166 MorpJiology under the Doctrine of [BOOK i. 



and attractive light. But the theory had a further advantage ; 

 it seemed not only to present the form of the plant in its 

 matured state, but to treat it genetically ; and in fact it did 

 possess an element of historical development, inasmuch as it 

 made the genetic succession of the leaves and of their axillary 

 shoots, which is at the same time the succession from the base 

 to the summit, the foundation of all consideration of the plant- 

 form. But it is also true that in this lay one of the weak sides 

 of the theory ; as long as it was a question only of continuous 

 spirals, the succession of matured leaves does also represent the 

 succession of their formation in time ; but this was not actually 

 proved in the case of leaf-whorls, and here, to save the theory, 

 genetic relations had to be pre-supposed for which no further 



4 



proof was forthcoming, while fresh researches have repeatedly 

 shown that a strict application of Schimper's theory is found 

 frequently to contradict the facts of development as directly 

 observed *. Moreover, regard was had only to those measure- 

 ments of divergence on the continuous genetic spiral which 

 were taken on the matured stem, while there was always the 

 possibility that the divergences might have been different at 

 the first, and been afterwards modified, as Nageli subsequently 

 suggested 2 . And again, the theory had a dangerous adversary 

 to encounter in the frequent occurrence of leaves that are 

 strictly alternate or crossed in pairs, and to conceive of this as 

 a spiral arrangement must at once appear to be an arbitrary 

 proceeding both from the mathematical point of view and from 

 that of historical development ; the assumption of a return of 

 the genetic spiral from leaf to leaf, as for instance in the 

 Grasses, like the prosenthesis in the change of divergence, 

 afforded, it is true, a construction which was geometrically 

 correct, but which could hardly be made to agree with the 



1 See Hofmeister, ' Allgemeine Morphologic' (1868), pp. 471, 479, and 

 Sachs, ' Lehrbuch der Botanik,' ed. 4 (1874), p. 195. 



1 See Nageli, ' Beitrage zur Wissenschaftlichen Botanik ' (1858), I, pp. 40, 

 49. 



