. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. 254 PRINCIPLES OF CRYSTi\XLOGRAPPIY. ?^j i^. "With regard to tbe selection of the three pinacoids, there may be a number of assumptions. Grailich and Lang talce (r > Z> > c: Schrauf selects, in substances which can be optically examined, 0 01, perpendic- ular to the bisectrix, 100 and 010, so that « > ?>; other authors follow no principle, but take the first method of exhibition. 4. EnoMBOHEDRAL SYSTEM.—Three phiues of s
. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. 254 PRINCIPLES OF CRYSTi\XLOGRAPPIY. ?^j i^. "With regard to tbe selection of the three pinacoids, there may be a number of assumptions. Grailich and Lang talce (r > Z> > c: Schrauf selects, in substances which can be optically examined, 0 01, perpendic- ular to the bisectrix, 100 and 010, so that « > ?>; other authors follow no principle, but take the first method of exhibition. 4. EnoMBOHEDRAL SYSTEM.—Three phiues of symmetry, A A'A", (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 •MhX ;, the planes of symmetry for the planes of ^^ the axes, because thej- are tautozonal. In order to observe the symmetry of the method of notation, we select for the i^lanes of the axes three faces of the crystal which are symmetrically situated with regard to the planes of symmetry, and so constitute a form. The faces 10 0, 010, 001, must be perpendicular to every plane of symmetry, because ouly one such form, composed of only three faces with their opposites, exists; every other one is composed 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 planes of symmetry, and is consequently simi- larly inclined to the three planes of the axes. Therefore— «, = & = c; (c = ^ = C) >90o • A single dimension, the angle of the axes, is undetermined. The three planes of symmetry have the symbols 101 = A ; 011 = A': 11 0 = 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 /; -f A- + 7 = o, because the symbol of the zone of symmetry is [111]. The other forms are scal
Size: 1570px × 1591px
Photo credit: © Library Book Collection / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookauthorsmithsonianinstitutio, bookcentury1800, bookdecade1840
