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372
Hereditary Genius
in the way of mathematicians, in framing a compact formula, based
on the theory of Pangenesis, to express the composition of organic
beings in terms of their inherited and individual peculiarities, and to
give us, after certain constants had been determined, the means of
foretelling
Derived unchanged
through Parents.
Modified through individual
variation.
The gemmules in any individual
Gr+
G (1-r)
The part Gr derived through the
parents is similarly composed of
two parts; namely
Gr2 +
Gr (1—r) =G(r—r2)
The part Gr2 derived through the
grandparents is composed of
Gr3+
Gr2(r—r2) =G (r2—r3)
&c.
&c.
&c.
That derived from the nth
ascending generation is
composed of
Gr
n+1
+
Gr (r
n-1
— r
n
) = G (r
n
—r
n+1
)
Hence G consists of Gr
n+1
unchanged gemmules derived from generations higher than
the nth + G multiplied into the sum of the following series, every term of which
expresses gemmules, modified by individual variation—1
1—r + [r—r2] + [r2—r3] + and + [r
n
—r
n+1
]=1—r
n+1
as r is a fraction less than 1 (it was 0.9 in the imaginary case discussed in my text, and
would generally be very small, but I have no conception what,— perhaps as small as
0.999., or some numbers still nearer unity), the value of r
n+1
will vanish if n be taken
sufficiently large, in which case the individual may be considered as wholly derived from
gemmules modified by individual variations posterior to the nth generation.
It must be understood that I am speaking of variations well within the limits of
stability of the race, and also that I am not speaking of cases where the individuals are
selected for some peculiarity, generation after generation. In this event a new element
must be allowed for, inasmuch as the average value of r cannot be constant. In
proportion as the deviation from the mean position of stability is increased, the
tendency of individual variation may reasonably be expected to lie more strongly
towards the mean position than away from it. The treatment of all this seems well
within the grasp of analysis, but we want a collection of facts, such as the breeders of
animals could well supply, to guide us for a few steps out of the region of pure
hypothesis.
The formula also shows how much of a man's nature is derived on the average from
any given ancestor; for if we call the father the 1st generation, the grandfather the 2d,
and so on, as a man has 2
n
parents in the nth generation, and as the formula shows that
1
Symbols enclosed in square brackets were originally over-lined. [Ed.]
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