34 



VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



It is evident that the graduations are as good as could reasonably be 

 expected, considering the small number of classes from which the 

 moments had to be calculated. 



I wish now to consider more fully a point that was raised earlier in 

 the paper. In the section dealing with the methods used in collecting 

 the material it was pointed out (p. 11) that in some cases the main stem 

 of a plant divided, forming what we have called secondary main stems, 

 and in some cases even a secondary main-stem was divided to form 



Leaf number 



Fig. 7,— Frequency histograms and fitted curves for variation in leaf-number in main-stem 

 and "all-branch" whorls of Series I, II, and III combined. Main-stem distribution and 

 curve in solid lines; "all-branch" distribution and curve in broken lines. 



"tertiary" stems. The statement was made that there was no difficulty 

 in practice in distinguishing such main stem divisions from primary 

 lateral branches. I wish now to present statistical evidence to indicate 

 that the variation in leaf-number in these portions of the plants shows 

 that they are parts of the main stem rather than branches. 



In table 11 are given the frequency distributions for all the secondary 

 main-stem whorls which were found in the course of the work, and in 

 table 12 are given the distributions for tertiary main-stem whorls. 



