. Botanical gazette. Plants. 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 cyc


. Botanical gazette. Plants. 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 c I 1 0 1 1 2 5 II 2 III 3 IV 5 1-5 1-5 2-5 3-5 V 8 VI VII 13 21 0-1 1-2 1-2 1 3-2 5-2 4 1-3 1-3 2-3 1 5-3 1-2 1-3 2-5 1-21 3-8 5-13 1-8 1-8 1-4 1-13 1-13 8-21 8 13 13-34 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 ; (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


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