Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-21T07:17:25.223Z Has data issue: false hasContentIssue false
  • English
  • Français

Some applications of the Gnomonic Projection to Crystallograhy

Published online by Cambridge University Press:  14 March 2018

Harold Hilton
Harold Hilton*
Affiliation:
Magdalen College, Oxford
Get access Rights & Permissions [Opens in a new window]

Extract

Let the crystallographic axes OA, OB, OC of a crystal, whose axial ratios are a : b : c, meet a plane p in A, B, C. Let a plane through O, parallel to a crystal-face whose indices are h, k, l, meet p in the line f (fig. 1) ; and let the line OF, perpendicular to the face, meet p at the point F. Let the perpendicular from O on p meet it in V, and let OV = m.

Type
Research Article
Information
Mineralogical magazine and journal of the Mineralogical Society , Volume 14 , Issue 64 , May 1905 , pp. 104 - 108
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 1905

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Page 105 note 1 Since in a plane triangles reciprocal with respect to a circle are homologous, we have incidentally proved that the ares joining corresponding vertices of a spherical triangle and its polar triangle are concurrent, and that the intersections of corresponding sides of the two triangles lie on a great circle.

Page 107 note 1 Another proof is given by von Fedorow, E., Abhandl. k. bayer. Akad. Wiss. Müuchen, Math.phys. Cl., 1900, vol. xx, p. 496 Google Scholar.