CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
269 
use of in direct experiments on breeding insects, where a record could be kept ad 
hoc. It follows at once from (i.), (v.), (vii.) and (viii.); 
Mb 
Mb 
:\i'b - 
M'b - Mb 
= r— = coefiBcient of resrression 
(xvii.). 
It is the second ratio which, I think, might with profit be experimentally 
evaluated. 
{/.} Since the mean fertility of daughters loaded with the fertility of their 
mothers is the fertility of the next generation, and we see that this is always greater 
than M2; if r be not zero, it follows that the inheritance of fertility marks a progres¬ 
sive change. The only means of cuunteracting its influence would be tlie reduction 
of M2 to or below Mi by the action of other equally potent factors of evolution. For 
the existence of such factors in man I shall later give evidence. 
( 4 .) Proposition III.—To extend the results obtained for fertility to the joroblem of 
fecundity. 
While the fecundity of an individual can often, at any rate approximately, be 
measured, the fertility is not ascertainable. Thus we can ascertain the number of 
occasions on which a brood mare has gone to the stallion and the number of foals she 
has produced, but her fertility, the produce she might have had, if she had 
throughout her whole career had every facility for breeding, is unknown to us. But 
if we proceed to form tables for the inheritance of fecundity, we are met by precisely 
the same difficulties as in the case of fertility. The more fertile individuals are d 
priori more likely to appear in the record, and will be likely to be weighted again 
with their fertility when we come to deal with their offspring.”" 
Now it is certain that fertility must be correlated with fecundity ; or, if x now 
represents the fecundity and y'the fertility, we shall have for the mean fertility for a 
given fecundity x an expression of the form Xq + Xi.-r, always supposing the regression 
to be sensibly linear. But the fertility must vanish with the fecundity, hence Xo = 0, 
and Xi is really the ratio of mean fertility to mean fecundity. Tims we may write for 
the fertility f 
f=\,x + C, 
where { may vaiy widely, but it is not correlated with x. 
If now all the symbols we have used with regard to fertility in Section (2) be inter¬ 
preted as referring to fecundity, we must weight with a factor kf instead of a factor 
kx, or with a factor kk^x X{. So long as this factor is linear, absolutely no change 
can be made in the results, for, ^ being uncorrelated with x, all summations including 
* In the case of sires especially, if we are dealing with thoroughbred horses, their comparative 
fewness at each period renders it quite imposfuble to deal with one offspring of each parent only. 
