37 



of Valeriana, of Centranthus, etc.; and some crystals, as e.g. those of 

 potassium-bichromate : K 2 Cr 2 O 7 , of sirontium-hydrotartrate : Sr (C 4 7/ 5 6 ) 2 

 + 4H 2 0, of calcium-thiosulphate: CaS 2 3 + 6 H 2 (fig. 28), etc. 



3. As to the special external aspect of all such symmetrical ob- 

 jects, we draw attention to the fact that 

 in general one end of the symmetry-axis 

 always shows a development of the 

 symmetrically arranged parts, which 

 is different from that at the other end 

 of the axis. This phenomenon can, in 

 accordance with the same phenomenon 

 often observed in crystallography, be 

 named hemimorphy. Generally speaking, 

 we can say that all objects possessing 

 a cyclic symmetry C n , have hemimorphic 



Calcium-thiosulphate (-f 6// 2 0) . 



In fig. 29 an imaginary fruitform 



is represented, which may serve to give some impression of vegetable 

 objects which perhaps may possess the symmetry of 

 one of the groups , namely that of C 6 . ] ) 



It is evident t ha t^allej these objects must differ from 

 their mirror-images; if the figures here reproduced, 

 are reflected in a mirror, this fact will be recognised 

 at once 2 ). In most cases only one of the two possible 

 forms is found in nature ; why the other is not produced, 

 can hardly be explained. With the problems relating 

 to this, we shall deal more in detail later on. 



4. II. We shall now proceed to the cases where several axes 



1 ) The symbols for these and the following groups are very convenient in 

 morphology for the purpose of description. They are partly analogous to 

 those of Schoenflies, partly analogous to those of P. Saurel, Zeits. fur 

 Kryst. 50. 1. (1911). 



2 ) It is a very remarkable fact that in several of the very ancient and 

 universally used religious symbols of many peoples, this axial symmetry is also 

 distinctly and preferentially 



expressed. So in the so-called 



fylfot-symbols, mystic emblems 



of doubtful significance, of 



which an Arabian, Hindu, and 



Scandinavian form are reproduced here; and also in a Japanese symbol- for 



"good luck". The symmetry indicated as C and C 3 is easily recognisable in 



these widely spread symbols. 



Fig. 29. 



