490 Proceedings of the Royal Society of Edinburgh. [Sess. 
difference in the correlation. Selection may raise or lower the correlation. 
In some cases there is a maximum and in others a minimum, these points 
being in general not far distant from the points of normal Mendelian distri- 
bution of the population. Selective mating is not, then, likely to interfere 
with the correlation coefficients to any appreciable extent except when the 
selection is stringent. 
28. There are a few other cases which demand attention, some of which 
will be referred to when the actual figures are discussed, while some others 
are added in this place. 
29. Case (A). — If both parents be equally selected and if the parentage 
is given being 
m (a, a) 2 (a, b) (b, b) 
m (a, a) 2 (a, b) (b, b), 
we have as the correlation of either parent and offspring, 
when the hybrid is distinct. 
_ i 
3m + 1 
2(m+l) 
Table of Values. 
m. 
r. 
m. 
r. 
0 
•353 
1-5 
•522 
•5 
•456 
2 
•577 
1*0 
•500 
00 
•612 
30. Case (B). — If the hybrid be present in normal numbers but the 
recessive present in defect and the dominant in corresponding excess. In 
other words, both parental populations consist of 
(1 +m) (a, a) 2 (a, b) (l-m)(b, b). 
This gives a correlation coefficient when the hybrid is distinct of 
\f 2 
2(4 - m 2 )’ 
m being always less than unity. 
\ 
Table 
OF 
Values. 
m. 
r. 
m. 
r. 
0 
•500 
•6 
•474 
•2 
•498 
•8 
•450 
•4 
•490 
31. Case (C). — Let the race be made up of such a population that a part 
only of the hybrid assumes dominant characters, that is, let it consist of 
parental populations of (1+m) (apparently dominant), (2— m) (hybrid), (1) 
(recessive), and let it mate indiscriminately. 
