RELATIVES ON THE SUPPOSITION OF MENDELIAN JNHERITANCE. 
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separate the two kinds of double heterozygote, 10, which, apart from inheritance, 
can be interpreted as the 4 homozygous and the 6 heterozygous phases of a 
tetramorphic factor. The 4 gametic types of this factor are the 4 gametic com- 
binations (1. l), (l . 2), (2 . l), (2 . 2). 
The mean deviations associated with these 4 gametic types are L 4-1/, M + M\ . . ., 
and we therefore write 
X = L + L', /||> = LH-M', 1R = M + L', © = M + M'. 
Further, if these gametic types occur with frequency, 
V- q=M'(i+f|r) 
V = q P ’(l+%MIj) 8 = 22 '(i+|MM') > 
it is clear that the frequencies wdth which the homozygous phases occur, 
such as 
P 2 P% 1 +/'u . n) =P 2 p' 2 1 1 + =^(L 2 + L' 2 + 4LL') | 
pqi + |(L + Lr}-p«(i + nq 
are exactly those produced, if there really were a single tetramorphic factor. 
In the same way the phases heterozygous in one factor also agree, for 
2jp W(1 +f u . 12 ) = W'/ { 1 + | L2 + L ' M ' + 2 H L ' + M') ) } 
= 2pq { 1 + |(L + L') (L + M') } = 2pq(l + |X/ID). 
Finally, taking half the double heterozygotes, 
2^V(l+/ 12 . a2 ) = 2^v{ 1+^(LM+L'M' + {L + M)(L' + M')) } 
2 PS { 1 + |(L + L') (M + M') [ = 2ps^l + |X©), 
or, equally, 
2qv [ i+^(L+M')(M + L') } =2qr(i + ^flMR). 
From this it appears that a pair of factors is analytically replaceable by a single 
factor if the phase frequencies be chosen rightly ; but the only difference in the 
inheritance in these two systems is that in the one case there is no coupling, and in 
the other coupling is complete. It would appear, therefore, that coupling is without 
influence upon the statistical properties of the population. 
17. The effects both of dominance and of environment may be taken into account 
in calculating the coefficient of correlation ; if we call x the actual height of the 
individual, y what his height would have been under some standard environment, 
and z what his height would have been if in addition, without altering the extent to 
which different factors are associated, each phase is given its representative value of 
