ASYMMETRICAL LEAST-CONCENTRATED TYPE. 159 



of the axis and the imbrication of the stout folded leaves. A 

 similar condensation in the case of E. liglandulosa would produce 

 equally good screw twists (fig. 776), while an identical exaggerated 

 spiral is seen in the winter-shoots of S. reflexum (fig. 766). 



Apicra spiralis, most commonly a five-spired form, (2-|-3), 

 varies to the three-spired form (1-1-2), and is then very similar 

 to Oyperus and Pandanus; owing to the greater succulence of 

 the leaves, however, the system appears less telescoped, and the 

 spiral twist less striking (fig. 59a). Section of the apex shows 

 the same phenomena as those figured for the three-spired Oyperus. 

 Pandanus is also identical. 



Other good examples of such constructions are afforded by 

 the shoots of Lycopodium Selago (4+5), (5-1-6) (fig. 78), where 

 they occur in conjunction with true whorled systems (3-F3), 

 (4+4), (5 + 5) (figs. 79,80). 



The production of " spired " types is of special interest in that 

 in several cases the spires are extremely well-marked {Pandanus), 

 and from their approximation to helices have been made the 

 chosen examples of torsion theories. As previously noted, the 

 appearance of Archimedean spirals, or true helices in the case of 

 cylindrical axes, will only be produced when the members attain 

 accurately equal bulk; i.e., when they definitely cease further 

 growth on reaching a certain specific volume. In such eases the 

 " orthostichy " curves become straight lines;' but so long as any 

 growth is taking place, however little it may be, the similar mem- 

 bers will retain the gradated series in which they were formed, 

 although the difference between adjacent members, consequent on 

 the retarded rate of growth, inay be so small as to be inappreciable 

 to the eye. 



Ultimate appearances are complicated by the fact that cessation 

 of growth may take place in two ways : either, as in typical and 

 theoretically uniform leaf production over a considerable length 

 of axis, members grow to a certain size and then stop ; or, growth 

 may diminish and cease uniformly throughout the whole system, 

 with the result that the completed system retains to a very con- 

 siderable degree the graduated sequence of its ontogeny; this 

 being weU seen in seasonal cessation of growth, as in the production 



