RELATIVE POSITIONS OF LATERAL MEMBERS. IJJ 



of phyllotaxis, states the general rule in the following words : — New lateral members 

 have their origin above the centre of the widest gaps which are left at the circumference 

 of the punctum vegetationis between the itisertions of the nearest older members of the 

 same kind. The rule is illustrated by the case of alternating whorls (especially of 

 pairs crossing one another at right angles, or 'decussating'), or by that of alter- 

 nating solitary leaves with a base which grows early in breadth, in Phanerogams, 

 where the punctum vegetationis consists of small cells. Where, on the other hand, 

 we have decidedly bilateral horizontal axes (as in Pteris aquilina, Salvinia, and 

 Marsilea), or definite relations of the leaf-formation to the segmentation of an apical 

 cell (as in Mosses), or distinctly successive formation of the members of a whorl 

 (as in Chara, Salvinia, flowers of Reseda, &c.), the mechanical importance of the 

 rule is, in my opinion, subordinate to the other causes which then have the greatest 

 influence in determining the position of the new members. Independently of the 

 points of view referred to in paragraphs 1-4, the genetic relationships indicated 

 in this paragraph show that it is scarcely possible to find a single rule which will 

 govern all cases of phyllotaxis. Causes which belong to altogether diff"erent cate- 

 gories must, according to circumstances, exercise the greatest influence in determin- 

 ing the point at which a new member is formed. 



(6) I consider it a circumstance of primary importance that the same or very 

 similar kinds of phyllotaxis may be brought into existence by very diff'erent com- 

 binations of causes, and positions apparently very diff'erent by very similar combi- 

 nations of causes. Among the causes here referred to I understand the previous 

 relative development of the axis and of its lateral members, the influence of the 

 primary on the secondary axes, of pressure, gravitation, light, and similar conditions. 

 The validity of this position becomes most evident when it is observed that the 

 same or similar divergences of leaves or lateral shoots may occur universally in 

 unicellular plants, in multicellular plants with a distinct apical cell, and in those in 

 which the punctuin vegetatiotiis consists of a small-celled tissue without any definite 

 relation to the segmentation of an apical cell, as in Phanerogams. The mechanics 

 of the processes of growth must undoubtedly be diff'erent when the lateral branches 

 of a Vaucheria are formed in two rows, and when the two rows of leaves of a 

 Fissidens or of a Grass are produced in the same or a similar position, in which 

 case the cell-walls in the primary meristem represent a multiplicity of causes of 

 growth and of hindrances to it. The similar arrangement of the outgrowths under 

 such different circumstances does not prove that the circumstances themselves are 

 similar or of but little importance, but only that altogether different combinations 

 of causes may lead to very similar relations of position. In Muscinea? and 

 Vascular Cryptogams the relation of the formation of leaves to the segmentation 

 of the apical cell is the more obvious the nearer to the apex the leaves originate. 

 It is most obvious of all in Mosses, where each segment grows out into a leaf- 

 forming protuberance immediately after its formation, and before further cell-division 

 takes place. Here the immediate conditioning cause of the position of the leaves is 

 the position of the leaf- forming ' segments' themselves; when these latter are formed 

 in two alternating longitudinal rows, as in Fissidens \ two rows or orthostichies of 



Lorentz, Moosstudien. Leipzig 1864, 



