138 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



homologous to two whorls of three and two respectively ; and this 

 spiral series (2 + 3) thus represented an intermediate condition 

 between a whorled (2 + 2) and a whorled (3 + 3). 



These were, in fact, the views of Eichler,* and constituted his 

 theory as to the origin of a pentamerous flower, the effect of which 

 is noticeable throughout the whole of his classical systematic work. 



That the (2 + 3) spiral system is intermediate between the 

 (2 + 2) and the (3 + 3) systems is obvious. The first is an asymmet- 

 rical construction, the two latter symmetrical systems ; but it does 

 not follow that the "intermediate condition" is therefore a second- 

 ary derivative, while the (2 + 2) and (3 + 3) are primary formations. 

 Eichler's interpretation naturally implies this peculiar standpoint, 

 and trimery and dimery are thus regarded as more primitive than 

 pentamery, notwithstanding the enormous preponderance of five 

 " orthostichies " in vegetative shoots, a fact first noticed by Bonnet. 

 However, this view being granted, it follows that Monocotyledons 

 and trimerous and dimerous apetalous Dicotyledons must be the 



* Reference to Eichler's Introduction (Bliithendiagramme I., II.) shows that 

 these views apparently arose from a misinterpretation of the facts represented 

 by the three types of flower in Berberis vulgaris. Thus a transverse section of the 

 winter-bud (September) of a shoot which will flower in the next season shows 

 foliage leaves in the contact relations of a (2 + 3) system while the inflorescence 

 bracts are apparently (3 -H 5). A longitudinal section of a later stage (November) 

 shows the flowers developing, and brings out the remarkable fact that the 

 terminal flower is the only one which has free space to grow. That this 

 terminal flower should under these circumstances continue the system of the 

 axis it terminates, and therefore present floral-members in five slightly spiral 

 " vertical rows," as in Delphinium Ajacis (androecium), is perfectly natural, 

 and this normally occurs. On the other hand, the lateral flowers, whether 

 owing to specific tendencies, or the stimulus of close packing, tend to vary, and 

 so give the natural symmetrical variants (2-t-2) and (3-)- 3) of the (2-)- 3) 

 system. One woiild not be surprised to find the normal type in a lateral 

 flower, or the (3-f-3) in a terminal, if these variations are determined solely by 

 the plant, and such again are the facts observed. The fact that the plant 

 selects a certain number of members to act as perianth segments and sporophylls 

 in the different cases, is wholly secondary to the mechanical construction which 

 originally produced them ; the rule the plant adopts is to take as many as will 

 completely flU a circle round the axis for each kind of member it requires, this 

 being 4, 5, 6 for the three types respectively, as shown by the proper geometrical 

 construction in terms of the numbers of curves. 



