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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1915 Excerpt: ...system. The four axes of ternary symmetry in the cubic system are hexagonal axes of combined symmetry in a sense that will be hereafter pointed out but do not occur as hexagonal axes in the same sense as in the hexagonal system. and are easily found. The arcs between the pole of any other face (e.g. 321 in Fig. 51) and the pinakoid poles can always be measured or calculated from a measurement to any of the above principal faces and the ratio of the intercepts made by this face on the axes ascertained in the manner above given for ascertaining the elements of tetragonal or rhombic crystals; the calculation being easier because all the angles at the pinakoid poles are = 90. This ratio of intercepts will give the indices of the face since the parametral elements are 1:1:1. The relation between the indices of faces connected by symmetry and constituting one "form" is in this case very wide. The form hkl consists of 48 faces whose indices are every possible group of three of the numerical values of hkl and Ml when h, k, and / are all different. This becomes a group of 24 faces when any two of h, k, and / are equal or when one of them is zero, a group of 12 faces when two are equal and one is zero, and a group of 8 faces when all three are equal. The merohedral subclasses in this system are four in number, characterized by the imputed incapacity of developing faces required for the full symmetry. The Thirty-two Classes Of Crystals. By the mode of classification above adopted; i.e. by treating the special nature of the "elements" to which a crystal complex can be referred as the They are given in most of the textbooks. In Miller's treatise (1839) they are given with a table of the arcs between them and mo3t of the other faces which occur in nat...
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