RELATIVES ON THE SUPPOSITION OF MENDELIAN INHERITANCE. 
405 
In general 
and if 
and 
then 
a 2 = /3 2 + S 2 , 
0-2 = Sa 2 (VIII) 
r 2 = S/8 2 (IX) 
e 2 =28 2 (X) 
<T 2 =T 2 + £ 2 . 
The regression due to a single factor of the mean of the offspring of parents of a 
ffiven array is 
Z 2 /S 2 
O- 2 ' 2 ’ 
and adding up the effects of all factors we find 
so that the parental correlation for a static population mating at random is simply 
1 
o 
T 2 
( 7 2 
(XI) 
We may regard this formula otherwise. The correlation between the actual 
somatic measurements such as a, d, — a, and the representative linear quantities 
c + b, c, c — b is -. Thus the correlation of parent and child is made up of three 
factors, two of them representing the relations between the real and the repre- 
sentative measurements, and the third the correlation between the representative 
measurements of the two relatives. Thus the effect of dominance is simply to reduce 
certain relationship correlations in the ratio 
The values of the correlations between the representative measurements for 
random mating, which may be called the genetic correlations, are given in the 
accompanying table : — 
Generations. 
Half 2nd 
Cousin. 
Half 1st 
Cousin. 
Half 
Brother. 
Ancestral 
Line. 
1 Brother. 
1st Cousin. 
2nd Cousin. 
Own ..... 
1 /64 
7x6 
74 
1 
72 
7s 
73 2 
Father’s . 
7x28 
7-3 2 
Vs 
7s 
74 
7x6 
764 
Grandfather’s 
7*56' 
764 
7X6 
74 
7s 
7s 2 
7X2 8 
Great-grandfather’s 
Vsia 
7x28 
732 
7s 
7x6 
764 
72 5 6 
Great-great-grandfather’s 
1 /l024 
725 6 
7 6 4 
7x6 
732 
7X28 
7sx 2 
6. The above reasoning as to the effects of dominance applies without modification 
to the ancestral line, but in a special class of collaterals requires reconsideration. 
The reason is that the deviations frotn linearity are now themselves correlated. In 
other words, a father who is heterozygote instead of recessive may have offspring 
