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H. S. REED 
causes which determine the relative sizes of the plants without pushing the 
mathematical analysis too far. Pearl and Surface (1915) found evidence 
that the height of the maize plants they studied was governed by Men- 
delian factors. We may with propriety inquire whether the relationships 
of the relative heights of the sunflowers give similar evidence. 
If we assume that there is one pair of allelomorphic characters for 
height, we should have in the F2 generation, four classes, AA, Aa, aA, 
and aa, each of equal frequency. In such a case, the distribution of the 
relative heights of the plants should be nearly regular. Also, since the 
plants in the end classes bearing the factors A A and aa are homozygous for 
the theoretical height-factor, they should be less variable than the hetero- 
zygous plants in the intermediate classes. We may examine the data to 
see if either of these assumptions can be supported. 
It was pointed out above that the mean quartile distributions are fairly 
evenly distributed in the several classes, though there is a slight tendency 
for them to be grouped in the middle classes. A smoother distribution 
might have been obtained by study of a larger population. 
As a measure of the relative variability of the mean quartile positions 
we may refer to the standard deviations obtained in table 14. The values 
for the first and fourth classes are .502 and .505 respectively, while those 
of the intermediate classes are .793 and .786. Certainly there is a signifi- 
cance about these results which seems to warrant the assumption that the 
plants in the extreme classes are less variable about their mean relative 
height than those in the intermediate classes. 
Objection may be raised to this assumption, since the sunflowers were 
not known to be the F2 progeny of a pair of individuals, and to the assump- 
tion of a definite ratio. In the work frequently quoted in this article, 
Pearl and Surface (19 15) have shown, however, that this is just what might 
be expected in any population in which independent Mendelian factors are 
distributed at random, since in such a population, where open fertilization 
occurs, the individuals will have the same factor constitution as individuals 
in the segregating generation. If we assume the presence of two factors 
for height, we should expect such a result as that obtained. There may be 
more than two factors for height, but the assumption of a larger number 
need not invalidate the argument. 
Attention may be called to a conclusion drawn from a study of the 
growth constants of these plants (Reed and Holland, 1919), wherein it was 
pointed out that the growth constants of plants ending in the several quar- 
tiles were practically identical. Differences in the mean relative heights 
are evidently determined by some internal factor other than differences in 
the growth constants. 
Summary 
I. The growth and variability of a small group of sunflower plants, 
grown under tolerably uniform field conditions, was measured by taking 
weekly records of the height of each plant during the grand period of growth. 
