459 
1911-12.] On Inheritance of Hair and Eye Colour. 
place for anything else to occur than that two constantly linked pairs are 
given off in equal numbers. Thus 
But when we consider the case of 
I dD 
bb 
D d 
Bb 
can only divide into 
and 
other things may easily happen. 
If D have a greater affinity for B than for b, then we may have more of the 
element I ^ given off than of the element 
i B 
* But here also there is a 
necessary arithmetical relationship between the different elements resulting, 
and if n 
d 
elements occur for one 
D . 
b 
it follows that there will also be 
n 
for one 
even although the attraction of D for B might be different 
from that of d for b. 
If the population (1) mate freely and if m 
occur with n 
(where 
m + n = 5 and 2 (ad + be) is denoted by h), the next generation will be 
given by 
( a 2 + ab + ac + mh ) 2 
DD 
BB 
+ 2 (a 2 + ab -f ac 4- mh)(b 2 + ab + bd + nh) 
DD 
B b 
+ ( b 2 + ab + bd + nh)‘“ 
1 DD 
m 
bb 
+ 2 {a 2 + ab + ac + mh)(c 2 + ac + dc + nh) 
BB 
+ 
2 (a 2 + ab + ac + mh)(d 2 + db + cd + mb) | D d 
+ 2 (b 2 -t- ab + bd + nh)(c 2 + ac + cd + nh) f Bb 
+ 2 (b 2 ab + bd + nbi)(d 2 + bd + dc -1- mil) 
( 2 ) 
+ 2 (c 2 + ac + cd + nh)(d 2 + db + cd + mh) 
bb 
dd 
Bb 
+ (c 2 + ac + cd + nh) 2 
+ (a 2 + db +■ cd + mh) 2 
dd 
BB 
dd 
bb 
This has exactly the same form as that from which it is derived, but 
the relative proportions of the different classes may be different. If the 
population is stable we have as the sufficient conditions, 
(a 2 + ab + ac + mh) 2 _ (b 2 + ba + bd + nh) 2 _ ( c 2 + cd + ca + nh) 2 _ (d 2 + db + dc + mh) 2 
ct 2 _ b 2 c 2 
d 2 
as all the similar relationships hold if these are true. 
Taking the first equation 
(a 2 + ab + ac + mh) 2 ( b 2 + ba + bd + nh) 2 
~a 2 = b 2 
* The assumption made here is that there is no special mortality or instability among 
the pairs which are actually formed. 
