444 
On the Inheritance of Coat-Colour in Cattle 
be multiplied by seeking for them and, not doing as we are here doing, dealing 
with the material provided in the pedigrees of a random sample from a few 
volumes of the Herdhook. It would thus seem that no simple Mendelian formula 
can possibly fit the shorthorn cases. Roughly, such a formula approaches the data 
in one or two points, but the roughness appears inconsistent with a theory of 
Mendelism being due to the purity of gametes. It is of course clear that the 
introduction of a complex allelomorph may improve matters, or the differentiation 
of whites and reds into different classes, homozygous and heterozygous. Increase 
in the number of available variables usually does give better fits. But the 
attempt to differentiate cows by the results of breeding from them must shatter 
on the paucity of their offspring. A cow will frequently give no more than 8 to 
10 calves, and, bred even to the same bull, or to the same type bulls, it may not 
be till the 9th or lOtli calf that she diverges from uniformity in her offspring. 
Thus one cow may throw 8 white calves and only the 9th be red or roan. This 
type of experience is not uncommon, and breeders not infrequently attribute it to 
the effect of age on the cow. To those who believe in individual prepotency — a 
view hardly consistent with Mendelism — this influence of age may not appear 
impossible. In the next place, the prejudice against white crosses on the part of 
breeders, indeed the dislike to white shorthorns in general, renders it almost 
impossible to effectively test the purity of any {RR) or (TriK) bull, although his 
offspring may be fairly numerous. Further, the bulls are often mated solely 
within their particular owner's strain, and it is not so evident what would happen 
if they were mated outside it. This tendency to assortative mating among 
shorthorn breeders will be discussed more fully in another section. We have seen 
that there is historically a possibility of two strains of red and two strains of 
white having been mingled in the shorthorn. Determinants representing parti- 
colour and white markings can undoubtedly be introduced also — we confess to 
having made an attempt from this standpoint, which shattered with further 
examination of Table I. — but the introduction needs a wider practice than we can 
boast of in inventing Mendelian formulae, and until we are more convinced than 
we are at present of the soundness of such formulae we should prefer to leave the 
invention to those who have had it. Goates Herdhook presents a wide range of 
material, and whatever we may think of the categories selected, the record has 
been made by persons in absolute ignorance of recent controversies about heredity. 
It is therefore really impartial material for Mendelians to unravel. 
For the remainder of this paper we shall confine ourselves to the biometric 
treatment of the problem, which, as we have already noted, is independent of the 
existence or non-existence of any Mendelian formula. We shall compare the 
results with other investigations of a like kind and endeavour to interpret the 
results in biometric language. 
(7) Assortative Mating in the Shorthorn Population. 
Three sets of matings were worked out, namely : («) the very recent matings 
of the parents of calves entered on the pedigree schedules, (6) the matings of the 
