502 Proceedings of the Royal Society of Edinburgh. [Sess. 
two generations and one-quarter thereafter, the following correlations are 
obtained. 
A. 
One Genera- 
tion *33 and 
two ‘25 
Recessive. 
A. 
Two Genera- 
tions *33 and 
two *25 
Recessive. 
B. 
One Genera- 
tion *33 and 
two ’25 
Recessive. 
B. 
Two Genera- 
tions - 33 and 
two ’25 
Recessive. 
Parental .... 
•578 
•578 
•638 
•638 
Grandparental 
•315 (-299) * 
•340 
•351 
•451 
Great-grandparental . 
T63 (-159)* 
T71 
T85 
•241 
Great-great-grandparental . 
•089 
T24 
It is thus seen that high ancestral coefficients may arise simply from 
the kind of mating, and when it is noted that even in recent years chestnut 
horses are present in excess of one-quarter it will he seen that the values 
given in this table should be exceeded. In fact, the whole is capable of 
explanation as a result of Mendelism and of method of calculation. In 
addition to the effects ascertained assortive mating must be considered. 
If this consists of an excess of like mating like it will raise the correlation 
(par. 13). Such is the probable mating, and so it is not necessary to assume 
that the ancestral coefficients are high because of the nature of inheritance ; 
a simple zygote formula is quite sufficient to explain the facts. 
Coat Colour in Cattle. 
In considering the value of the coefficients of inheritance in coat colour 
among cattle it is first necessary to see how far the coat changes can be 
expressed by a Mendelian law. In this instance we have the dominant 
group apparently divided into three classes : (1) red, (2) red with a little 
white, and (3) red and white, all of which seem for present purposes 
the same. In the accompanying table all the matings are given on the 
assumption that the red class is uniform. 
The red class when mated with the white give in general roan, so that 
in this case the hybrid is distinct. If we represent red by (R, R), white 
by (W, W), roan will be (R, W). Considering further the mating of red 
and white we get out of 135 cases 128 roan calves, while the remaining 7 
are red. Such a result might be expected on a Mendelian basis. All reds 
cannot be alike, nor all whites. There must be some variation among them ; 
* According to the method in which the population of parents is adjusted. 
