K. Pearson 
323 
all the organs A of a certain size or value have associated with them an array 
of 5-organs having a definite mean value, then this mean value changes with the 
change of A. The distribution of the means of 5-arrays for given values of J., 
whether expressed by curve or table, is in its most general sense the phenomenon 
which Mr Galton has termed regression. Thus there is regi'ession which may be 
determined between the number of court and plain cards in a hand at whist, 
between the head-lengths of two brothers, and between a measurement on the 
imago and another on its pupal case. Regression in its essence has no special 
relation to vital phenomena, nor to any hypothesis of parental foci and stable 
population. It is a fundamental conception of the theory of statistics*. 
It will bo clear to the reader that Mr Bateson does not use these terms in the 
biometric sense, possibly because he has not the preliminary biometric training. 
He is, of course, perfectly free to use them in his own sense, except on an occasion 
when lie is attacking a biometric memoir. In replying to Mr Bateson, if I use the 
words referred to in the biometric sense, then we have absolutely no common 
ground. On the other hand it is somewhat unusual in a discussion to give 
entirely different meanings to the terms originally used, and leave your adversary 
to find out with what significance you may be using them. Indeed Mr Bateson 
seems to rejoice in the idea that all definition is impossible. The kernel of his 
argument is that variation cannot be distinguished from differentiation ; possibly 
for this reason he avoids defining either term. He tells us that my memoir fails 
because this distinction cannot be made (p. 197, etc.). It is not a little curious to 
find Mr Bateson later admitting in a supplementary note that " these two classes 
of variation can broadly be recognised and treated as distinct " (p. 204), the two 
classes being apparently what he terms " Differentiant " and " Normal " types of 
diversity. But this I suppose was necessary in order to save his own theory that 
evolution takes place solely by the former kind of diversity, — i.e. the one which 
Mr Bateson asserts I cannot discriminate. He tells us that : " The attempts to 
treat or study them " (the context suggests his differentiant and normal variations) 
" as similar is leading to utter confusion in the study of evolution " (p. 204). But 
if we cannot distinguish them, how are we to study them by different methods ? 
Either they are distinguishable, in which case his criticism of my memoir is idle, 
or they are not distinguishable, in which case his theory of evolution by 
"differentiant variation" is also idle-f. Man soil das Kind nicht mit dem Bade 
verschutten ! 
But it is not only such terms as variation, correlation, and differentiation which 
Mr Bateson uses in a totally diverse sense from that used by me in my paper. In 
these cases, indeed, he departs from the current biometric senses, and we must 
search his own writings if we are to attach any meaning to them. But Mr Bateson 
takes away even my own definition from a word coined by myself I have 
* Half the obscurity consequent on its use by uon-statistically trained biologists would possibly have 
been avoided had it been called "progression"! 
t It is idle to attribute evolution to a factor you cannot distinguish from non-effective factors ! 
33—2 
