- Taylor , E. G. R. 1954 . The Mathematical Practitioners of Tudor & Stuart England 91 Cambridge John Pell in 'Collections relating to Commissions to Enquire into the Methods for Finding the Longitude' (London, 1673-76), British Library Add. MS 4393, states (fol. 37 obverse, paragraph 21) that Bond first made this forecast in The Sea-Mans Kalendar 'about 1636'; however suggests in that it may have been the issue for 1638, but his reasons for doing so are unclear
- Forbes , E. G. and Mayer , Tobias . 1723-62 . Pioneer of Enlightened Science in Germany Göttingen 1980
- 1648 . Discovery of finding the long hidden Secret of longitude by Henry Bond, Teacher of the Mathematickes at the Bulwark-gate neere the Tower London J. Tap and H. Bond, The Sea-Mans Kalendar or, An Ephemerides of the Sunne, moone, and certaine of the most notable fixed Starres. As also a Table of the Longitude and Latitude, of all the most eminent Places of the World, very exactly calculated by John Tap. The Twentieth Impression, newly Corrected and Marge d with many additions.,. Also a
- Gellibrand , H. 1635 . A Discourse Mathematical on the Variation of the Magneticall Needle. Together with its admirable diminution lately discovered London
- Thomas , K. 1971 . Religion and the Decline of Magic 151 – 78 . London Examples are discussed in repr. 1991)
- Tillyard , E. M. W. 1943 . The Elizabethan World Picture London
- Swan , J. 1635 . Speculum Mundi 9 – 27 . Cambridge
- Bond , H. 1668 . The Variations of the Magnetic Needle Predicted for Many Years Following' . Philosophical Transactions of the Royal Society , 3 : 789 – 90 . reproduced in Philosophical Transactions (abridged version), 1 (1809), 282
- 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 : 357 – 423 .
- Bond , H. 1674 . 'The Use of the Inclynatorie Magneticall Needle to Find the Longitude by the Use of the Carolina tables' London British Library, Add. MS 4393, fols 7-20; Pell (note 1), fol. 37 obverse
- 1676 . Inclination of the Magnetical Inclinatorle Needle 17 London 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
- Bryden , D. J. 1993 . 'Magnetic Inclinatory Needles: Approved by the Royal Society?' . Notes and Records of the Royal Society , 47 : 17 – 31 . Idem, pp. 19, 32. reproduces (Figure 1, p. 22) an illustration of a dip circle made in 1677 to Bond's design by the instrument maker Henry Wynne. Bryden states (p. 29, his note 26) that the original of this (unnumbered) plate, bearing the legend 'A figure of Mr: Bonds Inclinatory Needle', is bound in facing the title page of the Royal Society copy of Bond (note 29); the same plate faces page 17 of the copy in the collection of the University of Illinois at Urbana-Champaign; and a re-worked version of the plate with the legend 'These Instruments are exactly made by John Marke in the Strand neere Somerset House' faces page 17 in a Bodleian Library copy. Bryden knows of no other copies of Bond's book containing this plate
- 1678 . The Longitude Not Found London Bond's reasoning is not given. A naval officer, Peter Blackborow, suggested in his tract 1680), that Bond's figure of 8° 30' was the result of a miscalculation
- Descartes , R. 1637 . Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences Leyden Appendix I, 'La géométrie', it is translated in
- Smith , D. E. and Latham , M. L. 1925 . The Geometry of René Descartes Chicago repr. New York, 1954)
- Smith , D. E. 1923 . History of Mathematics 2 vols , 375 Boston 1925; repr. New York, 1958), I
- Boyer , C. B. 1968 . A History of Mathematics New York As noted byrepr. New Jersey, 1985) pp. 370-79, Descartes' account lacks any systematic discussion of rectangular coordinates and curve sketching and 'he did not lay down a coordinate frame in order to locate points as a surveyor or geographer might do, nor were his coordinates thought of as number pairs' (idem, p. 379)
- Rousseeuw , P. J. and Leroy , A. M. 1987 . Robust Regression and Outlier Detection New York For discussion, see
- Rousseeuw , P. J. 1998 . “ 'Robust Estimation and Identifying Outliers' ” . In Handbook of Statistical Methods for Engineers and Scientists, , 2nd edn Edited by: Wadsworth , H. M. New York
- Legendre , A. M. 1805 . Nouvelles méthodes pour la determination des orbites des comètes Paris
- Mayer , T. 1750 . “ 'Abhandlung Ober die Umwalzung des Monds um seine Axe und die scheinbare Bewegung der Mondsflecken' ” . In Kosmographische Nachrichten und Sammlungen 52 – 183 . for 1748
- Stigler , S. M. 1986 . The History of Statistics. The Measurement of Uncertainty before 1900 18 – 24 . Cambridge, MA for discussion
- Buteo , J. 1559 . Logistica, quae & Arithmetica vulgó dicitur Lyons
- Westfall , R. S. 1980 . Never at Rest. A Biography of Isaac Newton 202 Cambridge David Barraclough correctly recognized that since equation (1) concerns a rate, strictly speaking, the second term in equation (2) ought to be the integral of equation (1). This would give a predicted inclination of 57.0° at 1657.5, hence a declination of 3° 49' rather than zero. However, it must be borne in mind that Newton only discovered the calculus in 1665-66. A preliminary account of his methods, 'De analysi per aequationes numero terminorum infinitas' (On analysis by infinite series'), was privately circulated in manuscript in August 1669 but the first discussion to appear in print was in his Philosophiae naturalis principia mathematica (Mathematical Principles of Natural Philosophy), which was not published until 1687 (Westfall, idem, pp. 402-68). It must therefore be surmised that Bond used a naive approach to make his 1636 prediction. The method of calculation suggested here is the only one which the author has been able to find which provides an exact fit to Bond's predicted declination value. Of course, there is the possibility that he did make make his prediction solely on the basis of a graphical extrapolation of a trend from past data, but the evidence regarding use of graphical methods in the early seventeenth century (note 42) would seem to weigh against this
- Birch , T. 1757 . The History of the Royal Society of London, for Improving of Natural Knowledge. From its First Rise 3 vols , 319 London
- Marron , J. S. and Tsybakov , A. B. 1995 . 'Visual Error Criteria for Qualitative Smoothing' . Journal of the American Statistical Association , 90 : 499 – 507 . discuss the nature of the difference between what is measured by the usual statistical goodness-of-fit criteria and what the eye can see in a graphical presentation, which makes choice of a visually based smooth trend an effective guide to a suitable smoothing parameter
- Hobson , E. W. 1888 . Trigonometry', Encyclopaedia Brittanica , 9th edn Edited by: Baynes , T. S. and Smith , W. Robertson . Vol. XXIH , 566 Edinburgh According to these formulae, known as 'Napier's "Analogies" ', were first given in John Napier, Mirifici logarithmorum canonis descrlptio (A description of the marvellous rule of logarithms) (Edinburgh, 1614)
- Halley , E. 1683 . 'A Theory of the Variation of the Magnetical Compass' . Philosophical Transactions of the Royal Society , 13 : 208 – 21 . Halley disapproved of the fact that Bond's results only applied to London and did little to explain the world-wide changes in magnetic declination, and suggested that the phenomena were better accounted for by a four-pole geomagnetic model rather than the two-pole model advanced by Bond
- Simon Schaffer, The Longitude Not Found. Henry Bond and The Variation of the Compass' (unpublished dissertation for Natural Sciences Tripos, Part II (General) Section 2, University of Cambridge, 1975); I am grateful to David Barraclough for providing me with his copy of this work.
- Barlow , P. 1831 . On the Probable Electric Origin of all the Phenomena of Terrestrial Magnetism; with an Illustrative Experiment' . Philosophical Transactions of the Royal Society , 121 : 99 – 108 .
- Krafft , W. L. 1809 . 'Essai sur une loi hypothétique des inclinations de l'aguille aimantée en differents endroits de la terre' . Mémoires de l'Académie Impériale des Sciences de St. Pétersbourg , 1 : 248 – 70 .
- von Humboldt , F. H. A. and Biot , J. B. 1804 . 'Sur les variations du magnétisme terrestre, à différentes latitudes' . Journal de Physique , 59 : 429 – 50 .
- Biot , J. B. 1816 . Traité de physique expérimentale et mathématique 3 vols , 132 Paris
- 1971 . J. H. Lambert's Work on Probability' . Archive for History of Exact Sciences , 7 : 244 – 56 . The German mathematician and physicist, Johann Heinrich Lambert (1728-77), is best known to historians of geophysics for his publication of the first graph to show change in magnetic declination as a function of time in 'Theorie der Zuverlässigkeit der Beobachtungen und Versuche' ('Theory of reliability of observations and experiments'). Figure IV, plate V, in Beytrage zum Gebrauche der Mathematik und deren Anwendung (Berlin 1765), I, 424-88 O. B. Sheynin drew attention to the fact that Lambert appears to have been the first to introduce the concept of the 'theory of errors', and that he 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. See also discussion in HaId (note 46), pp. 103-07. However, Lambert's method of curve-fitting does not seem to have been widely adopted
- 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 1839(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 , : 184 – 251 .
- Pumfrey , S. 1989 . ' "O Tempora, O Magnes!" A sociological analysis of the discovery of secular magnetic variation in 1634' . British Journal for the History of Science , 22 : 181 – 214 .
Annals of Science
Volume 59, 2002 - Issue 4