240 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



As Schwendener's standpoint is somewhat involved and subject 

 to modification, the following example of his original method may 

 serve to illustrate the difference between the two conceptions. A 

 well-known figure from Schwendener's first plate has been copied 

 by Weisse into Goebel's Organography, and appears in the English 

 translation (p. 75). A phyllotaxis system is supposed to be repre- 

 sented by (1) a set of spheres — a legitimate hypothesis, but still 

 purely a hypothesis, since there is no evidence to show that the 

 transverse section of a primordium is ever mathematically circular. 

 (2) The spheres are taken as being all the same size : a condition 

 which is never reached in the plant until growth has uniformly 

 ceased, and the pressures with it. (3) They are arranged according 

 to a helical divergence system of Schimper and Braun, which is 

 all right once equal spheres have been postulated. (4) It is 

 assumed that such an arrangement will give orthogonal loose 

 packing; and finally, (5) an outside vertical force, an entirely 

 hypothetical conception so far as the plant is concerned, is applied, 

 with the natural result that the system may be ultimately thrown 

 into close hexagonal packing. It is difficult to see what exact 

 bearing such a conception, involving so many doubtful assumptions, 

 can have on the arrangement of the gradated primordia arising 

 on a radially symmetrical plant-apex ; but, by taking the vertical 

 force as a tension instead of a compressing force, it becomes clear 

 that such a construction might approximately represent the 

 changes produced in an adult system by passing it through the 

 second zone of elongation, and which have been previously regarded 

 as wholly outside the province of phyllotaxis, except in so far as 

 it may concern the descriptive writer. In discussing Schwendener's 

 standpoint, the first thing which requires to be clearly defined is 

 the exact significance of what is to be included under the term 

 phyllotaxis ; is it to include all secondary changes in the system 

 which may appeal to the eye, or has it to do solely with the 

 actual forces which produce the primary system within the proto- 

 plasmic mass of the apex, without any reference to the details 

 of cell-construction ? Thus all phenomena of packing must be 

 secondary : primordia must have been made and have reached a 

 certain bulk before they can be packed. The agencies which 



