22 PART I. — ORGANOGRAPHY. 



Usually, also, when there are three leaves in the whorl, they are 

 one-third of the circumference of the stem apart; when four, ■■ 

 one-fourth, and so on, and as a general rule also the leaves of 

 successive whorls stand over the interspaces of those imme- 

 diately below them. Good examples of opposite leaves are those 

 of the Mints, Maples and Lilac, and of whorled leaves in which 

 there are more than two leaves in the whorl, the Galiums, 

 Canada Lily, Leptandra and Silene stellata afford good illustra- 

 tions. 



In the alternate or scattered plan but one leaf occurs at a 

 node, and the leaves succeed each other in a spiral order. 



It is much the more common mode of phyllotaxy, and a con- 

 siderable number of different forms of it are recognized, the 

 greater portion of which may be reduced to a series mathemati- 

 cally represented by the fractions £, £, f , |, y 5 ^, etc. In these frac- 

 tions the numerator represents the number of turns to complete a 

 cycle, that is, to reach a leaf which stands directly above the 

 first ; the denominator represents the number of orthostachies or 

 perpendicular rows of leaves on the stem, or, what is the same 

 thing, the number of leaves, counting along the spiral from any 

 one of them, to the one which stands directly above it ; and the 

 whole fraction expresses the angular distance measured circum- 

 ferentially on the stem from one leaf to the next one on the spiral. 



It will be observed also that the third fraction of the series 

 is derivable from the first two by adding together the numerators 

 for a new numerator and the denominators for a new denomi- 

 nator ; that the fourth is derived from the second and third in 

 the same way, and so on. 



Examples of the \ or distichous arrangement occur in the Elm 

 and Basswood, and it prevails in the whole family of Grasses ; it 

 is illustrated in Fig. 41. The \ or tristichous arrangement occurs 

 in the Sedges, as shown in Figs. 42 and 43 ; the f or pentasti- 

 chous arrangement occurs in many common trees, as the Cherry 

 and Apple, and is illustrated in Fig. 44 ; the f or octastichous 

 arrangement is observed in Aconite, Osage Orange, Plantain 

 and Holly ; the more complex plans are rarer, but the -^ is 

 observed in the Houseleek and some other plants, and arrange- 

 ments represented by this and fractions still higher in the series 

 occur in the cones of various species of pines, spruces, etc. 



