A. Barrington and K. Pearson 
449 
TABLE V. 
Orandparental Inheritance in Shorthorns. 
Sex change 
Paternal Grandsire and Biill Calf ... 
•19 
0 
Paternal Grandsire and Cow Calf ... 
■25 
1 
Maternal Grandsire and Bull Calf . . . 
•18 
2 
Maternal Grandsire and Cow Calf ... 
•17 
1 
Paternal Grandam and Bull Calf ... 
•15 
1 
Paternal Grandam and Cow Calf ... 
■16 
2 
Maternal Grandam and Bull Calf ... 
•24 
1 
Maternal Grandam and Cow Calf ... 
•25 
0 
Mean = 
•20 
It will be seen at once that this is lower than the results obtained for man, 
horse, and dog ; i.e. about "2 instead of "3. This is what we might expect, as the 
parental correlations found for the shorthorn by mean square contingency are 
about "4 instead of the 'o for pigmentation in man, hoi'se, and dog. We are not 
prepared to assert, however, that it connotes an actual lessening of the intensity of 
inheritance, because other methods in the parental case seem to indicate that the 
resemblance is really greater than is shown by mean square contingency with only 
a classification into five vei^y unequal groups. 
The values are clearly somewhat irregular. If we group them according to the 
number of sex changes we find : 
Grandparental resemblance with no sex change = ^22 
„ „ one „ =^20 
,, ,, two sex changes = ^1 7 
It would thus appear that, as in the case of eye-colour in man, there is a 
weakening of the intensity of resemblance with each change of sex. But if this 
be more than an appearance, it must be screened by other factors in the case of 
parentage, for in that case the values are ^40 for no change of sex and ^40 for one 
change of sex. This result is remarkably consonant with what we have previously 
observed in the case of greyhounds* where we found no sensible influence of 
change of sex in the parental resemblance, but an apparent influence on the grand- 
parental relation. In eye-colour in the case of man it was found throughout all 
relationships f. We failed to demonstrate a change of sex influence in the case of 
coat-colour in horsesj, and it seems worth considering the matter further in short- 
horns. Accordingly in attempting to estimate the great-grandparental influence, 
when we gave up the excessive labour of forming the 16 great-grandparental 
tables which would have meant dealing with upwards of 16,000 entries, and a far 
* Biometrika, Vol. iii. p. 258. 
t Pearson : Phil. Trans. Vol. 195 A, pp. 114-117. Lutz : Biometrika, Vol. ii. pp. 237-240. 
+ Ihid. Vol. II. p. 232. 
Biometrika iv 57 
