461 
1911-12.] On Inheritance of Hair and Eye Colour. 
are at present of more importance than theories. The only difference in 
B 
this case is that either 
D 
d 
D . 
T - 
or 
-b 
B 
b 
b 
d 
must exist ; thus four different 
compounds cannot all appear together, but if an average of a large number 
of examples is taken the result must be the same. 
Referring back to the expression for a freely mating population, we see 
that the fact that it forms a perfect square is not a sufficient criterion of 
stability. All that is stable is the relation of the eyes alone or of the hair 
alone. Thus, taking formula (2) and summing each line as regards number, 
we have for the total of the first line, or the terms containing (DD), 
(a 2 + ab + ac + mh ) 2 + 2 (a 2 + ah + ac + mh)(b 2 + ab + bd + nh) 4 - ( b 2 + ah + bd + nh) 2 , 
or 
(a 2 + ab + ac + mh + b 2 + ab + bd + nh) 2 , 
or 
or 
(< a 2 + ab + ac + ad + b 2 + ab + bc + bd) 2 , 
since m + n = ' 5 
and h = 2ad 4- 2 be ; 
(a + b) 2 (a + b + c + d) 2 ; 
the second line, i.e. the terms containing (Dd), is equal to 
2 (a + b)(c + d)(a + b + c + d) 2 , 
and the third to 
(c + d) 2 (a + b + c + d) 2 , 
and the proportions of the original population (1) are exactly maintained. 
Shortly written as before shown, the general formula may be denoted by 
2 
D 
D 
d 
d \ 
a 
+ b 
+ c 
+ d 
B 
b 
B 
i) 
This is the typical stable Mendelian population without coupling if 
ad = bc\ if coupling exists, ^ is the criterion, and stability in the 
population is only established after many generations. 
Suppose equal numbers of two populations mix and mating is free : 
suppose also that the coupling ratio is 7, one actually found by Bateson 
and Punnett (3). Then if mating is free the first generation will be given 
by the ratio 
| DD 
i Dd 
+ 2 ! + 
dd 
BB 
: m ! 
bb 
With a ratio of 7 the next generation will be represented by 
( 
D 
D 
D 
d 
d 
i 8 
+ 7 
+ 
+ 
+ 7 
+ 8 
( 
B 
B 
b 
B 
b 
