98 



remarkable and fundamental investigations in detail now, but only 

 draw attention to the question of the symmetry of the obtained 

 R6 n t g e n-patterns. 



Now the close analogy of the Ron t gen-radiation with that of 

 common light, is also expressed in the fact that under all circum- 

 stances the Rontgen-radiation is a centrically-symmetrical pheno- 

 menon too, every Ron t gen-ray having a centre of inversion. 



The result obtained in crystals must therefore, according to what 

 was said before, always be as if the inversion were added to the 

 characteristic symmetry-properties of the crystal; i. e. if the patterns 

 obtained originated from a crystal whose symmetry in comparison 

 with the actual one is enriched "by a centre of symmetry. 



Let us see if experience is in accordance with this conclusion. For 

 that purpose we will compare the results obtained with plates 

 similarly cut from the trigonal crystals of turmaline, calcite, and quartz, 

 which have successively the symmetry of the groups C V 3 , D D 3 , and 

 Z) 3 , being thus radically different in this respect in all three cases. 



Quartz. 



x x 



Turmaline. 

 Fig. 94. 



Calcite. 



In fig. 94. the projection-figures drawn after Gadolin's method, 

 may elucidate the arrangement of the different symmetry-elements 

 in the three minerals considered. 



We will suppose that sections through these crystals are prepared 

 parallel to the basal plane (0001), to the prism-face (1010), and 

 to the face (1210) of the second prism. 



In turmaline the basal section has thus a ternary axis and three 

 symmetry-planes perpendicular to it, the section (1010) has no 

 symmetry-element whatever perpendicular to it, while the section 



H. Haga, Proceed. Akad. van Wet. Amsterdam, Vol. 16, 17, and 18. (1914 1916); 

 F. Rinne, Ber. d. math. phys. Kl. der Sachs. Akad. d. Wiss. Leipzig, (1915). 

 7. 303; II. 11; etc. 



