. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. FigiS. 7. Nine iDlanes of symmetry, three of which, A A'A", (Fig. 19,) are at right angles to each other, and similar. The other six, similar to each other, B B' B" . . B"^, intercalated between every two tautoz- onal A, and at an angle of 45°. Tesseral (isometric) system. § 2.—Characteristics of the Systems. From the above statement of the relations of symmetry in each crystal- line system we shall next derive the single fac
. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. FigiS. 7. Nine iDlanes of symmetry, three of which, A A'A", (Fig. 19,) are at right angles to each other, and similar. The other six, similar to each other, B B' B" . . B"^, intercalated between every two tautoz- onal A, and at an angle of 45°. Tesseral (isometric) system. § 2.—Characteristics of the Systems. From the above statement of the relations of symmetry in each crystal- line system we shall next derive the single faces belonging to each form as well as the most practical method of selecting the axes of the crystal. For axes we may select any three edges or zone-axes which are formed by three possible faces of the crystal not tautozonal with each other. We shall, however, on account of the existence of planes of symmetry, so select the axes that, wherever it is possible, they are placed sym- metrically to the planes of symmetry, by which we shall at once see that all the faces of a form will take the same numerical indices, but arranged in different orders. We understand by form the combination of all those faces which are symmetrical with each other, according to the planes of symmetry of the given crystal, and which, together, possess the same physical peculiarities. With regard to the selection of the axes, we only remark that it ap- pears necessary, on theoretical grounds, which were first developed by Frankenstein, so to select the axes that every acute axis-angle shall be greater than 60°, and that every obtuse one shall be less than 120°, which is always possible. "1. Triclinic system.—No plane of symmetry. The choice of the axes is arbitrary, as also the face 111, by which the jDlane of the axes is determined—. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these
Size: 1578px × 1584px
Photo credit: © Library Book Collection / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookauthorsmithsonianinstitutio, bookcentury1800, bookdecade1840
