236 HISTORY OF MINERALOGY. 



governs them, and is not affected by their casual 

 fluctuations, the fundamental relations of those 

 Dimensions according to which a multiplicity of in- 

 ternal oppositions, necessarily and mutually inter- 

 dependent, are developed in the mass, each having 

 its own polarity ; so that the crystalline character 

 is co-extensive with these polarities." 



The "Dimensions" of which Weiss here speaks, 

 are the Axes of Symmetry of the crystal ; that is, 

 those lines, in reference to which, every face is 

 accompanied by other faces, having like positions 

 and properties. Thus a rhomb, or more properly 

 a rhombohedron*, of calc-spar may be placed 

 with one of its obtuse corners uppermost, so that 

 all the three faces which meet there are equally 

 inclined to the vertical line. In this position, every 

 derivative face, which is obtained by any modifica- 

 tion of the faces or edges of the rhombohedron, 

 implies either three or six such derivative faces; 

 for no one of the three upper faces of the rhom- 

 bohedron has any character or property different 

 from the other two; and, therefore, there is no 

 reason for the existence of a derivative from one 

 of these primitive faces, which does not equally 

 hold for the other primitive faces. Hence the deri- 

 vative forms will, in all cases, contain none but 

 faces connected by this kind of correspondence. 

 The axis thus made vertical will be an Axis of 



2 I use this name for the solid figure, since rhomb has always 

 been used for a plane figure. 



