78 OEGANOGRAPHY AND GLOSSOLOGY. 



alternate ; as also (p. 42) that the floral organs (calyx, corolla, androeciuna and pistil) 

 are normally whorled; but we have warned the reader that very frequently the 

 leaves of each series, instead of forming a true whorl, are arranged in successive 

 flattened spirals, though still retaining the name of whorls. 



We will now advert somewhat in detail: 1. To the arrangement of leaves 

 properly so called, c,arpellary leaves, and bracts (this branch of Botany is called 

 Phyllotaxy) ; 2. To the arrangement of the petals and sepals, an arrangement 

 termed Vernation, because it can only be satisfactorily studied before the flower 

 expands. 



PHYLLOTAXY. 



When leaves are clearly whorled, either in twos (opposite), threes, fours, fives, 

 &c., they are generally separated by equal intervals, and consequently the arc com- 

 prehended between the bases of two contiguous leaves is equal to the circumference 

 of the stem, divided by the number of leaves in the whorl. This arc will therefore 

 embrace half the circumference if the whorl consists of two leaves ; one-third of the 

 circumference if it consists of three ; one-fourth, one-fifth, one-sixth, if it consists of 

 four, five, or six leaves. 



It has also been observed that the leaves of a whorl are not placed directly 

 above those of the whorl immediately above or below them, but opposite the 

 intervals which separate the leaves, and either exactly opposite, or to one or the 

 other side of the interval. When the leaves are opposite, and each pair crosses the 

 upper and lower pair at right angles, the leaves occupy four rectilinear lines, and, 

 seen from above, form a cross; such leaves are decussate (f. decussata). Whorls of 

 three or four leaves will in like manner occupy six or eight longitudinal lines. 

 Whorled leaves are relatively few ; many more plants have opposite leaves, and by 

 far the largest number have alternate leaves; and it is by the latter that the 

 arrangement of leaves on the stem must especially be studied. 



We have seen (p. 3) that the Oak presents five leaves (I, 2, 3, 4, 5), spirally 

 arranged around the stem, so that the one (6) which succeeds the fifth is placed 

 vertically above the first. In a longer branch, the seventh would be placed 

 above the second, the eighth above the third, &c. This spiral arrangement 

 prevails in many woody and herbaceous plants, as the Peach, Plum, Cherry, Rose, 

 Raspberry, Hawthorn, Spircea, Cytisus, Poplar, Willow, Sumach, Wallflower, Mignon- 

 ette, Heartsease, Groundsel, Poppy, &c. 



The naturalist Ch. Bonnet, who was the first to observe this arrangement of 

 alternate leaves, remarked that their points of insertion were separated from each 

 other by equal intervals, and discovered some more complicated arrangements, as 

 that, instead of the sixth leaf, it is often the ninth or even the fourteenth which is 

 placed vertically above the first, indicating a series of eight or of thirteen leaves. 

 Modern botanists have followed up this subject, and have formulated as laws 

 the facts which Ch. Bonnet had not generalized. 



To begin with the simplest example of alternation of leaves, that in which the 

 leaves alternate on opposite sides of the stem (Lime, Ivy, Elm, Hazel, &c.) : if a 



