218 On Theories of Association 
and therefore clearly not selected to obtain favourable or unfavourable results. 
These frequencies are 
1 
2 
3 
4 
5 
6 
7 
8 
Totals 
Father... 
36 
322 
264 
180 
5 
64 
101 
28 
1000 
Sou ... 
34 
301 
284 
137 
5 
100 
98 
41 
1000 
The reader should remember that the eye-colour groups are as follows : 
1 = light blue, 5 = light brown, 
2 = blue, dark blue, 6 = brown, 
3 = blue-green, hazel, 7 = dark brown, 
4 = dark grey, hazel, 8 = very dark brown, black. 
Group 5 has been usually clubbed with group 6 because in 5 only five fathers 
and five sons occur. 
The following table gives the class-index correlations for various groupings : 
TABLE XI. 
Table of Glass-Index Correlations *. 
Order of 
Divisions 
Class Correction 
Class Correction 
Corrective Divid- 
Table 
Fathers 
Sons 
ing Factor 
1st 7x7 
1 
: 2 + 3 : 4 
.5:6 
7 :8 
•9010 
•9011 
•8118,9110 
2nd 7x7 
1 
2:3:4 
5 + 6 
7 : 8 
•9624 
•9645 
•9282,3480 
1st 6x6 
1 
2 + 3 : 4 
• 5 + 6 
7 : 8 
•9009 
•9010 
•8117,1090 
2nd 6x6 
1 
: 2 : 3 : 4 
: 5 + 6 
7 + 8 
•9542 
•9553 
•9115,4726 
1st 5x5 
1 
: 2+3+4 
5 + 6 
7 :8 
•8070 
•8352 
•6740,0640 
2nd 5 x 5 
1+2:3:4 
5 + 6 
7+8 
•9259 
•9296 
•8607,1664 
1st 4x4 
1 
2 + 3 + 4 
5 + 6 
7+8 
•7971 
•8246 
•6572,8866 
2nd 4x4 
1+2 : 3+4 
5 + 6 
7 + 8 
•9054 
•9144 
•8278,9776 
3rd 4x4 
1+2:3:4 
5+6+7+8 
•9156 
•9130 
•8359,4280 
1st 3x3 
1+2+3 : 4 
5+6+7+8 
•8253 
•8191 
•6760,0323 
2nd 3x3 
1+2 : 3+4 
5+6+7+8 
•8949 
•8975 
•8031,7275 
3rd 3 x 3 
1 
. 2+3+4+5+6+7 : 8 
•5669 
•5968 
•3383,2592 
The reader should note that while the corrective dividing factor on the whole 
gets smaller and smaller as the classes get fewer and fewer, yet it is not possible 
to assert a priori that more classes will have a higher factor than fewer classes, 
e.g. our 1st 7x7 table has a lower corrective factor than our 3rd 4x4 table, and 
our 2nd 3x3 table a higher factor than our 1st 5x5 table. This point is 
important in reference to a criticism we shall make later of Mr Yule's statistical 
methods. 
* The justification for obtaining the class-index correlation by determining the mean by the 
Gaussian hypothesis is given later in this paper ; see also Biometrika, Vol. ix. pp. 127, 139, etc. 
