60 



Mr. F. Galton. 



[Jan. 21, 



The R.F.F. results refer to brothers only and not to transmuted 

 sisters, except in method (2), where the paucity of the data com- 

 pelled me to include them. I should point out that the data used in 

 these four methods differ. In (1) I did not use families under four. 

 In (2) and (3) I did not use large families. In (4) the method of 

 selection was as we have seen, again different. This makes the ac- 

 cordance of the results still more gratifying. I gather from the 

 above that we may securely consider the value of b to be less than 

 1'10, and allowing for some want of precision in the special data, the 

 very convenient value of 1*0 inch may reasonably be adopted. 



We are now able to deal completely with the distribution of 

 statures in every degree of kinship of the kinsmen of those whose 

 statures we know, but whose ancestral statures we are ignorant of or 

 do not take into account. We are, in short, able to construct tables 

 on the form of III, IY, and V, for every degree of kinship, and to 

 reconstruct those tables in a way that shall be free from irregularities. 

 The fraternal relation as distinguished from the co-fraternal has also 

 been clearly explained. 



In constructing a table of the form of III, IV, and V, we first find 

 the value of w for the degree of kinship in question, thence we deduce 

 / by means of the general equation iv 2 p^+f 2 =jp 2 (p is supposed to be 

 known, or for the general purpose of comparing the relative nearness 

 of different degrees of kinship as tested by family likeness in stature, 

 it may be taken as unity). The entries to be made in the several 

 lines are then to be calculated from the ordinary tables of the " pro- 

 bability integral." 



As an example of the first part of the process, suppose we are con- 

 structing a table of men and their nephews. A nephew is the son 

 of a brother, therefore in his case we have w = ^ X J = f ; and 



/= Pv /a-^ 2 ),=i-66. 



Form of Data for calculating Tables of Distribution of Stature 

 among' Kinsmen. 



Mean regression 

 to. 



Quartile of individual 

 variability, 

 f(=px V{l-w*). 



2/3 



1-27 



2/3 



1 27 



1/3 



1-fiO 



2/9 



1-66 



1/9 



1-69 



From any group of persons of the 

 same height, to their kinsmen as 

 below. 



Mid-parents 



Brothers , 



Fathers or sons 



Uncles or nephews 



Grandfathers or grandsons 



Trustworthiness of the Constants. — There is difficulty in correcting 

 the results obtained solely from the R.F.F. data, by help of the 

 knowledge of their general inaccuracy as compared with the 



