101 



by Bragg Sr. and Jr. l ), and by P. Debije. However, we will not 

 consider these remarkable and fundamental investigations in detail 

 now, but only draw attention to the question of the symmetry of 

 the obtained Ron t gen-patterns. 



Now the close analogy of the R on t gen-radiation with that of 

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

 stances the Ront gen-radiation is a centrically- symmetrical pheno- 

 menon, every Ront gen-ray having a centre of inversion. 



The result obtained in crystals will 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. as if the 



Quartz. 



XX 



Turmaline. 

 Fig. 96. 



Calcite. 



patterns obtained originated from a crystal whose symmetry in com- 

 parison with the actual one is enriched by a centre of symmetry. 2 ) 



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 , Z>?, and 

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



In fig. 96 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 



A ) W. H. and W. L. Bragg, Proceed. Roy. Soc. London; 89, A, 277, 477, 

 (1913); Zeits. f. anorg. Chemie, 90, 255, (1914); P. Debije, Phys. Zeits., 17,277, 

 (1916); 18, 291, 483, (1917). 



For the special questions dealt with here, see the papers of: G. Friedel, 

 Compt. rend, de 1'acad. d. Sc. Paris, 157, 1533, (1913); F. M. Jaeger and 

 H. Haga, Proceed. Akad. van Wet. Amsterdam, Vol. 16, 17, and 18. (19141916); 

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

 /. 303; //. 11; etc. 



2 ) A similar conclusion has already previously been drawn by G. Friedel, 

 Compt. rend, de 1'Acad. Paris, 157, 1533, (1913). 



