MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 313 
positive correlation, and we may conclude that the patent character in the daughter 
is inherited latently through the male line."^ 
But there is another and far more significant method of looking at this result, 
namely, by considering the meaning of E, on p. 274. We may treat the fecundity of 
daughters as really a character of the sire, and their mean fecundity as a measure of 
a latent character in him. B is then the correlation between a latent cliaracter in 
both a stallion and his sire, and we see that it is sensibly inherited for B = •1174. 
To compare with the law of ancestral heredity, we must use the coefficient of regres¬ 
sion, for the stallions are much more variable than their sires. We find 
Begression of stallion on sire = '2056, 
which carries us a long way in the direction indicated by that law. Thus it is 
extremely probable that this law of inheritance applies not only to the inheritance of a 
patent character, or of a character latent in one sex and transmitted to a second, but 
also to the inheritance of a character latent both in the transmitter and receiver. The 
present method accordingly seems applicable to the inheritance of a character latent in 
two individuals, if we take the mean of the character, wdien patent in the offspring, as a 
measure of its strength in the individual in whom it is latent. If li be the measure 
of a latent character in a parent, then the offspring will have a mean value qli Cj 
of this character, where q is the coefficient of parental regression and Cj a constant. 
If 4 be the measure of the same latent character in a relative, then the offspring in 
this case will have qlo + c.> of the character. But the correlation of li and 4 ^'hll be 
identical with that of ql^ -}- Cj and ql-i -j- c.,, as I have shown elsewhere.! Thus the 
mean of the patent character in the offspring may be used to measure the correlation 
between latent characters in their parents. 
To sum up our results for thoroughbred mares, we conclude that their fecundity, 
notwithstanding the imperfections and difficulties of the record, has been demon¬ 
strated to be inherited, and this, both through the male and female line, so far as 
we can judge, with an equal intensity. The apparent value of this intensity, except 
in the case of latent characters, is much below that required by the law of ancestral 
heredity, roughly, perhaps, 2/5 of that value; but there is considerable reason 
to think that this reduction may take place owing to the presence of fictitious values 
in the record arising from the peculiar circumstances under which thoroughbred 
horses are reared and bred. These fictitious values would hardly influence the 
means and variability of arrays like they must do the relationship between pairs of 
individuals. Hence, when we deal with such means and variabilities as in the cases 
on pp. 309 and 313, we find a much closer approach to the law of ancestral heredity. 
Fecundity is certainly inherited ; that it is inherited according to the Galtonian law 
* As a matter of fact, this conclusion is stronger than it appears here, for the correlation between 
nieces and aunts was worked out, without grouping, for fourteen distinct series, and in thirteen of them 
was found to be sensibly positive; in the fourteenth it was found to have an ijisignificant negative 
value. 
t “ On the Reconstruction of the Stature of Prehistoric Races,” ‘ Phil. Trars.,’ A, vol. 192, p. 183. 
VOL. CXCII.—A. 2 S 
