# Bauhaus-Universität Weimar

### Volltext Natural inheritance

Titel:
Natural inheritance
Person:
Galton, Francis
PURL:
https://digitalesammlungen.uni-weimar.de/viewer/image/lit26699/254/
```APPENDIX F.
247
step, and an additional 109 names in the second step, there are only
27 disappearances in the fifth step, and only six disappearances in the
tenth step.
If the curves of surnames and of population were drawn from this
case, the former would resemble the corresponding curve in the case
last mentioned, while the latter would be a curve whose distance
from the axis of x increased indefinitely, inasmuch as the expression
3<3+ 4i4+5f5
is greater than one.
Whenever fx (x) can be represented by a binomial, as above sug¬
gested, we get the equation
-”*-(ïî6T*{ }*
whence it follows that as r increases indefinitely the value of rm0 ap¬
proaches indefinitely to the value y where
that is where y = 1.
All the surnames, therefore, tend to extinction in an indefinite
time, and this result might have been anticipated generally, for a sur¬
name once lost can never be recovered, and there is an additional
chance of loss in every successive generation. This result must not
be confounded with that of the extinction of the male population ; for
in every binomial case where q is greater than 2, we have tx + 212 + etc.
+qtq> 1, and, therefore an indefinite increase of male population.
The true interpretation is that each of the quantities, rmv rm2,
etc., tends to become zero, as r is indefinitely increased, but that it
does not follow that the product of each by the infinitely large num¬
ber N is also zero.
As, therefore, time proceeds indefinitely, the number of surnames
extinguished becomes a number of the same order of magnitude as the
total number at first starting in N, while the number of surnames
represented by one, two, three, etc., representatives is some infinitely
smaller but finite number. When the finite numbers are multiplied
by the corresponding number of representatives, sometimes infinite in
number, and the products added together, the sum will generally ex¬
ceed the original number N. In point of fact, just as in the cases
calculated above to five generations, we had a continual, and indeed
```

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