12G NATURAL INHERITANCE. [chap. 



Deviation is determined by the same problem as that 

 which concerned the Q of the Mid-Parentages (page 87), 

 where it was shown to be b x i By similar reasoning, 

 when n = 3, the Prob. Deviation becomes b x -^, and 

 so on. When n is infinitely large, the Prob. Deviation 

 is ; that is to say, the (MF') values do not differ at 

 all from their common (MF). 



Now if we make a collection of human Fraternities, 

 each consisting of the same number, n, of brothers, and 

 note the differences between the (MF') in each frater- 

 nity and the individual brothers, we shall obtain a 

 system of values. By drawing a Scheme from these in 

 the usual way, we are able to find their Q ; let us call 

 it cl. We then determine b in terms of d, as follows : — 

 The (MF') values are distributed about their common 

 (MF), each with the Prob. Deviation of b x -1 , and the 

 Statures of the individual Brothers are distributed 

 about their respective (MF') values, each with the Prob. 

 Deviation d. The compound result is the same as 

 if the statures of the individual brothers had been 

 distributed about the common (MF), each with the 

 Prob. Deviation b, 



consequently b 2 = d 2 + — , or b 2 = — — d 2 . 



n 7i—l 



I determined d by observation for four different 

 values of n, having taken four groups of Fraternities, 

 consisting respectively of 4, 5, 6, and 7 brothers, as 

 shown in Table 14. Substituting these four observed 

 values in turns for d in the above formula, I obtained 



