11-1 
Research Bulletin No. 2 
have produced an F s range from 1 to 9 stalks (if belonging to 
group XV for stalk number), in which case the desired 26- 
decimeter, 9-stalked type would have been secured in F 3 . But 
since the chance is greater, let us suppose that the 26-decimeter. 
5-stalked F 2 plant belonged to group XI for number of stalks. 
Then by growing 50 F 3 plants from it, we would be fairly cer- 
tain of getting at least one 26-decimeter, 7-stalked plant which 
would breed true in both height and number of stalks. The 
next step, obviously, is to cross this homozygous 26-decimeter. 
7-stalked F 3 plant, or any of its F 4 progeny, with the 9-stalked. 
22-decimeter F 3 plant obtained from the other selection, or 
with any of its F 4 progeny. The two F 3 plants would have 
zygotic formula similar to the following : 
ill 26-decimeter. 7-stalked plant—- I A BBC ODD — A'A'B'B'- 
C'CWd'. 
i 2i 22-decimeter, 9-stalked plant— 4.1 BBCCdd—A 'A'B'B'- 
C'C'D'D'. 
It is clear, therefore, that since the two F 3 plants, (1) and (2), 
differ only in the factors D and D', only 16 F 4 plants — or say 50 
to make more sure — need be grown to give one plant that is 
homozygous in all eight factors. We have then grown 1.000 F 2 
plants, 100 F 3 plants, and 50 F 4 plants to accomplish what would 
perhaps have required a quarter-million F 2 plants alone. And 
it would have taken no more plants and no more time had we 
crossed the 9-stalked, 22-decimeter F 2 plant with the 7-stalked 
26-decimeter one instead of having first grown their F 3 progenies. 
In the same way it can be showm that the desired combina- 
tion of quantitative characters could be secured in comparatively 
few generations even if a sufficient uumber of plants could no1 
be grown in F 2 to recover the exact parent type of either char- 
acter. in any individual. But the theoretical possibilities have 
been sufficiently illustrated. 
Tn the detailed account of our experiments, several examples 
have been pointed out that illustrate the possibility of securing 
parent types in F s from F 2 lots thai contained no individuals as 
extreme as the parents. For instance, in certain crosses, no F 2 
plants had seeds quite like those of the parent varieties, but in 
F 3 the parent sizes were recovered in several cases. (See Tables 
20, 22, 24.) Perhaps the most striking case of this sort observed 
in our experiments is that of height of stalk. While in some 
crosses the parent heights were recovered in F 2 , in other crosses 
the most extreme F 2 heights lacked much of reaching the outer 
extremes of the parent ranges. In Tom Thumb X Black Mexi- 
can (Table 25), this was true of the F 2 families, but two of the 
F 3 lots — progenies of approximately the smallest F_. plants — 
