274 POPULAR SCIENCE MONTHLY. 



and GSb, have each one latent character, and each constitutes two 

 sixteenths of the whole. The type VgSb, having two latent characters, 

 constitutes four sixteenths. In general, a type having n latent char- 

 acters will be present in the second generation of any hybrid in a 

 proportion 2 n times as great as any type having no latent characters. 



Suppose now we sow all these nine kinds of seed and secure mature 

 plants from each. Those of the type GB can easily be distinguished 

 by their appearance. It can be selected out at once, as a new variety 

 fixed in character. The case is different with VS, VB and GS. 

 For example, if we attempt to select GS, we get also GSb, which has 

 exactly the same external characters. But if we take all the plants 

 with glabrous chaff and smooth heads ( GS -f- GSb ) and save the seed 

 of each plant separately, we can separate the next generation by noting 

 which j)lants re]3roduce true to type; for the seed of GS will produce 

 GS plants only, while that of GSb will produce one fourth GS, two 

 fourths GSb, and one fourth GB, according to Mendel's law. Or, 

 since GS and GSb appear alike, one fourth of the progeny of GSb 

 will be GB (glabrous and bearded), the remaining three fourths 

 being glabrous and smooth. In the same way we can separate VS 

 from VSb, VgS and VgSb, and VB from VgB. 



Now VS, VB, GS and GB are all the possible pure (homozygote) 

 combinations of the parent characters, two of them being identical 

 with the two parents, the others constituting new varieties. The 

 practical plant breeder, therefore, does not need to carry his hybrids 

 beyond the third generation to secure all the possible results of a 

 given cross, as far as new fixed varieties are concerned. It should 

 be remembered that this is true only of characters that obey Mendel's 

 law. It is plain, therefore, that it is a matter of the highest practical 

 importance to ascertain how general this law is. 



By the same methods outlined above, it is easy to ascertain what 

 types would result from a trihybrid, and from hybrids of all higher 

 orders. In the case of trihybrids, eight permanent combinations 

 result, one like each parent and six new ones. Quadrihybrids give 

 sixteen types, fourteen of which are new; and so on. In general, 

 the number of new fixed types springing from a hybrid is 2" 2, 

 where n is the order of the hybrid. 



The proportion of the various types in later generations of a 

 hybrid is a matter of more than curious interest. We have already 

 seen that, in the case of monohybrids, the later generations tend to 

 split up into the two parent types. It was stated above that this is 

 not so with hybrids of higher order. If we assume that each of the 

 nine types (four homozygote and five heterozygote) resulting from 

 a dihybrid is equally productive, the proportion of each of these 

 types in each generation to the sixth is as follows: 



