126 DESCRIPTIVE BOTANY. PART I. 



leaf which ranges vertically over the first on this spiral, 

 but without any reference to the number of coils which 

 the spiral makes before this happens. Thus, in each of the 

 annexed figures (fig. 136.), No. 8. ranges vertically over 

 No. 1 . ; but, in A, this happens after one coil ; and in 

 B, not until after three coils of the spiral. The 

 numbers are ranged at equal intervals, indicated by 

 the eight vertical lines drawn on the surface of the 

 cylinder. 



( 1 22.) Divergence of general in <j Spirulx. M. Braun 

 proposes to note the nature of this arrangement, by 

 giving it a numerical value, which shall be expressive of 

 the angular distance between two successive leaves on 

 the spiral, when they are projected on a plane perpen- 

 dicular to the axis. The expression obtained, is termed 

 the " divergence " of the generating spiral. Thus, the 

 divergence in A, is the angular distance between 1 and 

 2 (viz. | of the circle) ; but the divergence in B, 

 is f , as may be seen by inspecting the summits of the 

 two figures. The numerators of these fractions also 

 express the number of coils which the generating spirals 

 make, before one leaf ranges vertically over another ; 

 and their denominators, are the number of leaves distri- 

 buted upon this interval which is called the " length" 

 of the spiral. It is further evident, that the leaves 

 arrange themselves along as many lines drawn parallel to 

 the axis, as there are leaves on one length of the spiral, 

 viz. seven in each of these figures. 



Where the coils of the spiral are not very close, and 

 the numbers succeed each other at short intervals, it is 

 easy to trace its course round the axis ; but, in many 

 cases, the coils are so close together, and the leaves, or 

 other appendages, so disposed upon them, that all traces 

 of its course are either obliterated, or much confused. 



(123.) Secondary Sjiiralx. But still, the symmetry 

 with which the leaves are really disposed, is now ma- 

 nifested by the appearance of several " secondary" 

 spirals, which may be traced in various directions. 

 This is well exhibited in the arrangement of the scales 



