VARIATION IN DIFFERENT PORTIONS OF PLANT. 



29 



as compared with the "total" polygons given in fig. 3, indicating, of 

 course, that main-stem whorls are less variable. A more precise notion 

 of the variablity of the whorls on this portion of the plant may be gained 

 from table 6, which gives the means, standard deviations, and coefficients 

 of variation for the larger of the main-stem distributions. 



Table 6. — Constants for variation in leaf-number in main-stem whorls. 



"■Tlie constants were not separately calculated for plants in which there were only a few main- 

 stem whorls. 



On account of the small number of the main-stem whorls the results 

 are not as regular as could be desired. Even in very large Ceratophyl- 

 lum plants there are usually a comparatively small number of main-stem 

 whorls, and of those originally present a part are usually so mutilated 

 as to be uncountable. As the main stem is the oldest portion of the 

 plant, it suffers most from accidental injuries, the attacks of aquatic 

 animals (e. g., insects, snails, planarians) and from other injurious 

 factors. Consequently, when one deals with comparatively few indi- 

 vidual plants the results are bound to be irregular, because the propor- 

 tion of unmutilated whorls in different regions of the main stem will 

 differ from plant to plant. In spite of this irregularity in the constants 

 for different individual plants, however, we are able to reach certain 

 definite results. 



In the first place, it is quite clear, whether we compare single plants 

 or series, that the mean number of leaves to the whorl is higher for the 



