40 THIRD REPORT 1833. 



cussion as ever, I have dwelt upon it at an unusual length, in 

 the hope that some Member of the British Association may 

 have leisvire to prosecute the inquiry. Perhaps there is no 

 mode of proceeding to elucidate it which would be more likely 

 to lead to positive results, than a very careful anatomical exami- 

 nation of the progressive development of the Mangel Wiu'zel 

 root, beginning with the dormant embryo, and concluding with 

 the perfectly formed plant. 



Arrangemeni of Leaves. — It has for a long time been thought 

 that the various modes in which leaves, and the organs which 

 are the result of them, are arranged upon a stem might be re- 

 duced to the spiral, and that all deviations from this law of 

 arrangement are to be considered as caused by the breaking of 

 spires into verticilli. In the Pine Apple, for instance, the Pine 

 Cone, the Screw Pine, and many other plants, the spiral arrange- 

 ment of the leaves is so obvious that it cannot be overlooked ; 

 in trees with alternate leaves this same order of arrangement 

 may be discovered if a line is drawn from the base of one leaf 

 to that of another, always following the same direction; even 

 in verticiilate plants we not unfrequently see that the whorls 

 are dislocated by the praBternatural elongation of their axis, and 

 then become converted into a spire ; and the same pha3nome- 

 non is of common occurrence among the verticilli of leaves in 

 the form of calyx, corolla, stamens, and carpella, which com- 

 pose the flower. This will be the more distinctly apparent if we 

 consider that, as M. Adolphe Brongniart has shown*, what we 

 calLvvhorls in a flower often are not so, strictly speaking, but 

 only a series of parts placed in close approximation, and at dif- 

 ferent heights, upon the short branch that forms their axis. 



Dr. Alexander Braun has endeavoured f to prove mathema- 

 tically that the spiral arrangement of the parts of plants is not 

 only universal, but subject to laws of a very precise nature. 

 His memoir is of considerable length, and would be wholly un- 

 intelligible without the plates that illustrate it. It is therefore 

 only possible on this occasion to mention the results. Setting 

 out witli a contemplation of the manner in which the scales of 

 a Pine Cone are placed, to which a long and ingenious method 

 of analysis v/as applied, he found that several different series of 

 spires are discoverable, between which there invariably exist 

 peculiar arithmetical relations, v/hich are the expression of the 

 various combinations of a certain number of elements disposed 

 in a regular manner. All these spires depend upon the posi- 



* Annales des Sciences, vol. xxiii. p. 226. 



+ Verglekhendr Vritersuchunj iibcr die Ordininfj der Schuppen an den Tan- 

 nen~apfcn. Ito. IPjd. 



