Essays in Statistics. 187 



searched the biographies of great men, drawn out their genealogies, 

 traced their relationships, compared the results, struck averages, 

 and the following are his conclusions. 



He first entered this field with a work on English Judges from 

 1660 to 1865. These judges, always eight in number, constitute 

 the highest magistracy in England, and are, as he assures us, 

 universally admitted to be exceptional men. Their biography is 

 known, as are also their family connections. Here, then, is a fair 

 number of facts, which may be grouped together in order to 

 examine the results. 



In the course of 205 years there were 286 judges, and among 

 these the author has found 112 who had one or more illustrious 

 kinsmen. Hence, the probability that a judge has in his family 

 one or more illustrious members exceeds the ratio of 1 13 in itself 

 a striking result. 



Passing now from these general results to details, it may be 

 shown how this probability diminishes as we pass from relations of 

 the first degree (father, son, brother), to relations of the second 

 degree (grandfather, uncle, nephew, grandson), and those of the 

 third degree (great-grandfather, granduncle, cousin, grandnephew). 



Suppose 100 families of judges, and let N stand for the most 

 eminent man in each of them, the number of their illustrious 

 kinsmen will on the average be distributed as follows: Father, 26; 

 brother, 35 ; son, 36 ; grandfather, 15; uncle, 18; nephew, 19; 

 grandson, 19 ; great-grandfather, 2; granduncle, 4; first-cousin, 

 ii ; grandnephew, 17. This statement will be more readily 

 understood from the following table : 



TABLE I. 



2 great-grandfathers 



15 grandfathers 4 granduncles 



26 fathers 18 uncles 



100 N 35 brothers n cousins-german 



36 sons 19 nephews 



19 grandsons 17 grandnephews 



6 great-grandsons 



If now we pass from this partial work on the judges to broader 

 researches, we meet with results of very much the same kind. 



