124 



I'lIYLLOTAXY, OR LEAF-AKK AN<; KMKM . 



10 



and the sixth is the first to come over any one below: {ho 

 seventh comes over the second, the eighth over the third, &c. 

 The leaves are thus brought into five vertical ranks; l,uf these 

 live leaves are laid down on two turns of the 

 helix (the sixth beginning the second revolu- 

 tion) ; the angular divergence of the leaves in 

 order is :, or 144; the angular distance of 

 the vertical ranks. 72. This is a very advan- 

 -' taij;eons distribution for ordinary foliage on 



erect or ascending branches. Its formula is f , expressing the 

 angular divergence, the denominator also indicating the; number 

 of vertical ranks, the numer- 

 ator indicating the number 

 of revolutions made in add- 

 ing one leaf to each rank. 

 Fig. 244 illustrates this ar- 

 rangement on a cone of 

 American Larch, the scales 

 of which are homologous 

 with leaves, the numbers 

 in sight are affixed, and those of the whole 

 cone displayed on a plane at the side. 



Octostichous, or Enj/it-ranL-i',!. a less common 

 arrangement, occurs in the Holly, Aconite, 

 the radical leaves of Plantago. It has the 

 annular divergence of 135, or f of the cir- 

 cumference. and the leaves in eight ranks, 

 the ninth over the first and at the completion 

 of the third revolution : it is therefore repre- 

 sented by the fraction . 



240. The obvious relations of the fractions 

 ,': 5!' s- representing the primary forms of 

 spiral phyllotaxy, are that the sum of any two 

 numerators is the numerator of the next suc- 

 ceeding fraction, and the same is true of the 

 denominators ; also the numerator is the same 

 as the denominator of the next but one pre- 

 eecding traction. Following these indications, 



jj!. &< Now these 



i 



_ ' 



the series may be extended to 



/ T , 



FIG. 244. A enne nf Hi,. small-fruited American Lurch (Larix Americana), with 

 the BCalea uuml.ered, rxliil.itin- the live-ranked arrangement. 



l-'li;. L'lr,. AH otisrt <>r tlie Houseleek, exhibiting the 6-1 3 arrangement; the leaves 

 in sight, numbered, the 1 4th over the- tirst, the lilth over the lith. .Ve 



FIG. 246. Cotieof Whit,- Pine < I'iiius Strobus) with scales numbered from bottom, 

 and some secondary spirals marked. 



