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Gnomonic Projections on two planes

Published online by Cambridge University Press:  14 March 2018

John W. Evans
John W. Evans*
Affiliation:
Imperial Institute
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Extract

The gnomonic projection in which the faces of crystals are represented by the points where their normals through a fixed point–the centre of projection–meet a plane–the plane of projection–is already widely used by crystallographers. I propose in the following pages to show the advantages of the simultaneous use of two such planes of projection.

It is in most cases convenient for the two planes to be at right angles, and for the centre of projection to be at an equal (unit) distance from each. Circumstances, however, in some cases render it desirable to vary these conditions. When the planes are at right angles, one may conveniently be described as the horizontal plane, and the other as the vertical plane.

Type
Research Article
Information
Mineralogical magazine and journal of the Mineralogical Society , Volume 14 , Issue 65 , May 1906 , pp. 149 - 156
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 1906

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References

Page 154 note 1 Which would be equal in this position to the tangent of the circular measure of the side.

Page 155 note 1 Let N 1 be any point on the circle, and M 1 the point on the circle where K 1′ (produced) intersects it. Draw N 1 M 1 meeting D 1 D 1′ in L 1. Draw L 1 K 1′ meeting at Q 1 the perpendicular from N 1 on D 1 D 1′; then Q1 is s point on the ellipse. In the dlngram (fig. 6) Q1 is the extremity of the minor axis of the ellipse.