PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 307 
that in some manner repeated selection causes a progression of the “ focus of regres¬ 
sion,” by which term I would understand the mean of the general population from 
which selection has originally taken place. I have been very careful so far not to 
hazard any statement with regard to this focus of regression. I have measured only 
the amount by which the offspring of exceptional parents diverge, not from the mean 
of the parental population but from the mean of the offspring population. In this 
manner our formulas allowed for the play of secular natural selection. It is quite true 
that the word “ regression ” thus loses its accustomary meaning, which it can only 
bear if the population be stable and the means of two generations sensibly identical; 
this is the case for which, I think, the word was introduced by Mr. Galton. # The 
sense given to it in the present paper is accordingly a technical one; as already 
defined, it is the ratio of the mean deviation of the offspring of a selected parentage 
to the deviation in the parent which characterises the selection, the deviations in 
offspring and parents being respectively measured from the means of the corre¬ 
sponding general populations. Now here, at the very outset of our consideration of 
panmixia arises a very real difficulty, which is vital for the whole theory of evolution 
by natural selection. According to Mr. Galton the population being stable, or no 
secular natural selection or reproductive selection taking place, there is a regression 
of the offspring of selected parents towards the mean of a certain general population, 
and the “grandchildren” also regress to the same mean. We shall see then that 
unless correlation is perfect [r — = 1 j no amount of continued selection would suffice 
to prevent a race from regressing to an original general population when that selection 
was suspended. Panmixia in the sense of its most ardent supporters would be demon¬ 
strated. But the difficulty is not the establishment of panmixia, but as to what is to be 
considered the “ original general population.” On the theory of evolution by natural 
selection that general population has itself been produced by a series of selections, and 
selections probably affecting its mean as well as its standard-deviation, hence how is it 
possible to pick out any particular stage of general population as the “ focus of regres¬ 
sion,” and assert that regression of the offspring of parents now selected takes place 
towards that stage of evolution ? Where is the focus of regression to be placed for the 
profile angle of man ? About 80 ° to 90 ° or nearer the 40 ° to 70 ° of the anthropoid apes? 
The further back the better for those who believe that suspension and reversal of natural 
selection are identical, but no manipulating whatever of the human mortality tables 
would allow for a “ focus of regression ” very considerably below that of the current 
general population. Hence it would seem essential that successive selections must 
connote some progression of the focus of regression. This progression may be con¬ 
tinuous with continuous natural selection, or it may take place by starts and leaps, as 
* We can at once restore the trne notion of regression, as Mr. Galton points out to me, by measuring 
each organ or characteristic in terms of its own standard deviation. It will then be a coefficient of 
correlation and a proper fraction. 
2 R 2 
