INTRODUCTION. 9 



on orthostichies which cannot be proved to be straight and angles 

 which cannot be measured. 



Thus, if the angle of divergence within one cycle is constant, a 

 transition from one cycle to another of different value must involve 

 a special angle at the point of transition. To meet this difficulty 

 the theory of " prosen thesis " was added to the original conception 

 by Schimper and Braun ; a hypothesis again incapable of proof by 

 any actual measurements on the plant.* 



Prosenthesis was also called upon to explain the alternation of 

 cycles in the common type of flower; and, in the same way, in 

 the formation of whorls of foliage leaves which usually alternate, 

 prosenthesis was required at every node. 



Still more remarkable were the constructions adopted to explain 

 the " obliquely vertical rows " of stamens in the flowers of certain 

 Eanunculacese. In order to bring these into line with "ortho- 

 stichies," peculiar transitional divergences were adopted ; a f spiral 

 e.g. might, with a tendency to approach ^, give a somewhat larger 

 angle to every new cycle ; and, owing to this special form of pro- 

 senthesis, the true orthostichies would take an oblique position, in 

 this case, along the course of the genetic spiral.-f 



Once, however, it is admitted that such transitional divergences 

 may render orthostichies oblique, the whole theory becomes con- 

 siderably weakened, since no clue is given to the causes which may 

 produce such an effect in one case and not in another ; while the 

 fact that what it has been the custom of older writers to call ortho- 

 stichies should prove to be really a little curved, does not at first 

 strike the observer as necessarily affecting the validity of the 

 original hypothesis.:]: 



On the other hand, with all its faults, the definite notation of the 

 Schimper-Braun theory, and the brevity and apparent simplicity 

 with which it sums up complicated constructions, is so closely 

 interwoven with our whole conception of the subject, that it becomes 



* EicKler, Bliithendiagramme, i. p. 14. 



+ Eicliler, Bliithendiagramme, ii. p. 157. 



X Sachs, Physiology, Eng. trans., p. 497. " The theory of phyllotaxis, with its 

 assumption of the spiral as a fundamental law of growth, has, to the great injury 

 of all deeper insight into the growth of the plant, established itself so firmly 

 that even now it is not superfluous to show up its errors point by point." 



