GROWTH AND VARIABILITY IN HELIANTHUS 
265 
2. An analysis of the growth and relative superiority of the plants has 
been made to determine (a) whether the inferior plants grew slowly during 
the entire season, or whether they grew rapidly during their early history 
and came sooner to maturity; and (b) whether variability in size of indi- 
viduals, or of groups, was due to mere chance of environment or to some 
inherited factor. 
3. The quartile class was adopted as a basis for classifying the population 
into groups. The number of plants in each quartile was fixed at the outset 
and adhered to through the entire study. 
4. Plants which started in a given quartile showed a well marked 
tendency to remain in that quartile during the entire grand period of growth. 
Plants which were small at maturity were generally small from the beginning, 
those which were large at maturity had a well-marked superiority from the 
start. 
5. The actual standard deviations of the observed percentage values 
of the quartile positions of plants departed so widely and consistently from 
the theoretical standard deviations of the mean percentages that it seems 
quite certain that there was some agency operating to cause variability in 
height in excess of that to be expected upon the basis of pure chance. The 
assumption is made that the relative size of plants is dependent upon internal 
genetic factors, rather than upon external casual factors. 
6. The mean quartile position of each plant was taken as a measure 
of its relative size during the grand period of growth. The frequency of 
the mean quartile positions indicated a good random distribution, though 
there was a slight tendency toward grouping in the mid-classes. It seems 
probable, therefore, that the smaller relative size of the plants in the lower 
classes is an expression of the same definite factor as the relatively larger 
size of any of the other groups in this population. 
7. There was evidence that height was determined by factors which 
were distributed at random through the population. It was found that 
the distribution of the relative heights of the plants was nearly equal. 
Further support for the assumption was found in the fact that plants in the 
extreme classes were less variable in regard to their mean relative height 
than plants in the intermediate classes. 
8. The growth constants of plants ending in the several quartiles were 
practically identical. 
LITERATURE CITED 
Church, A. H. (1915). Quoted by Cockerell, T. D. A. Specific and varietal characters 
in annual sunflowers, Amer. Nat. 49: 609. 
Pearl, R., and Surface, F. M. (1915). Growth and variation in maize. Zeitschr. Indukt. 
Abstam.- u. Vererbungslehre 14: 97-203. 
Reed, H. S., and Holland, R. H. (1919). The growth rate of an annual plant, Helianthus. 
Proc. Nat. Acad. Sci. 5: 135-144. 
ShuU, G. H. (1908). Some new cases of Mendelian inheritance. Bot. Gaz. 45: 103-116. 
