428 
On the TnJierltance of Coat-Colour in Cattle 
been previously stated as to the scope of bioraetric work in this field. Our 
object is to state first the proportion in which sub-classes exist in a " population," 
to measure next the degree in wliich these sub-classes are mated at random, and 
then to determine the extent to which these sub-classes reproduce themselves. 
We believe that a statistical record of this kind is of fundamental importance 
whatever physiological theory of heredity be adopted. In treating cattle we have 
done precisely what was done in the case of thoroughbred horses and grey- 
hounds, namely, the latest available volumes of the studbook have been taken*, 
and the colour pedigree of individuals entered therein worked out. In the work 
on cattle this was done on standard pedigree slips, of which a sample is given 
on the following page. These were filled in where possible as far as the great- 
great-grandparents and these schedules, representing a random sample of the 
existing general population, form the basis of our tables. As in the case of the 
greyhounds, supplementary investigations were made by collecting special pedi- 
grees as those of white individuals. These special pedigrees were not embraced 
in the general sample except in so far as they fell into the period there dealt 
with, but they served to illustrate special points which it seemed desirable to 
elucidate. 
On the basis of the above random sample-]- we first determioed the extent to 
which random mating occurs in the general population. To what extent is there 
a fashion or taste in mating cattle ? We next enquired how far our tabulated 
results admitted of a Mendelian interpretation. Let us suppose this question 
answered in the positive or negative sense, as the case may be, it leaves the 
tabulated data absolutely where they were as to the further question we have to 
ask : What is the average degree of resemblance between relatives in a population ? 
To what extent do the features of the ancestry impress themselves upon the 
offspring ? This is not a matter of theory, it is simply a statistical enquiry as to 
the degree of independence of two distributions. It resolves itself mathematically 
into determining the degree of independence of probability in two " chance " 
distributions. In order to dispose of all doubts as to quantitative scale and as to 
" normal '' distributions of characters, we have adopted throughout the contingency 
method of measuring the deviation from independent probability, and in particular 
that form of it spoken of as mean square contingency. This makes all our results 
for one race strictly comparable intei' se. But the colour classifications being 
different for different species, it is not so legitimate to compare these results 
together. In order to throw light on this point other methods have been adopted 
occasionally for comparison and control ; these will be referred to in their proper 
places. 
* In the second paper on coat-coloui- in horses, we began with the earliest studbooks in order to 
test the influence of the far more frequent greys and blacks. 
t The word "random" is used with reference to coat-colour. When one or both parents had 
appeared several times, no further offspring of such individuals were taken, in order to avoid 
overweighting certain individuals. This affected the cows more than the bulls, because the former 
are classified in herds with sometimes close inbreeding. Thus 1000 consecutive cows might possibly 
have given only 50 to GO sires. 
