486 
Proceedings of the Royal Society of Edinburgh. [Sess. 
Table of Values of the Correlation of Parent and Offspring for Different 
Values of — by Fourfold Table Method. 
m 
Values of 
a. 
Assortive 
Mating. 
Parent-Offspring 
Correlation. 
•500 
•454 
•666 
•667 
•287 
•621 
•750 
•593 
1-000 
•boo 
*539 
1-5 
-•315 
•454 
2 
-•525 
•397 
20. The values of the grandparental coefficients can likewise be 
evaluated, but the labour is somewhat greater than in the previous sections, 
and does not seem to promise any results beyond what can be surmised 
from the previous argument. In this case a moderate degree of assortive 
mating in the parents has apparently little effect on the correlation 
coefficients. 
21. In general it is to be noted that a large variety of different values 
of the correlation coefficients arises on different hypotheses, and also that 
the correlation of parent and offspring differs greatly according to the kind 
of assortive mating of the parents, so that the value of the coefficient of 
assortive mating gives very little guide to the value of correlation between 
parent and offspring. It is also to be noted that the successive heredity 
correlation coefficients are not in an exact geometrical progression. 
Effect of Parental Selection on the Correlation Coefficient. 
22. The effect of parental selection has been investigated by Professor 
Pearson on the basis of the normal curve of error. On this basis it is shown 
that the higher the parental selection the lower the correlation coefficients. 
This, however, does not seem to follow on a Mendelian mechanism. Three 
cases occur on this basis which require to be considered separately: (1) 
Where the dominant is present in excess or defect ; (2) where the hybrid 
is present in excess or defect ; (3) where the recessive is present in excess 
or defect. These are very easily evaluated. 
The correlation tables here, however, are different from those which go 
before. Regression is not linear, so that the product method does not give 
an exact but only an approximate value of the correlation coefficient. 
23. Case I. — Let m (a, a) + 2 (a, b) + (b, b) be the population of the 
selected parent and p {(a, a) + 2 (a, b) + (b, b)} of the non-selected parent. 
