254 



PKINCIPLES OF CRYSTALLOGRAPHY. 



With regard to the selection of the three pinacoids, there may be a 

 number of assumptions. Grailich and Lang take « > & > c ; Schrauf 

 selects, in substances which can be optically examined, 001, perpendic- 

 ular to the bisectrix, 10 and 010, so that « > & ; other authors follow 

 no principle, but take the first method of exhibition. 



4. Rhombohedral system. — Three planes of symmetry, A A' A", 

 j,jZ3. ,., (Fig. 23,) which are tautozonal, similar, and 



inclined to each other at an angle of 60°. 

 In this case it is not admissible to select 

 the planes of symmetry for the planes of 

 the axes, because they are tautozonal. In 

 order to observe the symmetry of the 

 method of notation, we select for the planes 

 of the axes three faces of the crystal which 

 are symmetrically situated with regard to 

 the planes of symmetrj', and so constitute 

 a form. The faces 100, 010, 01, must 

 be perpendicular to every plane of symmetry, because only one such 

 form, composed of only three faces with their opposites, exists ; every 

 other one is comi^osed of six or of two. For the determination of the 

 planes of the axes we select a face, as 111, which is at right angles 

 to the zone-axis of the i)laues of symmetry, and is consequently simi- 

 larly inclined to the three planes of the axes. Therefore — 



a = 'b = C] (? =v; = :) >90o 

 A single dimension, the angle of the axes, is undetermined. 



The three planes of symmetry have the symbols 101 = A; 011= A'; 

 1 1 = A". The symbol of each, with the faces tautozonal to the plane 

 of symmetry, which are prisms according to the general notation, thus 

 deviating from usage in the other crystalline systems, is liable to the 

 condition li -{■ Ix + 1 = o, because the symbol of the zone of symmetry is 

 [111]. The other forms are scalenohedrons, which is the general form 

 of this system, with six faces, h Ic I, (Fig. 23,) and their opposites ; rhom- 



bohedrons, whose faces are perpendicu- 

 lar to every plane of symmetry; the 

 base 111. 



It is plain that the axis-angle = is equal . 

 to i)laue-angle of the faces at the vertex 

 of the primitive rhombohedron, (10 0). 

 5. Tetragonal system. — Four tau- 

 tozonal i^lanes of symmetry inclined at 

 an angle of 45° to each other ; every al- 

 ternate two, A A', BB', (Fig. 24,) simi- 

 lar; a fifth one, C, perpendicular to these, but not similar. For planes 

 of the axes we select two similar planes of symmetry, which are perpen- 

 dicular to each other, B A A', and the single i)lane of symmetry, C, at 



