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Original Articles

Fitting Geomagnetic Fields before the Invention of Least Squares: II. William Whiston's Isoclinic Maps of Southern England (1719 and 1721)

Pages 63-84 | Published online: 05 Nov 2010

References

  • Felgentraeger , W. 1894 . “ 'Die Isoklinen Karte von Whiston' ” . In Nachrichten der koniglichen Gesellschaft der Wissenschaften zu Göttingen (no. 2) 129 – 40 .
  • Bauer , L. A. 1895 . 'The Earliest Isoclinics and Observations of Magnetic Force' . Bulletin of the Philosophical Society of Washington , 12 : 397 – 410 . for 1892-94
  • Hellmann Halley , G. , Whiston , W. , Wilcke , J. C. , von Humboldt , [F. W. H.] A. and Hansteen , C. 1895 . “ Die ältesten Karten der Isogonen Isoklinen Isodynamen 1701 1721 1768 1804 1825 1826' ” . In Neudrucke von Schriften und Karten über Meteorologie und Erdmagnetismus Vol. iv , 1 – 25 . Berlin
  • Whiston , W. and Ditton , H. 1714 . A New method for Discovering the Longitude both at Sea and Land 10 London
  • von Humboldt , [F. W. H.] A. 1817 . 'Des lignes isothermes et de la distribution de la chaleur sur le globe' . Mémoires de Physique et de Chimie, de la Société D'Arcueil , 3 : 462 – 602 .
  • 1817 . 'Sur les lignes isothermes (Extrait)' . Annales de chimie et physique , 5 : 102 – 12 . His map is reproduced in Robinson (note 5, 1982), p. 72, Figure 22
  • Mayer , T. “ 'Abhandlung über die Umwalzung des Monds um seine Axe und die scheinbare Bewegung der Mondsflecten' ” . In Kosmographische Nachrichten und Sammlungen (1750, for 1748) 52 – 183 . His method was based on the solution of a series of simultaneous linear equations, each of which corresponded to a given set of data values; see
  • Stigler , S. M. 1986 . The History of Statistics. The measurement of uncertainty before 1900 18 – 24 . Cambridge, MA
  • Sheynin , O. [B.] . 1993 . On the History of the Principle of Least Squares' . Archive for History of Exact Sciences , 46 : 39 – 54 . for discussion
  • Eisenhart , C. 1961 . “ 'Boscovich and the Combination of Observations' ” . In Roger Joseph Boscovich Edited by: Whyte , L. L. 200 – 12 . London Sheynin (note 11, 1993)
  • Euler , L. 1749 . Pièce qui a remporté le prix de l'Académie royale des Sciences en 1748 sur la question des inégalités du movement de Saturn et de Jupiter Paris Observationes in praecedentem dissertationem' (Observations on the foregoing dissertation [of Bernoulli]), Acta Academiae Scientiarum Imperialis Petropolitanae (1777), part 1, 24-33
  • Gauss , C. F. 1839 . “ 'Allegemeine Theorie des Erdmagnetismus' ” . In Resultate aus den Beobachtungen des magnetischen Vereins im Jahre 1838 Edited by: Gauss , C.F. and Weber , W. 1 – 57 . Göttingen translated by E. J. Sabine and revised by
  • Herschel , J. 1841 . 'General Theory of Terrestrial Magnetism by Professor Carl Friedrich Gauss of the University of Göttingen' . Taylor's Scientific Memoirs , II : 184 – 251 .
  • Tulloch , J. 1875 . “ 'Arius' ” . In Encyclopaedia Brittanica , 9th edn Edited by: Baynes , T. S. and Smith , W. Robertson . 537 – 39 . Edinburgh [J. F. Smith], 'Unitarianism', idem (1888), xxm, 725-26;
  • Thomson , A. 1830 . “ 'Arianism' ” . In The Edinburgh Encyclopaedia Edited by: Brewster , D. Vol. II , 351 – 53 . Edinburgh
  • Snobelen , S. D. 1999 . 'Isaac Newton. Heretic: the Strategies of a Nicodemite' . British Journal for the History of Science , 32 : 381 – 419 .
  • Westfall , R. S. 1980 . Never at Rest. A Biography of Isaac Newton 649 – 53 . Cambridge Summarized by Thomson (note 21), p. 353, as being 'that the eternity of the Son of God was not a real eternity, but only a metaphysical existence, in potentia [Latin, virtue], or in some sublimer manner, in the Father as his wisdom or word; that Christ's real generation or creation happened sometime before the creation of the world; and that this was the doctrine… of Christ, of his apostles, and of the first Christians'. See also discussion in
  • Gunter , R. T. 1937 . Early Science in Cambridge 79 Oxford
  • Whiston , W. 1749-50 . Memoirs of the Life and Writings of Mr. William Whiston. Containing Memoirs of Several of his Friends 3 vols , London
  • Anonymous . 1858 . “ 'Whiston, William' ” . In Cyclopaedia of Biography Edited by: Knight , C. Vol. vi , 663 – 65 . London
  • Baynes , T. S. and Smith , W. Robertson , eds. 1888 . “ 'Whiston, William (1667-1752)' ” . In Encyclopaedia Brittanica , 9th edn Vol. xxiv , 548 Edinburgh
  • Lorimer , P. 1865 . “ 'Whiston, William' ” . In The Imperial Dictionary of Universal Biography Edited by: Waller , J. F. London in, 907
  • Taylor , E. G. R. 1954 . The Mathematical Practitioners of Tudor & Stuart England 285 Cambridge
  • Sobel , D. 1996 . Longitude London The lack of a means to locate the position of a ship accurately caused many vessels to be lost at sea by collision with unexpected rocks; see for a popular account of attempts to solve the 'longitude problem'
  • Malin , S. [R. C.] . 1987 . “ 'Historical introduction to geomagnetism' ” . In Geomagnetism Edited by: Jacobs , J. A. Vol. I , 27 London
  • Gilbert , W. 1600 . De magnete, magneticisque corporibus, et de magno magnete tellure; Physiologia nova, plurimis & argumentis, & experiments demonstrata London ; repr. Brussels, 1967), pp. 184-204; translated by
  • Mottelay , P. F. 1893 . On the Loadstone and Magnetic Bodies, and on the Great Magnet of the Earth. A New Phvsiology, Demonstrated with Many Arguments and Experiments London repr. New York, 1958),' pp. 275-304
  • von Humboldt , [F. W. H.] A. 1855 . Cosmos: Sketch of a Physical Description of the Universe Edited by: Sabine , E. J. and Sabine , E. 4 vols , Ii London Iauthor's note 144
  • W. Whiston The Longitude and Latitude Found by the Inclinatory or Dipping needle; Wherein the Laws of Magnetism are also discover'd. To which is prefix'd, An Historical Preface; and to which is subjoin'd, Mr. Robert Norman's New Attractive, or Account of the first Invention of the Dipping Needle (London. 1721). p. xxiv.
  • Whiston , W. 1719 . The Longitude and Latitude Found by the Indinatory or Dipping Needle 29 London emphasis as in original
  • Alexandrescu , M. , Courtillot , V. and Mouël , J.-L. Le . 1996 . 'Geomagnetic Field Direction in Paris Since the Mid-Sixteenth Century' . Physics of the Earth and Planetary Interiors , 98 : 321 – 60 . The data compilation of corroborates the Paris observation but casts no additional light on whom its originator might have been
  • H. Power Experimental Philosophy, in three books: containing new experiments microscopical, mercurial, magnetical, with some deductions, and probable hypotheses, raised from them, in avouchment and illustration of the now famous atomical hypothesis (London, 1663-64).
  • Thorndyke , L. 1958) . A History of Magic and Experimental Science. VIII The Seventeenth Century 215 New York In part as a refutation of the theories of the French physician and astronomer, Jacques Grandami, SJ (1588-1672) as set out in J. Grandamicus, Nova demonstratio immobilitatis terrae petita ex virtue magnetica ([n.p.], 1645); see also
  • Harrison , J. 1978 . The Library of Isaac Newton 261 Cambridge
  • Howarth , R. J. 2002 . 'Fitting Geomagnetic Fields before the Invention of Least Squares: I. Henry Bond's Predictions (1636, 1668) of the Change in Magnetic Declination in London' . Annals of Science , 59 : xxx H. Bond The Longitude Found: or, a Treatise shewing An Easie and Speedy way, as well by Night as by Day, to find the Longitude, having but the Latitude of the Place, and the Inclination of the Magnetical Inclinatorie Needle (London, 1676). Bond's work is discussed in Part I of this study,
  • Malin , S. R. C. and Bullard , E. C. 1981 . The Direction of the Earth's Magnetic Field at London 1570-1975' . Philosophical Transactions of the Royal Society , : A299 Interpolated from plate I
  • Rousseeuw , P. J. 1983 . 'Regression Techniques with a High Breakdown Point' . Bulletin of the Institute of Mathematics and Statistics , 12 : 155 Robust regression methods automatically down-weight the influence of outliers in the data when fitting the regression function. See
  • Rousseeuw , P. J. and Leroy , A. M. 1987 . Robust Regression and Outlier Detection New York for further explanation of method used
  • Shields , M. C. 1937 . The Early History of Graphs in Physical Literature' . American Physics Teacher , 5 : 68 – 71 .
  • Tilling , L. 1975 . 'Early Experimental Graphs' . British Journal for the History of Science , 8 : 193 – 213 . For a more general survey, see
  • Funkhouser , H. G. 1938 . 'Historical Development of the Graphical Representation of Statistical Data' . Osiris , 3 : 269 – 404 .
  • 1971 . 'J. H. Lambert's Work on Probability' . Archive for History of the Exact Sciences , 7 : 244 – 56 . O. B. Sheynin has drawn attention to the fact that in the section Theorie der Zuverlässigkeit der Beobachtungen und Versuche' (Theory of reliability of observations and experiments) of the book Bey trage zum Gebrauche der Mathematik und deren Anwendung, 2 vols (Berlin 1765), I, 424-88, by the German mathematician and physicist Johann Heinrich Lambert (1728-77), he appears to have been the first to introduce the concept of the 'theory of errors', and that he also fitted functions by dividing the data points into approximately equal-sized groups and drawing lines, or in some cases smooth curves, through the centres of gravity of these groups
  • Plackett , R. L. 1958 . The Principle of the Arithmetic Mean' . Biometrika , 45 : 130 – 35 .
  • Sheynin , O. [B.] . 1993 . The Treatment of Observations in Early Astronomy' . Archive for History of Exact Sciences , 46 : 153 – 92 .
  • Haid , A. 1998 . A History of Mathematical Statistics from 1750 to 1930 94 New York See Sheynin (note 11), p. 41; Stigler (note 11), p. 16, for opposing views
  • Bloxham , J. and Jackson , A. 1992 . Time-Dependent Mapping of the Magnetic Field at the Core-Mantle Boundary' . Journal of Geophysical Research , B97 : 19537 – 63 . A technique used to construct spatially smooth maps of the main magnetic field at particular points in time, using spherical harmonics and cubic B-splines as the basis functions for the time-dependent mapping. It is computed from all available post-1690 data; see for further details
  • Graham , G. 1725 . Observations of the Dipping Needle, Made in London, in 1723' . Philosophical Transactions of the Royal Society , 33 : 332 – 39 . or idem (abridged) 7 (1809, for 1724-34), 94-96

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