A. Barrington and K. Pearson 
455 
somewhat complex system of latent characters, because practically every colour 
group will be found — with larger or smaller frequencies — to reproduce every other 
colour group. The only alternative is to reject the records in bulk as patently in 
error, because they do not fit rigidly a simple Mendelian scheme. 
(b) When we turn to the statistical treatment of the data we are at once met 
by a further difficulty. The method of contingency enables us to free ourselves 
from any question of colour order or scale, and thus we are not troubled with any 
hypothesis as to a normal or Gaussian distribution. But while thus taking its 
place as the rational statistical process for dealing with colour data, we are 
dependent on breeders' colour classifications which are not made with a view to 
statistical treatment, and provide the statistician, as in this case of shorthorns, with 
groupings like those of red and roan not fine enough for his purposes. He obtains 
measures of intensity of resemblance comparable within the species — he can 
investigate the relative intensity of ancestral and collateral likenesses, but it is 
not so easy to compare the results for one species with a second. It would be a 
great advantage if red and roan could be recorded in light and dark shades, for 
the range in these colours is very wide and needs differentiation. With a 36- 
or 49-fold table we should undoubtedly get results better comparable with those 
for horses and greyhounds. 
(c) Notwithstanding these difficulties we actually find, however, that the 
shorthorns fit quite reasonably into the general range of results for man, horse, 
and dog. The "decay" of ancestral resemblance was found to be '64, a value 
lying between that found for man and dog, and expressible in round numbers 
by saying that the relationship decreases 2/3 at each upward gi'ade. Thus the 
geometrical series feature of the ancestral law is maintained in the case of short- 
horns. The parental relationship lies between '4 and "5, and is probably nearer 
the latter than the former number; the whole sibling resemblance is a little over 
•5 at a minimum, and appears to be very similar in range of value for that found 
for man and dog. There is a substantial assortative mating produced by breeders 
mating like with like, but while this would raise the apparent values of the con- 
tingency coefficients, the fact that red and roan are especially fashionable tends by 
its selective action to produce more than an equivalent lowering. Generally the 
shorthorn data strengthen our view that — whether it be Mendelian, or some 
other yet to be found — there is a single basal law of inheritance, manifesting itself 
notwithstanding assortative mating, selection, and environment in the clustering 
of the inheritance constants for all species of populations about the value '45 
to '5 for parental inheritance, and about '5 to '55 for fraternal inheritance, with a 
geometrical series of a ratio roughly about 2/3 for ancestral grades. Such an 
ancestral law will, we are convinced, be found to flow from the physiological 
basal law if it be discovered. Meanwhile each fresh series as it is worked out 
biometrically tends to strengthen the view that apparent variations in the in- 
tensity of hereditary resemblance are not real variations in nature. The hereditary 
process is one, producing in a population definite degrees of average resemblance 
