136 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



struction, and the character of the spiral must therefore be kuown ; 

 yet the circular plan has been generally adopted in the construction 

 of floral-diagrams. Take, for example, the " § " spiral, or quincun- 

 cial type, which characterises the calyx or perianth of the great 

 majority of Dicotyledonous types : in the floral literature of the 

 period which marks the evolution of the floral-diagram at the 

 hands of the Wydler-Eichler school, from a mere transverse section 

 of the flower-bud, one constantly comes across the tendency of 

 older observers to deduce an abstract ideal type of construction 

 which represented the general average of a mass of observations. 

 Thus the remarkable prevalence of whorled arrangements in 

 the floral members of the majority of floral types, which also holds 

 to such an enormous extent in the ontogeny of the essential organs 

 even when the calyx remains spiral, led to the assumption of a 

 series of concentric circles as the basis of the floral-diagram ; since 

 again such circles were easy to draw, and spiral construction was 

 not particularly obvious except in the case of a few of the Eanun- 

 culaceae and allied families, for which the application of theoretical 

 diagrams was recognised as being extremely difficult. The intro- 

 duction of the doctrines of evolution led to the result that these 

 ideal generalised types were frequently interpreted as actual 

 primitive forms, without any further phylogenetic evidence being 

 required ; circles were thus retained as being sufficiently accurate, 

 and the " | " spiral thus became conventionally represented in 

 terms of two circles, two members being placed on the outer and 

 three in the inner, constituting the Dicydic calyx* 



* Such a theory as that of the Dicydic calyx aflfords a good example of the 

 manner in which an abstract morphological generalisation, obtained from an 

 average of a large number of observations, becomes mistaken for a phylogenetic 

 one and ends by obscuring the very phenomena it was intended to elucidate. 

 It is clear that the number of members selected by the plant to serve as a pro- 

 tective investment, or an attractive cycle, depends primarily on the relative 

 tangential extension of these members: that 4=(2-t-2) are most frequently 

 selected in a dimerous flower, or 6 = (3 -I- 3) in the case of trimery, merely 

 indicates that the members are relatively narrow, and subtend, when adult, an 

 angle which is less than 180° or 120° as the case may be. Where the vridth is 

 relatively considerable (c/. 2 sepals, Paipaver, 3 sepals, Tradescantia), a single 

 cycle suffices and is therefore employed ; and the necessity for a dicyclic calyx 

 thus falls to the ground. This subject will be further considered under the 



