234 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



tion only applies to one special case, and does not hold for the 

 whorled and muUijugate systems, it is clear that the so-called 

 genetic-spiral also vanishes from theoretical considerations ; since 

 now it is seen to be merely a property of a special arrangement 

 of intersecting spirals, it can tell no more as to the meaning of the 

 phenomena then was previously known. The creation of Schimper, 

 it retains a certain interest as a relic of the past, but can now only 

 be regarded as a convention which is often useful in practice owing 

 to the fact that it admits of a method of attributing a numerical 

 value to the members which, so long as growth is distributed 

 equally around the growth-centre (i.e. centric), is actually a time- 

 sequence, and expresses the order of ontogeny as checked by 

 observation. It must, however, be remembered that this 

 sequence, obtained by resolving a certain number of inter- 

 secting curves along a single path, will necessarily cease to 

 be a time-sequence if once the growth-system becomes eccentric 

 (cf. Eccentricity). 



With orthostichies and the genetic-spiral both eliminated from 

 the subject, the parastichies alone remain, not only as the data 

 to be accumulated by observation of the plant, but as the ex- 

 pression of the working mechanism of the construction. Using 

 again what must be perfectly metaphorical language, since 

 borrowed from strictly physical conceptions, the log. spiral theory 

 suggests that new centres of lateral growth are originated at the 

 points of intersection of curves, which may be regarded as indi- 

 cating a type of segmentation of the protoplasmic mass, wholly 

 independent of cell-formation, along paths of distribution of 

 equal growth-potential which may be so far homologised with 

 " Lines of Force." To bring these curves into homology with 

 equipotential lines it is required to prove that the intersec- 

 tions are primarily orthogonal. The method adopted consists 

 in assuming the fact, and continuing subsequent mathematical 

 deductions with a view to render the error of the theory 

 apparent. So long as no marked discrepancy appears, the 

 theory may be regarded as a fair approach to the description 

 of the conditions actually prevailing in the field of a " growth- 

 centre." 



