35 



cases in which the symmetry of the figures considered is charac- 

 terised by the mere 

 existence of axes of 

 symmetry of the 

 first order, i. e. by 

 _j^ mere rotations. Such 

 figures and objects 

 therefore must al- 

 ways be different 

 from their mirror- 

 images', as we shall 

 see later, this kind 



Fig. 21. 

 d- Camphor-oxime. 



of symmetry plays an important role in many phenomena observed 

 in the domain of chemical and physical sciences. 

 I. The simplest cases are obviously those 



r\ 



where only one axis of the period - - exists. 



The corresponding symmetry-groups contain n 

 non-equivalent rotations, 

 as mentioned before. We 

 shall call them cyclic 

 groups, and indicate them 

 by the symbol C n , where 

 n may have any value 

 from i to oo . l ) 



Fig. 22. 

 Sodium-periodate. 



Fig. 23. 

 Wulfenite. 



As instances of symmetrical figures and objects of this kind, in 

 fig. 21, 22, and 23, the crystalforms of optically 

 active camphor-oxime: C 10 H 1& NOH, of sodium- 

 periodate: NaJO^ -\- jH 2 0, and of wulfenite: 

 PbMoO^ are reproduced; the values of n are 

 here 2, 3, and 4. respectively, and the axes are 

 all placed vertically, with the exception of that 

 of camphor-oxime, this being inhorizontal position. 



Many parts of plants and animals possess 

 this cyclic symmetry, as fig. 24. to 26 con- 

 vincingly show, where the blossom-diagrams of 

 Paris quadri folia (fig. 24.', C 4 ), 2 ) the fruits of Chlamydia tenacissima 

 (fig. 25', C 3 ) and of Helicteres baruensis (fig. 24', C 5 ) are reproduced, 



1 ) For n = oo we have, properly speaking, no longer a finite group of rotations. 

 This case will therefore be considered more in detail later on. 



2 ) The ternary symmetry is generally found in Monocotyledons, and Parts 



Fig. 24. 



Blossomdiagram of 

 Paris quadri folia. 



