330 
On the Fundamental Conceptions of Biology 
Such discontinuity must exist if correlation be not perfect, it is a well recog- 
nised result of statistical theory. 
(6) A variation is ti'eated as a finite deviation in type between one generation 
and a second. 
Only a comparison of parental and filial populations can test the existence or 
non-existence of such discontinuity. Measurements of such populations have been 
over and over again published by biometrical workers on heredity. I believe 
Mr Bateson has not published a single such comparison in his book. 
(c) Discontinuity is attributed to distributions of frequency which are bi- 
modal or multi-modal. 
The distinction of true from apparent modes is a very delicate problem in the 
logic of chance. But it is exactly the statistical processes of the higher mathe- 
matics — which Mr Bateson tells us have gone wide of their mark, if that be the 
elucidation of evolution — by which alone we can hope to solve the problem which 
according to this definition of Mr Bateson's is involved in discontinuity, and 
according to the biometrician lies in the heterogeneity of frequency or the diffe- 
rentiation of the organ in question. 
Thus Mr Bateson has given us three definitions. Which of them is to be 
considered as fundamental or ^^rimary ? I do not know. Not one of them has been 
used in Ids own treatise to test whether tJie cases lie adduces are variations, or, if so 
discontinuous variations. Which of them am I to suppose he refers to when he 
criticises my memoir on Homotyposis ? I do not know, I can only try them all. 
Now Homotyposis has nothing whatever to do with a comparison of deviation 
between parent and offspring, nor has it anything whatever to do with the 
question of whether the type changes infinitesimally or finitely between successive 
generations. Hence the only possible definition that applies to homotyposis is 
that considered under (c) above. I charitably suppose Mr Bateson to refer to his 
definition of 1897, and not to those of 1894, although he has in the words cited on 
p. 328 above expressly told us that discontinuity of variation is not this, but 
something very diff'erent. 
If so, the whole poiiit between Mr Bateson and myself turns on whether or not 
it is possible in the bulk of cases to detect heterogeneity or not in a frequency 
distribution. I contend that the mathematical statistician is doing this every day, 
but I also contend that the validity of his processes cannot be judged by biological 
reasoning. Mr Bateson's only hope lies in a discussion of the logic of chance, he 
must criticise the mathematical bases of the theory of statistics. To assert without 
a knowledge of the mathematics of the problem that a frequency distribution 
cannot be resolved, is like a statement made by one ignorant of harmonic analysis 
that curves cannot be analysed by a Fourier's series. 
In short if Mr Bateson means by discontinuous variation, what I understand 
by heterogeneity of frequency, he can only question the adequacy of our tests by a 
