430 On the Iiilieritance of Coat-Colour in Cattle 
Any simple or complex Mendelian system, any theory of hereditary deter- 
minants, must lead when it is applied to a " population " to its appropriate system 
of contingency coefficients between relational grades. It may be easy or it may 
be difficult to work out their theoretical values, but they undoubtedly exist, 
as soon as we know the nature of the mating. And without knowledge of the 
amount of mating of sub-groups no determinantal system can be applied to wild 
populations. If proven a theory of determinants would immensely assist breeders, 
but it is extremely difficult to see how it could be applied to wild populations and 
to the Darwinian theory of evolution by inheritance and selection. Hence, if we 
lay special stress on finding directly the coefficients which fix the intensity of 
inheritance in populations, it is not because we should in the least undervalue the 
discovery of a well-demonstrated determinantal theory of inheritance, but because 
we should then have, before applying it to populations and seeing its full bearing 
on the problem of evolution, to actually go through the theoretical determination 
of constants, which can without any such hereditary theory at all be determined 
from the material at our disposal. 
When, however, we have found the degree of resemblance between relatives 
quantitatively, that is to say, the empirical numbers which for any population 
mark the divergence from independent probability between any relational grades, 
we can next ask : Is there any connection between these numbers within the same 
species ? and are the coefficients for different species, or for different characters 
in the same species alike ? When we answer these questions we are determining 
whether heredity is the same or not for all characters and species, and to what 
extent ancestry and stock are of importance. It may be said that a valid 
determinantal theory would answer these questions also. So it undoubtedly 
would, but no such theory is, in our opinion, even approximately established as 
j^et ; and meanwhile there is and will remain every justification for attacking the 
problem by a method, which starts from no hereditary hypothesis, but merely 
endeavours to interpret the observed numbers of each class. 
So much may be said of the methods adopted in this paper. It is a repetition 
of what has already been written in this Journal, but it is desirable to restate it 
here in order to emphasize the aim of the present investigation. 
(2) Material. 
When we determined some years ago to consider the inheritance of coat-colour 
in cattle we directly sought for a simple case which might possibly enable us to 
convince ourselves of the efficiency of a quite brief Mendelian formula. The 
Guernsey cattle have a very considerable variety of coat-colour. With shorthorns 
a briefer classification is sufficient, but still it is wide enough to allow of the 
possibility of very complex allelomorphs. We were aware that the white short- 
horn breeds nearly true, and that the black Galloway does the same. Hence the 
cross of the white shorthorn and the black Galloway seemed to offer a possibility 
of testing the simplest Mendelian formula. Unfortunately the resulting blue-grey 
