RELATIVE POSITIONS OF LATERAL MEMBERS, 1 95 



geometrical rules, by means of which the genetic spiral can be easily deduced 

 from the parastichies \ 



It is evident that the constructions hitherto mentioned can only be more -or 

 less convenient aids to an understanding of the actual principles of the arrangement 

 of leaves. But in order to obtain, with their assistance, a deeper insight into the 

 processes of growth themselves of which these principles are the result, it is 

 necessary to follow the development, and in every single case to ask the question, 

 what circumstances are the cause of a new member being formed just in this place 

 and nowhere else. It may be well, therefore, to bring forward here some of the 

 points which must be considered in reference to this view. 



(i) The first point is always to determine with certainty the order of succession 

 in which the lateral members are formed. 



(2) Attention/must be paid not only to the lateral divergence, but also to the 

 longitudinal distance at which a new member is formed at the growing point above 

 the members last preceding it. The longitudinal distances of the youngest 

 lateral structures of a growing point from one another are usually very small ; 

 there is often no space to be distinguished between them, i. e. between the 

 planes of insertion of the youngest members. This circumstance may, on the 

 one hand, assist in the determination of the place where the next member must be 

 produced ; but, on the other hand, may give occasion, as the development of the 

 axis proceeds with its crowded lateral members, to compression and distortion, by 

 which the original arrangement is altered. 



(3) By the increase in length of the common axis, members which were at 

 first closely crowded become placed at a considerable distance from one another, 

 while others, in consequence of slower growth, remain closely packed; so that a 

 different distribution occurs in different parts of the 'stem, as in the leaf-rosettes and 

 flower- stalks of Crassulaceae, Agave, Aloe, &c. In the same manner the angle of 

 divergence frequently becomes changed by the more rapid increase in thickness of 

 the axial structure on one side than on the other; and still more commonly by 

 torsion round its own axis of growth. By such torsions lateral members, arranged 

 at first exactly in straight rows, become displaced so that the orthostichies appear as 

 if wound spirally round the axis. This occurs, for instance, according to Nageli 

 and Leitgeb, in the root-systems of Ferns, Equisetaceae, and Rhizocarpeae, as well as 

 in the three-rowed phyllotaxis of the Moss Fontinalis antipyretica, according to 

 Leitgeb. But the most striking example is furnished by the stem of the screw-pine, 

 Pandanus uHlis. In the bud, the numerous leaves, already strongly developed, 

 stand, as is shown by the transverse section, in three perfectly straight lines with 

 the phyllotaxis \ ; but, as the development of the stem advances, it undergoes so 

 severe a torsion that the three orthostichies are transformed into three strongly 

 curved spiral lines running round the stem (see Fig. 154). In these and similat 

 cases the change in the relative positions caused by the torsion of the actual 

 structure can be easily and certainly determined. But when the structures are so 

 arranged at the apex of the axial structure that the angle of divergence cannot 



* As the treatment of the subject is only of value to those who are practically concerned with 

 phyllotaxis, I must refer to the detailed description in Hofmeister's Allgemeine Morphologic, § 9. 



O 2 



