418 
R. A. FISHER ON THE CORRELATION BETWEEN 
Let 
L = Z + AL, 
then 
L= — — 
1 - A 
and 
A=S(2/»TL' + 2 ff WM' + 
therefore 
A(l-A) = ^2(2pT 2 + 2<?V2+ . . 
therefore 
A(1-A) = £t* 
■ ■ ■), 
•) 
(XXII*) 
so that the association constant, A, appearing now in the constant ratio l\ L, plays 
exactly the same part in the generalised analysis as it did in the simpler case. 
It may now be easily shown that the mean deviations, I and J, may be calculated 
from the equations 
T • , 2A l \ 
i= * i+ wa 
and (XXIV*) 
Jl2= ^ 2 + l^A (?+m) ’i 
and that the variance reduces, as before, to 
o - 2 + P^-t 2 (XXV*) 
16. Coupling. — In much modern Mendelian work coupling plays an important 
part, although the results of different investigators do not seem as yet to converge 
upon any one uniform scheme of coupling. The type found by Morgan in the 
American Fruit Fly ( Drosophila ) is, however, of peculiar simplicity, and may be found 
to be the general type of the phenomenon. 
An individual heterozygous in two factors may owe its origin to the union of 
either of two pairs of gametes, either (l . l) x (2 . 2) or (1 . 2) x (2 . l) ; when coupling 
occurs, the gametes given off by such an individual, of all these four types, do not 
appear in equal numbers, preference being given to the two types from which the 
individual took its origin. Thus in a typical case these two types might each occur 
in 28 per cent, of the gametes, and the other two types in 22 per cent. Coupling of 
this type is reversible, and occurs with equal intensity whichever of the two pairs are 
supplied by the grandparents. We may have any intensity from zero, when each 
type of gamete contributes 25 per cent., to complete coupling, when only the two 
original types of gamete are formed, and the segregation takes place as if only one 
factor were in action. 
The above analysis of polymorphic factors enables us to compare these two extreme 
cases ; for there are 9 phase combinations of a pair of dimorphic factors, or, if we 
