1909-10.] The Significance of the Correlation Coefficient, etc. 481 
When the hybrid is distinct from the dominant the value of the correla- 
tion coefficient depends only on the value of m, n, or r, though in the case 
when the hybrid is not distinct the value of p exercises an influence on 
the result. In a typical simple Mendelian distribution of the population 
m-\-n will be equal to 2 r and p to r. Those values, however, do not give 
an immediately stable population, the standard deviation of the offspring 
being higher than that of the parents. This population, however, quickly 
tends to stability. On the other hand, if the population is immediately 
stable it is easily seen that p must be equal to n, for the first generation 
gives a parentage and offspring as below : — 
Parent. 
Offspring. 
(a, a). 
(a, b). 
(b, b). 
Totals. 
(a, a) . 
m + r 
r+p 
m + 2r+p 
(a, b) . 
r + n 
2 (r+p) 
r + n 
4r + 2p + 2 n 
(b, b) . 
(r+p) 
m + r 
m + 2r+p f 
Totals . 
m + 2r + n 
4 (r+p) 
m + 2r + n 
2m + 2n + 8r + 4p 
and as the total is the same whether the addition is made by columns or 
by rows, the sum of each row must be equal to the sum of the corresponding 
column if the standard deviation remains the same. 
Or, 
m + 2r + p = m + 2r + n, 
which requires that n shall be equal to p. 
13. In the first place, the varieties of the correlation coefficients when 
m + n — 2p will be considered. In this case, changing the letters for 
convenience, the initial correlation table between husband and wife may 
be taken to be : — 
Husbands. 
Wives. 
(a, a). 
(a, b). 
(b, b). 
I 
Totals. 
(a, a) . 1 
n-a 
n 
a 
2 n 
(a, b) . 
n 
2 n 
n 
4 n 
(b, b) . 
a 
n 
n-a 
2 n 
Totals . 
2 n 
4 n 
2 n 
8 n 
