232 RELATION OP PHYLLOTAXIS TO MECHANICAL LAWS. 



subsequent mathematical form of these may be, will exhibit the 

 results of equal growth in equal times. 



Two points may be here conceded : there must be, as already 

 stated, some mechanical law implying a fundamental property of 

 force and matter underlying these phenomena of rhythm; and 

 it will again be hardly possible to discuss such speculations without 

 trespassing on the terminology of some branch of physical science, 

 the fundamental laws of which are reaUy equally obscure. Thus, 

 choice has been suggested between the terminology of the electro- 

 static field, vortex-motion, or even the crystallisation * which 

 constituted the basis of Nageli's micellar theory. There is no 

 suggestion that phyllotaxis has anything to do with any of these 

 physical phenomena ; but certain features capable of geometrical 

 presentation by orthogonal trajectories, common to these physical 

 phenomena, appear also to result from the determining causes of 

 phyllotaxis. The essential point at present is, — granted the 

 geometrical theory can be established for phyllotaxis, what 

 inferences can be drawn from it from a physical standpoint, any 

 or none ? When physicists are in a position to state that the 

 conceptions by means of which they are led to the mathematical 

 laws of phenomena are necessarily absolutely correct, it may be 

 possible to further discuss what ultimate bearing the similar 

 orthogonal construction may have in the case of living protoplasm. 

 Till then it is at any rate remarkable that such similarity should 

 be found, and few will doubt that, as Sachs pointed out for cell- 

 structure, some law evidently controls the whole series of 

 phenomena, which must again be a fundamental property of 

 living matter. If the introduction of a mathematical conception 

 of growth and growth-centres can lead to any better method of 

 dealing with the facts, there will be no harm in trying to apply 



* The general facts of crystallisation are even more remarkable in that thej' 

 refer to inanimate matter. Thus it may be possible to deduce mathematically 

 the number of crystalline forms, but the prime cause which determines why 

 crystallisation should ever take place, or why some forms should be commoner 

 than others, or why a given substance should select a special form, is as remote 

 as any indication of the prime cause of phyllotaxis. The number of arrange- 

 ments possible ia phyllotaxis is relatively small, and the observation and 

 tabulation of their occurrence comparatively simple. 



