Some Applications of the Gnomonic Projection to Crystallography

Harold Hilton
Fellow of Magdalen College, Oxford
Communicated by Professor Miers
University College, Bangor, North Wales

Summary: 1. In the gnomonic projection of the poles of a crystal on any plane the projection of the pole of (hkl) is the point (hkl), and the projection of the zone [HKL] is Hx + Ky + Lz = 0, a suitable triangle of reference and suitable triliteral coordinates being taken.

2. By means of this theorem simple proofs of well-known crystallographic theorems may be obtained.

3. Some relations between the number (ur) of zones of a crystal containing r faces, and the number of faces (vr) lying in r zones may be found; e.g., n(n−1)=∑2nr(r−1)ur, ∑2n{(r−1)vr−1−rur}=0 where ∑vr = n .

Mineralogical Magazine; May 1905 v. 14; no. 64; p. 104-108; DOI: 10.1180/minmag.1905.014.64.09
© 1905, The Mineralogical Society
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