230 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



be possible to give an explanation in physical terms ; but, on the 

 other hand, it is clear that, if the intersections are never ortho- 

 gonal, the data given by the plant are so obscure that the 

 phenomena of phyllotaxis only become the more hopeless of 

 explanation. So strongly is this standpoint suggested, that it 

 appears well worth while to assume the consequences of ortho- 

 gonal intersection and base all hypotheses on them; since, if 

 the view is a mistaken one, the error must become apparent 

 sooner or later ; while, so long as no such error appears, it 

 may be assumed that the hypothesis of energy-distribution is a 

 workable one. 



The use of the word action in previous chapters {cf. Part I. 

 p. 36), as a generalised expression, has been since avoided, as in 

 its strict mathematical sense the term undoubtedly places the 

 subject in too complex a light to be at present available for 

 botanical purposes : its introduction was mainly based on the 

 necessity for indicating that the systems presented phenomena 

 of movement, without reference to any obviously unattainable 

 data as to the actual velocity of any units which might be 

 regarded as component particles. Since the actual velocities of the 

 particles of a growing plant-apex are extremely small,a closer analogy 

 may perhaps be found, so far as the present purpose is concerned, 

 in a two-dimensional electrostatic magnetic field whose properties 

 may be considered as depending on each quasi-square portion of 

 space, enclosed by lines of force and equipotential lines, possessing 

 the same amount of potential energy. Just, in fact, as in the 

 above case the same amount of potential energy may be con- 

 sidered to be situated in each quasi-square, so in the plant-apex 

 the same amount of growth-energy, i.e. that required for the 

 production of a single leaf-primordium, is localised in a single quasi- 

 square of the phyllotaxis diagram.* Or, on the other hand, if 

 growth-energy be considered as more analogous to kinetic energy 



* A botanist would probably be more inclined to state the converse pro- 

 position : the fact that an equal amount of energy is presumably directed 

 into each lateral primordium, granted a constant relation between axis and 

 primordium, would involve such a geometrical construction. Either way of 

 looking at it is sufficient for present purposes. 



