210 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



The point therefore remains, — How far is this appearance of 

 orthogonally intersecting log. spirals possibly a secondary effect pro- 

 duced by building a system of approximately similar protuberances ? 



This problem may be attacked by assuming the orthogonal log. 

 spiral construction as expressing a distribution of growth energy 

 and seeing whither it will lead — that is to say, by deducing the 

 proper curves for the transverse component of the members, build- 

 ing the corresponding mathematical systems of what such phyllo- 

 taxis should be, and then comparing these constructions, and any 

 deductions which may be made from them, with the familiar 

 phenomena observed in a transverse section of a shoot-apex. 



If the appearances agree, or can be made to agree within an in- 

 telligible range, when other secondary factors are allowed for, the 

 orthogonal system may be -regarded as proved for phyllotaxis, as 

 one special case of a theory of growth distribution ; and while 

 proving this, the same deductions would further involve a con- 

 firmation of the original views of Sachs, which still remain some- 

 what hypothetical, in that they are based on appearances judged by 

 the eye ; and it at once becomes evident that this conception of 

 the distribution of growth-energy in orthogonally-intersecting 

 planes must be of the utmost importance in determining the 

 primary space-form of the whole of the plant-body. 



In thus dealing with phyllotaxis phenomena which present the 

 appearance in transverse section of a system of intersecting curves, 

 two points of view may be established. One, that of the builder, 

 in which the addition of new elements in time is made the leading 

 feature ; the other, that of the architect, to whom the actual order 

 of construction may be- immaterial. Is, that is to say, the space- 

 form of a plant determined by the visible structure of the growing 

 point — or is it an invisible property of the shoot, and the same 

 growth form may be worked out in terms of different units ? The 



highest degree characteristic ; the directions of the cell divisions are by no 

 means accidental, and an observer sufficiently acquainted with geometrical and 

 mechanical science at once recognises in the structures presented by the totality 

 of ceU-walls within an organ, cut in the proper manner, that we have here to 

 do with a conformity to law, the true meaning of which, however, is difficult to 

 decipher " (Sachs, Physiology, Engl, trans., p. 432). 



