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On the Fundamental Concej)tions of Biology 
(iv) Hence the fraternal correlation must be a function of the correlation 
between characters or organs of the gametes put forth by the same gonad. 
So far I do not see that any exception can be taken to the argument ; then, by 
the adoption of, I think, fairly legitimate limitations, it is shown mathematically 
that the average correlation between brothers for any character will be equal 
to the average correlation between the characters of gametes. To test this theory 
we must then endeavour to find out what is the quantitative relationship between 
the organs or characters of gametes. Now the production of gametes seems a 
process analogous to that of the production of any like organs by an individual, 
and the average value of the correlation of such organs ought to give us a value 
approximating to that of the average correlation between the scarcely measurable 
organs and characters of the gametes themselves. Such is the general tenor of 
my reasoning. What kind of like organs ought then to be dealt with in order to 
compare the results with those for the relationship between pairs of brothers ? 
Our data for brothers were drawn from types of life — man, horse, dog — in 
which there was no sensible class differentiation, tested by either biological or 
biometric methods*. Such differentiation where it exists must either be a result 
of environment, in particular of nurture, of period of production, or of differentiation 
in the gametes themselves. Its absence accordingly was the very sufficient reason 
for comparing the correlation of characters in the gametes with the correlation of 
undiferentiated like organs. Hence the source of my definition of homotypes as 
" undifferentiated like organs." It will be seen at once that the whole of Mr 
Bateson's argumentation is purely idle, and it is more than idle, it is, I venture to 
think, largely captious. Had I been comparing brothers of differentiated classes 
A and B, I should have tested whether for the characters I was dealing with 
differentiation did or did not exist — a test I again say we are perfectly able to 
make-f. I should then have correlated A with A, and B with B, and probably 
A with B, but not mixed pairs of A and B with pairs of A and A. This is 
precisely what we do with pairs of brothers and pairs of sisters, where there 
is a sexual differentiation. The possibility of dealing with pairs of A and B 
without introducing heterogeneity may surprise Mr Bateson, but I fear the 
mathematics of this must be passed over on the present occasion. 
Now Mr Bateson's charges were : 
(i) Differentiation between like organs is not distinguishable. 
My reply is that so far as it produces an effect comparable with the errors of 
random sampling it is distinguishable by well-known tests. 
* Stature and forearm, for example, have been frequently tested for heterogeneity. 
t Perhaps it may be as well to note that differentiation for the biometriciau denotes heterogeneity of 
mean and standard deviation for two or more parts of the population for the differentiated character, and 
this can be found by breaking up the population into classes. For Mr Bateson it seems as I have indi- 
cated to mean something quite different, but as he avoids in his paper definition I am unable to say 
what. No biometrician could use variation and differentiation as in any way synonymous. 
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