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On the determination the optic axes of a crystal from extinction-angles

Published online by Cambridge University Press:  14 March 2018

Harold Hilton
Harold Hilton*
Affiliation:
Bedford College (University of London)
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Extract

Various authors have discussed the problem how to determine the position of the optic axes of a biaxial crystal when the extinction-angles on n different faces have been observed. It has been proved that a unique solution is possible when n = 1, 2, or 4, according as the crystal is orthorhombic, monoclinic, or triclinic. It is assumed (and will be assumed in this paper) that the n faces have general positious. The result is uot true, if one or more of the faces has a specialized position. For instance, the extinction-angle ou a face of an orthorhombic crystal which is parallel to an axis of symmetry will obviously not suffice to determine the position of the optic axes.

Type
Research Article
Information
Mineralogical magazine and journal of the Mineralogical Society , Volume 19 , Issue 95 , December 1921 , pp. 233 - 239
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 1921

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References

page 233 note 1 Weber, L., Zeits. Krist., 1921, vol. 56, pp. 1–11, 96-103Google Scholar; A. Johnsen, Centralblatt Min., 1919, pp. 321-325 [Min. Abstr., vol. 1, p.222].

page 236 note 1 The approximate posiLions of the two hyperbola% and therefore of H and K, are obvious at once when A, B, p, p', q, q', are drawn. It may be preferable in practice to draw the portions of each hyperbola near H, K by freehand, and find where they meet. The first hyperbola is easily drawn by getting the point where it meets any transversal through A ; using the facb tha~ the parts intercepted on any line between a hyperbola and its asymptotes are equal. Similarly for the secoud hyperbola.

page 237 note 1 See Hilton, ‘Plane Algebraic Curves,’ 1920, ch. xv. The method of constructing the cubic will be intelligible without a knowledge of the theory of cubic curves, if the proofs of some of the statements are taken for granted.

page 238 note 1 We leave the simple geometric proof to The reader.

page 239 note 1 Klingatsch, A., Sitzungsber. Akad. Wiss. Wien, Math.-naturw. Kl., 1914, vol. 123, Abt. II a, p. 745Google Scholar.