POSITION REGRESSION— SECONDARY BRANCHES. 



79 



Series I, II, and III, as before. In this case, however, the origin of y 

 was taken at 6. 6 instead of at 7, as in the other case. The reason why 

 this was done will be obvious to the mathematical reader. 

 The curve obtained was 



y = 1.2662 + 1.8024 log {x - 0.7939) 

 whence, taking the origin of ?/ at we have finally 



Y = 7.8662 + 1.8024 log {x — 0.7939) II 



where Y indicates mean number of leaves to the whorl and x indicates 

 ordinal position on the branch. The observed and calculated ordinates 

 are given in table 40. The actual observations and the fitted curve are 

 shown in fig. 14. Considering the paucity of observations at the upper 

 end of the range, abetter graduation could not reasonably be expected. 

 We conclude, then, that the same type of curve expresses the regression 

 in secondary branches as in primaries. Or, in other words, the differen- 

 tiation of successively formed whorls follows the same general law in 

 both primary and secondary branches. 



9.6 

 9.2 



E 



>♦- 

 « 8.0 



C 



a 

 V 7.6 



7.2 



6.8 



I 2 3 •* 5 6 7 8 9 "0 II 12 13 



Position of whorl 



Fig. 14.— RogresHion of leaf-numbor on position In secondary branches, Kerios I, II, 

 and III combined. ObHervationn, • '— ; lltted curve, 



Having seen that the growth curve is fundamentally the same for 

 the two orders of branches, we may next examine the differences in the 

 two cases, and see what they signify. We may first notice how the 

 increment in mean leaf-number per unit advance in position compares 

 in the case of secondaries with what it is in primaries, for corresponding 



