INTRODUCTION. 3 



easily grasped simile of the twist on the girders of a span-roof, 

 remarks that it is readily shown on a model but not on paper. 

 When to this is added the puzzling results of abnormal cases, the 

 general feeling left is that the mechanical forces are so well under 

 the control of the living protoplasm of the plant that they may or 

 may not act in any given case.* 



Even if the diagrams and observations here recorded have no 

 permanent value, it is hoped that they may tend to revive an 

 interest in the methods of plotting out what may be termed 

 architectural studies of vegetable life. 



Phyllotaxis. 



By the oldest botanists the arrangement of leaves in series 

 which formed alternating rows, when viewed horizontally or 

 vertically, was very aptly described by the term " Quincuncial," 

 from the analogy of the familiar method of planting vines in the 

 vineyard (Daubeny, Lectures on Roman Husbandry, 1857, p. 152). 

 Though such a diagonal pattern was produced by the indefinite 

 multiplication of the quincunx (V), no reference to any special 

 number (5) was implied, and all cases of spiral phyllotaxis and the 

 great majority of whorled clearly come under this wide generali- 

 zation f (Fuchs, Be Historia Stirpium, 1542). 



A more detailed classification appears to have been first proposed 

 by Sauvages in 1743 (Sauvages, M4moire sur ime nouvelle Mithode 

 de Connoitre les Flantes par les Feuilles, 1743). 



* Goebel, Organography of Plants, Eng. trans., Weisse, p. 75. 



Schwendener, .Mechanische Theorie der Bktttstellungen, 1878, p. 12 : " Die 

 Sciumann'sohen Einwiinde gegen meine Theorie der Blattstellungen," Berichte 

 Konig. Preuss. Akad. Wise., Berlin, 1899, p. 901. 



+ The view put forward by Fuchs, that the quincunx (V) was formed by- 

 halving the X, is not endorsed by modern authorities ; the 5-dot arrangement 

 of a dice-cube being a more possible primitive form. 



This original signification of the term Quincuncial was revived by Naumann 

 in 1845 ("Ueber den Quincunx als Qrundgesetz der BlattsteUung vieler 

 Pflanzen "). From observations on Sigillaria, Lepidodendron, and Cactus stems, 

 he formulated a hypothesis of ridge and furrow construction, each ridge of a 

 cactus being a row of the Quincuncial system. 



