Page:History of botany (Sachs; Garnsey).djvu/186

 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 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 measurements 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 Nägeli subsequently suggested. 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