REPORT ON THE PHILOSOPHY OF BOTANY, 41 



tion of a fundamental series, from which the others are devia- 

 tions. The nature of the fundamental series is expressed by a 

 fraction, of which the nvmierator indicates the whole number 

 of turns required to complete one spire, and the denominator 

 the number of scales or parts which constitute it: thus /y in- 

 dicates that eight turns are made round the axis before any 

 scale or part is exactly vertical to that which was first formed, 

 and the number of scales or parts that intervene before this 

 coincidence takes place is twenty-one. 



It does not appear that this inquiry has as yet led to any 

 practical application, although one might have expected that 

 as the natural affinities of plants are determined, in a great de- 

 gree, by the accordance that is observable in the relative posi- 

 tion of their parts, the spires of which those parts are composed 

 might have had something in common which would be suscep- 

 tible of being expressed by numbers. If any practical applica- 

 tion can be made of Dr. Braun's fractions, it seems likely to be 

 confined to the distinction of species. His observations seem, 

 however, to have established the truth of the doctrine that, be- 

 ginning with the cotyledons, the whole of the appendages of 

 the axis of plants, — leaves, calyx, corolla, stamens, and car- 

 pella, — form an uninterrupted spire, governed by laws which 

 are almost constant. 



Structtire of Leaves. — The leaves of plants have been found 

 by M. Adolphe Brongniart to be not merely expansions of 

 the cellular integument of stems, traversed by veins originating 

 in the woody system, but to be organs in which the inteqjal 

 parenchyma is arranged with beautiful uniformity, in the man- 

 ner most conducive to the end of exposure to light and air, and 

 of elaboration, for which the leaves are chiefly destined. In 

 their usual structure leaves have been found by this observer 

 either to consist of two pi'incipal layers, — of which the upper, 

 into which the ascending sap is first introduced, is formed of 

 compact cells, more or less perpendicular to the plane of the cu- 

 ticle, and the under, into which the returning sap is propelled, 

 is formed of very lax cavernous tissue, more or less parallel with 

 the cuticle of the lower surface, — or else of two layers perpen- 

 dicular to the cuticle, with a central parallel stratum. 



The observations of Drs. Mohl and Meyen generally confirm 

 this ; but at the same tune the latter instances several cases in 

 which the texture of the leaf has been found to be nearly the 

 same throughout. 



Dutrochet* states, in addition, that the interior of the leaf 



* Aunales des Sciences, vol. xxv, p. 215. 



