PHYLLOTAXIS OR LEAF-AEEANGEMENT. 



105 



In cases where tiie internodes are very short, and the leaves are 

 .closely applied to each other, as in the House-leek, it is difficult to 

 trace what has been called the generating spiral, or that which passes 

 through every leaf of the cluster. Thus in fig. 216, there are thirteen 

 leaves which are numbered in their order, and five turns of the spiral 

 marked by circles in the centre (^ indicating the arrangement) ; but 

 this could not be detected at once. So also in Fir cones (fig. 217), 

 which are composed of scales or modified leaves, the generating spiral 

 cannot be determined easily. In such cases, however, there are 

 secondary spirals running parallel to each other, as is seen in fig. 217, 

 where spiral lines pass through scales numbered 1, 6, 11, 16, etc., 



Fig. 216. 



Fig. 217. 



and 1, 9, 17, etc., and by counting those which run parallel in differ- 

 ent directions, the number of scales intervening between every two in 

 the same parallel coil may be ascertained. Thus, in fig. 217, it will 

 be found that there are five secondary spirals running towards the 

 right and parallel to each other, the first passing through the scales 1, 

 6, 11, 16, etc. ; the second through 9, 14, 19, 24, etc. ; the third 

 through 17, 22, 27, 32, 37, etc. ; the fourth through 30, 35, 40, 45, 

 etc.; the fifth through 43, 48, 53, etc' The number of these second- 

 ary spirals indicates the number of scales intervening between every 



Fig. 216. Cycle of thirteen leaves placed closely together so as to form a rosette, as in 

 Sempervivum. A is the very short axis to which the leaves are attached. The leaves are 

 numbered in their order, from below upwarSs. The circles in the centre indicate the five 

 turns of the spiral, and show the insertion of each of the leaves. The divergence is expressed 

 by the fraction 5-thirteenths. Fig. 217. Cone of Abies alba, with the scales or modified 

 leaves numbered in the order of their arrangement on the axis of the cone. The lines 

 indicate a rectilinear series of scales, and two lateral secondary spirals, one turning from 

 left to right, the other ftom right to left. 



