35 



i>iirnt'nsis (fig. 24.', C 6 ) are reproduced, and in fig. 25 a part of a 

 nu-iin sii : Aurelia insulinda (H a e c k e 1), seen from below, and showing 

 ^__ _____ i _ ii ^__ the symmetry of group C 4 . 



As further instances the 

 blossom-diagrams of Tripha- 

 sia trifoliata (C 3 ), of Polemo- 

 nium coeruleum (C 5 ), of Hy- 

 drophyllum virginianum (C 5 ), 

 and perhaps of Roxburghia 

 gloriosoides (C.,), might be 

 mentioned. 



If n = 1 , the stereometrical 

 figure has no symmetry at all; 

 thus all asymmetric objects 

 belong to this group Cj. As 

 examples of natural objects 

 of this kind, we may mention 



Fig. 23. 

 Fruit of 



Fig. 24. 

 Fruit of 



the blossoms of Canna Sello- Helicteres baruensis. 

 wiana, of Valerianna, of Centranthus,etc.;a.nd 

 mydiatenacissima. soine crystals, as e. g. potassium-bichromate : 



( 7 , strontium-hydrotartrate : Sr (C 4 H 5 9 ) z -\- 

 H.,0, calcium-thiosulphate: CaS z 3 

 6H z O(fig. 26). 



3. As to the special external 

 pect of all such symmetrical 

 jects, we shall draw attention to 

 e fact that in general one end of 

 .e symmetry-axis always shows a 

 ivelopment of the symmetrically 

 nged parts, which is different 

 m that at the other end of the 

 This phenomenon can, in 

 :cordance with the same pheno- 

 icnon often observed in crystallo- 

 graphy, be named hemimorphy. 



1 . ~ 



Fig. 25. 

 Aurelia insulinda. 



quadrifolia, whose quaternary symmetry is present both in the blossom and in 

 the phyllotaxis of the plant (Cf. J. Sachs, Vorles. iiber Pflanzen- physiologic, 

 p. 600, Fig. 331), is a rare exception to this rule. On the other hand, the 

 five-fold symmetry seems to be most general for Dicotyledons; sometimes also 

 the fourfold symmetry appears to be of importance in this case. 



