128 NATURAL INHERITANCE. [chap. 



individual brothers in each Fraternity are dispersed 

 from their own (MF) with a Q equal to b. 

 Hence (l'24) 2 = ^ + 6 2 . 



be 

 But it is shown Problem 5 that v= , ,,» , — sr ; 



V (6 2 + c 2 ) ' 



7,2 2 



therefore (1 '24) 2 = b 2 + $r~. 



Substituting for c 2 its value of (l*7) 2 — 6 2 (see last para- 

 graph), we obtain 5 = 0"98 inch. 



Fourth Method ; from differences between pairs of 

 brothers taken at random : — In the fourth method, 

 Pairs of Brothers are taken at random, and the Differ- 

 ences between the statures in each pair are noted ; then, 

 under the following reservation, any one of these 

 differences would have the Prob. value of J 2 x b. The 

 reservation is, that only as many Differences should be 

 taken out of each Fraternity as are independent. A 

 Fraternity of n brothers admits of ^f^ possible pairs, 

 and the same number of Differences ; but as no more 

 than n— 1 of these are independent, that number only 

 of the Differences should be taken. I did not appre- 

 ciate this necessity at first, and selected pairs of brothers 

 on an arbitrary system, which had at all events the 

 merit of not taking more thau four sets of Differences 

 from any one Fraternity however large it might be. 

 It was faulty in taking three Differences instead of only 

 two, out of a Fraternity of three brothers, and four 

 Differences, instead of only three, from a Fraternity of 



