POSITION REGRESSION— PRIMARY BRANCHES. 



73 



leaf-number in the first 15 whorls on primary branches in Series IV, 

 as given in table 36. The data are not carried farther than the 15th 

 whorl, because from that point the material is too meager to yield very 

 reliable means. This will be evident by examining table 30. The contin- 

 uous curve is the graph of 



r = 8.2520 + 1.3608 log {x — 0.8015) 



the ordinates of which are given in the second column of the table. 

 That is, it is our first growth curve, changed only by a uniform addition 

 of 0.3 leaf in the absolute size of every whorl. 



10.2 



9.8 



9.4- 



9.0 



u 



E 8.6 



D 

 C 



ro 



8.2 



7.8 



7.4 



7.0 



7 8 9 10 



Position of whorl 



12 



14 



15 



Fig. 12.— Regression of leaf-number on position and the fitted curve for Series IV. The ordinates 

 give mean leaf-number and the abscissas position. ^^— — observation; theory. 



It will be seen that the agreement between the actual observations 

 and the values predicted by the growth curve is extraordinarily close. 

 Of course there is some irregularity in the observations after the 

 10th whorl, but this is only to be expected when we remember that the 

 means here are based upon comparatively few observations. Even 

 at the worst the maximum deviation of observation from prediction is 

 only a little over 0.2 leaf, while the average deviation is only 0.01 leaf. 



This result seems to me to be of considerable importance, because, 

 in the determination of the shape of the growth curve the observatioroS which 

 we see it here expressing so very closely were in no wise taken into account. 



