126 RELATION OP PHYLLOTAXIS TO MECHANICAL LAWS. 



obvious than the shorter ones, these paths may be studied as a 

 whole and mapped out by curved lines passing through the members 

 differing by these values, and the method of the forking of the long 

 curves of the system made more obvious (fig. 50). ,The method 

 of numbering may be checked by noting the proper differences in 

 adjacent members, and also by taking an approximate divergence 

 angle of 137°. 



Bearing in mind the convention previously laid down in the 

 type capitulum of fig. 44, that the member which originates a new 

 curve is always the external member of the two paths produced by 

 the forking, the system may be further analysed. 



Starting from the uppermost pair of decussate leaves 1 and 2, 

 No. 3 commences the asymmetrical condition and adds a new 

 curve j three long curves are now established and the original (2 + 2) 

 system completes the transition to (3 + 5) in the members 3, 4 

 and 5. 



Normal expansion commences immediately in 6, since 6 is the 



external member of the fork 2^ 



Thus 6 puts in the first new long curve, and similar relations 

 hold for 7, 8, 9, and 10. Five long curves are now added, and 

 the system is at this moment (8 + 5). As in the normal case, the 

 short curves immediately commence to be laid down, commencing 

 at 11, which is the internal member of the previous fork, but the 



, , i 4.V u u ^yll (difference of 5) 



external member or the branch 6^ ^ r 



\19 ( „ 13). 



Similar relations are established for the members 11-18 inclusive, 

 and 19 adds no curve, being the inside member of the last forking, 

 and falls in the gap left for it. No change takes place till 30 is 

 reached ; that is to say, 20 to 29 inclusive, or 10 leaves are formed 

 in a uniform (8 + 13) system. At 30, however, a long. curve is' 

 again added, since 30 is the outside member of the fork 



/30 (difference of 8) 

 ^\43( „ 21): 



as the first member of the ultimate transition, it also correctly 

 subtends a ray-floret. Similar relations hold for 30-42 inclusive. 



