422 
Miscellanea 
this Mendelian ' regression ' is linear, and can be written in the form r<j v \tr x . If, in the same 
way, the other 'regression' is linear, it can be written in the form ra- x /cr,j. Hence r can be 
obtained. 
In the case of somatic characters, the individuals with 1 and 2 protogenic elements are con- 
sidered to be somatically the same. Thus we have individuals with 0 protogenic elements, 
and others with a definite number, say, m. The correlation table (two rows and two columns) 
formed for this case will refer to individuals some concentrated at a point representing 0 proto- 
genic elements, and others concentrated at a point representing m protogenic elements. The 
correct method to apply in this case is that of (iii). As before, a value of C 2 can be found, to give 
a measure of relationship, but this will not be the true coefficient of correlation. The two obser- 
vations in each column have a mean, and these means can be joined by a line which may be 
called a ' regression : line. But this is less comparable to the actual regression lines found in 
practice for continuous distributions than in the case of gametic correlations, and it is doubtful 
if a correlation determined from it is of the same significance as one ascertained from a table 
with many rows and columns. But whether the comparison be legitimate or not, no other 
method of ascertaining correlation for a two-by-two table in which the observations are concen- 
trated at points seems to be as sound as that indicated in (iii). 
Dr Brownlee in his paper applies all methods to all cases indiscriminately and reaches very 
divergent results. In a particular case (p. 477) in which the product moment method gave 
r='33, the four-fold table method gave '53, and the mean square contingency (C 2 ) "37, the first 
and third of these not greatly differing. Dr Brownlee believed that " in a Mendelian instance 
such as this, the four-fold table seems specially applicable," but we can imagine no single case in 
which that method (assuming as it does a particular form of continuous distribution) is less 
applicable. The fact that its nse leads to a value more in accordance with results found for 
continuous characters could surely be used as an argument against the use of the hypothesis 
of the ' unit-character,' but this hypothesis is the essential foundation of Mendelism. In any 
problem on the determination of correlation it is very necessary to understand clearly the nature 
of the variation dealt with. When Dr Brownlee applies all methods to a single case, he is 
assuming that the distributions are at the same time both continuous and discontinuous, and we 
can get little information of value from his results. 
We need not point out in detail the many cases in which Dr Brownlee uses methods which 
strike at the very root of Mendelism, and which would be rejected with scorn, if they were 
understood, by the supporters of Mendelian principles. He has throughout stated the method by 
which he has obtained his many results, so that these results can easily be assessed at their true 
value. 
We may, however, point to one or two other instances of the looseness of thought which 
permeates the paper. On p. 476 Dr Brownlee uses the gametic distribution 2 ( A A ) + 4 (Aa) + 2 (aa). 
He then clubs together the (AA) and (Aa) groups and obtains 6 (A) + 2 (not A), and states "in 
this last case, however, the distribution is markedly skew." He then proceeds to use the four- 
fold table method, which should never be used if there is a suspicion that the distribution is 
more than slightly skew. But, in fact, Dr Brownlee knows nothing whatever about the 
distribution. Assuming that he was dealing with continuous variation, all he has done is to 
divide a frequency curve which may or may not be symmetrical into two parts, and this process 
of division does not in the slightest alter the distribution. If the one distribution be symmetri- 
cal, the other is also. Even such extreme numbers as 99(^1) to 1 (not A) may well represent 
a symmetrical distribution ; the actual numbers depend solely upon the point at which the 
division is made. 
Further evidence that Dr Brownlee appears to consider Mendelian distributions as perfectly 
continuous is given in his § 8, in which he states "if for the moment the distinguishing 
character of the hybrid and the dominant be assumed somewhat indefinite, we can make several 
