MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
149 
We have, accordingly, by the method of the present memoir :— 
Correlation of size of family with darkness of eye-colour 
= '0595, for fathers. 
= — '0239, for mothers. 
The former is just sensible, the latter hardly sensible relative to the probable error. 
So far as they can be relied upon, they would denote that fathers have more children 
the darker eyed they are, and mothers more children the lighter eyed they are. 
This is in accordance with the result given in the memoir, that the modern 
generation is darker than its male and lighter than its female ancestry, but it is not 
the explanation given in the text, although it is probably the true one. If it be the 
true one, dark fathers and light mothers ought to present the most fertile unions, 
and it seemed desirable to test this directly. We have already seen that there 
exists an assortative mating in eye-colour, like tending to mate with like, the 
co-efficient of correlation being about '1 ; hence if we were to correlate the eye-colour 
of mothers and fathers, i.e., husbands and wives weighted with their fertility, we 
ought to find this result substantially reduced. The following is the table :— 
Fathers. 
Light Eyed. 
Dark Eyed. 
Totals. 
t Ej'ed. 
1183 
612 
1795 
Jb 
i—5 
Dark Eyed. 
826 
455 
1281 
Totals 
2009 
1067 
3076 
We find r = '0239, or the correlation has been reduced to a fifth of its previous 
value, and is now of the order of its probable error. To mark still further this 
increased fertility of heterogamous unions, I add two further tables, giving the mean 
number of recorded offspring for various classifications of parental eye-colour. 
