10 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



extremely difficult to take up an unbiassed standpoint, or recast the 

 matter in a new phraseology ; while to deny the- actual existence of 

 the genetic spiral otherwise than, as Sachs has suggested, an unim- 

 portant accessory of the construction, savours of direct heresy. 



'The criticism of Sachs, which strikes at the root of the theory of 

 Schimper and Braun as applied to living organisms, applies equally 

 well to the work of other observers, and requires to be constantly 

 borne in mind.* 



Because, writes Sachs, we can describe a circle by turning a 

 radius around one of its extremities, it does not follow that circles 

 are produced by this method in nature. Because we can draw a 

 spiral line through a series of developing members, it does not follow 

 that the plant is attempting to make a spiral, or that a spiral series 

 would be of any advantage to it. Geometrical constructions do not 

 give any clue to the causes which produce them, but only express 

 what is seen, and this subjective connection of the leaves by a 

 spiral does not at aU imply any inherent tendency in the plant to 

 such a system of construction.-j- 



Much of this, again, applies to the methods adopted by 

 Schwendener. Because an empirical system can be forced by 

 pressiu:e into a condition resembling that obtaining in the plant, 

 it does not follow that a similar pressure acting on a similar 

 system is in operation in the plant itself. 



Schwendener,! it is true, made a great advance in dealing with 

 solid bodies and spheres, rather than the abstract geometrical points 

 of the Schimper-Braun theory ; and, so far, Goebel is undoubtedly 

 right in stating that further research must be conducted along the 

 lines laid down by him. But at the base of all Schwendener's con- 

 structions lies the fact that he begins by assuming the fractional 

 series of Schimper and Braun, and then arranges a mechanism to 

 convert these into systems more in accord with what is actually 

 observed in the plant. 



* Sachs, History of Botany, Eng. trans., p. 168. 



t Mechanische TTieorie der Blattslellwngen, 1878. 



Gf. Airy, Proceedings of the Royal Society, 1874, vol. xxii. p. 297, for a very 

 similar hypothesis of pressure on actual primordia without reference to the 

 actual structure of the growing point. 



X Goebel, Organography, Eng. trans., p. 73. 



