CONTACT-PRESSURES. 239 



between the developing primordia: the fact that the Schimper- 

 Braun formula did not hold for developing systems was common 

 knowledge, but his method of connection of these factors into 

 causal relation was extremely vague, and it may be noted that it 

 never appealed to the critical acumen of Sachs {of. also Pfeffer, 

 Physiology, Eng. trans., vol. ii. p. 144). It may also be pointed 

 out that, whatever importance be attributed to Schwendener's 

 conception of the alteration of primary systems by hypothetical 

 pressures, whether intrinsic, of the members themselves, or extrinsic, 

 of some compressing agency, they have after all little to do with 

 the fundamental facts of phyllotaxis, which is only concerned 

 with the production of the primary system itself, all secondary 

 alterations being subsidiary phenomena. Schwendener, in fact, 

 still requires to prove : — 



I. The existence of any force producing displacement ; 

 II. The fact that true displacements really are produced ; 



III. That such displacements are the result of the postulated 

 force, 

 whether, again, the force be regarded as a mechanical agency or 

 a still vaguer phenomenon of stimulation. The second of these 

 points has been attacked by Schumann and Jost,* their object 

 being to establish the fact, always sufficiently obvious to the 

 unprejudiced mind, that such extensive displacements do not take 

 place, and that the initial curve-system, as it first becomes visible 

 at the plant-apex, persists in the adult condition unless rendered 

 ambiguous by secondary elongation of the shoot. 



The standpoint here taken up is not so much that Schwendener's 

 theory is impossible, — it is founded on certain definite premises 

 from which mathematical results ensue, — but that it is entirely 

 gratuitous and unnecessary, since the phenomena it was intended 

 to explain, i.e. the secondary alterations of the Schimper-Braun 

 constructions, are non-existent; while the premises themselves 

 more than include all the data from which the log. spiral theory 

 is mathematically derived — the very data, in fact, for which in 

 previous pages stricter evidence has been demanded. 



* L. Jost, Bot. Zeit., 1902, p. 21 ; B. Leisering, Flm-a, 1902, p. 378 ; Prings. 

 Jahrb., 1902, p. 421. 



