BRANCHES AND LEAF-NUMBER. 



Ill 



(6) The variabilities, both absolute and relative, shown in this table 

 are comparatively low. Again they agree most closely with what has 

 been found for main-stem whorls. 



We get the same results, only still more marked, if we consider the 

 whorls at nodes Vv^here two branches originate. This "double" branch- 

 ing at one node does not occur very commonly in Ceratophyllum ac- 

 cording to our experience, but in one plant (No. 2, Series IV) such cases 

 were especially abundant. Table 56 shows the condition, in respect to 

 leaf-number, of these whorls on the plant mentioned. 



Table 56. — Frequency distribution for variation in leaf-number of whorls 

 where two branches originate. Plant 2, Series IV. 



The constants for this distribution are as follows: 



Mean = 9. 707 ±0.027 



Standard deviation = .518± .019 

 Coefficient of variation = 5.333 ± .199 



Comparing these with the values in table 55 for the same plant we 

 see that there is a still further raising of the mean and lowering of the 

 variability in the whorls at which two branches start. 



Now the question arises, can we consider the relatively high mean 

 and low variability of these whorls at which branches originate to be a 

 specific result of the presence of one or more branches at the node to 

 which the whorl belongs? Clearly, without further evidence, we can 

 not, because of the fact that among these whorls some are borne on the 

 main stem, others on primary branches, and still others on secondary 

 branches, and it has been shown that whorls are differentiated in respect 

 to leaf-number according to the part of the plant on which they are 

 borne. Further, according to the two laws of growth which have been 

 set forth above, it is clear that the number of leaves in whorls from 

 which branches originate will depend, in part at least, on the position 

 which such whorls occupy on their axes. Before we can reach conclu- 

 sions as to whether the presence of a branch influences the number of 

 leaves in the whorl we must determine the probable condition of such 

 whorls as a result merely of the operation of the usual laws of growth. 

 If, then, it be found that these v/horls differ considerably from the condi- 

 tion of "whorls in general" occupying the same relative position on the 



