These leaves, of a delicate, pale green, are cut into a thousand leaflets, which tremble in the lightest breeze, and tell you that the air is stirring even when the heat seems breathless. A more elegant and attractive diagram of the Phyllotaxis of ⅜ probably does not exist in nature. The common Cocoa-nut tree has its leaves arranged according to the fraction of 5/13; but, though the crown consists of several cycles of leaves, they do not form a close head, because the older ones become pendent, while the younger are more erect. The Pupunha, or peach palm (Guilielma), follows the Phyllotaxis of 8/21; but in this instance all the leaves are evenly arched over, so that the whole forms a deep-green vault, the more beautiful from the rich color of the foliage. When the heavy cluster of ripe, red fruit hangs under this dark vault, the tree is in its greatest beauty. As the leaves of this palm are not so closely set in the younger specimens as in the older ones, its aspect changes at different stages of growth; the leaves in the younger trees being distributed over a greater length of the trunk, while, in the adult taller ones, they are more compact. This arrangement is repeated in the Javari and Tucuma (Astrocaryum); but in these the closely-set leaves stand erect, broom-like, at the head of the long stalk. In the Mucaja (Acrocomia) the leaves are arranged according to the fraction 13/34. Thus, under the same fundamental principle of growth, an infinite variety is introduced, among trees of one order, by the slight differences in the distribution and constitution of the leaves themselves. In the Musaceæ, or Scytamineæ, the Bananas, another order of the same class of plants, a diversity equally remarkable is produced in the same way, namely, by slight modifications of this fundamental law. What can differ more in appearance than the common Banana (Musa paradisiaca), with its large simple leaves, so loosely arranged around the stem, so graceful and easy in their movements, and the Banana of Madagascar (Ravenala madagascariensis), commonly known as the Traveller’s tree, which, like the Baccába of Pará, has its leaves alternating regularly on opposite sides of the trunk, and so closely packed together as to form an immense flat fan on a colossal stem? Yet, in all these plants the arrangement of leaves obeys the same law, which is illustrated with equal distinctness by each one. This mathematical disposition of leaves is thus shown to be compatible with a great variety of essentially different structures; and though the law of Phyllotaxis prevails in all plants, being limited neither to class, orders, families, genera, nor species, but running in various combinations through the whole kingdom, I believe it can be studied to especial advantage in the group of palms, on account of the prominence of their few large leaves. The most abundant and characteristic palms of the Rio Negro are the Javari (Astrocaryum Javari), the Muru-Muru