106 



PHYLLOTAXIS OE LEAF-AEEANGEMENT. 



two scales in each of these spirals — the common difference being five. 

 Again, it will be found on examination that there are secondary spirals 

 running to the left, in which the common difference between every two 

 scales is eight, and that this corresponds to the number of secondary 

 spirals, the first of which passes through the scales 1, 9, 17, etc. ; 

 the second through 6, 14, 22, 30,.etc. ; the third through 3, 11, 19, 

 27, 35, 43, and so on. Thus it is that, by counting the secondary 

 spirals, all the scales may be numbered, and, by this means the gene- 

 rating spiral may be discovered. 



In the cone of the American larch (fig. 218) there is a quincuncial 

 arrangement of scales marked by the fraction ^. There are five 



vertical ranks, 

 15 



10 



11 



Fig. 218. 



12 



as marked in the tabular numerical view at the side of 

 . the cone— viz., 2, 7, 12 ; 4, 9, 14 ; 1, 6, 11 ; 

 14 : 3, 8, 13 ; 5, 10, 15, the common difference 

 13 ; ; i in each row being 5. On looking at the cone 

 we find also parallel oblique ranks, two of 

 which, ascending to the left, are marked by 

 the numbers 1, 3, 5, which, if the diagram 

 is coiled round a cylinder, continue in the 

 numbers 7, 9, 11, 13, 15 ; and 2, 4, 6, 8, 

 10, continued into 12, 14. There are thus 

 two left-handed spirals, with 2 as the com- 

 mon difference in the numbering of the scales. 

 Again, three oblique parallel spirals ascend 

 to the right, marked by the numbers 1, 4, 7, 

 6, 9, 12, going on to 15 ; and 5, 8, 11, 14; 

 scales is 3, corresponding 



running into 10, 13 ; 3, 



here the common numbering of the 



with the oblique right-handed spirals. 



The primitive or generating spiral may pass either from right to 

 left or from left to right. It sometimes follows a different direction 

 in the branches from that pursued in the stem. When it follows the 

 same course in the stem and branches, they are homodromom (o/io/os, 

 similar, and 5f o/ios, a course) ; when the direction differs, they are 

 heterodromous (iri^og, another or diverse). In different species of the 

 same genus the phyllotaxis frequently varies. 



Considering alternation as the usual leaf-arrangement, some have 

 supposed that opposite leaves are due to the development of two 

 spirals in opposite directions, whUe others look upon them as pro- 

 duced by two nodes coming close together without an intemode. A 

 verticil, in the latter view, wiU be the result of the non-development 

 of more than one intemode, and may occur in plants, the normal 



Fig. 218. Cone of a species of Larch (Larw; microcarpa), taken from Professor Asa 

 Gray's work, with the scales numbered so far as seen. The arrangement is J in the five- 

 ranked series. There are five vertical rows of scales, 1, 6, 11 ; 4, 9, 14 ; 2, 7, 12 ; 5, 10, 16 ; 

 and 3, 8, 13, as shown in the diagram. 



