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Published online by Cambridge University Press: 14 March 2018
In the following notes I have endeavoured to give in a convenient and simple form a complete account of the relations connecting different twinning-laws or operations, which, when applied to the same crystal-structure, produce indistinguishable results.
A rigorous analysis of the possible relations between the compound structures of twin-crystals, based on the principles of the equality of the structural distances in the plane of composition, will be found in the author's papers, ' The geometry of twin-crystals' (Proc. Roy. Soc. Edinburgh, 1912-1918, vol. xxxii, pp. 416-432, 433-457) and 'Die Geometrie der Zwillingskrystalle' (Zeits. Kryst. Min., 1918, vol. lii, pp. 827-371). See also the paper 'Twin-planes and cross-planes' in this Magazine (1910, vol. xv, pp. 390-397).
page 225 note 1 This nmst be distinguished from inversion as defined in the geometrical method of Stubbs and Ingram.
page 226 note 1 Evans, J. W., A modification of the stereographic projection. Mineralogical Magazine, 1910, vol. xv, pp. 401-402Google Scholar.
page 228 note 1 It is convenient to use the term 'line of symmetry' to include axes with an even number of symmetry—digonal, tetragonal, or hexagonal—but not those with 'contra-directional' digonal or hexagonal symmetry, as defined on p. 238. A line of symmetry is analogous in many respects to the normal to a plane of symmetry ; which is a line of symmetry, when a centre of symmetry is present; and, in its absence, an axis of contra-direetional digona] or hexagonal symmetry.
page 231 note 1 The manner in which a line of symmetry and an axis of reflection-twinning are respectively indicated in these projections is explained on pp. 228, 229.
page 237 note 1 These twin-crystals may also be formed by rotation round the principal axis through one.sixth of a circle. (See p. 240.)
page 238 note 1 Hilton, H., this Magazine, 1907, vol. xiv, pp. 261-263Google Scholar.
page 238 note 2 In a simple, or co-directional, axis of symmetry, there is, on rotation through a portion of a circle, coincidence, not only of every line of the crystal with the former position of an equivalent line, but also of the directions in them. A contra-directional axis, in which n = 4 or 6 is also a co-directional axis with n = 2 or 3, as the case may be, but a contra-directional axis in which n is 2 is not a co.directional axis. If the character of an axis of symmetry is not expressly mentioned, it must be assumed that a simple or co-directional axis is tritended.