X34 Pearl and Surface. 



Changes in the mean quintile position in the successive 

 stages of growth. 



a) Plants Starting in a Given Quintile. 



In the preceding section of this paper we have discussed the 

 quintile distribution of groups of plants takiug the season as a whole. 

 In this portion of the paper an attempt will be made to carry the 

 anal.vsis a step farther. It has been shown, for example, that there is 

 a tendency for plants relatively small at the beginning of the season 

 to be relatively small for the season as a whole. This result may 

 mean, on the one hand, that such a group of plants tended to remain 

 in or near quintile I during the whole season with only random 

 fluctuation from this value. Or, on the other hand, it may mean that 

 there was a gradual regression towards the mean of the poi)ulation 

 with the advance of the season. Thus it is conceivable that plants 

 relatively small at the beginning of the season become, gradually, 

 relatively larger untü at the end of the season they are on the average 

 not far different from the mean of the population. Similarly the relati- 

 vely large plants might become relatively smaller until they too are, 

 on the average, not far from the mean of the population. Either of 

 these conditions would give similar results with the methods used in 

 the preceding section. 



In order to study this question we have determined the mean 

 quintile position, at each successive measurement, for the plants 

 starting in a given quintile. These mean quintile positions are given 

 in tables 31 to 45. These values were determined from the distributions 

 in the respective rows of these tables. Both the mean and the standard 

 deviation of these means were calculated by the method of moments in 

 the usual way. 



Referring, for example, to table 31 it is noted that in the distri- 

 bution of June 12 all eleven plants were, by hypothesis, in quintile I. 

 The mean quintile position is of course 1"0 and the standard deviation 

 zero. In the distribution of June 15 three of these eleven plants fell 

 in quintile II and one in quintile III, while seven remained in quintile I. 

 The mean quintile position here is 1-45 and the standard deviation 0-66. 



The change in these constants can best be seen when displayed 

 graphically. Figs. 10, 11 and 12 show the mean (luiutilc positions for 

 the several groups of plants from each series. 



