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Hooke and Wren and the System of the World: Some Points Towards An Historical Account

  • J. A. Bennett (a1)
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I want to thank an anonymous referee for some very helpful comments and the President and Council of the Royal Society for permission to quote from manuscripts in their' possession.

1 For studies of Hooke's work, see Patterson, L. D., ‘Hooke's gravitational theory and its influence on Newton’, Isis, xl (1949), 327–41, and xli (1950), 32–45; Lohne, J., ‘Hooke versus Newton’, Centaurus, vii (1960), 652; Koyré, A., ‘An unpublished letter of Robert Hooke to Isaac Newton’, Isis, xliii (1952), 312–37, reprinted in Koyré, , Newtonian studies (London, 1965), chapter 5; Koyré, A., ‘Hooke on gravitational attraction’, ibid., pp. 180–4; Westfall, R. S., ‘Hooke and the law of universal gravitation’, The British journal for the history of science, iii (1967), 245–61; Centore, F. F., Robert Hooke's contributions to mechantes (The Hague, 1970), chapter 5. For Wren, see Lawrence, P. D. and Molland, A. G., ‘David Gregory's Inaugural Lecture at Oxford’, Notes and records of the Royal Society of London, xxv (1970), 143–78. Note also Koyré, A., ‘La gravitation universelle de Kepler à Newton’, Archives internationales d'histoire des sciences, iv (1951), 638–53, and Westfall, R. S., Force in Newton's physics (London, 1971).

2 See Whiteside, D. T., ‘Newton's early thoughts on planetary motion: a fresh look’, The British journal for the history of science, ii (1964), 117–37; ‘Before the Principia: the maturing of Newton's thoughts on dynamical astronomy, 1664–1684’, Journal for the history of astronomy, i (1970), 519.

3 See Armitage, A., ‘“Borell's hypothesis” and the rise of celestial mechanics’, Annals of science, vi (1950), 268–82.

4 Ibid., p. 278; Westfall, 1967, op. cit. (1), p. 253, note 22; Lawrence, and Molland, , op. cit. (1), pp. 152–3; Centore, , op. cit. (1), pp. 92–4.

5 Hooke, to Newton, , 6 01 1679/1980, in The correspondence of Isaac Newton, ed. Turnbull, H. W. (Cambridge, 1960), ii. 309.

6 Newton, to Halley, , 20 06 1686, ibid., ii. 435. As Koyré has pointed put, Newton is indicating that the duplicate proportion is not mentioned in Cometa; see Koyré, 1965, op. cit. (1), p. 234, note 2.

7 Newton, to Halley, , 27 05 1686, Correspondence, op. cit. (5), pp. 433–4. It seems fairly certain that, by combining Huygens's expression for centrifugal force, published ih 1673, and Kepler's third law, Wren had derived an inverse-square relation in the restricted case of a circular orbit. Lawrence, and Molland, , op. cit. (1), pp. 147–54, have collected together the evidence for this and have added the explicit testimony of David Gregory.

8 Newton correspondence, op. cit. (5), ii. 434.

9 Halley, to Newton, , 29 06 1686, ibid., ii. 441–2.

10 ‘The life of Dr. Robert Hooke’, in The posthumous works of Robert Hooke, ed. Waller, R. (London, 1705), p. iii.

11 Ward, S., Vindiciae academiarum (Oxford, 1654), p. 29. Curiously enough, in the same year Wren assisted John Wallis in observing a solar eclipse at Oxford; see Wallis, J., Eclipsis solaris Oxonii visae anno … 1654 (Oxford, 1655), p. 2. Walter Pope says that ‘The first thing Mr. Ward did, after his Settlement in Oxford [in 1649], was to bring the Astronomy Lectures into Reputation, which had been for a considerable time disused, and wholly left of … Besides this, he taught the Mathematics gratis to as many of the University, or Foreigners, as desired that Favour of him’; see Pope, W., Life of Seth Ward (London, 1697), p. 23. Hooke says that around 1655 he had ‘an opportunity of acquainting my self with Astronomy by the kindness of Dr. Ward’; see Waller, , op. cit. (10), p. iv.

12 From the English draft of Wren's inaugural address as Professer of Astronomy at Gresham College, in Wren, C. Jnr, Parentalia: or, manoirs of the family of the Wrens (London, 1750), p. 204.

13 Ibid., p. 239. For references to Wren's lectures on dioptrics, see ibid., p. 241; The diary and correspondence of Dr. John Worthington, ed. Crossley, J., Chetham Society, xiii (1847), 126–7; The life and works of the Honourable Robert Boyle, ed. Birch, T. (2nd edn., London, 1772), vi. 118; Birch, T., The history of the Royal Society of London (London, 17561757), i. 504.

14 For this distinction, see Russell, J. L., ‘Kepler's laws of planetary motion: 1609–1666’, The British journal for the history of science, ii (1964), 1719.

15 See Hall, A. R., ‘Wren's problem’, Notes and records of the Royal Society of London, xx (1965), 140–4. The printed solution in the Royal Society's archives is not unique; another is preserved in the Bodleian Library at Aubrey, x, ff. 155–6 (along with printed solutions by Sir Jonas Moore at ff. 157–61; for a reference to the printed solution of Thomas Harvie, see Collins, J., The mariners plain scale new plain'd [London, 1659], Book II, pp. 50–1). Wren's solution is considered in Huxley, G. H., ‘The geometrical work of Sir Christopher Wren’, Scripta mathematica, xxv (1960), 203–4.

16 ‘Since the famous gentleman's problem seems to have regard to the elliptical hypothesis of the planets (for he perhaps has it in mind to make the mean motion of the planets not about the focus of the ellipse but about some other point). Therefore it may be permissible to propose in return by way of extension a problem of the same kind: To divide the Area of a given Semi-circle or Ellipse, from any point in any diameter (or the diameter produced) in a given ratio’; Hall, , op. cit. (15), p. 143.

17 See Russell, , op. cit. (14), p. 3.

18 Hall, , op. cit. (15), p. 143.

19 See Wallis, J., Tractatus duo. Prior, de cycloide … (Oxford, 1659), p. 70.

20 Ibid., pp. 80 (1st pagination)- 73 (2nd pagination): ‘De problemate Kepleriano per Cycloidem solvendo’. Wren's solution is considered in Whiteside, D. T., ‘Wren the mathematician’, Notes and records of the Royal Society of London, xv (1960), 108–9.

21 Johnson, F. R., Astronomical thought in Renaissance England. A study of English scientific writings from 1500 to 1645 (Baltimore, 1937), chapter 7.

22 Ibid., p. 235.

23 Ibid., p. 237.

24 From the English draft, in Wren, Jnr, op. cit. (12), p. 204.

25 Ward, J., Lives of the professors of Gresham College (London, 1740), Appendix, p. 35. I hope to show, in a further paper, that in general Wren's work in astronomy must be seen in the context of an English tradition in the subject.

26 It is interesting that at a much later date, in September 1710, Flamsteed linked the names of Kepler, Wren, and Newton, when he referred to ‘Kepler's doctrine of magnetical fibres, improved by Sir Christopher Wren and prosecuted by Sir I. Newton’; see Baily, F., An account of the Rev. John Flamsteed (London, 1835), p. 277.

27 See Russell, , op. cit. (14), p. 3.

28 Quoted from the translation by Hall, , op. cit. (15), p. 141. Wren says:

‘Asseruit Keplerus, ex causis physicis, planetas ita ferri circa solem in Orbitâ Ellipticâ, ut velocitas planetae sit ubique distantiae ejusdem à Sole reciproce proportionalis; unde sequentem Hypothesin ingeniose commentus est. Secat scilicet aream Ellipseos Planetariae lineis à sole ductis in infinita Triangula Mixtilinae aequalia; unde fit ut Curva Ellipseos dividatur in portiones inaequales, minores quidem circa Aphelium, majores circa Perihel-ium: per has autem portiones ponit Planetam aequalibus temporibus ferri’; see Wallis, , op. cit. (19), p. 80 (1st pagination).

It seems that Wren still believed that these two expressions for the planet's velocity were equivalent in 1677, since on 20 September Hooke recorded: ‘To Sir Chr. Wren … Discoursd with him about [lunar] theory. he affirmed that if the motion were reciprocall to the Distance die Degree of velocity should always be as the areas, the curve whatever it will’; The diary of Robert Hooke, 1672–1680, ed. Robinson, H. W. and Adams, W. (London, 1935), p. 314. As is well known, Hooke still accepted the ‘inverse distance’ law in 1680.

29 Galileo, , Dialogues concerning two new sciences, trans. Crew, H. and de Salvio, A. (New York, 1954), p. 261.

30 For discussions of Galileo's ‘Platonic’ cosmogony, see Koyré, 1965, op. cit. (1). pp. 201–20; Cohen, I. B., ‘Galileo, Newton, and the divine order of the solar System’, in Galileo, mon of science, ed. McMullin, E. (New York, 1967), pp. 207–31; Drake, S., ‘Galileo's “Platonic” cosmogony and Kepler's Prodromus, Journal for the history of astronomy, iv (1973), 174–91.

31 Discorsi, e dimostrationi matematichi, p. 193, in Galileo, , Opere (Bologna, 1656, 5), vol. ii (Bodleian Library, Savile A. 19). A list of the books donated by Wren to the Sayile Library in 1673 is included in my Cambridge University Ph.D. thesis of 1974: ‘Studies in the life and work of Sir Christopher Wren’.

32 The Discorsi is annotated throughout, and the notes do seem to be in Wren's hand, though we have very few examples of his hand during the 1650s. However, compare the MS. ‘Anatomia Anguilla fluviatilis’ in the Heirloom copy of Parentalia (see Gregg Press reprint, 1965) and note Wren's 1656 reference to ‘schemes of several Fishes dissected’ in my ‘Study of Parentalia’, Annals of science, xxx (1973), 147. Most of the annotations to the Discorsi either indicate the content of, or are complementary to, the text. Some extended notes occur on manuscript pages inserted between pp. 88 and 89 and contain additional explantions and demonstrations, as well as a list of ‘Authoris principui à Galileo citati’. Six of these extended notes are referred to on the relevant pages of the text (see pp. 57, 89, 96, 103—in this case f. 2v of the MS. is mistakenly headed ‘Ad problema pag. 101’, 147, 204) and these references attribute the content of the notes to ‘D. Ward’, i.e. Seth Ward. At p. 96, for example, we find: ‘Vide D. Wardi Analysia hujus Problematis max generalius ppositi’. If then these notes were written at a time when Ward was involved in natural philosophy and in direct contact with Wren, they must date from the 1650s. Also, this two-volume edition of works by Galileo (Bodleian Library, Savile A. 18 and 19) dates from 1656. It is interesting that the annotations suggest that some kind of discussion, or perhaps a course conduc-ted by Ward, had centred round the Discorsi; cf. note 11. In his Gresham speech of 1657 Wren mentioned ‘Franciscus Sagredus, one of the Interlocutors in the Dialogues of Gallilaeus’; see Wren, Jnr, op. cit. (12), p. 204.

33 See below.

34 This emerged from Huygens's priority dispute with Hooke following the publication of Horologium oscillatorium, 1673. At first Huygens was unsure whether he had discussed the matter with Wren during his visit of 1661 or that of 1663 (Oeuvres complètes de Christiaan Huygens [The Hague, 18881950], vii. 314), but he later settled for 1661 (ibid., pp. 337, 391, 431). The question of which date is correct is not crucial in this context. We know that Wren met Huygens in 1663, as well as in 1661; see de Monconys, B., Journal des voyages (Lyons, 1666), ii. 76–7.

35 See Oeuvres de Huygens, op. cit. (34), xvi. 237311. Note also ibid., vii. 337, note 13, and Bell, A. E., Christian Huygens and the development of science in the seventeenth century (London, 1947), pp. 69, 120–1.

36 Hooke, R., An attempt to prove the motion of the earth from observations … (London, 1674), included in his Lectiones Cutlerianae (London, 1679), which is reprinted in Gunther, R. T., Early science in Oxford (Oxford, 1931), viii, see pp. 27–8. In the general preface to the Lectiones Cutlerianae Hooke says that this lecture was read at Gresham College in 1670 (and Birch, 1756, op. cit. [13], ii. 394, 434, 447, confirms that the observations were made in that year), but it is quite possible that the final paragraph at least was added just prior to publication. In 1690 Hooke claimed: ‘The Discovery of the Degree of Planetary Gravitation I first Communicated to Sr. Christopher Wren about 15 or 16 years Since Sometime before I published my attempt to prove the motion of the Earth …’; Hall, A. R., ‘Two unpublished lectures of Robert Hooke’, Isis, xlii (1951), 225. This may simply be false, or it may be that Hooke and Wren had discussed the possibility of the relation being inverse-square—a possibility which had not yet been verified by Hooke's experiments—and for Hooke this may have been sufficient ground for his later claim.

37 Gunther, , op. cit. (36), pp. 27–8.

38 Bacon, F., Sylva sylvarum: or a naturall historie in ten centuries … (2nd edn., London, 1628), pp. 1112.

39 Wilkins, J., The discovery of a new world. Or, a discourse tending to prove, that ‘tis probable there may be another habitable world in the moone … (2nd edn., London, 1640), pp. 203–42.

40 Ibid., p. 211.

41 Gilbert, W., De magnete, magneticisque corporibus, et de magno magnete tellure … (London, 1600), pp. 76–7, 95–6, 191.

42 Wilkins, , op. cit. (39), pp. 210–20. For Wilkins, gravity has properties analogous to those of magnetism, but is not magnetical in nature; see ibid., pp. 213–14.

43 Ibid., p. 216.

44 Ibid., p. 232.

45 Birch, 1756, op. cit. (13), i. 133–4. Note also ibid., pp. 125, 130, and Power, H., Experimental philosophy (London, 1664), p. 177.

46 Birch, 1756, op. cit. (13), i. 154.

47 Ibid., i. 163–4.

48 Ibid., i. 165.

49 See ibid., i. 234, 237.

50 Ibid., i. 461–2.

51 Ibid., i. 466–7, but see also Hooke's reports, in Works of Boyle, op. cit. (13), vi. 487–93. For later references to Hooke's experiments, see Sprat, T., The history of the Royal Society of London (London, 1667), pp. 224, 227, 247; Waller, , op. cit. (10), pp. 182, 563 (with hindsight Hooke could place the experiments in a much wider context). In De potentia restitutiva, in Gunther, , op. cit. (36), pp. 337–8, Hooke describes the scales he used at Westminster Abbey and St Paul's and says: ‘I propounded the same also to be tried at the bottom and several stations of deep Mines; and D. Power did make some trials to that end, but his Instruments not being good, nothing could be certainly concluded frorn them.’ This may be a useful example of Hooke's attitude in reports of earlier work; his account gives a false impression of the relation between his work and Power's.

52 For a contemporary reference to the question of the cause of gravity, see Hooke, , Micro-graphia (London, 1665), p. 246.

53 See Birch, 1756, op. cit. (13), i. 506–7.

54 Ibid., ii. 65.

55 Ibid., ii. 70. The paper is also printed in Works of Boyle, op. cit. (13), vi. 506–8.

56 Birch, 1756, op. cit. (13), ii. 72.

57 Ibid., ii. 75. ‘[Hooke] produced a pair of scales in a box, to make experiments with upon a good loadstone for the finding out of the decrease of its attractive force upon a body, according as it is placed at greater and greater distances, in order to find out, whether gravitation be somewhat magnetical; which he said might be done by comparing the distances of the bodies made use of in the experiments from the superficies of the earth and loadstone with the diameters; it being probable, that if they hold the same proportion, they have the same cause’; ibid., pp. 77–8 (cf. also pp. 85–6, 88).

58 Ibid. ii. 88.

59 Ibid. ii. 89.

60 Ibid. ii. 90.

61 Ibid. ii. 90.

62 Ibid. ii. 91.

63 Ibid. ii. 91.

64 Ibid., ii. 92.

65 Wallis's paper and his answers to varions objections are printed in Philosophical transactions, no. 16 (6 08 1666), 263–88; see pp. 272–3.

66 This was pointed out in Hall, A. R., ‘;Mechanics and the Royal Society, 1668–70’. The British journal for the history of science, iii (19661967), 26.

67 Birch, 1756, op. cit. (13), ii. 92.

68 For continued interest in the pendulum model for planetary motion, see ibid., ii. 97, 101, 103, 105–6, 388, 389.

69 Sprat, , op. cit. (51), pp. 313–14.

70 Note the edition of Sprat's History by Cope, J. I. and Jones, H. W. (London, 1966), pp. xiiixiv, and Purver, M., The Royal Society: concept and creation (London, 1967), pp. 915. It may be relevant to note that in Sprat's reply (first published in 1665) to Samuel de Sorbière's Voyage into England he mentions that he is working on the History, refers on several occasions to Wren's modesty (as he does in the History), and, noting that Sorbière did not mention Wren in connexion with the King's lunar globe, says: ‘Yet I intend to be juster to him’; Sprat, T., Observations on Monsieur de Sorbier's Voyage into England … (2nd edn., London, 1668), pp. 4, 11, 253, 151.

71 Lawrence and Molland have suggested that Wren may have provided the link between Horrox and Hooke; see Lawrence, and Molland, , op. cit. (1), pp. 152–3. Another useful article is Patterson, L. D., ‘Pendulums of Wren and Hooke’, Osiris, x (1952), 277321.

72 Oeuvres de Huygens, op. cit. (34), vii. 323.

73 See especially Armitage, , op. cit. (3), p. 278.

74 Compare Wallis, in his paper on the tides: ‘the Sun by it's motion about it's own Axis, is with good reason judged to be the Physical cause of the Primary Planets moving about it’; op. cit. (65), p. 270. Wallis had earlier stated a general, non-directional principle of inertia; ibid., p. 268.

75 See Birch, 1756, op. cit. (13), i. 386, 395 (it is interesting that Sir Paul Neile, who played an important role in Wren's career as an astronomer, should have had copies of some of Horrox's papers), 412–13, 414, 422, 456, 470, 473; ii. 48. For the prehistory of Horrox's Opera posthuma, see Plummer, H. C., ‘Jeremiah Horrocks and his Opera posthuma’, Notes and records of the Royal Society of London, iii (1940), 3952.

76 See The correspondence of Henry Oldenburg, ed. Hall, A. R. and Hall, M. B. (Madison, 1965–), ii. 162–4, 177; Oeuvres de Huygens, op. cit. (34), v. 73, 79.

77 See Birch 1756, op. cit. (13), i. 456; Oldenburg correspondence, op. cit. (76), ii. 209, 213, 231–2.

78 Wallis, , op. cit. (65), p. 288.

79 Ibid., pp. 271–2.

80 Ibid., p. 282.

81 Ibid., p. 264. For an earlier exchange between Wren and Boyle on the Cartesian explanation of tides, see Waller, , op. cit. (10), p. vii; Works of Boyle, op. cit. (13), i. 41; Birch 1756, op. cit. (13), iii. 464.

82 Moray, to Oldenburg, , 10 10 1665, Oldenburg correspondence, op. cit. (76), ii. 561.

83 For Huygens on this, see Oeuvres, op. cit. (34), vi. 383, 386; xvi. 204; xxii. 573; Oldenburg correspondence, op. cit. (76), v. 126–7; for Moray, see ibid., ii. 561, 624; Oeuvres de Huygens, vi. 371; for Wallis, see Oldenburg correspondence, v. 193. Note also Oldenburg at ibid., v. 371–4, 462–5.

84 Huygens said that, while Rooke and Wren had made experiments before April 1661, they had not evolved a theory; see Oeuvres, op. cit. (34), vi. 383, 386. When Wren presented his theory at the Royal Society on 17 December 1668, he affirmed ‘that he had this hypothesis several years before, when the society began to be formed; and that Mr. Rooke and himself made divers experiments before the society to verify the same: which affirmation of his was seconded and confirmed by several of the members, who were eye-witnesses of those experiments, as the president, Sir Paul Neile, Mr. Balle, and Mr. Hill’; Birch 1756, op. cit. (13), ii. 335. Cf. ibid., ii. 315, 337; Oldenburg correspondence, op. cit. (76), v. 117–18, 134–5; Sprat, , op. cit. (51), p. 312. Since the Society was formed in 1660 and Rooke died in 1662, it seems likely that Wren's theory dates from 1661. Compare Moray in Oeuvres de Huygens, vi. 424.

85 Wren's original paper is at Royal Society MS. CP. III (1). 43 (with copies at R.B., iv. 29, and Boyle Papers, xx, f. 157). It was printed in Philosophical transactions, iii, no. 43 (11 01 1668/1669), 867–8, and there is a full translation in Oldenburg correspondence, op. cit. (76), v. 320–1. The theory is discussed in Hall, , op. cit. (66), pp. 30–2, and in Westfall, 1971, op. cit. (i), pp. 203–6.

86 When Wren received Oldenburg's request, he replied that, having sorted out the relevant papers, ‘I found them somwhat indigested as I left them at first. & I could be glad you would give me a little time to examine them … I have noe doubt of the truth of the Hypothesis, but of some of the Experiments wch. I would trie over again’; Wren, to Oldenburg, , 3 11 1668, in Oldenburg correspondence, op. cit. (76), v. 125. See also note 84, above.

87 Ibid., v. 320.

88 Ibid., v. 320.

89 Westfall, 1971, op. cit. (1), p. 205.

90 Gregory, D., The elements of astronomy, physical and geomitrical (London, 1715) [English translation of Astronomiae physicae et geometricae elementa (Oxford, 1702)], i. 105–6.

91 Works of Boyle, op. cit. (13), vi. 501. Hooke saw the comet first on 23 December; see Cometa, in Gunther, , op. cit. (36), p. 223, also Birch, 1756, op. cit. (13), i. 511.

92 See Works of Boyle, op. cit. (13), vi. 501, with Birch, 1756, op. cit. (13), i. 504–5.

93 See Oldenburg correspondence, op. cit. (76), ii. 339.

94 See Birch, 1756, op. cit. (13), i. 508, 510–11; ii. 1.

95 Ibid., i. 511.

96 Oldenburg correspondence, op. cit. (76), ii. 341–2.

97 Brouncker also was involved in this. See ibid., ii. 354; Birch, 1756, op. cit. (13), ii. 1.

98 Oeuvres de Huygens, op. cit. (34), v. 212.

99 Birch, 1756, op. cit. (13), ii. 11, says that the author of the tract in question was Hevelius, but for Hall and Hall on this, see Oldenburg correspondence, op. cit. (76), ii. 356, note 1.

100 Ibid., ii. 353.

101 Ibid., ii. 353. Horrox is similarly cited in the paper on tides; see Wallis, , op. cit. (65), pp. 280–1.

102 See Oldenburg correspondence, op. cit. (76), ii. 353–4; and cf. Horrox, J., Opera posthuma, ed. Wallis, J. (London, 1678), pp. 310–11, 321, and Hooke, , in Gunther, , op. cit. (36), pp. 251–2. Wallis and Hooke say that there was no extant explanation by Horrox of the diagram of the 1577 comet.

103 Wallis's solution and construction are preserved at Bodleian MS. Don. d. 45, f. 283v; it is headed: ‘Problema. Dr Christopheri Wren, mihi propositur, 1st Jan. o. Ao 1665’.

104 Gunther, , op. cit. (36), pp. 236–40.

105 Wallis, to Collins, J., 22 02 1676/1677, in Correspondence of scientific men of the seventeenth century, ed. Rigaud, S. J. (Oxford, 1841), ii. 605.

106 See Oldenburg correspondence, op. cit. (76), ii. 353–4; Birch, 1756, op. cit. (13), ii. 11.

107 See Horrox, , op. cit. (102), pp. 309–14.

108 In a postscript to his letter of 21 January Wallis asked Oldenburg to present his service to Wren; see Oldenburg correspondence, op. cit. (76), ii. 356.

109 Oeuvres de Huygens, op. cit. (34), v. 228.

110 Birch, 1756, op. cit. (13), ii. 12. At the same meeting observations of the comet, made by the Earl of Sandwich, ‘were referred to Dr. Wren and Mr. Hooke’.

111 Gunther, , op. cit. (36), pp. 256–9. On 5 September 1674 Hooke ‘Had leave from Sir Ch: to publish his paper about the straight motion of Cometts’; Diary of Hooke, op. cit. (28), p. 120. And again, on 19 May 1676, Wren ‘gave me liberty to print his geometricall proposition about 5 lines’; ibid., p. 233. The geometry of Wren's solution has been discussed in Huxley, , op. cit. (15), pp. 207–8.

112 Birch, 1756, op. cit. (13), ii. 32.

113 Gunther, , op. cit. (36), p. 257.

114 Ibid., p. 258.

115 All Souls Drawings, i. no. 3; published in Wren Society, xii (1935), plate XLVII. Hooke has continued the line of the comet's motion in one of his diagrams (see Figure 1, diagram marked ‘Fig. 19’) to early February, whereas Wren's last entry was 20 January. Also, in Figs. 19 and 21 he omits the early section, i.e. 20–31 October 1664.

116 See the ‘Synopsis’, prefixed to Cometa, in Gunther, , pp. cit. (36), p. 215. Hooke referred to Wren's method on two later occasions, see Waller, , op. cit. (10), p. 104; Philosophical collections, no. 4 (10 01 1681/1682), p. 108.

117 If we look at the diagram (Fig. 1), where Wren has applied his ‘theory’ to the comet of 1664–5, in Fig. 19 the semicircle represents the earth's orbit, seen from the south; the con-tinuous line above is the path of the comet, which is moving in the opposite direction to the earth; the dotted line is the projection of this path on to the plane of the ecliptic. Fig. 20 represents observations of the comet's longitude, beginning in November (N). These longitude values are transferred to Fig. 19, where they are represented by lines drawn from the corresponding positions of the earth. The dotted line is then located using four of thèse longitude lines, given the ratio of the time intervals between the observations. We now have the true distances from the earth to the projections of the comet's positions on to the plane of the ecliptic. These distances are transferred to the line EC in Fig. 21, where E is the earth, and the distances from E to where the latitude values for the comet meet perpendiculars from the corresponding positions on EC, represent the true distances from the earth to the comet. This is what we wanted to find. The perpendiculars can be transferred to Fig. 19, so that we may represent the comet's motion, drawn here on a flat sheet, but in fact inclined to the ecliptic.

118 Birch, 1756, op. cit. (13), ii. 12, 13.

119 Oeuvres de Huygens, op. cit. (34), v. 235–6. From the information contained in his letters, Moray seems to have been close to Wren's work about this time.

120 Ibid., v. 263. Moray says: ‘… Je m'en remets a ce que vous en fera voir ce que Monsieur Wren va publier sur cette matiere.’ The catalogue of Wren's works in Wren, Jnr, op. cit. (12), p. 240, includes the entries ‘De natura & motibus cometarum’ and ‘Of the Comet in the Year 1664. N.B. Hypothesis and Theory of Comets; produc'd to the Royal Society. 1665’. An early draft for Parentalia, British Museum MS. Add. 25, 071, f. 91, also mentions ‘Tractatus, De Cometis’.

121 Pepys records that on 1 March 1664/5 Hooke delivered ‘a second very curious Lecture about the late Comett’; see The diaty of Samuel Pepys, ed. Latham, R. and Matthews, W. (London, 1972), vi. 48.

122 Oeuvres de Huygens, op. cit. (34), v. 286.

123 Ibid., v. 320.

124 Ibid., v. 322.

125 Wren, to Moray, , 11 04 [1665], Royal Society MS. EL. W. 3, no. 5.

126 See Birch, 1756, op. cit. (13), ii. 24; Philosophical transactions, i. no. 2 (3 04 1665), 17; Oldenburg corresbondence, op. cit. (76), ii. 359–67.

127 Wren, to Hooke, , 20 04 [1665], Royal Society MS. EL. W. 3, no. 6.

128 Hooke, to Wren, , 4 05 1665, in Wren, Jnr, op. cit. (12), p. 219; note Oldenburg correspondence, op. cit. (76), iii. 82–3, 84–5. We know that Hooke was using Wren's double-telescope while making these observations; see Gunther, , op. cit. (36), p. 77, and note also ibid., p. 54, and Waller, , op. cit. (10), pp. 498503.

129 Wren, Jnr., op. cit (12), p. 220.

130 Note Birch 1756, op. cit. (13), ii. 48. As late as 21 June, at a Royal Society meeting, ‘Dr. Wren being desired to leave what he had done about the late comets, promised to do so’; ibid., 59. Wren discussed the comets with Auzout, while he was in Paris (see Oldenburg correspondence, op. cit. [76], iii. 36, 38, 82–3, 84–5) and later applied his theory to a comet which appeared in 1680; see Birch, 1756, op. cit. (13), iv. 67.

131 Moray, to Oldenburg, , 28 09 1665, Oldenburg corrcspondence, op. cit. (76), ii. 529; note also Wallis at ibid., iii. 342.

132 Gunther, , op. cit. (36), p. 260. This section covers pp. 223–60.

133 Birch, 1756, op. cit. (13), ii. 107: ‘Mr. Hooke exhibited his observations of the comet in the end of the year 1664, intimating, that he intended topublish them very shortly.’

134 The fact that different sections are inconsistent with one another is useful in distinguishing between them. A central section (Gunther, , op. cit. [36], pp. 241 ff.) is definitely of an early date and contains Hooke's conclusion that the first comet is moving in a circle (p. 246). Pepys, , loc. cit. (121), records that at Gresham on 1 March Hooke argued that the first comet had appeared before, in 1618, and would return at a future date; cf. Gunther, , op. cit. (36), p. 243. Also, on p. 244, Hooke predicts that the first comet will be seen (with a telescope) in a month or six weeks' time, after it has passed the sun. Comparison with Hooke's letter to Wren in Wren, Jnr, op. cit. (12), pp. 219–20, similarly dates this section to March. Note also that Hooke tells Wren that this is so ‘whether we take the Supposition of the Motion of the Earth, and imagine the Comet to be moved in a Circle, one Side of which touches, or rather goes within the Orb of the Earth on one Side, and without the Orb of Saturn, or at least that of Jupiter on the other … or whether we suppose the Earth to stand still, and the Comet to be moved in a great Circle whose convex Side is turned towards the Earth’, and compare his argument in this section of Cometa. Also, on p. 246, Hooke refers to ‘this present Comet’. The section before this (Gunther, , op. cit. [36], pp. 223 ff.) is definitely later and is probably part of the paper of August 1666. Here the physical discussion is consistent with a comet's path including straight and curved components. Hooke sets himself a number of queries, which he proceeds to answer in turn. This gives the section a certain coherence, in a structure typical of a Royal Society ‘history’. It is a survey of a completed piece of work; see ibid., pp. 224, 235, 237. Hooke refers to the results of Hevelius, Gottignies, and Petit (ibid., p. 238) and generally to ‘a multitude of other Histories, which I have received concerning that Comet of 64’. For Hooke's connexion widi the work of Petit in particular, see Birch, 1756, op. cit. (13), ii. 66, 93. Wren had brought Petit's book back from France; see Oldcnburg correspondence, op. cit. (76), iii. 48. Following what I have called the central section, a slight change is noticeable from p. 247 onwards: Hooke reintroduces physical questions and the comet now seems to be past. The reference to the ‘Queries’ on p. 247 seems to indicate later insertions. However, the content is still consistent with the central section. There is a more definite change on p. 250, when Hooke describes how he turned to a study of Tycho's observations of the comet of 1577. He then makes the very interesting reference to Horrox's hypothesis, with a reproduction of Horrox's diagram of the 1577 comet, presumably that sent to the Royal Society by Wallis; see Oldenburg correspondance, ii. 353. From p. 250 onwards, the discussion concerns the possible rectilinear motion of comets and ils modification by gravitational effects and is consistent with the opening section.

135 Gunther, , op. cit. (36), p. 259.

136 Ibid., pp. 253–4.

137 Ibid., pp. 251–2, and Tab. IIIa, Fig. 9.

138 Ibid., p. 228.

139 Ibid., p. 229.

140 Ibid., pp. 254, 259–60.

141 Wren was in London in June 1665. He and Hooke were appointee to a committee to observe the magnetic variation and they discussed ‘the art of flying’ at a Royal Society meeting on 21 June; when Wren's work on the comets was mentioned; see Birch, 1756, op. cit. (13), ii. 54–9. Hooke dated his interest in the conical pendulum to 1665; see Gunther, , op. cit. (36), p. 105.

142 See Birch, 1756, op. cit. (13), ii. 66, 74; Works of Boyle, op. cit. (13), vi. 506. For Wren's return, note Oldenburg correspondence, op. cit. (76), iii. 48.

143 See Works of Boyle, op. cit. (13), vi. 501–5.

144 Birch, 1756, op. cit. (13), ii. 72. Compare Hooke's later ideas in his.‘Discourse on the nature of comets’ of 1682, in Waller, , op. cit. (10), pp. 177, 178, and note his reference to the 1664 comet (ibid., p. 168). It is interesting that on 28 September 1665 Moray wrote to-Oldenburg: ‘I do intend to write within a day or two to Dr Wilkins, to put Mr Hook to the finishing his observations &c concerning the Cometes … pray do you solicit the same thing’; Oldenburg correspondence, op. cit. (76), ii. 529.

145 Gunther, , op. cit. (36), p. 260.

146 Birch, 1756, op. cit. (13), ii. 92.

147 See, for example, Westfall, 1971, op. cit. (1), pp. 80–1.

148 See ibid., p. 211; Westfall, 1967, op. cit. (1), p. 259; Lawrence, and Molland, , op. cit. (1), pp. 151–2. Huygens sent a copy of Horologium oscillatorium to Wren; see Oeuvres de Huygens, op. cit. (34), vii. 303, 321. Hooke records reading this work on 14 November 1675 and that on the following day he ‘Meditated upon motion of Planets of circular pendull’; Diary of Hooke, op. cit. (28), p. 194.

149 For Hooke's discussions with Wren, see entries for 16 August 1677, 20 September 1677, 18 October 1679, 21 October 1679, 27 October 1679, 8 November 1679, 26 January 1679/80, at ibid., pp. 307, 314, 427–30,436; also Newton correspondence, op. cit. (5), ii. 442.

150 Ibid., ii. 305, 309, 313.

151 Ibid., ii. 309.

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