246 
On Theories of Association 
D 
1+2 
o 
4 
5 + 6 
7+8 
Totals 
1+2 
494 
275 
88 
42 
32 
931 
275 
308 
142 
86 
90 
901 
4 
88 
142 
81 
56 
76 
443 
5 + 6 
42 
86 
56 
44 
69 
297 
7+8 
32 
90 
76 
69 
161 
428 
Totals 
931 
901 
443 
297 
428 
3000 
We have the scheme : 
B-D 
1 + 2 
O 
4 
5+6 
7 + 8 
1+2 
+ 2 
- 51 
-25 
+ 26 
+ 48 
3 
-51 
+ 110 
-45 
-30 
+ 16 
4 
-25 
- 45 
+ 87 
- 9 
- 8 
5+6 
+ 26 
- 30 
- 9 
+ 26 
-13 
7 + 8 
+ 48 
+ 16 
- 8 
-13 
-43 
Here 225 individuals must be transferred to the diagonal to get from D to B, 
i.e. there is an increase to this extent of the correlation, but 223 have got to be 
transferred outwards to the ends of the other diagonal, although not in such a 
concentrated fashion. There can be small doubt, we think, that the correlation of 
B is nearly, if not slightly greater than, that of D. B is the correlation table for 
Brothers, A, G and D have correlations respectively of "28, "45 and '50. We feel 
confident in asserting that the unknown correlation of B is far nearer to that -of 
G or D, than of A, which Mr Yule gives as its limit ! Nor can the reader who 
examines these tables fail to obtain true insight into the peculiar nature of the 
con-elation of B. It is clear that B fails of normality because there is an excess of 
dark brothers having brothers with blue eyes. The excess is greater than in the 
case of father and son and this is actually what we should expect, if the excess be 
due to the inclusion in the record of infants. For an infant will be reckoned 
once as a son, but if he is one of n brothers, he will appear n(n — 1) times. If 
our surmise be correct there may be no failure at all of approximately Gaussian 
frequency in these eye-colour tables, but anomalous lumps in the second and 
fourth quadrants due to this unconscious inclusion of infants. If these lumps, 
which the inclusion of a dozen to twenty infants would suffice to produce, be 
removed, we should expect the correlation to rise as in the Huxley Lecture to 
about '60. What the final value would be after the correction for the more 
gradual changes in eye-colour, which occur after infancy*, remains to be deter- 
mined ; we may be quite certain, however, that it is likely to be 80 to 100 °/ Q 
above Mr Yule's maximum of - 28. 
* The influence of age on parental and fraternal tables of eye-colour will be shortly considered 
de novo. 
