134 Proceedings of the 



parts sometimes rise to the same height, in which case they form a 

 verticilli^ and sometimes to different heights. Although the latter 

 case is much more frequent than the former, the authors who have 

 written on the subject generally speak of these flowers as composed 

 as verticilli, probably because the difference of height between the 

 various parts of each system is so small as to appear to them 

 unworthy of notice. But M. Jussieu, by taking a minute account of 

 these differences, seeks to establish that the most general law rela- 

 tive to the disposition of the leaves of a branch may be equally ap- 

 plied to the parts of the flower. Let us suppose the parts inserted 

 in different points of a spiral line turning on the conic spindle 

 (noyau) of the flower. Let us divide the surface of the cone into 

 five equal parts, by so many lines let fall from the summit to 

 the base, by which each spiral turn will be cut by these lines at five 

 points. Let us then suppose an insertion at any of the points of in- 

 tersection, and place them upon these points alternately (de deux) : 

 after two spiral turns we shall find the sixth insertion situated 

 directly over the first, and the first five will form what Bonnet calls 

 a quincunx. When the parts are large enough for the borders 

 or edges to pass each other, they will cover or lap over each other in 

 such a manner as to form two exterior, two interior, and one inter- 

 mediary, that is to say, covering on one side and covered on the other. 

 The two exteriors will be placed first and second, the intermediary 

 third, and the two interiors fourth and fifth. It is necessary to re- 

 member these characteristics, because they serve to point out the 

 order of insertion where the difference of height is too small to serve 

 as a guide. When the parts are large enough to lap over each 

 other, not only with their borders or edges, but by the greater part 

 of their surface, one will envelope, or lap over, two, two over three, 

 three over four, and four over five. This is the inflorescence 

 which has been called enveloping, and which differs from the quin- 

 cuncial only by the enlargement of the parts. The parts of a quin- 

 cunx in the flower are generally placed alternately with those of the 

 two quincunces which are immediately above and below it. It is 

 difficult to account for this disposition on the hypothesis of a single 

 spiral, but it is perfectly intelligible if we admit the existence of a 

 second spiral entirely similar to the first, and revolving on the same 

 cone, but commencing from the opposite point of the base like the 

 worms of a double screw. It is upon these two spirals that the 

 concentric spirals are inserted alternately. This supposition is 

 justified by observing the flowers on which the parts which are mul- 

 tiples of five, or some other number, alternate among themselves in 

 various rows ; it is evident that this alternation results from the parts 

 being inserted at equal intervals upon several spiral parallels. The 

 petals of the cactus, the stamina and fruits of several of the magno- 

 lias and ranunculi, furnish examples of this. The disposition of the 

 scales in the common pine cone is also an illustration, if not a posi- 

 tive proof, of this. 



