30 



VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



whorls on the main stem than for the plant as a whole. Further, we 

 see that both absolutely and relatively the main-stem whorls are on the 

 whole distinctly less variable than are those from the entire plant taken 

 together. But obviously the fair comparison is not between main-stem 

 whorls and all whorls in the plant, but between main-stem whorls and 

 all whorls on branches. Accordingly we may examine the distributions 

 and their constants for the whorls on all branches of the plant. In 

 table 7 are given the frequency distributions for variation in such whorls 

 for the totals for the six series. It is not necessary to tabulate these 

 distributions for each plant separately, for reasons which will appear 

 as we go on. 



Table 7. — Frequency distributions for variation in leaf-number in whorls on all 

 branches. Totals for series. 



The difference between these distributions and the corresponding 

 ones for the main stem given in table 5 is apparent. The "all-branch" 

 distributions resemble closely those for the plant as a whole. The most 

 frequently occurring whorls are those with 9 leaves (except in Series 

 VI) as against 10 in the case of the main-stem whorls. The constants 

 for the "all-branch" distributions are given in table 8. 



Table 



-Constants for variation in leaf-number in whorls on all branches. 

 Totals for series. 



It is at once apparent that the whorls on the main stem have on the 

 average a higher number of leaves than do whorls on branches. Further, 



