50 



THE ROOT, OR DBSCENDING AXIS. 



etc., the common difference being also five) ; two sets (one of tliree, the other of 

 eight) turning left; and stih another set, of thirteen, steepest of all, turning right 

 (1 — 14 — 27, etc.). Now the sum cf the spirals contained in the two steepest sets gives 

 the denomincUor of the fraction expressing the true formative spiral sought. Thus, 

 8-|-13=21. The numerator corresponding is already known, and the fraction is 

 Jj. See also the white pine cone, whose cycle is J^. 



238. Diagram 97 represents the leaves of a cherry oyde as seen from ahove, and 

 verified in the aestivation of the fiowers in the rose-family. 



V 

 MORPHOLOGY OF THE LEAF. 



239. General character. The leaf may be regarded as an expan- 

 sion of the substance of the bark, extended into a broad thin plate by 

 means of a woody frame work or skeleton, issuing from the inner part 

 of the stem. The expanded portion is called the lamina or blade of 

 the leaf, and it is either sessikj that is, attached to the stem by its base, 

 or it is petiolate, attached to the stem by a footstalk called the petiole. 



240. Stipules. But the regular petiole very often bears at its base 

 a pair of leaf-like appendages, more or less ap- 

 parent, called stipules. Leaves so appendaged 

 are said to be stipulate, otherwise they are ex- 

 stipulate. 



241. Therefore a complete leaf consists of 

 three distinct parts ; the lamina or blade, the 

 petiole, and the stipules. 



242. Transformations. Both the petiole, 

 blade and stipules are subject to numerous mod- 

 ifications of form. Either of them may exist 

 without the others, or they may all be transformed 

 into other organs, as pitchers, spines, tendrils, 



I and even into the organs of the flower, as will 

 /' hereafter appear. 



OF THE PETIOLE. 



243. The form of the distinct petiole is 

 rarely cylindrical, but more generally flattened 

 or channeled on the upper side. When it is 

 flattened in a vertical direction, it is said to be 

 compressed, as in the aspen or poplar. In this 

 case the blade is very unstable, and agitated by 



93. Leaf of willow (Saiix ^he least breath of wind. 



lucida) ; s, the stipules. The , 



raidvein is S-lined ; veinlets 244. The WINGED PETIOLE IS flattened or ex- 



2-iin«i ;veinuiets single-lined, panded into a margin, but laterally instead of 



99, clover leaves ; s, stipules, . „ . i , c ■ 



p, petiole, I, leaflets. Vertically, as in the asters, bometimes the 



