EXPLANATION OF THE PRINCIPLES OF CRYSTALLOGRAPHY 

 AND CRYSTALLOPHYSICS/ 



By Aristides Brezina. 

 [translated for the smithsonian institution by professor t. egleston.] 



INTEODUCTION. 



Among all the metbocls in crystallograpby there is not a single one 

 which has remained so completely coufied within special limits as Mil- 

 ler's. The reason for this is not the abstract method in which the sub- 

 ject is treated, nor its difficult mathematical principles, but is principally 

 owing to the fact that, up to this time, it has never been treated separ- 

 ately from those operations which serve for the derivation of certain 

 special mathematical formul* in the first principles of geometry. 



Miller's method is really capable of an elementary treatment, which, 

 almost without the use of mathematics, renders xiossible not only the 

 quick and certain explanation of all combinations in the way of zone- 

 observations, but also the recognition of the physical characters of 

 cr^'stals on the basis of their relations of symmetry. 



These characters of this known method are especially useful for min- 

 eralogists and lithologists, who make microscopical observations : for the 

 first, because he, without many measurements and calculations, can 

 show, from only the simple inspection of a crystal, the connection of the 

 different faces, together with the explanation of the combination ; and 

 for the latter, because he is in position, on account of a precise knowl- 

 edge of the relations of symmetry, to recognize, in thin sections, both 

 the crystalline system and the elements of a crystal ; and in both cases, 

 without presumption of such mathematical knowledge, which is without 

 the departments of mineralogists and lithologists. This method is, for 

 this reason, not only simple and fundamental, but is in eYery way supe- 

 rior to the others in use, which have originated with Weiss, Naumann, 

 and Levj. 



One of the most important advantages of it is the possibility of a 

 simultaneous development of the crystallographic and physical rela- 

 tions of every system from its known symmetry. This method of pro- 

 cedure gives, from the very commencement, a complete insight into its 

 habits and characteristics, and secures, during its development, a survey 

 of the whole theoretical structure. But while this method of derivation 

 was first carried out for the crystallographic part by von Lang^, the in- 



' Miuenilogische Mittbeiluuf^eu. Wien, 1872. 



^ Laog, Krystallograpbie. Wien, Braumiiller, 1866. 



