PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 2 75 
Finally, it is impossible to more than hazard suggestions as to reproductive selec¬ 
tion in relation to mothers’ height. It will be noticed that both mothers of sons and 
mothers of daughters are taller than wives, and, further, daughters, while taller than 
wives, are not so tall as mothers of daughters. Hence, while the difference in height 
of daughters and wives might be due to natural selection or improved physical 
training, it might also be accounted for by greater reproductivity as to daughters in 
tall women, i.e. , mothers of daughters taller than wives, and this tallness being trans¬ 
mitted in a lesser extent to daughters. This would be a case of secular change due 
to reproductive selection. The statistics are, however, too few to make the differences 
in the mean heights of wives, daughters and mothers, very definitely significant. 
(iv.) Inheritance. —Mr. Galton has concluded from his data that the coefficient 
of regression is ’3333 from father to son or from son to father, and by the assumption 
of the “midparent” has practically given the mother an equal prepotency with the 
father in heredity. The fuller theory developed in this paper does not seem in entire 
agreement with these conclusions. In the first place, the theory of uni-parental 
inheritance shows us that it is not the constancy of variation in two successive gene¬ 
rations with which we have to deal, but the question whether sons have the same 
degree of variability as the “ fathers of sons,” and this must be definitely answered in 
the negative. Table II. shows us that there are undoubtedly significant differences in 
the coefficients of correlation, which may be summed up in the words 'prepotency in 
heredity of the father. It must be remembered that this is only for one characteristic, 
height, but in this characteristic both sons and daughters, on the average, take very 
considerably more after their father than after their mother. Turning to Table V., we 
see that the ratio of the mean heights of the two sexes, considered in three different 
classes, is practically the same, i.e., 1'08, or 13 to 12, as Mr. Galton has expressed it. 
Now, in Table III. we see that the coefficients of regression in paternal inheritance 
are not only sensibly greater than those of maternal inheritance, but, as these coeffi¬ 
cients have to be multiplied by the absolute deviations of father or mother from their 
means to obtain the absolute deviations of offspring, and as these absolute deviations 
will be in the ratio of 13 to 12, there is a considerable further reduction to be made 
in comparing the strength of maternal with that of paternal heredity. 
Thus it may be said that paternal heredity is to maternal heredity, in the case of sons, 
as *4456 to ‘3384 X xt or to ‘3124, and in the case of daughters, ’3096 X xf or ’3354 to 
'2932. Thus, while daughters inherit less from both their parents on the average than 
sons, both—and sons especially—take more after their father than their mother. The 
inferior inheritance of daughters may, to some extent, be counterbalanced by the law 
already noticed, that exceptional fathers have more often daughters than sons. 
We may illustrate this by two examples—the regression of grandson on grand¬ 
father, and of great-grandson on great-grandfather when the inheritance is respectively 
through the male and female lines. 
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