46 



VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



the constants be made, because of the large probable errors. It is of 

 interest to note that the number of tertiary whorls is greater in Series 

 III, than in Series II or I. The relative increase is greater than is indi- 

 cated by the figures in table 21, since the total of Series III is smaller 

 than that of either I or II. This increase in tertiary whorls is a rough 

 index of the change which took place in the Carp Lake population, due to 

 growth in the interval between the collection of Series I and Series III. 



Table 22.— Frequency distributions for variation in leaf-number in whorls on 



quaternary branches. 



In order that some judgment may be formed of the characteristics 

 of tertiary-branch whorls I have prepared table 23, which gives, in addi- 

 tion to the constants for the distributions of table 21, the absolute 

 differences between these and the constants for secondary-branch 

 whorls. Only totals for series are tabled, because of the paucity of 

 material. The difference is taken as positive when the secondary-branch 

 constant is the greater. 



The probable errors are very large, as was to be expected, and the 

 results are not as smooth as could be desired. Still, I think, we may 

 safely draw the following conclusions: 



(a) The mean number of leaves to the whorl is distinctly lower for 

 tertiary than for secondary branch whorls. In only one case out of the 

 five is the difference between the means negative, and then it is sensibly 

 zero, in comparison with its probable error. In Series II, IV, and VI, 

 the difference is 0.6 to 0.7 leaf, a very considerable amount, and cer- 

 tainly significant in comparison with the probable error. It is of the 

 same order as the difference between main-stem and primary-branch 

 whorls (cf. table 16), and is distinctly greater than the difference 

 between primary and secondary branches in respect to mean number 

 of leaves per whorl. 



(6) The tertiary-branch whorls tend on the whole to be less rather 

 than more variable than those borne on secondaries. The differences in 

 the variability columns are all very small, and, taken singly, quite insig- 

 nificant in comparison with their probable errors. Due weight, however, 

 must be given to the fact that the sign of the differences is uniformly 



