POSITION REGRESSION— SECONDARY BRANCHES. 



81 



may compare the developing branches of a Ceratophyllum plant with a 

 machine, of which the whoi-ls are the product, we may say that the 

 machine works more smoothly the longer it runs. 



The fact that the increments in mean leaf -number with successive 

 whorl formation are greater in the case of secondary branches is shown 

 in the growth equation by the higher value of the constant C. This 

 indicates that C may be regarded as the constant which expresses the 

 action of the internal formative factors, in contradistinction to A, which, 

 as we have seen above (p. 75) in the case of primary branches, expresses 

 the effect of external environmental conditions. We should expect C, 

 then, to remain practically constant for the same division of the plant 



C 0.8 



E 



u 



<J 0.6 



5-6 



Whorls 



9«-IO 



Fig. 15.— Curves comparing growth of secondary and primary branch whorls. The ordinates 

 give the increments in mean leaf-number as we pass to successive whorls, the positions 

 being given by the abscissas. Primary-branch whorls ; secondary-branch whorls 



(i.e., primary or secondary branches) without regard to external influ- 

 ences, while A changes with change of environmental conditions. In 

 other words, it would appear that external conditions affect chiefly the 

 absolute size of the elements of the plant while the internal morphoge- 

 netic factors which determine the way in which the proportionate 

 differentiation of the elements shall occur are practically independent 

 of environmental change. These relations hold for primary branches 

 very clearly, so far as the present material goes. We might test the 

 matter for the secondaries in the same manner as before by determining 

 whether with an appropriate change of the constant A in the secondary- 

 branch growth equation (II) which has been deduced from Carp Lake 



