422 
R. A. FISHER ON THE CORRELATION BETWEEN 
Thus for three human measurements : — 
Stature. 
Span. 
Forearm. 
/* ■ 
. '2804 
•1989 
•1977 
p . 
•5066 
•4541 
•4180 
C 1 C 2 
•7913 
•7575 
•6980 
A . 
. -2219 
•1507 
T377 
1(1 + A) 
. '6109 
•5753 
•5689 
These figures are deduced from those given by Pearson and Lee ( loc , 
are there found to be insignificant, and taking the weighted means. 
cit.), neglecting sex distinctions, which 
These values for |(I+A) agree very satisfactorily with the two ratios of the 
ancestral correlations which have been obtained, '6167 for eye colour in man, and 
'6602 for coat colour in horses. It is evident that if we also knew the ratio of the 
ancestral correlations for these features, we could make a direct determination of A 
and ascertain to what extent it is the cause and to what extent an effect of the 
observed marital correlation. 
20. The correlations for sibs, double cousins, and more distant relations of the 
same type, in which all the ancestors of a certain degree are common, may be found 
by considering the variance of the group of collaterals descended from such ancestors. 
The variance of a sibship, for example, depends, apart from environment, only upon 
the number of factors in which the parents are heterozygous, and since the proportion 
of heterozygotes is only diminished by a quantity of the second order, the mean 
variance of the sibships must be taken for our purposes to have the value appropriate 
to random mating, 
+ f e 2 = -^-[2c 2 (l - A) + 3(1 - c 2 )] 
plus the quantity — — V due to environment. But the variance of the population 
is V/cx; and the ratio of the two variances must be 1 —f where f is the fraternal 
correlation. Hence 
/=ii(l + C2 + 2c 2 A). 
4 
In the same way, the variance for a group of double cousins is unaffected by 
selective mating, and we find the correlation coefficient for double cousins to be 
A(i + 3c 2 + 12c 2 A), 
lo 
showing how the effect of selective mating increases for the more distant kin. 
On the first hypothesis, then, we must write, 
