150 BOTANY. 



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

 succession on the punctum vegetationis at a distance equal 

 to two 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 each 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, 

 21, 23, 29, 34, 37, 47, 55, and 144 ranks. 



198. The distance between any two succeeding leaves is 

 called the angular divergence; it may generally (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 -J-) ; in 7-rauked, f ; in 8- 

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

 13-ranked, -^ ; in 14-ranked, ^ ; in 18-ranked, ^ ; in 21- 

 ranked, 2 R T ; in 23-ranked, -fa ; in 29-ranked, ^ ; in 34- 

 ranked, |f ; in 37-ranked, 7 \ ; in 47-ranked, ffi j i n 55- 

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



Examples of the more common of these arrangements are to be 

 found as follows .* 



(a.) 2-ranked in Fagus, Cdtis, Ulmux, Vitis, Tilia, most Viciea, and 

 all grasses. 



(b.) 3-ranked in Carex, Scirpus, and most Jungermannia. 



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

 Restio erectus and Thamnochortus scariosus. 



(d.) 5-ranked in Quercus, Populus, Robinin, most Rosacece, Borra- 

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



(e.) 7-ranked in Melaleuca ericcefolia, EupJiorbia heptagona, Sedum 

 sexangulare, etc. 



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

 jus, Raphanus, Brass'ca, Hieracinm piloseUa, etc. 



(g.) 9-ranked in Lycopodium selago. 



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



(k.) 13-ranked in Verbascum, Rhu* typhina, Twga canadensis. 



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

 ogic der Qewachse," p. 448 et seq. 



