100 
PROFESSOR K. PEARSON AND DR. A. LEE ON 
in this case we had to seek back for each sire—the year of whose birth was unknown 
—until we found the record of his coat-colour given under the heading of his dam in 
the year of his birth. 
The average of our two cases gives a coefficient of correlation = '3353, the colt 
having a greater degree of resemblance to the grandsire than the filly. This value is 
substantially greater than the '25 we might expect for exclusive inheritance, and 
more than double the value T5, to be expected for the grandparental correlation 
with Mr. Galton’s unmodified law for blended inheritance. Of course the ‘25 is to be 
expected as the mean of the eight grandparental series, and, as we shall see for eye- 
colour in man, these may vary very much in magnitude. But allowing for this, it 
seems quite impossible that the average value could be reduced to T5. I take it 
therefore that the grandparental, like the parental, data point to a law of inheritance 
other than that which has been described in my paper on the Law of Ancestral 
Heredity. This peculiar strengthening of the grandparental heritage has already 
been noted by me in my paper on the Law of Reversion,* and the difficulties of 
dealing with it on the principle of reversion therein discussed. There may be some 
opinion among breeders as to the desirability of emphasising the dam’s strain in the 
choice of a sire which leads to this result, but if so it is unknown to me, nor do I see 
how it would work without also emphasising the correlation of the dam and foal. 
The mean value of the correlation for the maternal grandfather and grandchildren for 
eye-colour in man is ’3343—a result in capital agreement with that for coat-colour in 
horses. In that case the average of the eight series, as we shall see later, is con¬ 
siderably above ‘25, and we must, I think, suspend our judgment as to whether this 
could possibly in the case of horses be the true mean value. As to the value '15 
it seems quite out of the question. 
As already remarked, the influence of the maternal grandsire (unlike that of the 
sire) is substantially greater on the colt than on the filly. 
(c.) Collateral Heredity, First Degree. —Here we have more ample data to go 
upon, namely, a complete set of six tables of both whole and half siblings of both 
sexes. 
We notice one or two remarkable features straight off. In the first place, in the 
case of both fillies and colts, the whole siblings of the same sex have not a correlation 
the double of that of the half siblings, but have a correlation very considerably less 
than this. A priori we might very reasonably expect the one to be the double of 
the other. This is what would happen in the case of blended inheritance on the 
hypothesis of equipotency of the parents. As the half siblings are on the dam’s side, 
we might assert a considerable prepotency of the dam over the sire. This cannot 
indeed be the explanation of the divergence in the case of Basset Hounds, where the 
half siblings have a correlation considerably less than half that of whole siblings,! 
* ‘Roy. Soc. Proc.,’ vol. 66, p. 140 et seq. 
f ‘Roy. Soc. Proc.,’ vol. 66, p. 140 et seq. 
