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 Gl to S) will on the average possess 3D. Similarly that each. of the four grandparents of F (who will stand in the order of G2 to S) will on the average possess 3D, and so on. Again we have seen that F, on the average, transmits to S only I of his peculiarity ; that Gl transmits only i-; G2 only -,IT, and 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(4+2(3 x24)+-4(94 2Q)+ &c. }

=D' 22 + 23 3 + 24 32 + &c. j =D x 0.30.

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 Eyecolour, must be taken to mean that that same fraction