136 MENDELISM CHAP. 



nature. This view, however, he gave up later, be- 

 cause he thought that the relatively rare sport or 

 mutation would rapidly disappear through the 

 swamping effects of crossing with the more abund- 

 ant normal form, and so, even though favoured by 

 natural selection, would never succeed in establishing 

 itself. Mendel's discovery has eliminated this diffi- 

 culty. 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 hetero- 

 zygotes 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 stable con- 

 dition 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/ homozygotes 

 of one kind, r homozygotes of the other kind, and 2q 

 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 f =pr was fulfilled. If the conditiorr is 

 fulfilled to start with the population remains in 



