The Inheritance of Quantitative Characters in Maize 19 
recombination of gametic factors of some kind must have taken 
place, for in no other way could this greater variability be ex- 
plained. Contributions toward such proof have been given by 
the essential agreement of the investigations reported by at least 
eight investigators. 
Perhaps before giving a brief resume of the results of these 
investigations, however, it may be well to illustrate by concrete 
hypothetical examples just what sort of complexities the data 
from actual crosses are likely to show if the theory of multiple 
factors is correct. The practical difficulties of proving this 
theory have been mentioned in general terms; let us see in what 
form these difficulties are likely to present themselves to us in 
our actual experiments. 
Returning to a simple case like that used before, in which the 
difference in height between a 10-inch plant and a 26-inch plant 
is supposed to be due to four independent, interchangeable, allelo- 
morph] c pairs, let us examine the results that are to be expected 
in the F 1? F 2 , and F 3 generations and in back crosses between an 
F a individual and either parent. In this example the presence 
of any single factor is supposed to add 2 inches to the height of a 
zygote and all effects of environment on development are assumed 
to be absent. 
Plant A, 10 inches high, has the zygotic formula ( x =10 in.) 
+ aabbccdd = 10 inches, the plant B has the zygotic formula 
(x = 10 in.) + AA BBCCDD = 26 inches. Since all F t plants 
have the zygotic formula (x = 10 in.) + AaBbCcDd, they are all 
16 inches high. If we apply the formula (-J + i) 8 for determin- 
ing the frequency distribution of the F 2 generation, the following 
result is obtained : 
10 
12 
14 
16 
18 
20 
22 24 26 
No. of individuals 
1 
8 
28 
56 
70 
56 
28 8 JL_ 
Thus, while the plants of the F 1 generation are alike, the F 2 
generation is variable. The class of greatest frequency is the 
same as that of the F ± generation, but it is really made up of 
individuals unlike in zygotic constitution and which therefore 
breed very differently in F 3 as is shown in Table 1. 
One can see clearly what different progenies these various 
zygotes will produce. Zygotes selected at random from the ex- 
tremes will be more likely to breed comparatively true to their 
type than will those near the class of greatest frequency. Thus 
of the 74 zygotes 10 to 14 and 22 to 26 inches high, 10. or 13.5 
per cent, will breed true; 16, or 21.6 per cent, will produce 
progenies with ranges of variation of only four inches ; and 48, 
or 64.9 per cent, will produce progenies with ranges of eight 
