W. F. E. Weldon 
369 
A clear proof that Professor Pearson's view of the facts of regression is wrong, 
although it is in accord both with the theory of chance and with the results of the 
numerous statistical studies of inheritance which he and his pupils have made 
during the past seven years, is absolutely essential, if the view held by Professor 
de Vries is to be maintained. No proof whatever is offered throughout the 
Mutationstheorie. The only observations which bear upon the point, and are 
sufficiently extensive to serve as serious evidence, are the observations on maize. 
In 1886 Professor de Vries had a race of maize plants in which the mean number 
of rows of seeds per head was 12 to 14. By a process of selection, sowing in the 
first year seed from a head with 16 rows, and in later years seeds from plants with 
a greater number of rows, he succeeded by 18.94 in producing a race in which the 
mean number of rows per head was 20 — a number which rarely occurred, and was 
practically never surpassed, in the original race. The means of the successive 
generations are given graphically on p. 53 of his work; but I find it difficult to 
reconcile the diagram with the statements on p. 88 ; it is therefore impossible 
to discuss these results in detail, but certainly neither the diagram, nor the 
statement on p. 54 that the line on the diagram which shows the mean character 
of each race "nahert sich im Laufe der Jahre derjenigen der Aussaatkolben immer 
mehr," is consistent with the view that the ratio between the deviation of the 
parents of any generation from the original race-mean, and the deviation of their 
offspring from the same original race-mean, is even approxitnately constant. 
A further proof that regression to the original race-mean does not occur is 
given by the subsequent history of this maize. In 1897 an attempt was made to 
reverse the process of selection, and for this purpose individuals were chosen out of 
the generation of that year which had only 16 rows of seeds per head, the mean 
of the generation being 20. Now 16 is a greater number than the mean number 
of rows in the original race; and if regression to the original race-mean occurred, 
the number of rows of seeds per head among the offspring of individuals with 
16 rows should have been at all events less than 16. As a matter of fact it was 
20 ! Not only so, but the individuals with the smallest number of rows per head 
were taken out of this generation, and their offspring had on an average 18 rows 
per head. From these again the individuals with the smallest number of rows of 
seeds were chosen as parents, and the mean number of rows in the third generation 
was 14 — 16. 
So that this experiment, taken as a whole, forms a fairly conclusive proof that 
the statements concerning the focus of regression on which the whole theory of 
the instability of varieties depends, are erroneous, and a main part of the argument 
fails. 
In supposing that his view of i-egression is identical with that of Mr Galton, 
Professor de Vries seems to overlook a fundamental difference between the two. 
When Mr Galton says that parents which exhibit a known deviation D in any 
character produce offspring whose mean deviation is JD, he is careful to explain 
that the parents spoken of are the whole series of parents of their generation 
Biometrika i 39 
