2 B ELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



And in this, of all older botanical generalizations, perhaps, it is 

 alone worthy a place beside the linnaean system of classification, 

 that it first introduced methods of precise observation, record, and 

 geometrical representation into the interpretation of the growth of 

 the plant body as one whole organism, and thus paved the way for 

 the classic morphological researches of Wydler, Irmisch, and Eichler. 



To Hofmeister and Sachs, as founders of the modern school, 

 the theory of Schimper and Braun, based on the observation 

 of matured organisms, struck on the rock of development; but, 

 while Hofmeister convinced himself of the utter inadequacy of the 

 theory, he did not substitute any more comprehensive view, and 

 Sachs did not investigate the matter at all deeply, regarding it as a 

 mere playing with figures and geometrical constructions, of little 

 interest except to those to whom it was practically useful.* 



Further attempts at a more mechanical solution of the problems 

 have been made by Sehwendener ; and an admirable summary by 

 Weisse in Goebel's Organography of Plants presents the methods 

 adopted in explaining the phenomena observed by the action of the 

 mechanical forces of contact-pressure. 



The subject can, however, by no means be regarded as placed 

 on a satisfactory footing. It is clear, that if mechanical agencies 

 come into play, they should be referable to the established laws of 

 mechanics, capable of resolution into their component forces, and 

 of diagrammatic representation in the different planes ; while the 

 part, if any, that is not mechanical, but due to some inherent 

 "organizing property" of the protoplasm, requires to be clearly 

 isolated from the products of known mechanical laws. 



From a mechanical standpoint, it is perhaps in the diagrams 

 that one feels most the absence of geometrical or mathematical 

 constructions. Thus Weisse, in using Schwendener's not at all 



* Sachs, On the Physiology of Plants, Eng. trans., p. 499 : " For my part 

 I have from the first regarded the theory of phyllotaxis more as a sort of geo- 

 metrical and arithmetical playing with ideas, and have especially regarded the 

 spiral theory as a mode of view gratuitously introduced into the plant, as may 

 be read clearly enough in the four editions of my text-book." 



Sachs, Text-book, edit, i., Eng. trans., p. 174 : "The treatment of the subject 

 {Parastichies) is only of value to those who are practically concerned with 

 phyllotaxis." 



