122 



VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



are 4 branches, etc. Clearly the maximum number of branches possible 

 is 5. Proceeding in the way just illustrated for the first 10 secondary 

 branches on all plants of Series I, II, III, and IV, the results shown in 

 table Q6 were obtained. No branch was counted which did not have 

 at least 7 whorls distad of it on the primary axis. 



Fia. 25. — Diagram of a portion of a plant. I, "first" branch; II "second" branch; III, "third" branch 

 etc. These secondaries are for convenience represented without leaves. Further explanation in 

 the text. 



We see at once from the table that the more distad the branch with 

 which we are dealing lies the larger is the number of branches occurring 

 in the next 5 nodes. When we get beyond the sixth branch less than 

 four occur very rarely. These tables show very plainly the gradual 

 approach towards a condition where each node bears a branch. It will 

 help to make the point still clearer if we examine the means of the 

 arrays in table 67. 



Table 67. — Mean number of branches in the five nodes immediately following 



a designated branch. 



Branch. 



First... 

 Second 

 Third... 

 Fourth 

 Fifth... 



Branch. 



Sixth.... 

 Seventh 

 Eighth., 

 Ninth... 

 Tenth..., 



Series I. II, 



and III I Series IV. 

 combined. 



3.86 

 4.60 

 4.20 

 4.75 

 4.75 



4.58 

 4.36 

 4.25 

 4.40 

 5.00 



The increase in the mean number of branches is evident. A little 

 inspection shows, however, that this increase is not uniform in all parts 

 of the table, but is on the whole distinctly more rapid in the first few 

 branches than in the later ones. In other words, the increment in the 

 character under discussion becomes smaller and smaller for the successive 

 branches. This at once suggested that the law of change here might 



