148 MENDELISM chap. 



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 gener- 

 ation, and that this position is thereafter maintained. 

 The proportions of the three classes which satisfy the 

 equation q 2 = pr are exceedingly numerous, and popula- 

 tions in which they existed in the proportions shown in 

 the appended table would remain in stable equilibrium 

 generation after generation : — 



p 



2 q. 



r. 



I 



2 



1 



I 



4 



4 



I 



6 



9 



I 



8 



16 



I 



20,000 



ioo,oco,ooo 



I 



2 n 



n 2 



This, of course, assumes that all three classes are equally 

 fertile, and that no form of selection is taking place to the 



