RELATIVES ON THE SUPPOSITION OF MENDELIAN INHERITANCE. 
421 
the mean z of their mates is 
and the grandparental correlation coefficient will be 
c e lAf 1 liA 
1 2 2 2 
Similarly, that for the (n + l) th parent will be 
giving the Law of Ancestral Heredity as a necessary consequence of the factorial 
mode of inheritance. 
18. If we suppose, on the other hand, that the association is essentially in y , the 
coefficient of correlation between y of husband and y of wife must be — in order to 
c i 
yield an apparent correlation m. Also 
T 2 
62 “ O' 2 — A € 2 ’ 
and 
A = ^c 2 . 
c i 
The parental correlation found as before is now 
L\C 2 + A C x ’ 
2 ’ 
and the higher ancestors are given by the general form 
c 1 c 2 + Ac 1 ^1 + AJ l 
although A is now differently related to c 1} Cz, and m. 
In the third case, where the essential connection is between z of husband and z of 
wife — and this is a possible case if the association is wholly due to selective fertility 
or to the selection of other features affected by the same factors — the equation between 
the correlations for y and z is changed, for now the marital correlation for y is equal 
to Ac 2 when we retain the definition 
Hence also 
T 2 
C2 = o- 2 -Ae 2 ' 
(A. = ACjC 2 , 
and the correlation coefficients in the ancestral line take the general form 
T+AV+ 1 
19. On the first of these theories a knowledge of the marital and the parental 
correlations should be sufficient to determine cqca, and thence to deduce the constant 
ratio of the ancestral coefficients. 
