References

1. Halley, E. , “An account of the cause of the change of the variation of the magnetical needle with an hypothesis of the structure of the internal parts of the Earth” , Philosophical transactions, xvi ( 1692 ), 563 – 87 . The paper was read to the Royal Society on 25 November 1691 .

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2. Newton, I. , Philosophiae naturalis principia mathematica ( London , 1687 ), 466 (Book 3, Prop. 37, Cors. 3 and 4).

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3. Kollerstrom, N. , “Newton's lunar mass error” , Journal of the British Astronomical Association, xcv ( 1985 ), 151 – 3 .

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4. Halley , op. cit. (ref 1), 568 .

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5. Wilson, C. , “D'Alembert versus Euler on the precession of the equinoxes” , Archive for history of exact sciences, xxxvii ( 1987 ), 233 – 73 , p. 252 .

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6. Aiton, E. J. , “The contributions of Newton, Bernoulli and Euler to the theory of the tides” , Annals of science, xi ( 1955 ), 206 – 23 , p. 211 .

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7. Young, C. A. , A text book of general astronomy ( London , 1889 ), 282 : “Since the tide-raising power varies as the cube of the distance inversely, while the attracting force varies only with the inverse square, it turns out that although the Sun's attraction on the Earth is nearly 200 times as great as that of the Moon, its tide-raising power is only about two-fifths as much”.

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8. Westfall, R. S. , “Newton and the fudge factor” , Science, cli ( 1973 ), 751 – 8 , p. 756 .

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9. Newton , op. cit. (ref. 2), 2nd edn ( London , 1713 ), 430 (Book 3, Prop. 37, Cor. 3). See also Kollerstrom, N. , “Newton's two moon-tests” , The British journal for the history of science, xxiv ( 1991 ), 369 – 72 .

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10. Halley's review of the Principia appeared in Philosophical transactions, xvi ( 1687 ), 291 – 7 ; further comments of his appeared in his “True theory of the tides” , ibid., xix ( 1696 ), 445 – 57 .

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11. Halley, E. , “A theory of the variation of the magnetic compass” , ibid., xiii ( 1683 ), 208 – 21 .

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12. The nonexistence of two of Halley's four magnetic poles was demonstrated in 1817 , when the first complete chart of magnetic meridians appeared: Chapman, Sydney , “Edmond Halley and geomagnetism” , Nature, clii ( 1943 ), 231 – 7 .

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13. Halley , op. cit. (ref. 11), 221 .

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14. Bennett, J. A. , “Cosmology and the magnetical philosophy, 1640–1680” , Journal for the history of astronomy, xii ( 1981 ), 165 – 77 .

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15. Chapman , op. cit. (ref. 12), 234 .

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16. Forbes, E. G. , History of Greenwich Observatory, i ( London , 1975 ), 15 – 17 .

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17. Birch, T. , History of the Royal Society ( London , 1756 ), iii, 131 .

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18. Forbes , op. cit. (ref. 16), 74 ; Baily, F. , An account of the Revd. John Flamsteed ( London , 1835 ), 194 . A letter to Flamsteed by Thomas Perkins of 12 December 1700 recalled the purchase of his late brother's papers in 1680 by Edmond Halley.

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19. For Perkins's theory see Birch , op. cit. (ref. 17), iv, 18 – 19 ; no-one has ever taken Flamsteed's claim seriously, see McPike, E. F. , Hevelius, Flamsteed and Halley ( London , 1937 ), 92 .

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20. See Kircher, Athanasius , Mundus subterraneus ( Amsterdam , 1665 ). For discussion of Kirchner and magnetic cosmology, see Baldwin, M. , “Magnetism and the anti-Copernican polemic” , Journal for the history of astronomy, xvi ( 1985 ), 155 – 74 .

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21. Schaffer, S. , “Halley's atheism and the end of the world” , Notes and records of the Royal Society, xxxii ( 1977 ), 17 – 40 , p. 18 .

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22. Halley , op. cit. (ref. 1), 573 .

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23. Zircle, C. , “The theory of concentric spheres: Halley, Mather and Symmes” , Isis, xxxvii ( 1947 ), 155 – 9 .

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24. Kubrin, D. , “Such an impertinently litiginous lady” , in Standing on the shoulders of giants, ed. by Thrower, N. J. ( Oxford , 1990 ), 55 – 87 , pp. 59 , 64 .

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25. Oldroyd, D. R. , “Geological controversy in the seventeenth century: Hooke vs Wallis and its aftermath” , in Robert Hooke: New studies, ed. by Hunter, Michael and Schaffer, Simon ( Woodbridge, Suffolk , 1989 ), 207 – 33 , p. 230 .

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26. For Hooke's geological theories in the 1690s, see Ito, Y. , “Hooke's cyclic theory of the Earth” , The British journal for the history of science, xxi ( 1988 ), 295 – 314 .

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27. Hooke, R. , “A discourse of earthquakes” , Posthumous works, ed. by Waller, R. ( London , 1707 ), 279 – 450 , p. 349 .

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28. Halley, E. , “Some account of the ancient state of the city of Palmyra” , Philosophical transactions, xix ( 1695 ), 160 – 75 , p. 174 .

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29. Schaffer , op. cit. (ref. 21), 22 .

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30. Ibid., 18 .

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31. Halley, E. , “Emendationes ac notae in vetustas Albatenii observationes astronomicas” , Philosophical transactions, xvii ( 1693 ), 913 – 21 .

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32. Royal Society , Journal Book, 31 October 1694 . See Kubrin, D. , “Newton and the cyclical cosmos” , Journal of the history of ideas, xxviii ( 1967 ), 325 – 46 , p. 337 .

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33. In the mid-nineteenth century the true character of the phenomenon called ‘secular acceleration’ of the Moon came to be understood, as due to the slowing of the Earth's rotation rate. The increasing day-length causes the lunar month to appear shorter over the centuries. The apparent effect has been regarded as sufficiently similar to credit Halley with the discovery of the Moon's ‘secular acceleration’. See Kusher, D. , “Secular acceleration of the Moon's mean motion” , Archive for history of exact sciences, xxxix ( 1989 ), 291 – 316 .

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34. Halley, E. , “An account of the cause of the change of the variation of the magnetic needle” , Philosophical transactions abridged, 1705 edn, ii, 610 – 20 ; 1809 edn ( 5th edn ), iii, 470 – 8 ; Miscellanea curiosa, 3rd edn ( 1726 ), i, 43 – 59 .

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35. The aurora of 1716 marked the conclusion of the sixty-year Maunder Minimum (Eddy, J. , “The case of the missing sunspots” , Scientific American, May 1977 , 80 – 92 , p. 82 ), whereby the Sun largely bereft of sunspots had refrained from causing magnetic storms or aurorae, as it has done ever since.

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36. Halley, E. , “An account of the late surprizing appearance of the lights seen in the air, on the sixth of March last, with an attempt to explain the principal phaenomena thereof” , Philosophical transactions, xxix ( 1716 ), 406 – 28 , p. 427 .

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37. Whiston's, W. Astronomical lectures ( London , 1715, 1728 ) gave the relative densities as: Sun 1.00, Earth 3.87, Moon 7.00 (Frontispiece). This Frontispiece did not appear in the original Latin edition of this work, Praelectiones astronomicae ( Cambridge , 1707 ).

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