50 



THE ROOT, OR DESCENDING AXIS. 



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

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

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

 the denominator of the fraction expressing the true forviative spiral sought. Thus, 

 84-13=21. The numerator corresponding is already known, and the fraction is 

 J-. See also the white pine cone, whose cycle is _= '< . 



238. Diagram 97 represents the leaves of a cherry cycle as seen from above, and 

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



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 sessile, 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 be?irs at its baso 

 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 



}f\ into other organs, as pitchers, spines, tendrils, 

 //£[ and even into the organs of the flower, as will 

 I hereafter appear. 



OF THE PETIOLE. 



243. The form of the distinct petiole \% 

 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 



98. Leaf of willow (Salix t fo e ] east Drea th of wind, 

 lucida) ; «, the stipules. The _ . „ . 



midvein is 3-lined ; veinlets 244. The WINGED PETIOLE IS flattened or GX- 



2-iined jveinuiets single-lined. p an( ] e( j [ u i a margin, but laterally instead of 



99, clover leaves ; s, stipules, ... ,i ci j.- x\ 



p, petiole, ueafleu. vertically, as in the asters. Sometimes tha 



