268 On the Effect of a Differential Fertility on Degeneracy 
i.e. the regression owing to differential fertility, S2 is the variability of the offspring 
generation and should be compared with cr^ or o-j, while R is the correlation 
between offspring and effective parentages. 
An examination of this table shows the following general results : (a) the mean 
value of the character in the population is reduced 8 to 13 per cent, of its standard 
deviation according to the hypothesis we make with regard to the influence of the 
character on fertility. That is to say, the mean character of the population stands 
one-third to a half-decile lower with each new generation, {b) In the next place 
the variability is lowered two to five per cent. The probability therefore of 
extreme deviations is sensibly reduced ; but this reduction tells only on excess of 
the character because the mean of the distribution has been markedly shifted 
towards defect of the character ; in other words, if extremes of the character 
in excess correspond to noteworthy men, they are much less likely to occur in 
a population where this differentiation of fertility has set in. Suppose we term 
one man in a thousand "noteworthy," then such a man corresponds to the grade 
3"090o-i in our original population. His position in the offspring generation will be 
+ 3 090O-1 = 3-216 0-1 = ^2 = 3-37 So. 
But this corresponds to four such individuals in 10,000, or 1 in 2500 ; or there 
will be less than half as many noteworthy men. This is on the first hypothesis ; 
the second hypothesis shows only 1 in 3300, and the fourth or less influential 
hypothesis 1 in 1700. It will therefore be obvious that if mental powers are 
hereditary, any differentiation of fertility will not only alter rapidly the average 
intelligence of the community, but will produce that dearth of noteworthy ability, 
or of genius, which is fatal to the continued existence under modern competitive 
conditions of a great national life. The whole system of curves corresponding 
to this first Illustration is given in Diagi'am I. 
Illustration II. In the previous illustration we considered a case where the 
maximum fertility did not coincide with the minimum of the character, although 
the lowest values of the character had markedly higher fertility than the highest. 
It will be of interest to determine what, if any, differences arise in our general 
conclusions, if we fix on the fertility of individuals high and low in the scale, 
instead of on average fertility values. We will suppose that the individual 
parentage which stands sixth in the 1000 for the given character has only a fertility 
of 1"5, and that which stands last but six has a fertility of 6'5 ; the maximum 
fertility of any grade shall be 7, and this shall occur helow the grade of the 
individual parentage with a fertility of 6"5. Using the notation of p. 264, we may 
take mi = = 2'5, say. Hence 
iyi<!2|lzi2|il)=2..,X + .= ±, -75525, 
■434.2945 
^-<'Ml^).,,,_,.,,S50B. 
