120 



VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



We may turn now to another question with reference to the distri- 

 bution of branches, which may be put in this way: What proportion 

 of first branches have their succeeding (i. e., second) branch on the 

 node immediately distad of that on which they themselves are borne, 

 and in what proportion of cases are there one or more nodes without 

 branches intervening between the two? Similarly, what are the propor- 

 tions of cases for second and third, third and fourth, etc., branches, 

 where successive branches are borne on contiguous nodes? The data 

 on these questions have been extracted for the first to the sixth secondary 

 branches in the first four series and are shown in table 64. In this table 

 a double column is given to each series, one half being headed + (plus) 

 and the other half — (minus) . Whenever the succeeding branch to the 

 one designated in the first (left-hand) column of the table was borne on 

 the next node it was entered in the + (plus) column. When branchless 

 nodes intervened between the two an entry was made in the — (minus) 

 column. Unless at least three whorls of leaves were formed beyond 

 a branch no record was made regarding it. That is, only cases were 

 included where it was possible for a succeeding branch to have been 

 formed. 



Table 64. — Position of succeeding branches (secondary). 



This table shows that there is a decided difference between first 

 branches and those farther distad on the axis, in respect to the matter 

 under consideration. Thus we see that there is more than an even 

 chance that one or more branchless nodes will follow the first branch, 

 while for all the others the chance of a succeeding branch occurring on 

 the next node is greater than the chance that it will not so occur. 

 Further, this chance increases the farther out on the axis we go. This 

 is shown most clearly if we calculate the percentage (in the total number) 

 of the cases in which the immediately succeeding branch occurs at the 

 next node. This has been done for the last two columns of the table 

 (Series I, II, and III combined and Series IV), with the results shown 



