RELATIVES ON THE SUPPOSITION OF MENDELIAN INHERITANCE, 
409 
wholly heterozygous individual, is related to two other quantities, such as e u and e 3 i, 
by just the same equation as that by which / is related to i and k, and occurs in the 
9x9 table with corresponding coefficients. The elimination of the five deviations 
621; ei2) e 32, ^23, e22 is therefore effected by rewriting the 9x9 table as a 4 x 4 table, 
derived from the quadratic in i and k corresponding to the relationship considered. 
Thus the variance, found by squaring the individual variations, is derived from 
the 3x3 table 
f- 
- 
- 
- 
2 pq 
— 
— 
- 
q> 
which yields the 2x2 table 
|(P + 2g) ( 
\.P9 
02 P+-q) 
and the quadratic in eu, e 13 , e 31 . e 33 
' ,F (P + 2 q){p' + 2 q')p s p' 3 e. 
ipqP 9 L 
n 2 + 3 similar terms + 2 p 2 q' 2 p' s (p 
■2 
hi e 33 + e i3 e 3l)J> 
which also takes the form 
r K-\(p 2 P , \r-P*4\z- 
Ipqpql 
q 2 p'%i + ( N\ 
i3 ) 2 + 2pqp' 3 (pe n - 
The parental table 
-\pq 
yields 
-\P% 
q*/4p 
1 
-v\ f 
16. pqp'q 
°13 11 31 1 1 t 
and the fraternal table 
p 2 iM 
IT 
— 
<? 2 / 4 P 
leads us to the simple expression 
+P3q ' 3e ^ + fPV + 2 3 ?' 3e 33 2 J- 
For uncles and cousins we obtain respectively \ and x 1 ^ of the parental contribution, 
while for double cousins the table 
16 p 
( P + 2 ?) 
and a quadratic similar to that for the variance. 
