344 
On the Fundamental Conceptions of Biology 
My conclusion was that the homotypic factor and the fraternal correlation had 
both values lying between "4 and o. If I incline more definitely to the higher 
limit to-day, it is because we have far more and better data available for both 
heredity and homotyposis than we had when my memoir was written in August 
1900. 
My sole reason in anticipating unpublished results here is to emphasise how 
very unadvisable such a statement as that made by Mr Bateson is, if he has not 
data of his own upon which he can base such an opinion as that : there is no 
clustering of hereditary or homotypic constants. Without a strong opinion that 
such is the case I presume he would not have felt bound to remark on the 
" suspicious circumstance." It is exactly the same rapid jumping to conclusions 
which I also note when Mr Bateson says that I restrict myself to undifferentiated 
like parts and miss the point that relationship is not lost when we pass to diffe- 
rentiated parts. If Mr Bateson had studied my paper he would have found 
fundamental theorems in cross-homotyposis fully considered, and possibly had he 
studied my other memoirs previously published he would have found more than 
one theorem in cross-heredity, and have known that we had worked out whole 
series of correlations between differentiated parts in related organisms. 
In conclusion then I must state that Mr Bateson much confirms my belief in 
biometry. He tells us that neither differentiation between like organs nor between 
brothers can be biologically detected. I believe it can be detected, where it has 
any sensible influence, by biometric methods. He tells us further that evolution 
takes place by " specific," " differentiant " or " discontinuous " variation, not by 
normal variation, so that the statistical work of my co-workers and myself " has 
gone wide of its mark if that mark is the elucidation of Evolution " (p. 203). There 
is only one conclusion to this argument, namely, that as long as Mr Bateson refuses 
to apply mathematics to biology, he will not be able to discriminate this mysterious* 
" differentiant " variation from normal variation, and he too will not be able to 
elucidate Evolution. Personally I do not despair, for I see great progress in the 
last eight years, and it is chiefly marked by a tendency to define, so that we can be 
quantitatively exact and so drop nomina quae carent rebus. 
Twenty years hence our successors, working by improved methods and with 
better training, will no doubt reach fitter definitions and more exact values for 
vital coefficients. But of one thing I am sure: Biometric methods will not then 
have to justify themselves to a non-mathematical biological world; mathematical 
knowledge will soon be as much a part of the biologist's equipment as to-day of 
the physicist's. Its function will not be to replace observation by symbols — all the 
biometric workers that I know even to-day are striving to keep in touch with 
nature — but to interpret observation in certain fields of biological enquiry, especi- 
ally in that of Evolution, where without mathematics further progress has become 
impossible ; impossible, for the very simple reason that we have to deal with the 
vital statistics of large populations, where no tabulation of individual instances 
can possibly lead to definite conclusions. 
* "Subtle and evasive quality of differentiation " is Mr Bateson's term. 
