^oo LECTURE XXIX, 



mechanical and geometrical considerations, among which the mutual pressure of 

 the young organs on a common axis plays an important part. It would require 

 far too much space here, however, to go more in detail into Schwendener's somewhat 

 prolix account: it suffices that, as he shows, it is possible to demonstrate by means of 

 simple models (figures in a displaceable frame) how from purely mechanical causes 

 arrangements corresponding to the divergence f , for example, must pass over into such 

 as correspond to | and J^, the transition from one divergence into the other being 

 accomplished somewhat suddenly. Schwendener's description is based on the 

 circumstance, previously made evident by Hofmeister and myself, that the laws of 

 phyllotaxis assumed by the spiral theory only appear at all where the young organs 

 (leaves or shoots) arise on the growing-point of a mother-shoot in large numbers, 

 and quite close beside one another, so that at first no free surface whatever of the 

 axis is presented. By means of this very close position, the place of origin of the 

 outgrowths newly added acropetally is in part determined, and at the same time, 

 in consequence of the close packing, pressures and torsions must make their ap- 

 pearance during growth, by which the relations of position assume their definitive 

 condition. 



Where the oifshoots of an axis appear at some distance from one another from 

 the commencement, none of the relations spoken of occur. Apart from some Algse 

 which we might adduce here, I may refer the reader to the known case of the whorls 

 of branches of the Pines. The leaves of these trees arise close above and beside one 

 another on the main shoot, and since they are from the first numerous and small 

 in relation to the growing-point, they present complicated and somewhat constant 

 divergences : the position of every new leaf which makes its appearance at the 

 growing-point is simply determined by these conditions. The whorl of branches 

 developed in any one year on a Pine, on the contrary, only arises after the growing- 

 point of the main shoot which produces it has grown far beyond the whorl of branches 

 of the previous year ; the consequence is that the consecutive whorls do not alternate 

 regularly as elsewhere, but are situated one above another in any direction on the 

 stem. 



Since the older morphology as expressed in the genetic spiral with its parastichies 

 and constant divergences which were supposed to stand in mysterious connection 

 with one another, and further with its principle of axillary branching, cannot exist 

 in the face of an unbiassed criticism of the facts, simply because it sets up a few 

 relations of position, which only occur on radial orthrotropic shoots, as the funda- 

 mental law of all vegetable growth, we must now rather acknowledge that there is no 

 general law which can be formulated for the arrangement of the organs on a parent- 



read clearly enough in the four editions of my text-book. That the whole doctrine of Schimper 

 and Braun depends, not, as it Were, merely upon the inaccurate interpretation of single facts, but 

 that it rather stands in direct opposition to scientific investigation, and was based on the founda- 

 tion of the idealistic direction of the 'Naturphilosojihie' was clearly expressed by me in my 'GeschichU 

 der Botanik' (1875). The fundamental ideas of this criticism were also subsequently placed by 

 Schwendener, in his ' Mechanischen Theorie der Blattstellungen' (1878), in the foreground of his 

 considerations. A historical description well worthy of note of all the views on leaf-position 

 hitherto held, as well as a theory of his own, is contained in Casimir de CandoUe's 'Considerations 

 sur Vitude de la phyllotaxie'' (Genf, 1881). 



