Royal Academy of Sciences of Paris. 135 



From what has been said, the five folioli of the calyx of a flower 

 may be considered as placed on the first spiral. At the point cor- 

 responding to that of the sixth insertion, but on the second spiral, the 

 quincunx of the petals will commence, which will also be disposed 

 upon two spiral turns, nearer to the summit than those which bear 

 the folioli. When the system of the petals is finished, that of the 

 stamina will begin, and form a third quincunx, situated on the same 

 spiral as that of folioli, but on the fifth and sixth turns. Lastly 

 comes the quincunx of the ovaries, which will be inserted on the 

 seventh and eighth turns of the second spiral. It has here been sup- 

 posed that each spiral begins to form the first part of one quincunx 

 at the moment at which the other spiral completes another ; but this 

 regularity does not always occur. Thus the second, instead of bear- 

 ing the first petal at the point corresponding with that which a sixth 

 foliolus would occupy, may bear it at the point corresponding with the 

 seventh, eighth, ninth, or tenth ; whence there are four other combi- 

 nations possible ; and although the alteration of the parts in the two 

 successive quincunces, and the corresponding opposition of those 

 of every other quincunx, is apparently unaltered, the regularity is less 

 perfect, because, although a stamen will always be found correspond- 

 ing to a foliolus of the calyx, and an ovary to a petal, it will not cor- 

 respond with the foliolus and petal bearing the same number. The 

 nearer the spiral rises towards the summit of the cone, the more its 

 turns contract and approach each other. The lower, therefore, 

 a quincunx is situated in a flower, the more its parts are separated 

 from each other. This remark may give rise to several deductions. 

 In the first place the principles just laid down will be the less easily 

 recognised in proportion as their exemplification is sought for 

 in a higher or more interior quincunx, because the contraction of the 

 spiral turns tends to give it the appearance of a verticillus, and the 

 slightest deviation in the insertion of a part will tend to change its 

 apparent order: it is therefore in the calyx that these principles may 

 most frequently be verified. The inequality of height in the inser- 

 tion of the petals can rarely be observed, except by their situation 

 being a little more exterior and interior, and even this can rarely be 

 perceived in the flower when open; in the bud it is more per- 

 ceptible. The laws of the quincunx, being once admitted for the 

 calyx and corolla, should also by analogy be admitted for the 

 stamina and the ovaries, although the latter more generally present 

 the appearance of a perfect verticillus. Several instances, how- 

 ever, may be found in which this appearance does not exist ; added 

 to which the developement of the parts of each of these pretended 

 verticilli is much less contemporaneous than is generally supposed. 

 This developement, indeed, would naturally be slower in the highest 

 parts, which must be impeded by want of space ; whence it arises 

 that total or partial abortions are more frequent in proportion as the 

 quincunx is in a more elevated situation in the flower. Thus abor- 

 tions are rare in the calyx, less so in the corolla, still less so in the 



