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 small proportion of dominants and one containing a similar proportion of recessives are equally stable. The term dominant is in some respects apt to be misleading, for a dominant character cannot in virtue of its dominance establish itself at the expense of a recessive one. Brown eyes in man are dominant to blue, but there is no reason to suppose that as years go on the population of these islands will become increasingly brown eyed. Given equality of conditions both are on an equal footing. If, however, either dominant or recessive be favoured by selection the conditions are altered, and it can be shown that even a small advantage possessed by the one will rapidly lead to the elimination of the other. Even with but a 5 per cent selection advantage in its favour it can be shown that a rare sport will oust the normal form in a few hundred generations. In this way we are freed from a difficulty inherent in the older view that varieties arose through a long-continued process involving the accumulation of very slight variations. On that view the establishing of a new type was of necessity a very long and tedious business, involving many thousands of generations.