322 RELATION OP PHYLLOTAXIS TO MECHANICAL LAWS. 



upwards to form a lamina in which " dorsiventrality " is not so 

 excessive as in a more typical foliage-leaf. The growing-point is 

 sunk to the level of the bases of all the leaves, and in spirit- 

 material may be contracted below the insertion of the great 

 majority. Sections of the bud may therefore be compared from 

 different levels (fig. 83, T., II.). A section across the whole bud 

 portion of a full-grown plant shows for the most part five clear 

 curves, pointing therefore to a phyllotaxis system (5-t-8). The 

 members may be thus readily numbered up along these curves 

 and the system checked to the centre by tracing a hypothetical 

 ontogenetic spiral with a divergence angle of 137'^ : the parastichies 

 are, however, seen to be imperfect at the centre, and the overlap- 

 ping of members in sets of three points to a phyllotaxis of (2-|-3) 

 (fig. 83, members 28-36). On the other hand, a section which 

 just grazes the top of the axis shows that the actual system in 

 which the members are laid down is (3 + 5). The apex is broad 

 and flat, the members arise apparently without close contact, and 

 their boundaries are difficult to recognise along the shallow groove 

 which separates them ; it is, in fact, only by taking a section that 

 their shape can be defined. There is no doubt, however, as to the 

 construction of the curve-system being (3 + 5). The explanation 

 of these phenomena appears therefore quite simple ; the lamina of 

 the younger members increases rapidly at first, and sliding-growth 

 is sufficient to bring three members into lateral contact ; a section 

 taken through the upper part of the younger members in this 

 condition presents the appearance of a (24-3) system. On the 

 other hand, the bulk of the section passes through the outer 

 leaves lower in their course, at a point at which tangential 

 extension is at a minimum; the members thus apparently draw 

 away from each other laterally, and the " 8 " curves are thus 

 opened up, and the system assumes the form of a (5-f-8) type with 

 the " 5 " curves smooth-edged. 



A similar effect is seen in species of Sedum, in which the 

 members tend to round off and form so-called "centric" leaf- 

 forms. Thus S. pruinatum (fig. 103), developing as a (5-|-8) 

 system, presents the secondary appearance towards the periphery 

 of the section of an (8-1-13), the " 8 " curves being now the smooth- 



