84 



WILD LIFE IN CALIFORNIA 



cision of their attachment or insertion on the 

 stems or branches. There are three modes, but 

 no species of plant uses more than one. The 

 different systems are known as alternating, 

 opposite and whorled. 



In the first or alternate, one leaf after an- 

 other occurs along- the stem, or perhaps more 

 accurately stated, a single leaf from each 

 node or joint. In the second or opposite sys- 

 tem there are two leaves at each stem node, 

 opposite to each other, and each pair of 

 leaves occur at right angles to the other as 

 they are produced by the growing stem, so 

 that looking down a stem it would appear 

 as if it bore four ranks of leaves. The last 

 or third mode is the whorled, where more 

 than two leaves spring from a stem joint, the 

 places of attachment being uniformly spaced, 

 that is, when there are five leaves in a whorl 

 they will be located one-fifth of the cir- 

 cumference of the stem or stalk apart. 



No two of these modes are ever seen on 

 any one species, but several different families 

 of plant life may have the same system. How- 

 ever, the systems, except in the "opposites" 

 vary in the order and number of leaves 

 circling a stem and the differences are uni- 

 form for each species. The variations in the 

 "alternating" are most remarkable in their 

 mathematical arrangement and division of 

 space in the attachment of the leaves to their 

 stems or branches. When this peculiarity 

 came to the notice of that great naturalist, 

 Darwin, he marveled at it, but said he could 

 give no explanation. 



The arrangement of leaves in this system 

 with all its modifications is spiral. This will 

 be readily detected by taking a stem well 

 studded with leaves and noting that the first 

 leaf above the leaf directly in front of you 

 is located part way around the stem and the 

 next leaf in order is still higher and farther 

 on around, and so on until you find a leaf 

 attached to the stem directly above the one 

 from which you started. The variations 

 referred to as occuring in this mode are in 

 the number of leaves and tMe times around 

 the stem until there is reached a leaf at- 

 tached directly above the starting point; and 

 in these numbers and circles comes the 

 wonderful mathematical features. 



The simplest and very common form is 

 with the growths where leaves are attached 

 on opposite sides of the stem, but each suc- 

 ceeding one above the other. Counting the 

 leaves in this arrangement the leaf on the 

 opposite side is one, and the next leaf in 

 order located directly above the starting 

 point, completing the circle around the 

 stem, is two. This system is styled two- 

 ranked, as only two leaves are attached to 

 the stem in making the spiral turn complete. 

 There being only two leaves, the space of at- 

 tachment horizontally is one-half the circum- 

 ference of the stem apart; though vertically, 

 or the distance in height between the leaves, 

 may vary considerably. The arrangement is 

 also expressed by the fraction %. 



The next in the series is the three-ranked 

 or three leaves in one spiral turn around 

 the stem, and attached one-third of the 



circumference apart; and expressed by the 

 fraction % . 



Now it would seem as if there might be 

 growths with four, five or six leaves with 

 one turn, but none such exist, for nature 

 controls this matter with mathematical sys- 

 tem. The arrangement of all other series is 

 in accordance with the peculiar law that each 

 succeeding series is composed of as many turns 

 and number of leaves as there are turns and 

 leaves in the two preceding series. Therefore 

 you will find the next in the series is ex- 

 pressed by the fraction 2-5, the numerator 

 and denominator of which are the sums of 

 those of the first two of the series. These 

 figures indicate that there are two spiral turns 

 and five leaves in the series and also that 

 spaces of attachment of the leaves are two- 

 fifths of the circumference. 



We have for the first three series 1-2, 1-3, 

 2-5, and following the law mentioned in the 

 last paragraph the next series should be the 

 sum of the numerators and denominators of 

 the last two fractions, to wit: 3-8, and that 

 is what happens, three spiral turns and eight 

 leaves three-eighths of the circumference 

 apart. 



The next arrangement is 5-13, following 

 the same method of addition. Then fol- 

 low 8-21 and 13-34, which is about the high- 

 est commonly noted and is as far as we need 

 go to explain this peculiarity. Observe that 

 these last also are the sums of the numera- 

 tors and denominators of preceding fractions. 



The structure of an ordinary leaf consists 

 of green pulp, known in botany as paren- 

 chyma, through which, extending to all parts, 

 is a fibrous frame of harder growth called 

 ribs and veins. The veins are so styled for 

 the reason they are hollow tubes connecting 

 with the ribs and main stem or petiole of the 

 leaf, also tubular, which besides stiffening 

 and supporting the green softer part, give 

 passage to the saps that flow back and 

 forth from the trunk of the tree to the leaf. 

 The veining of a leaf is called venation, and 

 varies in accordance with the origin of the 

 plant, but is so consistently uniform therewith 

 that a mere glance enables one to identify the 

 class to which the plant belongs. 



The shapes and forms of leaves are many, 

 and seem to serve no other purpose than to 

 render ready identification of the various 

 trees and plants, or make ornament and 

 shade. One might think the Oriental palm 

 tree with its large broad leaves would throw 

 more shade than a tree with smaller leaves, 

 but where do we find a denser shade than 

 that of our live oak with its small leaves? 

 But there are exceptions where the shape and 

 form have a special purpose. Among which 

 may be mentioned the hollow tubed leaves of 

 the pitcher plant which, when partially filled 

 with water, become traps for insects. Then 

 there are the extraordinarily shaped leaves of 

 the Venus Fly-trap plant which works some- 

 thing after the manner of a steel trap. When 

 an insect alights or touches the inner face of 

 either of the hinged lobes of the leaf they 

 suddenly close together capturing the in- 

 truder, but what is more remarkable the leaf 



