120 BOTANICAL GAZETTE. 



within an extensive forest contains, in summer, almost double the 

 proportion of carbonic acid in the air over the open country. On 

 the other hand, forest soil is in summer very much poorer in carbonic 

 acid tlian the soil of the open fields and the amount in the latter 

 rises with elevation of temperature much more rapidly than does that 

 in the former. The diffusion of carbon in the soil seems to be slow, 

 as its quantity appears to vary greatly in places close to each other. 



The Phyllotaxis of Leaves, by A. P. Morgan, M. D. — 1. The ar- 

 rangement of leaves upon the stem is denominated phyllotaxis. Leaves 

 are arranged upon the stem in three principal ways; (1) they are 

 alter 110 fr, (2) they are opposite, (3) they are verticillate or wJiorled. 

 Leaves are alternate upon the stem when but a single leaf grows at 

 each node. Leaves are opposite when two leaves grow at each node 

 upon opposite sides of the stem. The leaves are verticillate or whorl- 

 ed when more than two leaves grow in a circle or wdiorl around each 

 node of the stem. 



L Alternate Leaves. — 2. Alternate leaves are arranged upon I he 

 stem in a succession of spiral cycles. The length of each cycle is de- 

 termined by the distance from anv one leaf to the leaf directly above 

 it upon the stem. The cycle is represented by a fraction of which 

 the numerator denotes the number of times the spiral winds around 

 the stem, and the denominator indicates the number of leaves in tha 

 cycle. 



3. The various arrangements of alternate leaves are designated in 

 accordance with the numbers of their vertical ranks upon the stem ; 

 these are always the same as the number of leaves in the cycles. 



4. It has been ascertained that with rare exceptions the cycles in 

 the various arrangements of alternate leaves are represented by the 

 series of fractions ; 



1-2, 1 3, 2-5, 3-8, 5-13, 8-21, 13-34, (fee. 

 It is here proposed to amerul tliis series hy placing at its beginning 0-1. 

 Li this series the numerator of each fraction after the first two is ob- 

 tained by adding the numerators of the two preceding fractions, and 

 the denominator is obtained by adding their denominators, 



5. The series 1, 1-2, 1 3, 2-5, &c , represents the different cycles 

 of arrangement wlien we follow the shortest path around the stem. 

 If we go around in the opposite direction, by the longest route, the 

 series will be, 1-1, 1-2, 2-3, 3-5, 5-8, 8-13, 13-21, 21-34, &c., in which 

 each fraction is the complement of the corresponding fraction in the 

 preceding series. 



