458 
Proceedings of the Royal Society of Edinburgh. [Sess. 
XXXI. — On Inheritance of Hair and Eye Colour. 
By John Brownlee, M.D., D.Sc. 
(MS. received June 17, 1912. Read same date.) 
Some time ago, in a paper published by the Royal Anthropological Institute, 
I applied a Mendelian analysis to that part of the observations made by the 
late Dr Beddoe (1) which refers to the colour of the hair. In that paper (2) 
I showed that these observations obeyed in a highly remarkable degree 
the law referred to, and that this result held from the north of Scotland, 
through the whole of England, Ireland, France, and Germany, to the south 
of Italy. At that time I was unable to make any application to the 
observations on eye colour also published in the same work, but I have now 
succeeded in completing the analysis. 
The whole depends on a theorem of population stability which may be 
easily proved. 
Let the population consist of a mixture of two races having two 
characters such as hair colour and eye colour inherited according to the 
Mendelian law of segregation. Let these qualities be denoted by (BB),, 
(bb) for the hair, and (DD), ( dd ) for the eyes. Then the population may 
be considered given by 
DD I DD 
BB +2ai ! B& 
+ & 2 
DD | 
bb 
+ 2 bd 
+ 2 ac 
D d 
BB 
+ (2 ad + 2 be) 
D d 
Bb 
D d 
\ dd 
dd 
dd 
+ c 2 
+ 2 cd 
+ d 2 
bb 
1 BB 
Bb 
bb 
(i> 
If this population mate freely, and if all matings possess equal fertility,, 
the relationship of the constants required for a stable population depends 
on whether coupling exists or not. 
The meaning of the term “ coupling ” may be easily seen from a considera- 
tion of the different units in the above expression. It will be noticed that 
every term of the expression except that in the middle has either two eye 
units or two hair units the same. It is thus impossible when division takes 
* The factors outside the brackets are the proportional numbers of each variety. The 
simple case is : if x(A, A) mate at random with itself and with y(a , a) and all subsequent 
matings are equally probable, the stable population is given 
£c 2 (A, A) + 2xy(A f a) + y 2 (a, a). 
Gf. p. 462. 
