MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
99 
both parents than the colt does. There is certainly (judged from coat-colour) no 
preponderance of the sire’s influence over the dam’s such as breeders appear occasion¬ 
ally to imagine. The average influence of the dam on the offspring indeed appears 
to be slightly greater than that of the sire, but the difference is of the order of the 
probable error, and not of the overwhelming character exhibited in the case of Basset 
Hounds. There is indeed in the case of thoroughbred horses not the same chance of 
carelessness produced by a misalliance afterwards screened by the defaulter. There 
exists, however, a far greater premium—considering the great value of yearlings from 
fashionable sires—set upon dishonesty. Again it is possible that when stallions 
receive too many public or private mares, or are still used in their old age, that they 
may, without losing the power of fertilising, lose some of the power of transmitting 
their characters. The divergences, so far as the probable errors are concerned, are 
not such that we are forced out of our way to explain them. With the single 
exception of sire and colt we see that our table shows the universal prevalence of the 
rule that : 
Relatives of the same sex are more closehj correlated than relatives of the same 
grades of the opposite sex. Thus :— 
A colt is more like his sire than his dam. 
A filly is. more like her dam than her sire. 
A dam is more like her filly than her colt. 
A grandsire is more like his grand-colt than his grand-filly. 
A colt is more like his brother colt than his sister filly. 
A filly is more like her sister filly than her brother colt, 
the latter two cases being true for both whole and half siblings. 
The solitary exception is that a sire is more like his filly than his colt. 
If we were to assume it a rule that a filly in the matter of coat-colour has stronger 
inheritance all round than a colt, we should find it agree with our results for parental 
inheritance, and receive considerable support for the much stronger correlation of 
fillies than of colts, when either whole or half siblings. But it would not be in 
accordance with our results for grandparents, for which, however, we have only 
details for two out of the eight possible cases. On the whole, I think we must 
content ourselves with the statements that parental correlation is certainly about '5, 
and that with high probability each sex is more closely correlated with its own sex of 
the same grade of relationship. 
(b.) Direct Line, Second Degree .—My data here are unfortunately only for two 
cases out of the possible eight. I hope some day to finish the series, but the labour 
of ascertaining from the studbooks the coat-colour of 700 or 800 separate sires is 
very great. Indeed it is not easy to follow up the pedigree through the male line 
when the sire is not one of the famous few. On the other hand, it is much easier 
through the female line. For this reason the maternal grandsire was taken. Even 
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