RELATIVES ON THE SUPPOSITION OF MENDELIAN INHERITANCE. 
417 
those of the other factor from 1 to n, then, as the phase (12) of the first factor occurs 
with frequency 2pq{l+i 12 ), and of the second factor, with frequency 2p'q'(l +f' 12 ), 
we shall write the frequency with which these two phases coincide in one individual 
as Apqpq(l +/ 12 . 12 ), or as 4pqpq{l +f 12 ) (l +/' 12 ) (l +f 12 . 12 ), so that 
f 12.12 = /l2 • 12 + f 12 +/ 12 • 
The proportional increase of frequency of the gametic combination (l . l) is 
PP'fu . ii +P2'/'n . i2 +prf ' n . is + • • • 
+ ?P'/'l2.11 + 22 / / , 12.12 + 2 7 ''/'l2.13+ • • • 
and so on. 
By virtue of the equations connecting the f’s of a single factor, this expression, 
which we shall term F n , has the same value, whether written with dashed or 
undashed f’s. 
Individuals having the constitution (12. 12) may be formed by the union either 
of gametes (l . l) and (2 . 2), or of gametes (1 . 2) and (2.1); hence the equations of 
equilibrium are of the form 
2/n . 12 = F u + F 22 + |(L + L')(M + M') 
but 
therefore 
+ F 12 +F 2l +^(L + M')(M + L'), 
l/l2 . 12 = 2/ 12 • 12 “ 3/l2 - 2/ 12 
= 2/ 12 .i2-^(LM + L'M'), 
2/ 12 . 12 = t l n + F 22 + F 12 + F 21 + fi(L + M)(L' + M') 
By analogy with Article 12, the solution 
J 12 . 12 = 
suggests itself, and on trial it leads to 
Do 7 
/i2.12 = ^( L + M )( L ' + M' 
F - ^LL' 
and is thereby verified. 
Hence we may evaluate L, L', . . . , for 
but 
L = pli + #12 + >'Jl3 + • • • 
= 1 + ' 2 {P H '(vfn . 11 + <jfu . n + ■ • •) + lp<l/n(pfn , 12 + 2/12 12 + 
Pf 11 . 11 + Sfn . 11 + • • • “ yL(L' + M'), 
■) + 
(XIX*) 
L = Z + ^ L2 { p'H'(L' + L') + 2p’q'j' 12 (L' + M') + . . .} 
= l + ^L'2(2p'l'L' + 2qm'M.' . . .). 
therefore 
