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On a protractor for use in constructing stereographic and gnomonie projections of the sphere. (With Plates III, IV, IV a and V.)

Published online by Cambridge University Press:  14 March 2018

A. Hutchinson
A. Hutchinson*
Affiliation:
University of Cambridge
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Extract

The protractor of which an account is given in the following pages is intended to facilitate the construction of stereographic and gnomonie projections of the sphere, especially on the part of students of crystallography. The fundamental properties of these projections, on which its design depends, have long been known, and have been the basis in the past of methods somewhat similar to those about to be described. Any novelty there may be in the device is to be sought therefore in the convenient arrangement of its parts, and in the ease with which it may be constructed and used, rather than in the principles which it embodies. We will consider first the construction of the protractor, then its application in tile case of the stereographic and gnomonic projections, and in conclusion will deal with a few points of interest in the history of these projections.

Type
Research Article
Information
Mineralogical magazine and journal of the Mineralogical Society , Volume 15 , Issue 69 , November 1908 , pp. 93 - 112
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 1908

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References

Page 99 note 1 Penfield, S. L., Amer. Journ. Sci., 1901, ser. 4, vol. xi, p. 19.Google Scholar

Page 101 note 1 The point N' is the ‘Winkelpunkt’ of V. Goldschmidt, and may be termed the ‘angle-point’ of N.

Page 103 note 1 This construction may also be utilized to find the angle between two given points. For let H and D be the two points. Find F the pole of the zone HD and join DF. Then find E and proceed as above. Another construction, due to E. S. Fedorov, is given on page 105.

Page 104 note 1 Zeits. Kryst. Min, 1908, vol. xliv, p. 89. See also ibid, 1903, vol. xxxvii, p. 141.

Page 104 note 2 Annuaire Géol. Min. Russie, 1905-1906, vol. viii, p. 26.

Page 106 note 1 ‘Ptolemaei Planisphaerium.’ Vonetiis, 1558.

Page 106 note 2 ‘Christophori Clavii Bambergensis e Societate Iesu Astrolabium.’ Romae, 1593.

Page 106 note 3 ‘Christophori Clavii Bambergensis e Societate Iesu Operum Mathematicorum Tomus Tertius.’ Moguntiae, 1611.

Page 106 note 4 Adrianus Metius, ‘Primum Mobile’. Editio nova. Amsterdami, 1633.

Page 107 note 1 ‘Francisci Aguilonii e Societate Iesu Opticorum Libri Sex.’ Antverpiae, 1613. (See Book vi, p. 573.)

Page 107 note 2 J. Harris, ‘Elements of Plain and Spherical Trigonometry.’ London, 1706.

Page 107 note 3 J. Wilson, ‘Trigonometry with the Doctrine of the Sphere.’ 2nd edit. Edinburgh, 1724.

Page 107 note 4 C. Leadbetter, ‘A Compleat System of Astronomy.’ London, 1728.

Page 107 note 5 W. Emerson, ‘The Projection of the Sphere.’ 2nd edit., London, 1769.

Page 107 note 6 G. S. Klügel, ‘Geometrische Entwickelung der Eigenschaften der stereographischen Projection.’ Berlin und Stettin (Friedrich Nicolai), 1788.

Page 107 note 7 E. Reusch, ‘Die stereographische Projection.’ Leipzig, 1881

Page 107 note 8 A. Germain, ‘Traité des Projections.’ Paris [1866?].

Page 107 note 9 G. J. Morrison, ‘Maps, their Uses and Construction.’ 2nd edit., London, 1902.

Page 107 note 10 C. F. Close, ‘A Sketch of the Subject of Map Projections.’ London, 1901

Page 107 note 11 K. Zöppritz, ‘Leitfaden der Kartenentwurfslehre.’ New edition by A. Bludau, Leipzig, 1899.

Page 109 note 1 Phil. Trans., 1695-1697, vol. xix, No. 219, p. 202.

Page 110 note 1 F. E. Neumann, ‘Beiträge zur Krystallonomie.’ Berlin and Posen, 1823.

Page 110 note 2 W. H. Miller, ‘A Treatise on Crystallography,’ 1889. ‘Mineralogy,’ 1852.

Page 110 note 3 Des Cloizeaux, A., ‘Manuel de Minéralogie,’ vol. i, 1862, vol. ii, 1874–1898 Google Scholar.

Page 110 note 4 Fedorov, E. S., Zeits. Kryst. Min., 1898, vol. xxi, p. 617 Google Scholar, and 1908, vol. xxxvii, p. 188.

Page 110 note 5 G. Wulff, ibid., 1898, vol. xxi, p. 258, and 1902, vol. xxxvi, p. 14,.

Page 110 note 6 B. Hecht, ‘Anleitung zur Krystallberechnung.’ Leipzig, 1893.

Page 110 note 7 Sommerfeldt, E., Zeits. Kryst. Min., 1906, vol. xli, p. 164 Google Scholar.

Page 110 note 8 V. Goldschmidt, ibid., 1899, vol. xxx, pp. 260-271.

Page 110 note 9 Panfield, S. L., Amer. Journ. Sci., 1901, ser. 4, vol. xi, pp. 1–24 CrossRefGoogle Scholar and 115-144 ; see also vol. xiii, pp. 245-275 and 347-376, vol. xiv, pp. 249-284.

Page 111 note 1 Goodchild, J. G., Proc. Roy. Phys. Soc., Edinburgh, 1897-1901, vol. xiv, pp. 823–859 Google Scholar and 403-484.

Page 111 note 2 A. von Braunmühl, ‘Vorlesungen über Geschichte der Trigonometric.’ Leipzig, 1900.

Page 111 note 3 Huller, S., ‘Bibliotheca Mathematica.’ 1899, vol. xiii, p. 71 Google Scholar.

Page 111 note 4 J. Moore, ‘A New Systeme of the Mathematicks.’ London, 1681. (See ‘Cosmography,’ p. 162.)

Page 111 note 5 W. Emerson, loc. cir.

Page 111 note 6 A. de Morgan, ‘An Explanation of the Gnomonic Projection of the Sphere.’ London, 1836.

Page 112 note 1 Goldschmidt, V., ‘Ueber Projection und graphische Krystallberechnung’, Berlin, 1887. See also, Zeits. Kryst. Min., 1890, vol. xvii, p. 97 Google Scholar, and 1892, vol. xx, p. 143.

Page 112 note 1 Miers, H. A., Min, Mag., 1887, vol. vii, p. 145 CrossRefGoogle Scholar.

Page 112 note 1 Smith, G. F. H., Min. Mag., 1903, vol. xiii, pp. 809–821 Google Scholar.

Page 112 note 1 Evans, J. W., Min. Mag., 1906, vol. xiv, p. 149 CrossRefGoogle Scholar.

Page 112 note 1 Hilton, H., Min. Mag., 1904, vol. xiv, pp. 18–20 CrossRefGoogle Scholar, 1905, vol. xiv, 99-103, 104-108.

Page 112 note 1 Wright, F. E., Amer. Journ. Sci., 1907, ser. 4, vol. xxiv, p. 321 Google Scholar.