RELATIVE POSITIONS OF LATERAL MEMBERS. 



169 



lateral axes (here axial shoots) are interposed between the "insertion of the respective 

 leaves and their stem-axis. 



If the axial members are greatly shortened, the view (from above) of an 

 axis, with its lateral members, often itself supphes the diagram ; as, for instance, in 

 the leaf-rosettes of Crassulaceae, and in most flowers. In other cases a transverse 

 section through the bud enables the observer to examine the divergence of the 

 leaves; but in many other cases the relative positions are more obscure, and can 

 only be ascertained by careful examination. In addition to the study of the history 

 of development, peculiar methods, depending on geometrical principles, are often 

 necessary in order to represent the relative positions correctly and at the same 

 time clearly. 



There are also circumstances in which it is desirable, instead of representing 

 the relative positions on a horizontal projection, to project them on the unwound 

 surface of the axial structure, the latter being considered as a cylinder the surface 

 of which is supposed to be flattened out. The transverse sections of the axis 

 lying one over another are denoted on this surface by straight lines on which the 

 positions of the members are drawn. 



Among the diff"erent arbitrary constructions which may be attempted on 

 paper, for the purpose of comparing the relative positions of the members of an 

 axis, or of reducing them to short geometrical or arithmetical expressions, the fol- 

 lowing is of peculiar interest, and has been specially employed to denote the re- 

 lative positions of the leaves and lateral shoots of the stem : — A line is imagined 

 proceeding from any one of the older members in such a direction that, travers- 

 ing the axis towards the right or the left, it includes the points of insertion 

 of all the successive lateral members according to their age ; the horizontal 

 projection of this line is called the Gaieiic 

 Spiral ; in reality it is a helix ^ running 

 round the stem more or less regularly. The 

 importance of this construction has been very" 

 much overrated, and it has been employed 

 where it is not only inapplicable to the eluci- 

 dation of the history of development, but even 

 where it has no longer even a geometrical 

 meaning, and no longer assists a conception of 

 the relative positions, but even makes it more 

 difficult and complicated. 



When we are dealing with solitary leaves or 

 shoots standing on the axis in three, four, five, 

 eight, or more directions, and when the diver- 

 gences are not too variable, the construction of 

 the genetic spiral is of excellent service for a 

 ready understanding of the position of the leaves (Fig. 141); and a more exact 



Fig. 141. — Transverse section through the convolu- 

 tion of the leaf-sheaths i— 6 of Snbal ambractilifera, 

 in the centre of the section of a young Jeaf-blade. 

 The arrangement of the leaves 'S a ^ divergence. 

 If the numbers i— 6 are united by a line, the genetic 

 spiral is obtained. 



' If the spiral winds from right to left, the right edge of the leaves is called the kathodic, the 

 left (ascending) edge the anodic ; the reverse in the spiral of an opposite direction seen from 

 without. 



