1909-10.] The Significance of the Correlation Coefficient, etc. 487 
These are equal if m-j-3 = 4p ; but p may be neglected as occurring in every 
term and therefore not affecting the result. 
The correlation table for the selected parents and offspring, if mating 
be random, is then the following: : — 
o 
Selected Parents. 
Offspring. 
(a, a). 
1 (a, b). 
(b, b). 
Totals. 
(a, a) . 
m 
1 
m + 1 
(a, b) . 
m 
2 
1 
m + 3 
(b, b) . 
1 
1 
2 
Totals . 
2m 
4 
2 
2m + 6 
This gives 
if the hybrid be distinct, or to 
' 6 m + 2 
m 2 4-1 4 m +17 
m + 1 
2(m + 2) 
if the dominant include the hybrid ; 
reducing: if 
m =1 to r = *5, 
and to 
r' = -333, 
respectively, as before seen to be the case. 
The correlation table for the non-selected parent and the offspring is : — 
Non-Selected Parent. 
Offspring. 
(a, a). 
(a, b). 
(b, b). 
Totals. 
(a, a) . 
m+1 
m + 1 
2m + 2 
(a, b) . 
2 
m + 3 
m+1 
2m + 6 
(b, b) . 
2 
2 
4 
Totals . 
m + 3 
2m + 4 
m + 3 
4m + 12 
* r s . 0 . signifies the correlation of the selected parent and offspring. 
r n-0 . „ „ „ non-selected parent and offspring. 
vol. xxx. 32 
