lU 



BOTANICAL GAZETTE. 



of scales in the cone is 2x13 = 26. The number of cycles in the cones 

 of Black spruce (Abies nigra) vary from 4 to 7, averaging about 5. 

 Hence its cycle and the number of cycles will be represented by 

 TA-BLE II. 5 (5-13 j, and the number of scales 



by 5x13=65. In like manner the 

 cone of White Pine {Pinus Strobus) 

 is represented by 5 (5-13); of Pitch 

 Pine (Pinus rigidus) by 4 (13-34). 

 of American Larch (Larix Ameri- 

 cana) by 2 (2-5), etc. 



19. Table II exhibits the num- 

 ber of turns or parts of a turn made 

 by each order of spirals in a single 

 cycle. Or, the denominator shows 

 the number of cycles required for 

 the spirals to make the number of turns indicated by the numera- 

 tor. 



Opposite Leaves. — 20. Opposite leaves also exhibit cycles of ar- 

 rangement analogous to those of alternate leaves. 



The OS Cycle— (Fig. 1.) The 0-2 cycle represents 



21. 



Fig. 7 



the two-leaved ancestor of all Dicotyledons; it yet stands 

 for the cotyledonary leaves of many of them, the succeed- 

 ing leaves being alternate. The 0-2 cycle, however, is not 

 at all liable to tht' objection of being an ideal one. "Ln 

 many fossil plants the pairs of leaves do not alternate, but are 

 placed directly one over the other." (Henfrey's Elementary 

 Botany, p. 45.) Hence 0-2 represents a two-ranked ar- 

 rangement of opposite leaves. 



22. The l-Jf Cycle.— (Fig. 8.) In the case of op- 

 posite decussate leaves, the cycle is complete in 

 two nodes. The leaves are borne upon two spirals, 

 each of which makes half a turn round the stem. 

 The cycle, therefore, is represented by 2(l-2)-2 

 (2)= 1-4. This is the most common arrangement 

 of opposite leaves. Examples are furnished by the 

 Maple, and by plants of the Mint Order. 



23. The Higher Cycles. — When the fourth pair of 

 leaves stands directly over the first pair, three nodes 

 complete the cycle and there are six ranks. There 

 are two spirals each bearing three leaves in half a turn about the 



1 



Fig. 8. 



