90 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



II. Constant Fhyllotaxis. 



With such an assumption that growth is more or less uniform so 

 long as the apex remains in the condition of Zone I., and absolutely 

 so at some central point at which the new impulses are originated, 

 it is possible to build up any system of phyllotaxis, the results of 

 uniform growth being expressed by taking circles whose radii are in 

 the requisite geometrical progression. For example : — Taking a case 

 in which the lateral members are assumed to have a bulk-ratio with 

 the main axis of 1 : 2, a (3 + 5) system may be produced by adding 

 one new member at a time, and allowing each to grow along the 

 same series of circles in geometrical progression. 



Fig. 37, 1, shows the insertion of one such primordium. Now, if 

 the second member be laid down on the side exactly opposite the 

 first, the system assumes at once a symmetrical condition, and the 

 symmetrical construction of one member at a node thus induced, 

 giving rise to the phenomenon of exactly alternating leaves in two 

 rows, is general among Monocotyledonous types {Iris, Canna, 

 Gramineae.) If the axis is growing asymmetrically, however, the 

 primordium is formed at an approximate angle of 137° on a log. 

 spiral system, the ratio of the curves of which approaches 1 : 1'62 ; 

 since this angle and ratio gives, as concluded from Wiesner's obser- 

 vations, the optimum oscillation effect in constructing the nearest 

 approach to a radial system, one member at a time. The second 

 member thus falls (fig. 37, 2) on one side of the diameter passing 

 through the first one. 



As it must fall either right or left of this line, it would appear 

 probable that the chances are equal in either case, and that in 



