K. Pearson 
325 
I have said enough to show that Mr Bateson and I do not speak the same 
language. I must now pass to my second point : 
(ii) What is the sense in which Mr Bateson uses his terms? 
In order to answer this question I was forced to postpone my reply to 
Mr Bateson until I had read his Materials for the Study of Variation. But I fear 
I am not much wiser now that I have done so. Mr Bateson nowhere gives concise 
definitions, to which he consistently keeps in the course of his treatise. His whole 
thought seems in flux, and if the reader believes he has Mr Bateson's sense on 
one page, he will find that the context connotes something totally different on 
the next. 
Variation. I start first with Mr Bateson's definition of variation : " For though 
on the whole the offspring is like the parent or parents, its form is perhaps never 
identical with theirs, but generally differs from it perceptibly and sometimes 
materially. To this phenomenon, namely the occurrence of differences between 
the structure, the instincts or other elements which compose the mechanism of the 
offspring, and those which were proper to the parent, the name Variation has been 
given " {Materials, p. 3). 
Mr Bateson suggests that Specific Differentiation has resulted from this 
Variation. Later he tells us that : 
" To study Variation it must be seen at the moment of its beginning. For 
comparison we require the parent and the varying offspi'ing together" (p. 7). 
There is no doubt here as to Mr Bateson's meaning: variation is a study of 
the difference between two organisms which stand in the relation of parent and 
offspring, and to study it we require both these organisms for comparison. 
Now two points appear to flow from these statements : 
(i) Mr Bateson's conception of variation is not that of a measure of the 
deviations of a population from its mean. To the biometrician variation is a 
quantity determined by the class or group without reference to its ancestry. To 
Mr Bateson it is a measure of the deviation of the offspring from the parent. 
The biometric expression for such a measure might well be taken for any law 
of distribution, as the root mean square of such deviations, or : 
V (mi - ma)'^ + (cTi - ro-g)". 
In other words it would involve in^, m.,, the means of the parental and filial 
generations, their variabilities or standard deviations cti, ct.j, and the coefficient r 
of parental inheritance. This is a highly complex expression, and it is noteworthy 
that the data for determining it are not in one single case given by Mr Bateson. 
In the great mass of cases for which I have seen data — at least 60 and probably 
100 now — the population is either stable or approximately so, thus m^ = nu and 
cTi = o-o nearly. In other words, unless r=l, i.e. inheritance be complete, the 
offspring on the average differs by a finite quantity from the parent. This is true 
