500 
Proceedings of the Royal Society of Edinburgh. [Sess. 
The first generation of parentage (A) mating freely gives offspring in 
the following proportions i— 
Parent. 
Offspring. 
(a, a). 
(a, b). 
(b, b). 
Totals. 
(a, a) . 
8 
8 
16 
(a, b) . 
10 
18 
12 
40 
(b, b) . 
10 
15 
25 
Totals . 
18, or 2 x 9 
36, or 4 x 9 
27, or 3 x 9 
81 
Which shows that the hybrid offspring are in number twice the geometric 
mean of the pure races as should be (par. 3). To obtain the next genera- 
tion with a like parentage an increase in the number of the pure races is 
required, so that the last table becomes : — 
Parents. 
Offspring. 
(a, a). 
(a, b). 
(b, b). 
(a, a) . 
1 
10 
10 
20 (2 x 10) 
(a, b) . 
10 
18 
12 
40 (4 x 10) 
(b, b) . 
12 
18 
30 (3 x 10) 
Let these mate freely and we have for the correlation table of grand- 
parents and grand -offspring the following distribution : — 
Grandparents. 
Grand- 
offspring. 
(a, a). 
(a, b). 
(b, b). 
Totals. 
(a, a) 
300 
380 
120 
800 
(a, b) . 
475 
895 
630 
2000{</(800xl250)} 
(b, b) . 
125 
525 
600 
1250 
Totals . 
900 
1800 
1350 
