CHAP, iv.] Metamorphosis and of the Spiral Theory. 163 



appeared in these publications with a formal completeness 

 which could not fail to attract the attention of the botanical 

 world and indeed of a larger audience ; and justly so, for, as 

 unfortunately so very seldom happens in botanical subjects, 

 a scientific idea was in this case not merely incidentally sug- 

 gested, but was worked out in all its consequences as a complete 

 structure, and this structure gained in external splendour from 

 the circumstance that its propositions, dealing with geometrical 

 constructions, could be expressed in numbers and formulae, 

 a thing hitherto unknown in botanical science. 



That the leaves are arranged on the stems that produce 

 them according to fixed geometrical rules had been noticed by 

 Cesalpino and by Bonnet in the middle of the eighteenth 

 century ; but nothing more resulted than weak attempts at 

 mere description of different cases. Schimper's theory is marked 

 by that which is at once its greatest merit and its fundamental 

 error, the referring of all relations of position to a single prin- 

 ciple. This principle lies in the idea that growth in a stem 

 has an upward direction in a spiral line, and that the formation 

 of leaves is a local exaggeration of this spiral growth. The 

 direction of the spiral line may change in the same species, or 

 in the same axis, and may even change from leaf to leaf. 

 The important variations in the arrangement of leaves are not 

 shown in their longitudinal distances, but in the measure of 

 their lateral deviations on the stem. The characteristic point 

 in this theory is the mode of considering these lateral de- 

 viations or divergences of the leaves as they follow one another 

 on an axis, the referring them to a more general law of posi- 

 tion. Means were at the same time skilfully supplied for 

 discovering the true conditions of arrangement, the genetic 

 spiral, in cases where the genetic succession of the leaves, and 

 consequently their divergence, could not be immediately re- 

 cognised. After innumerable observations, it appeared that there 

 is a wonderful variety in the disposition of leaves, but that at 

 the same time a comparatively small number of these variations 



