488 Proceedings of the Royal Society of Edinburgh. [Sess. 
This gives 
if the hydrid be distinct ; 
r nn = 
771 + 3 
J{2(m 2 + 14m + 17)} 
“ v /(3*m + 2) 
if the dominant includes the hybrid ; 
reducing if 
m= 1 to r — 5, 
and 
r = ’333. 
24. Case II. — In like manner, if the parentage be such that hybrid is in 
excess or defect we have, if the population of selected parents be 
(a, a) + 2m, (a, b) + (b, b), 
and the population of non-selected parents 
p{(a, a) + 2, (a, b) + (b, b)}, 
1 
if the hybrid be distinct ; 
J2(m + 1) 
1 
s-0 ‘ ~~ 3(2m + 1) 
if the hybrid be included in dominant. 
The correlations in this case of the non-selected parents and offsprings 
are constant and identical with those where there is no selection, namely, 
r = ’5 and r'^333, for the correlation table for the non-selected parents 
when written out is as follows : — 
Non-Selected Parent. 
Offspring. 
(a, a). 
(a, b). 
(b, b) 
(a, a) . 
m + 1 
m + 1 
(a,b). . 
m+ 1 
2m + 2 
m + 1 
(b, b) 
m+ 1 
m+ 1 
and m + 1 being a factor throughout, the result is not affected. 
25. Case III. — If the recessive be in excess or defect we take again, 
the population of the selected parent, (a, a) -f 2, (a, b) + m (b, b), 
and „ „ non-selected parent, p{ (a, a) + 2, (a, b) + (b, b)}. 
From this the correlations, if the hybrid is distinct, are obviously the same 
as in Case I., but if the hybrid be included in dominant then we have — 
4m 
3(m + l)(m + 5) 
(m + 1)* 
