Church. — The Principles of Phyllotaxis. 



229 



of such intersecting curve systems are not specially studied in an ordinary 

 school curriculum, a preliminary sketch of some of their interesting features 

 may be excused, since geometrical relationships have clearly no inherent 

 connexion with the protoplasmic growth of the plant-shoot, but are merely 

 properties of lines and numbers. 



Thus, by taking first, for example, a system in which spiral curves 

 of any nature radiate from a central point in such a manner that 5 are 



Fig. 35. Curve-system (5 + 8) : Fibonacci series. A full contact-cycle of eight members is 

 represented by circular primordia. 



turning in one direction and 8 in the other, giving points of intersection 

 in a uniform sequence, a system of meshes and points of intersection is 

 obtained, and to either of these units a numerical value may be attached. 

 That is to say, if any member along the ' 5 ' curves be called i, the next 

 inmost member along the same series will be 6, since the whole system 

 is made of 5 rows, and this series will be numbered by differences of 5. 



