VARIATION IN DIFFERENT PORTIONS OF PLANT. 33 



For the "all-branch" distribution the criterion *<! (=2/?.,— 3^—6) is 

 negative, indicating that a curve of Type I is demanded for graduation. 

 In the case of the main-stem distribution, however, '<i is positive, whence 

 at first thought it would be concluded that a curve of Type IV was 

 demanded. But it has been shown by Pearson (:01) that ^ positive, 

 while a necessary condition, is not a sufficient condition for Type IV. 



In addition, 



A (/3.+3)^ 

 "■' 4 (4A-3/8i) (2)8-3/8-6)" 



must be > and < 1. We see at once that the main-stem distribution 

 does not fulfill this latter condition, since «, = 1.2455, or is > 1. Clearly, 

 then, one of the transition curves of Type V or Type VI is wanted. 

 The condition for Type V is that <, = 1, while for Type VI we must 

 have ^2 > 1 and < oo . Strictly speaking, then, our main-stem distribu- 

 tion should be graduated by a curve of Type VI, but insomuch as k, 

 differs from 1 by only a small amount we shall probably get sufficiently 

 good results with Type V. I have accordingly fitted the main-stem 

 distribution with a Type V curve and the "all-branch" distribution with 

 a Type I curve. The equations to the curves are: 

 Main-stem distribution (Type V) :' 



Log ?/=19. 6849467-18. 34909 log 0^-26.092355 (-) 



Origin at 13.2096; x positive towards small whorls. 

 All branch distribution (Type I) : 



j/=581.6454 (l+^:69ro) (l-lTMs) 



Origin at mode = 9.2345. 



The histograms and their fitted curves are shown in fig. 7. The 

 frequencies for both curves were reduced to percentages before plotting, 

 so that, since the base elements are the same, both curves have the 

 same area in the diagram. This method brings out most clearly the 

 points of difference between the two distributions. 



^For obvious reasons I have put the curve in the logarithmic form. The equation 

 to a curve of this type is of the form 



~P — y/* 



where y^, p, and y are constants. 



