MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
117 
than maternal aunts ('2338). I consider, however, that the correlation of paternal 
aunt and nephew ('2837) in our series is abnormally high. 
Now it will, I believe, be seen that the investigation of the eight avuncular and 
the eight grandparental relationships, here made for the first time,* enables us to 
draw far wider conclusions than when, as hitherto, only parental and fraternal corre¬ 
lations are dealt with. In making the subjoined general statements, however, I 
must emphasise the following limitations :— 
(a.) The rules are deduced only from data for one character in one type of life. 
(J3 .) This character appears to be undergoing a secular change, a change very 
possibly due to a correlation between eye-colour and fertility in woman. Thus such 
a change might not unlikely differentiate the male and female influences in heredity. 
My conclusions, definitely true for eye-colour in man, and at the very least 
suggestive for investigations on other characters in other types of life, are :— 
(i.) That the younger generation takes, as a whole, more after its male than its 
female ascendants and collaterals. 
(ii.) That the younger generation is more highly correlated with an ascendant or 
collateral of the same than of the opposite sex. 
(iii.) That the younger generation is more highly correlated with an ascendant or 
higher collateral reached by a line passing through one sex only than if the line 
changes sex. 
Thus correlation is greater with a paternal uncle than with a maternal uncle, or 
with a maternal grandmother than a paternal grandmother. 
(iv.) Males are more highly correlated with their ascendants and collaterals than 
females are. 
The above rules apply to the averages; individual exceptions will be generally 
found to arise from a conflict of rules. Thus (ii.) and (iii.) may in special cases come 
into conflict with (i.). When we have more data for a greater variety of characters, 
we shall see better the relative weight of these rules in cases where they conflict. 
(/) Exclusive Inheritance in Eye-Colour .—A cursory examination of the eye- 
colour records shows at once how rare is a blend of the parental tints. Even when 
such is recorded, it is by no means clear that we have not to deal with a medium tint 
which is really a case of reversion to a medium tinted ancestor. The failure of eye- 
colour to blend is, I think, well illustrated by what Mr. Galton has termed cases of 
“ particulate ” inheritance. In the thousands of eye-colours I have been through, I 
noticed some half-dozen cases only in which the two eyes of the same individual were 
of different tint, or the iris of one pupil had streaks of a second tint upon it. f 
* I anticipate equally valuable results when characters are first correlated for the nine possible cousin 
series. 
t In the same manner the occurrence of particulate inheritance in coat-colour in horses may be really 
an argument against the existence of blends. In the many volumes of the studbooks I have examined, 
the recorded instances of piebalds are vanishingly few in number. 
