Hostname: page-component-7479d7b7d-rvbq7 Total loading time: 0 Render date: 2024-07-10T06:37:51.287Z Has data issue: false hasContentIssue false
  • English
  • Français

On the advantages of the face-adjustment for two-circle goniometry

Published online by Cambridge University Press:  14 March 2018

Max H. Hey
Max H. Hey*
Affiliation:
Mineral Department of the British Museum of Natural History
Get access Rights & Permissions [Opens in a new window]

Extract

In two-circle goniometry as usually practised, the zone-adjustment is almost invariably used. It would be difficult to discover the reasons which have led to this unfortunate neglect of the face-adjustment; actually the face-adjustment has all the advantages of the zone-adjustment without its defects.

Type
Research Article
Information
Mineralogical magazine and journal of the Mineralogical Society , Volume 23 , Issue 145 , June 1934 , pp. 560 - 565
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 1934

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 560 note 1 This primary function is not fulfilled by the tables of angles sometimes given, containing calculated angles only.

page 561 note 1 The author would add a fifth independent sub-division of crystallography to the four given by Rogers, A. F. (Amer. Min. 1933, vol. 18, p. 538)Google Scholar ; determinative crystallography differs sufficiently in its aims and methods from pure morphology or from structural crystallography to form a separate sub-division.

page 562 note 1 The formal proof of this construction is simple. Let OB extend to infinity, to meet RPQ in B, which will then be the gnomonic projection of b (010). Draw PY parallel to TR to cut OB in Y. Then BPY is the gnomonic projection of a right-angled spherical triangle, the right angle being at Y. And the angle YBP of this triangle = 90°-[ab] : [bP] = 90° ϕ. Hence cot BY = cot bP. cosec ϕ. But in the gnomonie projection, RP = OY = cot BY. And RP = RT. cot bP by construction. Hence if RT = cosec q), the construction is correct. Now by construction,

page 562 note 2 The face b (010) can almost always be adjusted, even if it is not developed. Thus the zone ac [010] may be adjusted, which comes to the same thing, since the face b is perpendicular to this zone-axis ; or the zone ab [001], or any other zone containing b (010), may be adjusted parallel to the axis of the horizontal circle, the zone measured, and the position of b(010) calculated. Then any face is brought into the reflecting position, the horizontal circle turned through the angle which the normal to b(010) has been found to make with the axis of the vertical circle, and the face brought, back into the reflecting position by means of the crystal-adjusting segments. With the three-circle goniometer, this adjustment is made with the greatest ease by means of the third circle.

page 562 note 3 The principal advantage of projection on b (010) lies in the assistance given in selecting the most suitable axes. Cf. Barker, T. V., Systematic crystallography. London, 1930, p. 44.Google Scholar

page 562 note 4 Projection is assumed to be on a plane perpendicular to the zone ab, and the y-axis is parallel to the zone-line bc. The radius of projection is taken as unity. With the zone ab in zone-adjustment, x = tan p. sin ϕ, y = tan p. cos ϕ

page 564 note 1 It is necessary that a zone shall contain at least two faces other than the face selected for adjustment, if it is to serve as a test of the accuracy of adjustment

page 565 note 1 The face c (001) can very well be adjusted, provided projection is made on a plane normal to one of the zone axes ac [010] or bc [100].