1886.] 



Family Likeness in Stature. 



59 



mean of all them, is such that its quartile = — Now the dis- 



tribution of values in each line of Table V, whose quartile = /, is 

 due to the combination of two variables. The one is the variability 

 of CiC 2 . . about C ; the other is the variability of the individual 

 brothers in each family, about C x , C 2 , &c, respectively. Therefore 



27^2 



p = — p + ^' 2 - Substituting for c 2 its value jp 2 —6 2 , we obtain 



The observed value of / in Table V is 1*24, whence we obtain 

 6=1-10. 



(4.) Pairs of brothers may be taken at random, and the differences 

 noted between their statures ; then under the following reservation, 

 as regards the differences to be taken, we should expect the observed 

 quartile of the differences to be = x b. The reservation is, that 

 only as many differences should be taken oitt of each family as are 

 independent. A family of n brothers admits of n.n — 1/2 possible 

 pairs, but no more than n — 1 of these are independent and only these 

 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 pairs of differences 

 from any family, however numerous. It was faulty in taking three 

 differences instead of only two from a family of three, and four 

 differences instead of only three from a family of four, and therefore 

 giving an increased weight to those families, but in other respects 

 the system was hardly objectionable. On the whole the introduced 

 error would be so slight as scarcely to make it worth while now to go 

 over the work again. By the system adopted I found a quartile value 

 of 1*55, which divided by a/2 gives 6=1*10 inch. 



Thus far we have dealt with the special data only. The less trust- 

 worthy R.F.F. give larger values of b. An epitome of all the results 

 appears in the following table. 





Values of b obtained by 

 different methods and 

 from different data. 



Specials. 



R.F.F 



(2.) From to (Tables V and IV) 



(3.) From / (Tables V and IV) .... 



1-07 

 0'98 

 110 

 110 



1 -38 

 1:81 

 1-14 

 1-35 



1-06 





