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A. D. Darbishire. 
interesting one. Bateson has suggested that many cases, which in 
the early days after the rediscovery of Mendel’s papers, were inter¬ 
preted as instances of a 1 : 2 : 1 proportion, may in reality have 
been instances of a 3 : 9 : 4 proportion ; for it is obvious that if the 
numbers from w r hich the ratio is calculated are not very great, 
it will not be easy to determine whether a particular ratio is to be 
classed as 1:2:1 (or, as we may call it, 4 : 8 : 4 for the moment), or 
as 3 : 9 : 4 ; especially when it is remembered that many Mendelian 
investigators are, quite rightly in many cases, contented with a 
qualitative as opposed to a quantitative result. But now that it is 
known that this 9 : 3 : 4 or 3 : 9 : 4 proportion is sometimes 
attained, it becomes extremely important to determine whether the 
ratio in any given case is of the 1 : 2 : 1 or 3 : 9 : 4 type, because, of 
course, the causes underlying these two proportions are entirely 
different. And it becomes important, therefore, to breed one’s 
material on so large a scale that there can be no question to which 
of these two types the ratio obtained belongs. The determination 
of this point is not a question of individual arbitrary taste, but is 
based on a statistical formula which we shall come to consider 
later on. 
The suggestion that some ratios which were interpreted in the first 
place as instances of the 1:2:1 type might really be instances of 3 : 9 : 4, 
raises the question in one’s mind whether all cases of 1 : 2 : 1 may 
not be of the 3:9:4 type. This suggestion of course strikes at 
the root of Mendelian principles, and if an examination of the ratios 
obtained, by the statistical formula to be described, prove that the 
proportion 1 : 2:1 never occurs, the most elementary and funda¬ 
mental tenets of Mendelian doctrine will have to be given up. For 
instance it is obvious that no case of Mendelian inheritance can be 
explained on a hypothesis involving a single pair of characters ; and 
that all instances of the common Mendelian phenomena of dominance 
and segregation, in the 3 : 1 proportion, are to be explained by a 
hypothesis relating to two pairs of factors, one of which (as in the 
case of the seed-coats in Pisum ) demands the co-existence in the 
zygote of two factors for its manifestation. If some theory of this 
kind should, after experimental and statistical analysis, prove to fit 
the facts more closely than the one at present held, we should, I 
think, at least have a theory which helps to explain the phenomenon 
of dominance ; for it has long seemed to me, long in fact before the 
9:3:4 proportion was known, that dominance is merely a type 
of reversion. My idea has been somewhat as follows :—When two 
