240 
On Theories of Association 
correlation of ^ as representing the heredity of eye-colour in man. And here it 
may be well to point out a very distinct difference between the problem which 
Pearson set himself and the problem for which the Mendelians profess to provide 
a solution — both speak of the heredity of eye-colour — but in no sense deal with 
the same problem*. The Mendelian says: " I treat the heredity of the character, 
presence or absence of anterior pigment." The correlation in this case should 
be ^. This problem, however, is not that of the heredity of the various grades of 
pigment in the iris. There is very little doubt that grade of pigment is a perfectly 
continuous variate. The pigment of the iris is not solely confined to anterior and 
posterior faces, and quite different grades of pigment can occur in both these 
Diagram VII. Eegression of eye-colour of brothers, the grade intervals being supposed equal. 
Inset, the same, colours 4 to 8 only, to illustrate the reduction in the regression — which 
is here the correlation — produced on the pseudo-rank hypothesis. 
5+6 
5+6 
1 2 
(Light) 
5+6 
First Brother. 
7 8 
(Dark) 
situations, until you get in the albinotic eye almost a complete absence of pigment. 
The accompanying diagrams, which have been drawn by two different methods, 
show how the heredity of eye pigment holds as well inside the blue-grey group as 
inside the hazel-brown group. They have been obtained in two ways, (i) by the 
use of the Gaussian to obtain the means of the arrays, and the relative ranges of 
* Even in the treatment of this problem we have only the papers of Hurst and Davenport which 
have been assumed to confirm each other. As a matter of fact on Hurst's postulates as to the methods 
of observation, Davenport ought to have reached results discordant with Mendelism instead of con- 
firmatory ! For the nature of these authors' work on similar problems, see p. 209 above and Biometrika, 
Vol. vii. p. 403 and Vol. vm. pp. 269, 271, 272. 
