. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. 254 PKINCIPLES OF 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 0 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&qu
. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. 254 PKINCIPLES OF 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 0 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, 0 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'; 110 = 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
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