348 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



General Conclusions. 



I. The log. spiral theory, as already indicated,* is put forward 

 solely as a mathematical conception, admittedly gratuitously 

 introduced into plant-morphology, as a fundamental hypothesis 

 founded on a mathematical theory of centric growth (Part I., 

 p. 16), and is intended to replace the helical theory of Bonnet, 

 which, being deduced from an ideal adult construction, was only 

 required to imitate appearances of leaf-distribution on a full- 

 grown shoot. In the preceding pages this new view of the 

 growth of a plant-shoot and its appendages from one "growth- 

 centre " has been elaborated from a simple standpoint of uniform 

 growth which does not necessarily ever obtain in any living 

 body. 



II. The mathematical data corresponding to such a standpoint 

 have been deduced and tabulated, in accordance with the simple 

 numerical data afforded by plant phyllotaxis systems ; and thus it 

 has been shown that the divergence angles of such uniformly 

 growing asymmetrical systems can be deduced mathematically, 

 while by simple geometrical constructions very reliable results 

 may be obtained by one quite ignorant of mathematics. Also, 

 granting the reasonable hypothesis that the lateral members of a 

 plant are formed in one growth-system controlled by the shoot- 

 apex, the curves of the transverse components of such members 

 for different systems have been deduced and figured. 



III. Given these data, it now remains to take them to the 

 plant and note how far confirmation of the theory of orthogonal 

 construction can be obtained, as implying an orthogonal distribu- 



* New Phytologist, 1902, p. 49 ; Arnials of Botany, vol. iviii., p. 227. 



