270 On th( Effect of a Differential Fertility on Deaeneracy 
We now turn to the distribution of offspring. We have : 
m. = -2728^(7,, 2, = a, Vl -•06986p^ 
R/p = 8-6490/\/r4-8152-p^ 
We can now determine these in precisely the same manner as they were tabled 
for the four hypotheses in Illustration I. 
Govstavts of Offspring Distribution. Illustration II. 
Hypothesis . . . 
(i) 
(ii) 
(iii) 
(iv) 
•1585 
•1736 
•1228 
•1002 
•9881 
•9858 
•9929 
■9953 
Rip 
•9759 
•9783 
•9713 
•9689 
We see at once from this table that whichever hypothesis we take the 
variability of the new generation is only lessened about 1 per cent, and the 
correlation about 3 per cent., values markedly less than in the case of Illustration 
I. This is obviously due to the fact that the fertility distribution is markedly 
less concentrated. But the shift of the population average is now 10 to 17 per 
cent, of the standard deviation, or roughly the avtjrage has receded through | to | 
of a decile in the character. We may measure the extreme effect of this by 
inquiring how far "noteworthy" individuals, the individual one in a thousand of 
the old generation, have been reduced in number. What we have to find is the 
value of ('»io + 3'090o-i)/S., ; for the first hypothesis this is 3"288, which corresponds 
to 1 in 2000, or the halving of these noteworthy individuals in the second 
generation, and we have practically the same rate on the second hypothesis. We 
thus see that on the numbers of this second Illustration, the average population 
will degenerate considerably faster, 25 per cent, faster approximately, but the 
dearth of noteworthy individuals will be slightly less. The reader must not, 
however, conclude from these numbers that our second Illustration represents 
a less undesirable type of degeneracy. Beside the dearth of the noteworthy, 
the multiplication of the extremely unfit has to be measured. Let us suppose 
that the individual whose character has the least value in the 1000 of the original 
population is by virtue of this deviation a non-useful member of the community — 
physically or mentally unfit. We must clearly then find out in the second 
generation to what number of the population this standard applies, i.e. we want 
(3-090O-1 - /HoJ/So. This is equal to 2-967 on the first and 2-958 on the second 
hypothesis, corresponding in both cases to 1 in 667 instead of 1 in 1000. On the 
other hand it will be found that in the first illustration the corresponding numbers 
are 3"107 and 3"125 on hypotheses (i) and (ii) respectively, giving practically 1 in 
1000, and the same standard of unfitness repeating itself in the second generation. 
Thus Illustration II, with a slightly reduced rate of decrease of noteworthy 
individuals, has an increased rate of unfit individuals, when compared with 
