110 NATURAL INHERITANCE. [CHAP. 



to either of his Parents as he is to his Brother. In 

 other words, the Parental kinship is only half as close 

 as the Fraternal. 



We have now seen that there is Kegression from the 

 Parent to his Son, from the Son to his Parent, and from 

 the Brother to his Brother. As these are the only three 

 possible lines of kinship, namely, descending, ascending, 

 and collateral, it must be a universal rule that the un- 

 known Kinsman, in any degree, of a known Man, is on 

 the average more mediocre than he. Let PD be the 

 stature of the known man, and PD' the stature of his 

 as yet unknown kinsman, then it is safe to wager, in 

 the absence of all other knowledge, that D' is less 

 than D. 



Squadron of Statures. It is an axiom of statistics, 

 as I need hardly repeat, that every large sample taken 

 at random out of any still larger group, may be con- 

 sidered as identical in its composition, in such inquiries 

 as these in which we are now engaged, where minute 

 accuracy is not desired and where highly exceptional 

 cases are not regarded. Suppose our larger group to 

 consist of a million, that is of 1000 x 1000 statures, and 

 that we had divided it at random into 1000 samples 

 each containing 1000 statures, and made Schemes of 

 each of them. The 1000 Schemes would be practically 

 identical, and we might marshal them one behind the 

 other in successive ranks, and thereby form a " Squad- 

 ron," numbering 1000 statures each way, and standing 



