THE SYMMETRICAL CONCENTRATED TYPE. 149 



very constantly pentamerous, in which 4 sepals were followed by 3 

 petals and the anther lobes of 2 stamens, would form so marked an 

 exception that it would be readily recognised as a deformity. It 

 will further be noted that, expressed in terms of the parastichy 

 curves, a symmetrical whorl of 4 members will be contained by (4 

 + 4) curves, and a whorl of 5, (5 + 5), etc. It thus follows that any 

 change in a symmetrical system, in which symmetry is retained 

 from node to node, implies the addition or loss of at least two curves 

 simultaneously, one in either direction, since the addition or loss of 

 an uneven number would at once throw the construction into an 

 asymmetrical form. 



That the increase or reduction of the members of a whorled system 

 may often be due to variations in nutrition, so that the bulk-ratio 

 may be involved in a manner similar to that described for asym- 

 metrical types, is clearly suggested by the enormous range of varia- 

 tions observable in some flowers, especially Papamr somniferum ; 

 under varying conditions of cultivation the number of carpels which 

 may reach 15 in a strong plant readily falls to a minimum 4 in 

 progressively starved plants, while the aggregate number of stamens 

 which present an irregularly symmetrical system may be simul- 

 taneously reduced from over 500 to 8. 



Better examples are met with in the progressive reduction along 

 successive axes of the same plant, homologous again with the reduc- 

 tion along the members of the Fibonacci ratios in successive 

 ramifications previously noted (Helianthus, etc.), but differing again 

 in the complete absence of these values, and thus affording a much 

 more gradual decline : e.g., Buta commonly produces terminal 6-5- 

 merous flowers, while 4-merous are practically constant in the 

 ultimate scorpioid cymes. Most striking is the case of Sempervivum : 

 three plants of S. italicum, growing in the same pot, gave the 

 following numbers for the sepals and petals of successive floral axes 

 (the construction is not absolutely constant throughout individual 

 flowers) : — 



Ti Til- Jill- Tiv- Tv- Tvi. 



(12 13 12 11 11 10 



I. . . 14 < 13 



