Miscellanea 
423 
tentative divisions, either bisecting the hybrid or dividing it into such divisions that one-fourth 
resembles the recessive." He then applies the four-fold table method to these cases and finds the 
corresponding correlations are "44 and - 50 and concludes "again, Mendelian principles do not lead 
to low correlations but to figures approximately equal to those found by observation." But 
these "tentative divisions," by assuming continuity of distribution, throw over the whole 
Mendelian case. 
Later on Dr Brownlee deals with the cases of two and three pairs of zygotes, looking at the 
problem solely as one in continuous variation. For he states " it is evident that when two and 
three pairs of zygotes are condensed* we do not go straight back to the normal distribution. 
The reason of this is that the normal surface obtained when the elements are considered 
separately, represents something different from the surface which is condensed into the last 
tables." It is difficult to find the meaning of this paragraph, but at any rate it shows that 
Dr Brownlee has overlooked the fact that Mendelism was rediscovered by biologists who were 
seeking for a theory to explain discontinuous variation. 
Dr Brownlee devotes part of his paper to an investigation, on the Mendelian basis, into 
the effects of selection and of assortative mating. His confusion between continuous and discon- 
tinuous variation is evident in this part as elsewhere. As regards selection, he concluded that on 
a Mendelian mechanism it does not follow that the higher the parental selection the lower the 
correlation coefficients, the result which had been reached by Prof. Pearson by biometric methods. 
The question is an important one and can by no means be got over so simply as Dr Brownlee 
appears to have done, and we have attempted to investigate it elsewhere. We may state here, 
however, that our results do not agree with those of Dr Brownlee, and that we find that the 
assumption of Mendelian discontinuous variation leads to qualitative (and often quantitative) 
conclusions similar to those discovered by Prof. Pearson on the assumption of continuity of 
distribution. There is one point, however, in Dr Brownlee's work on this subject to which we 
may refer. In certain cases he obtains an approximate value of the correlation coefficient for 
three-by-three tables and by the product moment method when the regressions are not linear. 
We take, for example, the table from his p. 487, which we give below. 
Parent. 
(AA) 
(Aa) 
(aa) 
Totals 
(AA) 
a 
m+l 
m + 1 
2m + 2 
(Act) 
2 
mi + 3 
m + 1 
2m+ G 
(aa) 
2 
2 
4 
o 
Totals 
m+3 
2m + 6 
mi + 3 
4m + 12 
Proceeding by the ordinary product moment method the expression found for r is 
,_ mi + 3 
r_ x '2(™ 2 + 14m+17) ' 
If both regressions were linear this expression should be the square root of the product of 
those regressions. Now the regression of offspring on parent in the above table is linear, and 
equal to "5. But the regression of parent on offspring is not linear unless m=l. 
* This phrase is a typical example of Dr Brownlee's looseness of language. The definition of a 
zygote as "the cell formed by the fusion of a male with a female gamete " seems to render impossible 
the operation of condensing 'pairs of zygotes.' So far as we can ascertain, Dr Brownlee merely 
means that the character considered depends upon a number of Mendelian couplets, and not on a 
single one. 
