128 NATURAL INHERITANCE. [CHAP.

individual brothers in each Fraternity are dispersed from their own (MF) with a Q equal to b.

Hence (1.24)2 =v2 + b2.

But it is shown Problem 5 that v= be

',l (b2 + C2) ~

b2c2

therefore (1.24) 2 = b2 + b2 + c2.

Substituting for c2 its value of (1.7)2-b2 (see last paragraph), we obtain b=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 Differences 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 ± 2 1~ 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 appreciate this necessity at first, and selected pairs of brothers on an arbitrary system, which had at all events the merit of not taking more than 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