72 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



common, and are met with in anomalous specimens of plants other- 

 wise exhibiting the normal series, and especially in plants growing 

 under unfavourable conditions of environment, it is extremely 

 doubtful whether the determination of any particular set of 

 parastichy ratios affords any adequate reason for constructing a 

 series to contain it. 



Such series expressed in the Schimper form are — 



«• h h f, A> A= ■ • ■ • 99° 30' 6" 

 i- h h I -h, A, . ■ . . 77° 57' 19" 



/.I i _2_ _3. 5_ RA." A.' AV' 



''• 5' 6' 11' ]7' 28' ... 01 * to 



"-• 5' 7' 12' 19' 31' .... i-Oi- o o 



In the form of parastichy ratios — 



a. 1, 3, 4, 7, 11, 18, 29, 47. 

 6. 1, 4, 5, 9, 14, 23, 37, 60. 

 c. 1, 5, 6, 11, 17, 28, 45, 73. 

 d 2, 5, 7, 12, 19, 31, 50, 81. 



Expressed in the former system, by turns of the genetic spiral and 

 indefinite orthostichies, the fact is elicited that the first three tend 

 to a smaller limiting angle than the normal series, while the last 

 {d) approaches a larger one ; but when expressed as parastichies, it 

 becomes clear that from the standpoint of an approach to symmetry 

 they form very uneven systems. In the higher terms the ratios 

 are practically identical with those of the normal series (1 : 1'6) : — 

 {a) (6) 



3 : 4 : : 1 : 1'3 4 : 5 : : 1 : 1-25 



4: 7:: 1:1-75 5: 9 : : 1 : 1-8 



7:11::1:1-571 9 : 14 : : 1 : 1-5 



11 : 18 : : 1 : 1-63 14 : 23 : : 1 : 1-642 



18:29: :1:1-61 23 : 37 : : 1 : 1-608 



29:47: : 1 : 1-62 



(c) {d) 



5 : 6 : : 1 : 1-2 2 : 5 : : 1 : 2-5 



6 : 11 : : 1 : 1-83 5 : 7 : : 1 : 1-4 

 11:17: :l:l-54 7 : 12 : : 1 : 1714 

 17 : 28 : : 1 : 1-647 12 : 19 : : 1 : 1-583 

 28:45 : :1: 1-607 19 : 31 : : 1 : 1-632 



