72 PROCEEDINGS OP THE AMERICAN ACADEMY, 



R in approximately equal numbers. Tiiis result is probably broiight 

 about by the expulsion, in maturation, of the D or the R character from 

 the germ containing these two elements. This phenomenon is the so- 

 called principle of segregation. If one hybrid be fertilized by another 

 like hybrid, there will thus be possible, according to the laws of chance, 

 two combinations of a D with an R gamete to one each of a D with a D 

 and an R with an R, thus : 



D+R 



D + R ^ 



J ,D + 2D(R) + R '^■ 



This result may be expressed by formula (2) : 



D(R) X D(R) = D + 2D(R) + R. 



Generation F^ will thus consist of three sorts of individuals : (a) indi- 

 viduals D, which are pure dominants and reproduce their kind only ; 

 (b) individuals D(R), which, though indistinguishable in somatic charac- 

 ters from those of class (a), are nevertheless heterozygotes and, like their 

 parents, produce gametes D and R in equal numbers ; and (c) individuals 

 R, which have the recessive character alone, and when paired with other 

 R individuals produce only R offspring. 



For class (a), if kept by itself, we may then construct formula (3) : 

 D X D = 4 D ; and for class (c) formula (4) : R X R == 4 R. The 

 formula for class (b) is of course the same as that for their parents, the 

 primary hybrids, viz., formula (2) above. In addition to these crosses, 

 the D(R), or heterozygous, individuals may be back-crossed with the 

 original parent forms. Thus, if the D(R) animal, producing gametes D 

 and R in equal proportions, be bred to one of the pure dominant type, pro- 

 ducing gametes D and U, there will be two sorts of combinations possible, 

 one of which will be a combination of D with D, the other a combination 

 of D with R. The chances for the occurrence of each are equal. The 

 result may be expressed by formula (o) : D(R) x D= 2D(R) + 2D. 

 In external appearance, the entire progeny of this cross may be similar, 

 but the existence of the two sorts of individuals may be demonstrated by 

 crossing each with the recessive form, R. In the case of the D individ- 

 uals, such a cross will produce only heterozygotes, 13(R), in accordance 

 with formula (1). But the D(R) class, producing equal numbers of D 

 and R gametes, on being crossed with the recessive type, will give in 

 equal proportions the two sorts, D(R) and R individuals. This result we 

 may express by formula (6) : D(R) X R = 2D(R) + 2R. Thus in a 

 cross of two heterozygotes, there are obtained, — formula (2), — in addition 



