VARIATION STEPS 185 



Similar experiments were carried out by DE BRUYKER, on 

 the whole with similar results. 



In the Corymbiferous Composites the number of marginal 

 florets may pass through a long series of values, let us say from 



to 100 (and still more). When the variation of this property 

 is observed : 



(i) Within the limits of a complex species [Senecio nemor- 

 ensis, § 124) or a genus {Senecio, § 124) ; 



(2) In one monotypic species under the influence of plasticity ; 



(3) In one monotypic species under the influence of gradation, 

 the nde is always the same. The Fibonacci terms are always 

 predominant (if they are of the first or the second degree), 

 coinciding with the humps of the curves. 



Adopting the view that any value whatever of the property 

 under consideration corresponds to a state of equilibrium (§ 43) 



1 conclude that the Fibonacci terms are the expression of states 

 of equilibrium which are more stable ^ than those expressed by 

 other values. The Fibonacci terms are, therefore, the expres- 

 sion of a certain mechanical predisposition which is a specific 

 energy of the property. This conclusion is applicable on any 

 series of variation steps whatever. (See § 123.) 



Two more conclusions may be drawn from the above obser- 

 vations : 



(i) The existence of a two- (or more) humped variation curve 

 does not give proof of the existence of different subspecies 

 (races) in the material (§ 130). In other words, dimorphism or 

 polymorphism of a curve may depend on the existence of varia- 

 tion steps without any complexity. This remark is appUcable 

 on certain curves, from which the coexistence of different sub- 

 species or races has been deduced, without any information 

 about the specific energies of the measured property. 



(2) A monomorphic (one-humped) variation curve may be 

 transformed into a dimorphic (or polymorphic) one by a simple 

 change in the conditions of existence — if variation steps are at 

 play. Therefore, when the variation curve of a given property 

 of a given species is one-humped in a first country (or locality), 

 and two-humped in a second country (or locality), we are not 

 allowed to conclude without more information that the species is 

 monotypic in the first case and complex in the second case. 



In Primula elatior the number of flowers of the so-called 

 umbel is very variable, with distinct variation steps which coin- 

 cide with the terms 3, 5, 8 . . . (Fibonacci series). Dr DE 

 BRUYKER has observed that specimens collected from dry 

 spots give a variation curve in which the lower terms (3 or 5, or 

 both) are predominant, whereas specimens collected from wet 

 spots in the same locality show a distinct predominance of the 

 ^ I discern three degrees of stability (§ 124). 



