GROWTH AND VARIABILITY IN HELIANTHUS 
that there is some agency operating to cause variability in height in excess 
of that to be expected upon the basis of pure chance. Moreover, regarding 
the higher values obtained for the plants in quartiles I and IV, we must 
conclude that these agencies are more influential on the plants varying most 
greatly from the mean height of the population on the 14th day. It will 
be seen that the actual standard deviation is an extremely useful constant, 
since it measures the influence of those factors (aside from pure chance) 
which determine the relative height of the plants during their grand period 
of growth. 
Before discussing the growth characters further, it will be well to examine 
their behavior when studied from the point of view of the growth rate of 
plants ending in the several quartiles. 
The Quartile Deviations of Plants Ending in a Given Quartile 
The population was divided into four groups according to their heights 
at the end of the growing season. On the 84th day 15 plants were in quar- 
tiles I and III, and 14 plants in quartiles II and IV respectively. The 
quartile positions of these plants were then determined on each of the days 
of observation. 
Tables 8, 9, 10, and 11 show the number of plants in the several quartiles 
at each measurement and the mean quartile positions. The plants which 
ended in any given quartile were distributed through all the quartiles on 
the 14th day, yet even then the tendency to be grouped in or near the quar- 
tile in which they ended was manifest. It will be noted that on the 14th 
day the mean quartile position for the plants ending in the several quartiles 
was nearly the same and that it was near the mean quartile position (2.5) 
of the population as a whole. By the 42nd day the plants ending in quar- 
tiles I and IV had come within less than a quartile of reaching their final 
position, while those ending in quartiles II and III were very close to their 
final position. In each case the percentage of observations falling in the 
particular quartile in which the plants ended was somewhat higher than 
similar values for plants starting in the several quartiles as given in tables 
4 to 7, inclusive. From this it appears that the final quartile position of 
the plants was a better means of judging their average position during the 
grand period of growth than the initial position. The opposite relation in 
the case of maize plants was found by Pearl and Surface (1915). It may be 
remarked in passing that the plants ending in a given quartile showed 
little change in the mean quartile positions after the 42d day. 
Turning now to table 12, where the data are more compactly assembled, 
it will be noted that much the same tendency to deviate is shown by these 
figures as by those in table 7. The observations show that the plants were 
more frequently in the quartiles in which they finished than in any other. 
On the basis of pure chance the observations should fall between 15 
and 35 percent approximately, yet only 6 out of 16 observations obey this 
