82 MINERALOGY 



In type 25, the ditetragonal polar, where there is a vertical plane 

 of symmetry crossing the prism face and the vertical axis is a dite- 

 tragonal axis and no equatorial plane or digonal axes, the etch 

 figure on each face is symmetrical to a vertical plane only ; and re- 

 volved around the vertical axis c 90 will become congruent with 

 those on the adjacent face, as a', a will also be a reflection of a', 

 across the plane of symmetry containing the edge between them. 



In type 24, the tetragonal equatorial, where the vertical axis is a 

 tetragonal axis of symmetry and has an equatorial plane, the etch 

 figure will be symmetrical to the equatorial plane By a revolution 

 of 90 around the vertical axis it will become congruent with a', 

 on the adjacent prism face, but a is not a reflection of a', as here 

 there is no plane of symmetry between them. 



In type 23, the tetragonal holoaxial, where there are no planes of 

 symmetry and the vertical axis is a tetragonal axis and there are 

 four digonal axes in the equatorial plane, the etch figure must 

 have a center of symmetry ; and if revolved 90 around the vertical 

 axis or 180 around the crystallographical axis, it must become con- 

 gruent with a', the etch figures on the adjacent crystal faces. The 

 figure a' is not a reflection of a, as there is no plane of symmetry 

 between them. 



In type 22, the tetragonal alternating, where there are no planes 

 of symmetry arid the vertical axis is a tetragonal alternating axis, 

 the etch figure a will be asymmetric ; and if revolved around the 

 vertical axis c 90, then reflected over the equatorial plane, will 

 become congruent with a', on the adjacent prism face. 



In type 21, the tetragonal polar, where the vertical axis is a te- 

 tragonal axis, the etch figure a will be asymmetric and will become 

 congruent with a' by a rotation of 90 around the vertical axis c. 



From the several diagrams it will be seen that each of the seven 

 possible prisms of the first order, though alike in outward form, 

 possesses the symmetry of the type, which is revealed by the shape 

 and relation of the etch figures on the form. 



Crystalline elements. In the isometric system, as the axes are 

 all interchangeable, the crystalline characters are fixed and are the 

 same for all substances crystallizing in the system. In the tetrag- 

 onal system the axial ratio - varies with the substance ; its value 



a 



is constant, however, for each chemically pure substance. The 

 axial ratio is calculated from the angles of the fundamental forms, 

 or those forms which intercept the axes at unity. 



