150 BOTANY. 



(6.) It is very common for the young leaves to appear in 

 succession on the punctuui vegetationis at a distance equal 

 to tvro fifths of the circumference from each, producing a 

 five-ranked arrangement. 



(7. ) A seven-ranked arrangement is rarely seen ; it is pro- 

 duced by the leaves following eacli other at a distance of two 

 sevenths of the circumference. 



(8. ) An eight-ranked arrangement, which is a very common 

 one, results from the leaves appearing at the constant distance 

 of three eighths of the circumference. 



(9.) In like manner there may be formed 9, 11, 13, 14, 18, 

 31, 23, 29, 34, 37, 47, 55, and 144 ranks. 



198. — The distance between any two succeeding leaves is 

 called the angular divergence; it may genei-ally (but not always) 

 be deduced directly from the number of ranks (orthostichies); 

 thus in the 2-ranked leaves it is \ ; in the 3-ranked, ^ ; in 4- 

 ranked, | ; in 5-ranked, f (rarely \) ; in 7-ranked, f ; in 8- 

 ranked, f (rarely ^) ; in 9-ranked, f ; in 11-ranked, -^^ ; in 

 13-ranked, -^^ ; in 14-ranked, ^ ; in 18-ranked, -^ ; in 31- 

 ranked, ^; in 33-ranked, ^; in 29-ranked, •^; in 34- 

 ranked, If ; in 37-ranked, -^ ; in 47-ranked, |4 ; in 55- 

 ranked, ^ ; in 144-ranked, ^;^f. 



Examples of the more common of these arrangements are to he 

 found as follows .* 



(a.) 2-ranked in Fagus, Celiis, Vlmus, Vit's, Tilia, most Videa, and 

 all grasses. 



(6.) 3-ranked in Garex, Scirpus, and most JiingermannicB. 



(c). 4ranked in the bracts of the principal axis of inflorescence of 

 Besiio ereetus and Thamnochortus seariosus. 



(d) S-ranked in Quercus, Popuhts,. Robinia, most Rosacem, Borra- 

 fjiiiace.m, etc. ; this is the most common arrangement in Dicotyledons. 



(«.) 7-ranked in Melaleuca ericcefolia. Euphorbia heptagona, Sedum 

 sexangulare, etc. 



(/.) 8-ranked in Polytrichum, Parietaria erecta, Antirrhinum ma- 

 jus, Raphanus, Brassica, Hieraoium piloseUa, etc. 



(g) 9-ranked in Lycopodium aelago. 



(h.) 11-ranked not rarely in Sedum reflexum and Opuntia vulgaris. 



(Je.) 13-Tanked in Verbaacum, Rhus typhina, Tauga canadensis. 



* This list of examples is from Hofmeister's " Allgemeine Morphol- 

 ogie der Gewachse," p. 448 et seq. 



