104 



obtained by H. Hag a and the author 1 ) in the case of the three 

 minerals discussed here. There can be no doubt whatever about 

 the full agreement between the experimental results and the theo- 

 retical deductions. 



That in all cases of crystalline symmetry this agreement really 

 takes place, and that, therefore, conversely it may be safely concluded 

 that the Ron t gen-radiation is in all circumstances actually a 

 centrically '-symmetrical phenomenon, was demonstrated for the first 

 time by the same authors l ) in a series of papers, in which were 

 described experiments with crystals of almost all the 32 classes 

 of crystallography. 



If accidental abnormalities, caused by occasiona lirregularities 



Fig. 99 a c. 



Stereographical Projection of the R 6 nt g e n-patterns of quartz, turmaline, 

 and calcite. Plates parallel to J12TOJ. 



of the molecular structure or by twinning-phenomena, be left out 

 of account here, we can say that the centrically- symmetrical nature 

 of the radiation considered, as well as the agreement of the theore- 

 tically deduced and experimentally found symmetry of the R on t gen- 

 patterns, have now been exactly stated in all cases. 



14. The same thesis about the apparent increase of symmetry 

 of a crystalline medium in which a phenomenon of a special sym- 

 metry occurs, appears to be true for all other physical phenomena 

 in crystals. In the same way we find that the 32 possible symmetry- 

 classes of crystallography are reduced to the following eleven: 



/, Cl, D 1 }, Cl, D?, Cj, C D 3 , Cl, D?. T", and K*. 

 for all phenomena which have likewise a centrically-symmetrical 



!) H. Haga and F. M. Jaeger, Proceed. Akad. v. Wetenschappen Amster- 

 dam, Vol. 17, 18, (1914 '16). On accidental abnormalities of the patterns of 

 quartz caused by twinning, vid. the papers mentioned here. 



