116 THE PHENOMENON OF 



to the axis, as a ray, or in relation to the spiral series to 

 which it belongs, as a wave, we recognise in any case, in 

 the intimately connected origin of the stem and leaf, an 

 alternation of emerging and retiring formation, of rising 

 and sinking, radiation and concentration ; and this it is 

 which we have characterised above as a course of de- 

 velopment advancing in repeated acts of Rejuvenescence, 

 as it were in an undulating flow of the metamorphosis. 

 This would be the place to examine the definite pro- 

 portions which the leaf-formation adheres to in its spiral 

 undulation, and the conditions of arrangement of the 

 leaves arising from these ; to trace them from the simple 

 rudimentary plans ({, i,) with which the plant, as a whole, 

 commences and which are mostly repeated at the begin- 

 ning of a new branch, through all the complications 

 which come in during the progress of the metamorphoses, 

 and mostly attain their maximum in the hypsophyllary 

 region ;* then, further, to show how the simpler plans 

 (3, I, >) recur, but in cyclic combination, in the flower, 

 how here a new series of complications is established in 

 the harmonious combination of the cycles, and how finally 

 in the fruit, the arrangement frequently returns to the 

 simplest condition. But to carry this out would demand 

 an exposition of the theory of Phyllotaxy, which would 

 far exceed the limits allowable in the present treatise. 



Note. The more recent researches on the Phyllotaxy 

 of Plants will be found compared in Schleiden's ' Grund- 

 ziige/ 2te Ausg.ii, p. 1 77 ('Principles of Botany,'pp. 263-6), 

 to which are to be added, a later treatise by the brothers 

 Bravais ('Essai sur la disposition generale des feuilles 

 rectiseriees/ 1840), an essay by the Swede Silverstrahle 

 (translated in Hornschuch's 'Archv. scandinavischen 

 Beitrage/ i, p. 382), agreeing in its conclusions with the 

 first treatises of the brothers Bravais ; and the works of 



* Vide Composite, Dipsaceac, Plantagineae, Proteacese, Fipcracpfe, 

 Zingiberacese, Cyperacea;, Aroidesc. 



