84 



VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



It is seen at once by mere inspection of the table that there is clearly 

 a change in the mean number of leaves per whorl, with successive whorl 

 formation. The precise amount of this change is shown in table 43, 

 which gives the actual mean for each array of table 42. 



Table A3.— Regression of leaf-number on position in main-stem whorls. 



Position 

 of whorl. 



1-10 

 11-20 

 21-30 



Mean number 



of leaves 



per whorl. 



9.045 

 9.233 

 9.580 



Position 

 of whorl. 



31-40 

 41-50 

 51-60 



Mean number 

 of leaves 

 per whorl. 



9.689 

 9.700 

 9.697 



Position 

 of whorl. 



61-70 

 71-80 

 81-90 



Mean number 

 of leaves 

 per whorl. 



9.800 



9.800 



10.000 



This result shows that in main-stem whorls, just as in primary and 

 secondary branch whorls, there is a definite relation between the number of 

 leaves and the position on the axis. The later-formed whorls tend to have 

 a higher mean number of leaves than those formed earlier. The data of 

 table 43 are shown graphically in fig. 16. 



The increase in mean leaf-number in main-stem whorls is clearly very 

 gradual. We have now to determine whether it is according to the same 

 law which holds for other divisions of the plant. On account of the paucity 

 of material we can not get at this directly as we have in the other cases, but 

 must resort to an indirect method. For reasons which have been stated 

 above, we know nothing about how the main-stem curve starts. The first 

 array in table 42 (whorls 1 to 10) is unfortunately largely composed of 

 whorls above the fifth, the lower ones being in most cases broken. The 

 consequence is that the mean for this group has an unduly high value. 

 Further, there can be no doubt that the main-stem curve actually starts at 

 a considerably higher level than does that for primary branches, so that 

 it would be obviously unfair to compare the absolute values predicted 

 from our primary-branch growth curve (equation I) with main-stem 

 means. The fairest way of approaching the problem seems to me to 

 compare the increment in mean leaf-number occurring between whorls in 

 different situations on the main stem with the increment between similarly 

 situated whorls on primary branches as predicted by equation I. If 

 there is reasonable agreement between the observed and predicted 

 increments we may fairly say that the growth and differentiation of 

 leaf -whorls follows the same law in the main stem and the branches. 

 The data for this comparison are given in table 44. 



On the whole these results are quite satisfactory. Of course there 

 is wide divergence between observed and predicted results at the two 

 ends of the series. At the lower end (whorls 5 to 15) the observed incre- 

 ment is much too small, but, as has been pointed out, our first mean 



