K. Pearson 
331 
complete study of the mathematical methods of modern biometry. The moment 
he does this he will have to recognise that his own treatise on variation contributes 
nothing whatever to the study of discontinuity. 
I have said enough, perhaps, to show that Mr Bateson and I do not use the 
same language, and to indicate how very difficult controversy must be when we 
have no common definitions. Yet many biologists will read Mr Bateson's paper 
who have neither the opportunity nor perhaps the inclination to study ray original 
memoir. In biology I have been told that a statement made by any individual 
biologist is considered true vintil some other biologist takes the trouble to contra- 
dict it. Then it is considered doubtful and one authority is weighed against a 
second. In case absence of contradiction should imply acceptance of statements 
as true, I wish to state once for all that for years I have not replied to English or 
German critics because the publication of further results obtained by biometric 
methods seemed the best answer to those who suppose silence synonymous with 
discomfiture. But if one is forced against one's will into controversy, let it be 
complete ; and so let me state once and for all that I consider Mr Bateson's peculiar 
theory of evolution by discontinuous variations untenable. It is, as he recog- 
nises, quite incompatible with much of my own work on evolution. I have not, 
however, spent my energies in criticising it, nor do I intend to do so on the 
present occasion. I doubt even whether I fully understand what he means by the 
term " discontinuous " ; I am far from certain that he himself is clear on the 
point — several definitions may be extracted from the Materials. But I do know 
that I have gone through hundreds of populations now, each involving several 
hundred up to a thousand individuals for a great variety of characters in both the 
animal and plant kingdoms, and I find, when really comprehensive populations 
are examined, so little of anything like this discontinuous variation in which 
Mr Bateson puts his faith*, that I doubt whether it has any statistical validity in 
that mass struggle for existence which occurs in nature. On the other hand, 
taking variation in its biometric sense for a continuous homogeneous distribution 
of frequency, I do find definite evidence of progressive change in races. I think 
we have now sufficient data, for example, to show that selection has taken and is 
taking place in man. If we take a long series of measurements of the skull in 
prehistoric and dynastic Egypt there can, from the measurements themselves, 
be no reasonable doubt that we are dealing with the same race, nor again in the 
case of Englishmen to-day and of Englishmen 250 years ago. But a change, a 
* Mr Bateson cites Dr F. Ludwig's interesting researches as showing "discontinuous variation " in 
plants, and spealts definitely of the "laws such distributions commonly obey." Here again we have 
evidence of the impossibility of testing the truth without adequate statistical theory. In many cases the 
multimodal character of Dr Ludwig's curves is simply due to the divergencies of random sampling, and 
without a theory of the probable errors of random sampling we may make "discontinuous variations " 
out of statistically insignificant differences ! In other cases there is undoubted heterogeneity, but whether 
Mr Bateson will consider it due to "discontinuous variation" when he sees its real cause is another 
matter. The clue to the mystery was given in a note to Part i. of Biometrika and is more fully 
developed in a series of papers in this Part. 
34—2 
