Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T15:49:11.978Z Has data issue: false hasContentIssue false

Theories of Polar Motion from Tisserand to Poincaré (1890 – 1910)

Published online by Cambridge University Press:  12 April 2016

P. Melchior
Affiliation:
Royal Observatory ofBelgium

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The discovery by Seth C. Chandler (1891) that the motion of the pole (the reality of which had been established by K.F. Küstner and by the simultaneous latitude observations at Honolulu and Berlin by German astronomers) resulted from two components i.e. a free circular motion with a period of 427 days and a forced elliptical motion with a period of 365.25 days, raised considerable interest in the scientific community of astronomers and geophysicists.

The celebrated Mécanique Céleste of Tisserand (1890) had been published just one year before at a time when doubts still persisted and arguments could be presented in favor of the fixed pole. Starting with Tisserand’s arguments, we describe in this paper the impact of the successive contributions by A. Greenhill, S. Newcomb, Th. Sloudsky, S. Hough, G. Herglotz, A. Love, J. Larmor and H. Poincaré to the solution of the problems raised by the Chandler period.

The lines of reasoning taken by these eminent scientists were rigorously correct so that, after about one hundred years, contemporary researchers, who benefit from a far better knowledge of the inner structure of the Earth and are able to take advantage of modern computing power, do not contradict any of their conclusions and instead refine them with an accuracy which was not imaginable one century ago.

Type
Part 1. History of Early Polar Motion Research
Copyright
Copyright © Astronomical Society of the Pacific 2000

References

Chandler, S.C., 1891. On the variation of Latitude. The Astron. Journal, XI, pp 6570.Google Scholar
Dehant, V. and Defraigne, P., 1997. New transfer functions for nutations of a non rigid Earth. J. Geophys. Res. 102, B 12, pp 2765927687.Google Scholar
Greenhill, A.G., 1879. “On the rotation of a liquid ellipsoid about its mean axis,” Proceedings Cambridge Phil. Soc. 3, pp. 233246.Google Scholar
Greenhill, A.G., 1880. On the general motion of a liquid ellipsoid under the gravitation of its own parts. Proceedings Cambridge Phil. Soc., 4, pp 414.Google Scholar
Herglotz, G., 1905. “Ueber die Elastizität der Erde bei Berücksichtigung ihrer variablen Dichte,” Zeitschrift f. Math, und Phys. 52, pp 275299.Google Scholar
Hopkins, W., 1839. On the Phenomena of Precession and Nutation, assuming the Fluidity of the Interior of the Earth. Phil. Trans. Roy. Soc. London A 219, pp 381423 and A 220, pp 193208.Google Scholar
Hough, S.S., 1895. The Oscillations of a Rotating Ellipsoidal Shell containing Fluid. Philosophical Transactions Royal Society, London, 186, pp 469506 awarded a Smith’s Prize.Google Scholar
Hough, S.S., 1896. The Rotation of an Elastic Spheroid. Philosophical Transactions Royal Society, London, 187, pp 319344.Google Scholar
Jeffreys, H., 1949. Dynamic effects of a liquid core. Monthly Notices Roy. Astr. Soc., 109, pp 670687.Google Scholar
Kelvin, , Lord, , (Thomson, W.), 1863. On the rigidity of the Earth. Phil. Trans. Roy. Soc. London 153, II, pp 573582. Revised in Math. And Phys. Papers III, art. XCV, pp 312336. Cambridge Univ. Press, 1890.Google Scholar
Kelvin, , Lord, , (Thomson, W.), 1885. On the Motion of a Liquid within an Ellipsoidal Hollow. Proc Roy. Soc. Edinburgh, XIII, pp 370378. Math, and Phys. Papers IV, pp 193201, Cambridge Univ. Press.Google Scholar
Kelvin, , Lord., , (Thomson, W.), 1890. Motion of a Viscous Liquid. Math and Phys. Papers III, art XCIX, pp 436442, see §14. Cambridge Univ. Press.Google Scholar
Larmor, J., 1909. The Relation of the Earth’s Free Precessional Nutation to its Resistance against Tidal Deformation. Proceedings Royal Society, London, 82, pp 8996.Google Scholar
Love, A.E.H., 1909. The Yielding of the Earth to Disturbing Forces. Proceedings Royal Society, London, 82, pp 7388.Google Scholar
Melchior, P., 1971. Precession - Nutations and Tidal Potential. Celestial Mechanics 4, pp 190212.Google Scholar
Melchior, P., 1983. The Tides of the Planet Earth. 2nd edition Pergamon Press, 641 pages — see page 52.Google Scholar
Melchior, P., 1986. The Physics of the Earth’s Core. An Introduction. Pergamon Press, Oxford, 256 pages.Google Scholar
Melchior, P., 1992. Tidal Interactions in the Earth Moon System. Intern. Union of Geodesy and Geophysics. Union Lecture IUGG Chronicle 210, pp 76114.Google Scholar
Newcomb, S., 1891. On the periodic variation of latitude and the observations with the Washington Prime-Vertical Transit. The Astron. Journal XI, pp 8182.Google Scholar
Newcomb, S., 1892. On the Dynamics of the Earth’s Rotation with respect to the Periodic Variations of Latitude. Monthly Notices Roy. Astr. Soc., 52, pp 336341.Google Scholar
Poincaré, H., 1910. Sur la Précession des Corps Déformables. Bulletin Astronomique XXVII, pp 321356.Google Scholar
Rochester, M.G., Jacobs, J.A., Smylie, D.E. and Chong, K.F., 1975. Can Precession Power the Geomagnetic Dynamo? Geoph. J. R. astr. Soc. 43 661678.Google Scholar
Ross, F.E., 1912. Tables of Correction to the Nutation Terms of the Berliner Jahrbuch. Astronomische Nachrichten, Bd 192, no 4587, pp 4748.Google Scholar
Schiaparelli, I.V., 1889. De la Rotation de la Terre sous l’Influence des Actions Géologiques. St.-Petersbourg, Acad. Impériale des Sciences, 32 pages.Google Scholar
Sloudsky, Th., 1895. De la rotation de la Terre supposée fluide á son intérieur. Bulletin Soc. Impériale des Naturalistes, Moscou, vol IX, n 2, pp 285318, suite:.vol X, pp 162-170, 1896. This important paper is repeatedly referred in the literature as published in 1896. However it was published in 1895, being dated 5-17 mai 1895.It follows that which was published in 1896.Google Scholar
Smith, M.L. and Dahlen, F.A., 1981. The period and Q of the Chandler wobble. Geophys. J.R. astr. Soc. 64, pp 223281.Google Scholar
Tisserand, F., 1890. Traité de Mécanique Céleste, Tome II. Théorie de la Figure des Corps Célestes et de leur Mouvement de Rotation. Gauthier-Villars, Paris, 549 pages.Google Scholar
Von Oppolzer, Th., 1881. Praecessions - und Nutationscoefficienten. Astronomische Nachrichten, Bd. 100, Nr. 2387, pp 166170.Google Scholar
von Oppolzer, Th., 1886. Traité de la Détermination des Orbites, des Comètes et des Planètes. Edition franéaise par Pasquier, E.. Gauthier-Villars, Paris, cf. pages 146154.Google Scholar
Wilson, C.R. and Haubrich, R.A., 1976. Meteorological excitation of the Earth’s Wobble. Geophys. J.R. astr. Soc. 39, pp 539550.Google Scholar