PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 293 
or, since oq and cr 4 are nearly, if not practically, equal, and oq and oq also, we have— 
regression from grandfather to grandson through the female line = r 23 r v Ji Y . 
This may be a very sensible quantity, if the correlation coefficients are of consider¬ 
able magnitude. What we have here, then, is the shipping of a generation , the 
inheritance of an especially male characteristic through the female line. The same 
reasoning would apply to the inheritance of an especially female characteristic through 
the male line. The formula, of course, gives no explanation of why oq is small and 
r 14 finite. It is only suggested that these outlying facts of heredity are not neces¬ 
sarily inconsistent with the formula. It may be argued that this account of skipping 
a generation would only apply to a characteristic which actually exists in both sexes, 
even if only in a small degree in one of them, and further, it assumes the distribution 
of this small degree to be of a normal character. This argument would certainly 
touch characteristics functionally necessary and peculiar to one sex; it may be 
doubted how far it would affect the question of secondary sexual characteristics, 
which may have rudimentary values in the sex of which they are not characteristic. It 
must further be remembered, however, that our correlation formulae are perfectly true 
for cross heredity, and accordingly the idea of rudimentary value may be pushed a 
good way, even to the idea of latency in a second closely-allied organ. The idea of 
latency here is not to be pressed into airy theory of panmixia or of germ plasm. 
Given that certain bulls get good milkers, we have the problem, what organ or 
characteristic, rudimentary or not, in bulls has the highest numerical coefficient 
of correlation with the milk-giving capacity of the cows they beget ? We may not be 
able to ascertain this organ or characteristic, but the problem is really a statistical 
one, and does not assert anything as to the mechanism of heredity. The skipping of 
a generation in secondary, or even in primary, sexual characteristics, does not seem 
accordingly to present anything of a character which our formula fails to cover. In 
particular, in the case of morbid inheritances, such as gout and colour-blindness, 
which, while peculiarly male diseases, are yet handed down through the female line, 
our formula seems to be of considerable suggestiveness. This suggestiveness 
essentially depends on the independence of the two factors—correlation and varia¬ 
tion—which are components of the formula. Thus, while there appears to be no 
necessary relation between power of transmitting and capacity for developing a 
disease, the independence of correlation and variation will probably allow us to 
• 
account for most special cases. The reader must be careful to note that we are not 
compelled to give r or <x meanings relating directly to the intensity of the disease; 
they may refer to the size of organs or intensity of characteristics on which the 
liability to the disease or its intensity directly or indirectly depends. Bearing this in 
mind, we have only to put r 13 finite, or vanishingly small, while both oq and oq 
are finite, to grasp (i.) how gout may be transmitted from grandfather through either 
son or daughter to grandson, and yet (ii.) how colour-blindness and haemophilia are 
transmitted, as a rule, through daughter only to grandson—in both cases the 
