THE BILATERALITY OF APPENDAGES. 305 



in the diagram: thus in young growing shoots of Phyllodinous 

 Acacias (fig. 105) the development of the phyllode lamina along 

 slightly spiral vanes (spires) is readily recognisable; and the 

 same generalisation holds for the secondary protuberances which 

 constitute the ridges of the Cactaceae (spiral of phyllody). 



On the other hand, with the assumption of the special case 

 of true symmetrical construction, these geometrical relationships 

 vanish, in that the complementary diagonals of the quasi-squares 

 become circles and radii respectively ; so that in a whorled type 

 the leaf-laminae lie in a strictly horizontal plane from the first, 

 and a whorled phyllode is also wholly orientated in a vertical 

 plane. 



Finally, it may again be noted that all these generalisations, 

 being applicable to the rhomboidal section of a leaf-primordium 

 presented in a phyllotaxis system in which the leaves tend to 

 take the form of quasi-squares under mutual pressure, do not 

 directly concern the relationships of the free primordia of the 

 primary system. The nature and symmetrical properties of the 

 primary primordia, which in section present the form of an ovoid 

 curve, which in the theoretical construction is to be regarded 

 as a quasi-circle, require to be considered separately, when the 

 mathematical properties of such constructions have been more 

 fully described (cf. Mathematical Notes); the special point, 

 of interest being that, while in asymmetrical constructions the 

 rhomboid sections are also asymmetrical and obliquely placed, 

 the fundamental curve of the primordium is mathematically 

 orientated from the first along a radius of the whole system 

 passing through its centre of construction, and about which 

 radius the member is truly bilaterally symmetrical. 



A clear distinction is thus required to be drawn between the 

 behaviour of the leaf-base, as seen at the insertion-area (or leaf- 

 scar), which is the surface of the axis, and the properties of the 

 free portion of the lateral appendage. 



As general examples of these various phenomena, comparison 

 may be made of the sections of the terminal buds of Pinus (fig. 

 88) and Araucaria (fig. 41), in which the amount of sliding- 

 growth is relatively small. The transition is shown very perfectly 



