244 
On Theories of Association 
can be no doubt that tbe correlation of B is very much greater than the correlation 
of A. To convert G into A the changes are given by the scheme : 
B-C 
1+2 
3 
4 
5 + 6 
7 + 8 
1+2 
+ 1 
-14 
+ 3 
- 1 
+ 11 
O 
-17 
+ 39 
- 13 
- 6 
- 3 
4 
- 9 
+ 24 
- 1 
- 9 
5 + 6 
+ 9 
- 16 
- (i 
+ 13 
0 
7 + 8 
+ 10 
- 4 
- 8 
- 5 
+ 1 
Here again the candid reader will, we believe, admit that B has more correla- 
tion than C. The general difference is again a transfer to the diagonal cells of 
frequency to the right and left of this diagonal, the total number so transferred is 
78 ; but the transfer is rendered more complex by the appearance of 36 units in 
the cells in the top right-hand and bottom left-hand corners. This transfer is 
only half the size of the other towards the diagonal, and it probably measures 
the frequency of senile blues in the parents and of infantile blues in the offspring. 
We hold that we must still credit B with more correlation than C, although this 
secondary movement can now be well recognised. B is the contingency table for 
Father and Son's eye-colour (see p. 186). A is a table for a Gaussian surface with 
•3 correlation, G is a similar table for a Gaussian surface with "5 correlation, both 
beiug adjusted to give frequencies to unit places only with the same marginal 
totals as the Father and Son eye-colour table. These comparisons suffice to 
indicate that the correlation of Father and Son is far greater than "30 and is 
probably slightly greater than - 50. 
Precisely similar treatment of the Brother-Brother eye-colour table leads to 
like conclusions, as the reader may judge from what follows. 
Consider the three tables : 
J 
1+2 
g 
4 
5 + 6 
7 + 8 
Totals 
1+2 
398 
283 
113 
66 
71 
931 
0 
283 
281 
135 
87 
115 
901 
4 
113 
135 
72 
50 
73 
443 
5 + 6 
66 
87 
50 
36 
58 
297 
7 + 8 
71 
115 
73 
58 
111 
428 
Totals 
931 
901 
443 
297 
428 
3000 
B 
1+2 
3 
4 
5 + 6 
7+8 
Totals 
1+2 
496 
224 
63 
68 
80 
931 
224 
418 
97 
56 
106 
901 
4 
63 
97 
168 
47 
68 
443 
5 + 6 
68 
56 
47 
70 
56 
297 
7 + 8 
80 
106 
68 
56 
118 
428 
Totals 
931 
901 
443 
297 
428 
3000 
