76 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



Again, the impulses in the mass of growing protoplasm, constitut- 

 ing the first zone of growth, have no necessary connection with 

 the presence of cell-walls or any subsidiary current-movements 

 within the component cells of the apex, where these are 

 present.* 



Thus, in S'elianthus or Hippuris, each impulse, when first observ- 

 able, involves a whole group of cells ; in Uqidsetum several impulses 

 forming about one-third of a complete whorl of members can be 

 definitely localized as belonging to the derivatives of a single seg- 

 ment of the initial cell; while in the coenocytic Dasycladaceae, 

 the impulses are clearly independent of the non-existent ceU walls, 

 but the phyllotaxis is none the less perfect in its symmetrical 

 relations, and bears comparison as a symmetrical concentrated type 

 with members exhibiting cellular structure. Thus Neomeris dumetosa 

 presents alternating whorls of thirty members, Hguisetum Telmateia 

 30-40, Hippuris 6-12. Without insisting on any special dynami- 

 cal interpretation of the complicated phenomena exhibited by such 

 a living mass of protoplasm, it appears evident that the transverse 

 components of the forces involved in the production of symmetrical 

 phyllotaxis may he expressed by a diagram illustrating the uniform 

 motion of a free circular vortex, the construction lines of which are 



* Modern researches (Vocliting, Weisse, Schumaim) have tended mainly to 

 the observation of the actual facts of ontogeny, on the lines laid down by 

 Hofmeister. But such methods have one weak point, they can only result in 

 the statements of the facts observed without giving any reason for such pheno- 

 mena. Thus in the case of the rise of a semi-fluid protoplasmic protuberance on 

 a similar semi-fluid mass, it is clear that the causes which led to the initiation of 

 such a formation are practically over so far as that protuberance is concerned, 

 as soon as it becomes visible, and other forces may come into play quite different 

 from the primary cause. Phyllotaxis is therefore concerned primarily with the 

 forces which produce new-growth centres at or below the surface of the proto- 

 plasmic mass of the growing point, and suggestions as to their modes of operation 

 can only be deduced from physical standpoints. The large broad apex (8-10 

 mm.) of a full-grown specimen of Aspidivm Filix-Mas shows, in the early part 

 of the year, the primordia of the leaves of the next succeeding year already 

 commencing as slight elevations spaced out without any contact relations to one 

 another in the spiral series (5-1-8). The protuberances are visible to the naked 

 eye, without the section-cutting required for smaller buds, but no amount of 

 observation of the facts of development will explain the reason why these eleva- 

 tions appear in their appointed places. (Of. (3 + 5) system of fig. 35, Plate VIII.) 



