416 
R. A. FISHER ON THE CORRELATION BETWEEN 
from it is, however, exactly one half of that obtained above, so that the contribution 
of a single factor to the parental product moment is J/ 3 2 . Hence the parental 
correlation is 
where r and <r retain their previous meanings. 
Moreover, from the fraternal table we may obtain a quadratic expression having 
for its typical terms 
1 +p) V. + ipy h*2 + P 2 ?( 1 + P)hi]2+PVv'i3 
i??(l +P + q + 2pq)jn +pqr(l + 2 p)j l2 j n + 2 pqrsj n j u , 
which, when simplified by removing one quarter of the square of the expression in 
(XII*) becomes 
+ 2p)*j* +/>V 1 i 12 + ip?(l +p + <i)h 2 2 %PVi , 2 ii3 , 
or, simply, 
I(a 2 + /? 2 ). 
Here, again, the introduction of multiple allelomorphism does not affect the 
simplicity of our results ; the correlation between the dominance deviations of 
siblings is still exactly 3-, and the fraternal correlation is diminished by dominance 
to exactly one half the extent suffered by the parental correlation. The dominance 
ratio plays the same part as it did before, although its interpretation is now more 
complex. The fraternal correlation may be written, as in Article 6, 
-L(t 2 -+Ae 2 ). 
15 . Homogamy and Multiple Allelomorphism . — The proportions of these different 
phases which are in equilibrium when mating is assortative must now be determined. 
As in Article 10, let Ii, I 2 , . . . be the mean deviations of the homozygous phases, 
and J12, J13, . . . those of the heterozygous phases. Let the frequency of the first 
homozygous phase be written asy> 2 (l +/u), and the others in the same way. Then, 
since p is the frequency of the first kind of gamete, 
Pfi i + zfofrfx3+ • = 0 , 
and 
P/12 + 9/22 + r M _ + ■ ■ • =°> 
and so on. 
Let 
pIi + g'J 12 + rJi 3 + . . . =L, 
pJ"i 2 L 9I2 4 * r J28 + • • • = M, 
and so on, then L, M, . . . represent the mean deviations of individuals giving rise 
to gametes of the different kinds ; hence, by Article 9 , 
2pq(l+f lz ) = 2pqev' LM , 
that is, 
/i2 = /V v - LM (XIV*) 
The association between the phases of two different factors requires for its repre- 
sentation the introduction of association coefficients for each possible pair of phases. 
Let the homozygous phases of one factor bo numbered arbitrarily from 1 to m, and 
