viii.] DISCUSSION OF THE DATA OF EYE COLOUR. 149 



is known with certainty of any of the ancestors of 

 S except F. We have seen that though nothing may 

 actually be known, yet that something definite is implied 

 about the ancestors of F, namely, that each of his two 

 parents (who will stand in the order of relationship 

 of G 1 to S) will on the average possess ^D. Similarly 

 that each of the four grandparents of F (who will stand 

 in the order of G 2 to S) will on the average possess 

 ^D, and so on. Again we have seen that F, on the 

 average, transmits to S only ^ of his peculiarity ; that 

 GK transmits only T ] F ; G 2 only ih> anc ^ so on - Hence 

 the aggregate of the heritages that may be expected 

 to converge through F upon S, is contained in the 

 following; series : — 



D is + 44) +4 (^4°) +&c - } 



=D U + 2^ + 2^ +&C -J Dx0m 



That is to say, each parent must in this case be 

 considered as contributing; 0*30 to the heritage of the 

 child, or the two parents together as contributing 0*60, 

 leaving; an indeterminate residue of 0'40 due to the 

 influence of ancestry about whom nothing is either 

 known or implied, except that they may be taken as 

 members of the same race as S. 



In applying this problem to Eye-colour, we must bear 

 in mind that the fractional chance that each member 

 of a family will inherit either a light or a dark Eye- 

 colour, must be taken to mean that that same fraction 



