FACTOR RELATIONS IN QUANTITATIVE INHERITA NCE 181 
intermediate, for in quantitative inheritance in general the factors ap- 
parently do not display dominance but the phenotypic expression of Aa 
is approximately equal to the average of that of the two parents. If 
this idea be correct the F, should consist in this case of LAA: 2Aa: laa, 
which has been shown to be approximately true, if the boundaries shown 
in Fig. 86 be accepted. It is to be noted, however, even for as simple a 
case as this that the two parents and the F; each have their typical ranges 
of fluctuation. Considering the parental and I’, distributions, the upper 
limits of the smaller parent run into the lower portion of the range of the 
F,, and the lower limits of the larger parent run into the upper limits of 
the Fi. It follows that in F2, even if there should be only a single factor 
difference between the two parents, the F, classes would overlap. Con- 
sequently some of the plants assumed to belong to the lower class and 
also some of those assumed to belong to the upper class really belong to 
the middle group, and some of those arbitrarily included in the middle 
class belong either to the upper or to the lower class. 
The only accurate method of classifying those individuals lying near 
the boundaries of the classes is to test them by growing their F’3 progenies. 
If they belong to the upper or lower classes they should then give uni- 
modal distributions corresponding to the parental distributions, whereas 
if they belong in the middle class, they should give trimodal distributions 
corresponding to the distribution obtained in F,. In another case 
Leake has endeavored to apply this test to an entire F’; distribution, and 
although the evidence indicates some discrepancies probably due to the 
presence of minor factor differences, nevertheless the agreement is such 
as to lend support to the idea of a single main factor difference. 
Most size differences however are not so readily interpreted as this 
one, apparently because a larger number of factors is concerned in them. 
The general statement with regard to such size differences is that two 
contrasted races, each of which displays a certain characteristic amount 
of variability when grown in the pure line, when crossed produce an Fy 
intermediate between the two parents and no more variable than either 
of them. The F from such a hybrid when grown in large populations 
displays on an average an intermediate position, but some few indi- 
viduals at either extreme approach the sizes of the parents, and between 
these extremes lies a continuous series of forms, in distribution usually 
approximating a normal curve. The evidence of segregation here is the 
increased variability in the second generation, and subsequent genera- 
tions display a similar conformity to such an interpretation. 
This type of inheritance may best be illustrated by a typical example, 
but one which has, perhaps, been more thoroughly investigated than 
any other, namely the inheritance of length of corolla in tobacco. East 
has investigated the inheritance of length of corolla in crosses between 
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