POSITION OF BRANCHES. 



123 



be a logarithmic one, similar to what we have previously demonstrated 

 for the growth of leaves. Accordingly the data of this table were fitted 

 with logarithmic curves of the type used in the previous cases, by the 

 same method. The resulting equations were. 



Series I, II, and III combined, Y = 2.4061 + 2.2194 log a; (I) 



Series IV, Y = 3.8440 + .8931 log (x-.S) . . (II) 



in which Y denotes mean number of branches occurring in the five 

 nodes immediately following any designated branch, the ordinal position 

 of which is given by x. Calculating the values of Y for values of x 

 from 1 to 10 we have the results shown in fig. 26. 



5 6 



Branch 



Fig. 26.— Curves showing mean number of branches (ordinates) In five nodes Imme- 

 diately following a designated branch (abscissas) on a primary axis. Series I, II, 

 and III combined r-\ Series IV . 



The numbers with which we are dealing here are so small relatively 

 that great regularity in the observations can not be expected. There 

 can be no doubt, however, that the general trend of the observations is 

 adequately represented by the logarithmic curves. This means that 

 the growth processes concerned in branch production, so far as may be 

 judged from our present material, follow a logarithmic law. The mean 

 number of branches formed in a constant number of nodes (5) increases 



