*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 characters 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* *GSb*) and save the seed of each plant separately, we can separate the next generation by noting which plants reproduce 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: