THE SYMMETRICAL CONCENTRATED TYPE. 145 



of whorled trimery is further shown by the case of reduced 

 Monocotyledonous flowers ; e.g., individual flowers of Iris, 

 Lilium. 



The case of three symmetrical pairs of curves at angles of 120° 

 which gives the typical trimerous Monocotyledonous flower, here 

 represents the full symmetrical case of the system (2 + 3), as is 

 shown by the partial retention of the spiral in ontogeny (Lilium 

 candidum, etc.) ; but it may also occur as a variation of a decussate 

 type, as in the assimilating shoots of Fuchsia gracilis, Fraxinus, 

 Tmpatiens, and again as an extreme reduction of a pentamerous 

 flower passing through the tetramerous phase and thus independent 

 of the ratio series (Oenothera biennis). 



Similarly the case of whorls of four members may have a threefold 

 origin, to be separated carefully in the consideration of floral 

 phylogeny : firstly, as an extreme variation of the decussate system 

 (foliage shoots of Fuchsia gracilis) ; secondly, an advance variation 

 of trimery, flowers of Crocus, Iris, Leucojum, Lilium (more constant 

 in Paris); and lastly, a reduction variation from pentamery, the 

 most general case of tetramery, as found in the flowers of Oenothera, 

 Alchemilla, Cruciferae ; and less frequently, Btota, Jasminum, 

 Euonymus, Ampelopsis, Viburmcm, etc., etc. In the same way true 

 hexamery may be produced as a variant of pentamery, as in 

 flowers of Euta, Jasminum, Ampelopsis, Viburnum, Heracleum, 

 etc., supplying increasing evidence that with perfect symmetry 

 in construction the value of the series of Fibonacci is com- 

 pletely lost, although the phylogenetic relics persist to a very 

 considerable degree; due, no doubt, in many cases to the fact 

 that symmetry is only attained in the specialised floral mechanism, 

 while the parent shoot still retains its unmodified asymmetrical 

 and mechanical construction, so long as there is no direct ad- 

 vantage to be gained by substituting either radial or dorsiventral 

 symmetry. 



As in the case of asymmetrical constructions, it is easy by 

 making geometrical drawings to obtain an idea of the bulk-ratio 

 for any given symmetrical system with a degree of accuracy quite 

 sufficient for any practical purposes, the ovoid curves inscribed 

 in the log. spiral meshes being taken as circles. 



