460 
Proceedings of the Royal Society of Edinburgh. [Sess. 
we have, since the positive root must be taken, 
7 wifr 7 , , 7 . nh 
a + b + c H b + ci + d + — , 
a b 
or 
or 
c + , — =d + — 
a b 
abc + Amabel -f- 2 mb 2 e = abd 4- 2 na 2 d + 2 nabc, 
since h = 2{ad + be) ; 
= abd + ( 1 - 2m)a 2 d + ( 1 - 2m)abc, 
since 2 (m + n) = 1 ; 
or 
or 
\m(abd + b 2 c + a 2 d + abc) = abd + a 2 d, 
2m(a + b)(ad + be) = (a + b)ad 
2m(ad + be) = ad 
2mbc = (1 - 2 m)ad 
= 2 nad. 
The other equations also reduce to this, so that 
ad m 
be n 
is the criterion of stability if coupling exists. If there is no coupling, 
m — n and ad = be. 
Some remarks may be made in this place concerning the meaning of 
coupling. It has two forms : either each unit has a special attraction for 
the corresponding unit originally associated with it, or on the other hand 
for the one with which it has come in contact when hybridisation occurs. 
The theory at present advanced by Mendelian biologists makes in my 
/ 7Tb 
notation — = 2 P — 1 when p is a positive integer. I confess that I cannot 
follow the arguments on which this is based. The facts seem to me much 
more in line with the conditions of stability in chemical solutions. If 
there be a solution, say, of Na 2 S 0 4 and HC 1 , the relative proportions of the 
four possible substances depend on the rate at which the reactions between 
Na 2 S 0 4 and HC 1 and between NaCl and H 2 S 0 4 take place. Denoting these 
respectively by n and m, if the amount of these four substances be respec- 
tively a, d, b, c , equilibrium will exist if nad — mbc . Or, in other words, the 
equation of chemical equilibrium is the same as that of the stability of the 
population considered. The advantage of this method of looking at the 
matter is that it implies no special values of m and n. Short, therefore, of 
some fundamental reason for the value — = 2 P — 1, it is better to consider 
n 
that other values may be possible and that facts on one side or the other 
