A. Barrington, a. Lee and K. Pearson 257 
It would thus appear that the grandparental correlation cannot be very 
different from the mean value J. 
If we compare the results now obtained with earlier pigmentation series we 
have the following table : 
TABLE VII. 
Gixmdparental Relationshij). 
Grandparent and Offspring 
Man 
Eye-Colour 
Horse 
Coat-Colovu' 
Greyhound 
Coat-Colour 
Mean 
Paternal Grandfather and Son 
•421 
•324 
•314 
•353 
Paternal Grandfather and Daughter... 
•380 
■361 
■2G1 
•334 
Maternal Grandfather and Son 
•372 
■359 
•301 
•344 
Maternal Grandfather and Daughter. . . 
•297 
•312 
•384 
•331 
Paternal Grandmother and Son 
•272 
•309 
•368 
•316 
Paternal Grandmother and Daughter 
•221 
•204 
•311 
•245 
Maternal Grandmother and Son 
•252 
•261 
•332 
•282 
Maternal Grandmother and Daughter 
•318 
•235-* 
•386 
•313 
Mean 
•317 
•296 
•332 
•315 
We conclude from this that as in the case of parents, so in the case of 
grandparents, there is no substantial difference in pigmentation inheritance 
between man, horse and greyhound. We may reasonably hold that a geometrical 
series : 
i ix(in ix(fn... 
will express the decreasing correlations between offspring and ancestry as closely 
for the greyhound as it does for man and horse "f*. 
The evidence in favour of a change of sex weakening the intensity of here- 
ditary influence is of a rather doubtful kind. It has been shown to hold for 
eye-colour in man by Pearson |, both in the case of direct and collateral heredity, 
and by Lutz§ for further data in the case of direct inheritance. It does not 
appear to be markedly true for coat-colour in horses. For greyhounds it is not 
absolutely true, although the differences are of the probable-error order in the 
case of the unselected parental relations. Here the sire, as in the case of the 
horse, has a more marked influence on the coat-colour of the daughter than 
on that of the son, while the dam for man, for horse and for both cases of dogs 
is more influential in the case of the daughter than in that of the son. In the 
grandparental series it does however appear to be true ; thus we find : 
* Erroneously given as •239^2 instead of •2351 owing to a slip in the value used for log k in finding 
the equation for r in Blometrika, Vol. ii. p. 231. The value for k is correct, the equation for r slightly 
incorrect. 
t See " The Law of Ancestral Heredity," Biomctrikti, Vol. ii. pp. 211 et seq. 
t Phil. Trans. Vol. 195, A, pp. 114—117. 
§ Biometi ika, Vol. ii. pp. 237—240. 
Biometrika in 33 
