On the Relation of Phyllotaxis to Mechanical 



Laws. 



By 

 Airthixr H. Churcli, ^Mi.A.., ID.Sc., 



Lecturer in Natural Science, Jesus College, Oxford. 



PAET I. 



CONSTRUCTION BY ORTHOGONAL TRAJECTORIES. 



I. Introduction. 



In the doctrine of Metamorphosis and the enunciation of the 

 Spiral Theory we have handed down to us two remarkable 

 generalizations which, originating in the fertile imagination of 

 Goethe, have passed through the chaos of Nature Philosophy and 

 emerged in a modern and purified form, quite different from their 

 primary conception, to form the groundwork of our present views 

 of Plant morphology. 



That leaves are usually arranged in spiral series had long been 

 recognized by botanists; but it was left for Goethe, in 1831, to 

 connect the spiral-twining and torsion of stems, the spiral thicken- 

 ing of vessels, and the spirals of leaf-cycles into one ever-present 

 " spiral-tendency " of vegetation. 



The Spiral Theory proper, as applied to Phyllotaxis, owes its 

 elaboration and geometrical completeness to Sehimper and Braun 

 (1830-1835), by whom it was worked out with such precision, and 

 the ideas carried to their ultimate logical conclusion with such 

 uncompromising vigour, that it still forms, in the early pages of 

 text-books, the starting-point for our consideration of the relative 

 positions of the members of the plant body. 



A 



