ts of crossing with the more
abundant normal form, and so, even though favoured by natural selection,
would never succeed in establishing itself. Mendel's discovery has
eliminated this difficulty. For suppose that the sport differed from the
normal in the loss of a factor and were recessive. When mated with the
normal this character would seem to disappear, though, of course, half of
the gametes of its progeny would bear it. By continual crossing with
normals a small proportion of heterozygotes would eventually be scattered
among the population, and as soon as any two of these mated together the
recessive sport would appear in one quarter of their offspring.

A suggestive contribution to this subject was recently made by G. H. Hardy.
Considering the distribution of a single factor in a mixed population
consisting of the heterozygous and the two homozygous forms he showed that
such a population breeding at random rapidly fell into a {148} stable
condition with regard to the proportion of these three forms, whatever may
have been the proportion of the three forms to start with. Let us suppose
for instance, that the population consists of p homozygotes of one kind, r
homozygotes of the other kind, and 2 q heterozygotes. Hardy pointed out
that, other things being equal, such a population would be in equilibrium
for this particular factor so long as the condition q^2 = pr was fulfilled.
If the condition is fulfilled to start with, the population remains in
equilibrium. If the condition is not fulfilled to start with, Hardy showed
that a position of equilibrium becomes established after a single
generation, and that this position is thereafter maintained. The
proportions of the three classes which satisfy the equation q^2 = pr are
exceedingly numerous, and populations in which they existed in the
proportions shown in the appended table would remain in stable equilibrium
generation after generation:--

p. 2q. r.
1 2 1
1 4 4
1 6 9
1 8 16
1 20,000 100,000,000
1 2n n^2

This, of course, assumes that all three classes are equally fertile, and
that no form of selection is taking place to the {149} benefit of one class
more than of another. Moreover, it makes no difference whether p represents
the homozygous dominants or whether it stands for the recessives. A
population containing a very sma