of the offspring, however, the limitation cuts off' the dis- 

 tribution somewhat abruptly with a finite ordinate at 20 — 25, five 

 years being our unit of grouping. 



3. Now duration of life is a very different character to eye-colour, or 

 to some extent to the size of organs in adult life. Eye-colour is fairly 

 well determined, it may change with old age slightly, but it cannot 

 transform itself from light blue to brown. Again, nourishment and use 

 undoubtedly affect the size of organs, but they are likely to influence 

 father and son, or, at any rate, brother and brother, in much the same 

 way, for they are members of the same family and the same class. On 

 the other hand, death depends not only on inherited constitution but 

 on innumerable chance elements of environment and circumstance. 

 The environment both of home and period is much more alike for two 

 brothers than for a father and son; food, sanitation, habits of life, 

 change considerably in a generation, and two brothers have more equal 

 chances of life than a father and son. But even with two brothers, 

 one may live on the family estates and the other ruin his health in 

 Africa or India. Hence, while the non-differential death-rate will not 

 materially alter the correlations between most characters in relatives, 

 it must seriously affect the correlation between the durations of life in 

 father and son, and to a lesser extent between brother and brother. 

 A good stock may be better protected against death than a weak one, 

 but no stock at all can resist certain attacks. Hence if we look upon 

 death as a marksman, p per cent, of his shots are, we may say, sure to 

 be effective whatever they hit, this is the non-differential death-rate, 

 the remaining 100 —p per cent, of his attacks will only be successful 

 on the weaker stocks. Now the effect of this conception of death's 

 action is that the correlation table for ages at death of any pair of 

 relatives must be looked upon as a mixture of uncorrelated material — 

 deaths due to the non-differential death-rate, and correlated material — 

 deaths due to the differential or selective death-rate. At different 

 periods of life also one of these death-rates may give more material to 

 the table than at another. In the case of fathers and sons we should 

 expect the non-differential death-rate to be more numerous in its con- 

 tributions than in the case of brother and brother. 



Now it has been shown by one of us that when correlated material 

 is mixed with uncorrelated material, the result is approximately to 

 reduce the coefficient of correlation in the ratio of the amount of corre- 

 lated to the total amount of material.* Hence, if we assume that the 

 * ' Phil. Trans.,' A, vol. 192, p. 277. 



