152 



BOTANY. 



parastichies passing to the right, while leaves 3, 6, 9, 13, 

 15, 18 belong to the parastichies which pass to the left. 



(5.) Upon counting, 

 in Fig. 129, it is found 

 that there are three 

 parastichies passing to 

 the left and five to the 

 right ; the smaller 

 number is the same as 

 the numerator of the 

 fraction expressing the 

 angular divergence, 

 while the sum of the 

 two equals the denomi- 

 nator ; similar rela- 

 tions may be shown to 



Fig. 130. — niagram of eight-ranked arrange- ■ / • r\ 



ment, viewed from above. Tlie ortlioBtichles, which exISt m Other CaseS. 

 hiTS appear to be radial lines, are numbered, as in ^^^ t£ 



Fig. 1S9, f rem /. to F7/7. The leaves are number- 200. — It noW We 



ed from Uol6.-After Sachs. g^^^^ ^j^^ ^^^^^^^ ^_ 



rangements by projecting the stem upon a flat surface in 



such a way that the successive 



nodes, in ascending the stem, 



are represented by smaller 



and smaller concentric circles 



(Fig. 130) (as would, in fact, 



be the case if we made sections 



through the nodes of the 



lounctum vegetationis), it is 



at once evident that each leaf 



is so placed as to stand over 



the vacant space between the 



previously formed ones, and 



that as regards the leaves 



formed after it, it is equally 



well situated. 



Pig. 130a.— Cross-section of a leaf-bud 

 of the Hemlock Spruce (TsugaCanadea- 



TT J! ■ L £ 1 i. XI • »««)• Magnified.— After Hofmeister. 



lioimeister formulates this ^ 



to tlie morphologist. So much has tliis been done, that the study of 

 Phyllotaxis lias in some quarters become little more than a species of 

 Kjatberoatical gymnastics, 



