GROWTH AND VARIABILITY IN HELIANTHUS 
Variation in the Growth and Final Size of Plants 
The growth rate of this group of plants has been studied and found to 
agree closely with that of an autocatalytic reaction in which one of the 
products catalyzes the reaction (Reed and Holland, 191 9). We may, 
therefore, turn from the question of the growth rate of the population as a 
whole, to consider some problems of growth and variability relating to 
smaller groups within the large group. We should attempt to discover 
whether the large and the small members of the group differ from each 
other in their growth rates as well as in their final size ; to be specific, whether 
the small plants grew slowly during the entire season, or whether they grew 
rapidly during their early history and came sooner to maturity. 
Closely related to this, is the question of relative position in the popu- 
lation during the whole period of growth. Do plants which are undersized 
at the start grow rapidly enough to get into higher groups as they become 
older, or do they remain undersized to maturity? 
Another question, and one which is also wrapped up in the questions 
previously propounded, is that of the nature of the variability of the groups. 
Are their variations those which are due to mere chance of environment, 
or are they due to some other cause, which may be referred to the genetic 
constitution of the plant? 
For purpose of study, it is convenient to classify the sunflower plants 
upon the basis of their size each week during the growing season. The 
quartile^ was used because it gave enough plants in each class to offset minor 
errors, such as are bound to occur in quantitative work. In order to make 
comparisons more valid, the number of plants in each quartile was fixed at 
the outset and adhered to throughout. The divisions were as follows: the 
first and third quartiles contained 15 plants each; the second and fourth 
14 plants each. The first quartile contained the 15 shortest plants at each 
time of making measurements; the second quartile contained the 14 next 
taller; the third quartile contained the 15 next taller and the fourth quartile 
contained the 14 tallest plants. In some few cases, one or more plants fell 
on the quartile boundaries. It was then necessary to assign them to one or 
the other adjacent quartile. This was done in as impartial a manner as 
possible, in order that the assignments might have a purely random nature. 
The boundaries of the quartiles never varied widely from the limits obtained 
from the value xja = 0.675. 
^ In using the term "quartile" to designate a portion of the population, I am aware of 
some danger of confusion of terms. Strictly speaking, a quartile is a point so situated on 
the base of a frequency polygon that one fourth of the individuals lie on one side and three 
fourths on the other. Yet there seems to be some authority for using it to designate one 
fourth of the area of the frequency polygon (cf. use of term "quintile" by Pearl and Surface, 
1915). In this paper the term "quartile" will be used to designate one fourth of the 
population. 
