LESSOX 10.] 



IN A SIMIIAI 



73 



first, and llio fourth over tliP socoml. This brinpjs all the h-avos into 

 two ranks, one on one sitlc of the, stem and one on tin- oilier; and 

 is therefore called the two-ranked arrangement. It occurs in all 

 Grasses, — in Indian Corn, for instanee ; also in the Siiiderworl, the 

 lielhvort (I'^ig. 1'>1) and Iris (Kig. 132), in the liasswood or Lime- 

 tree, ScQ. This is the simplest of all arrangements. 



18G. Ne.\t to this is the three-ranked arrangement, such as \vc 

 see in Sedges, and in the Veratrum or White Ilellehore. The plan 

 of it is shown on a Seclge in Fig. 141, and in a diagram or cross 

 section underneath, in Fig. 142. Here the 

 second leaf is placed one third of the way 

 round the stem, the third leaf two thirds of 

 the way round, the fourth leaf accordingly 

 directly over the first, the fifth over the 

 second, and so on. That is, three leaves 

 occur in each turn round the stem, and they 

 are separated from each other by one third 

 of the circumference. 



187. The next and one of the most com- 

 mon is the ^tT-ra?j/ter£ arrangement ; which 

 is seen in the Apple (Fig. 143), Cherry, 

 Poplar, and th'^ greater part of our trees 

 and shrubs. In this case the line traced 

 from leaf to leaf will pass twice round the 

 stem before it reaches a leaf situated di- 

 rectly over any below (Fig. 144). Here 

 the sixth leaf is over the first ; the leaves 

 stand in five perpendicular ranks, equally 

 distant from each other; and the distance 

 between any two successive leaves is just 

 two fifths of the circumference of the stem. ua 



1S8. The five-ranked arrangement s expressed by the fraction f. 

 This fraction denotes the divergence of tlie successive leaves, i. e. the 

 angle they form with each other : the numerator also expresses the 

 number of turns made round the stem by the spiral line in complet- 

 ing one cycle or set of leaves, namely if ; and the denominator gives 

 the immber of leaves in each cycle, or the number of perpendicular 



FK;. 1 II. Pircp of the stalk of n .'^oilce. with (Iip IpavpK nit awny, lonvini; thrir tm^on ; 

 tlip loavoH arc iiiiiiiliprpil III ordtT. froin '. to (".. Wi. Uiagraiii or crusi-aecliuu of Uio aaiiift 

 til ill Olio iil.iiio ; tlic lo.'iv»« fiiiiilnrly miiuborutl. 



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