290 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



V. The Bilaterality of Appendages. 



Since it follows from the mathematical construction of a circular 

 system of lateral members, making close contact and exhibiting 

 uniform growth expansion, that no absolutely radially symmetrical 

 member can be primarily produced from the growth-centre and 

 remain a part of the system, a comprehensive definition of a foliar 

 member is thus obtained, in that all leaf -structures must be by 

 construction inherently Mlateral from their first inception; and 

 although the true curve of the transverse section of a member 

 may differ from a circle only within the error of drawing, these 

 primordia are always eccentric with regard to the point which 

 has been termed the " centre of construction." 



The biological observation that "stems" bear "leaves" in 

 acropetal series is thus correlated with the mathematical fact 

 that such inherently bilateral primordia can alone be primarily 

 produced by a growing apex so as to satisfy the observed 

 phenomena. Radially symmetrical " branches," on the other hand, 

 are to be regarded as secondary productions, and arise at a 

 greater distance behind the growing-point; as, for example, in 

 the apparent axil of a previously formed primary primordium, 

 these areas being the only spots left vacant in a normal growing 

 system. 



Every leaf, or lateral member of the first degree, whether borne 

 on the axis of gametophyte or sporophyte, whether an assimilatory 

 appendage or a sporophyll, is thus structurally bilateral from the 

 first ; and however much certain types may subsequently become 

 "centric" in form, they remain nevertheless eccentric internally, 

 with regard to the centre of construction, so long as any growth 



