126 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 12. By similar reasoning, when n = 3, the Prob. Deviation becomes b x and so on. When n is infinitely large, the Prob. Deviation is 0 ; that is to say, the (MY) 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 (MY) in each fraternity 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 d. 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 -n, 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,

2

consequently b2 = d2 + - n , or b2=

nn-1 d2.

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