PRINCIPLES OF CRYSTALLOGRAPHY. 



253 



Five elements are undetermiDed, two relations and three angles of the 

 axes. Because no plane of symmetry exists, a single face, It 1c I, (Fig. 20,) 

 with the one parallel to it, constitutes a form. It is only necessary to 

 consider this analogy in the selection of the axes, where there exists a 



similarity in the angle and in the composition of the faces, with a more 

 highly symmetrical system, as the monoclinic or orthorhombic, 



2. Monoclinic system. — One plane of symmetry, B, (Fig. 21.) We 

 first select this plane as one of the i)lanes of the axes, especially for the 

 plane XZ, so that it takes the symbol 010. For every face, lilcl, a 

 second one is now possible, which, with it, is placed symmetrically with 

 regard to the plane of symmetry 010, and, therefore, as is easily seen, 

 takes the symbol hid. These two fiices, with those opposite to them, 

 constitute together the general form of the monoclinic system. A zone- 

 axis is determined by every two such pairs of faces, which, as is easily 

 perceived, must lie in the plane of symmetry, because 010 lies in the 

 zone [ {h Jc I) {h 7:1)]. If two such zone-axes are taken for the axis of X Z, * 

 it is at once clear that the angles of the axes will be — 



X T = C = 90° ; Y Z = .- = 90° ; (KZ = rj)% 90° 

 A fourth face gives the sections of the axes a^h^c, and we have in 

 this system three unknown elements, two ratios, and one angle of the 

 axes. 



3. Orthorhombic system. — Three planes of symmetry, ABC, (Fig. 

 22,) at right angles to one another, which 

 we select for the planes of the axes, with 

 the symbols 1 0, 1 0, 1. The three 

 axes will, for this reason, be at right an- 

 gles to each other, and we Lave now, by 

 means of a fourth plane, to determine 

 their lengths, so that — 



a> & > c; ? = >5 = : = 90o 

 In this system we have, therefore, two un- 

 known elements, - , - ; the four faces, 

 ' c c 



h h I, 11 A: 1, h ic J, 111- 1, with their opposites, are similar, so that the general 

 form is an eight- sided rhombic pyramid. 



Fij 22. 



