80 VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



whorls in the two cases. The value of the constant C in the case of the 

 secondaries (=1.8024) shows us at once that the increment in Yper 

 unit change in x will be greater in the secondary-branch whorls than 

 in the primary. That this in fact is the case is obvious enough to the 

 eye if we compare fig. 14, with plate I. The upward slope of the secondary 

 curve is much more rapid than is that of the primary curve. The fact 

 may be shown in another way. The successive increments in mean leaf- 

 number for the first 10 whorls of primary and secondary branches are 

 given in table 41. 



Table 41. — Increment in leaf-number in successive whorls. 



It is evident that the increments are larger on the secondary branches. 

 The nature of the change in the increment is very clearly shown if we 

 plot the data from table 41 to the same scale for the two orders of 

 branches. This has been done with the result shown in fig. 15. 



We see that though the secondary branches start lower, they attain 

 any designated mean leaf- number in a smaller number of whorls. Thus 

 while in the case of the primary branches a mean leaf-number per whorl 

 of 11 would only be reached after the formation of 175 successive 

 whorls, the secondaries would reach this mean after the formation of 

 only 56 whorls in round numbers (55.58 exactly). That is to say, if we 

 may speak in terms of analogy, the morphogenetic mechanism attains 

 its results more rapidly in the case of the secondary branches. This is 

 an expression of the fact noted above (p. 77) that the positional corre- 

 lation is higher in secondary than in primary branches. The law 

 of growth in the plant is, as we have seen, that the mean leaf- 

 number per whorl increases with successive whorl formation, the rate 

 of increase at any point varying inversely as the number of whorls 

 which have been formed up to that point. Clearly the production of a 

 maximum mean leaf-number may be regarded as the "end" towards 

 which the morphogenetic process here tends. But the secondaries 

 attain this "end" more quickly than do the primaries; that is, with the 

 formation of fewer successive whorls. If, merely as an analogy, we 



