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

Published online by Cambridge University Press:  05 January 2009

J. A. Bennett
J. A. Bennett
Affiliation:
13 Sleaford Street, Cambridge CB1 2PW.
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Abstract

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Presidential Address
Information
The British Journal for the History of Science , Volume 8 , Issue 1 , March 1975 , pp. 32 - 61
Copyright
Copyright © British Society for the History of Science 1975

References

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), 327–41CrossRefGoogle Scholar, and xli (1950), 32–45; Lohne, J., ‘Hooke versus Newton’, Centaurus, vii (1960), 6–52CrossRefGoogle Scholar; Koyré, A., ‘An unpublished letter of Robert Hooke to Isaac Newton’, Isis, xliii (1952), 312–37CrossRefGoogle Scholar, reprinted in Koyré, , Newtonian studies (London, 1965), chapter 5CrossRefGoogle Scholar; Koyré, A., ‘Hooke on gravitational attraction’Google Scholar, ibid., pp. 180–4; Westfall, R. S., ‘Hooke and the law of universal gravitation’, The British journal for the history of science, iii (1967), 245–61CrossRefGoogle Scholar; Centore, F. F., Robert Hooke's contributions to mechantes (The Hague, 1970), chapter 5.Google Scholar 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.CrossRefGoogle Scholar Note also Koyré, A., ‘La gravitation universelle de Kepler à Newton’, Archives internationales d'histoire des sciences, iv (1951), 638–53Google Scholar, and Westfall, R. S., Force in Newton's physics (London, 1971).Google Scholar

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), 117–37CrossRefGoogle Scholar; ‘Before the Principia: the maturing of Newton's thoughts on dynamical astronomy, 1664–1684’, Journal for the history of astronomy, i (1970), 5–19.Google Scholar

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

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

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

6 Newton, to Halley, , 20 06 1686Google Scholar, 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.Google Scholar

7 Newton, to Halley, , 27 05 1686Google Scholar, Correspondence, op. cit. (5), pp. 433–4.Google Scholar 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. 147–54Google Scholar, have collected together the evidence for this and have added the explicit testimony of David Gregory.

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

9 Halley, to Newton, , 29 06 1686Google Scholar, 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.Google Scholar

11 Ward, S., Vindiciae academiarum (Oxford, 1654), p. 29.Google Scholar 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.Google Scholar 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.Google Scholar 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.Google Scholar

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.Google Scholar

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), 126–7Google Scholar; The life and works of the Honourable Robert Boyle, ed. Birch, T. (2nd edn., London, 1772), vi. 118Google Scholar; Birch, T., The history of the Royal Society of London (London, 1756–1757), i. 504.Google Scholar

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), 17–19.Google Scholar

15 See Hall, A. R., ‘Wren's problem’, Notes and records of the Royal Society of London, xx (1965), 140–4.CrossRefGoogle Scholar 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)Google Scholar. Wren's solution is considered in Huxley, G. H., ‘The geometrical work of Sir Christopher Wren’, Scripta mathematica, xxv (1960), 203–4.Google Scholar

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.Google Scholar

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

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

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

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.Google Scholar

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

22 Ibid., p. 235.

23 Ibid., p. 237.

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

25 Ward, J., Lives of the professors of Gresham College (London, 1740), Appendix, p. 35.Google Scholar 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.Google Scholar

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

28 Quoted from the translation by Hall, , op. cit. (15), p. 141.Google Scholar 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).Google Scholar

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.Google Scholar 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.Google Scholar

30 For discussions of Galileo's ‘Platonic’ cosmogony, see Koyré, 1965, op. cit. (1). pp. 201–20Google Scholar; 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. 207–31Google Scholar; Drake, S., ‘Galileo's “Platonic” cosmogony and Kepler's Prodromus’, Journal for the history of astronomy, iv (1973), 174–91.CrossRefGoogle Scholar

31 Discorsi, e dimostrationi matematichi, p. 193Google Scholar, in Galileo, , Opere (Bologna, 1656, 5), vol. iiGoogle Scholar (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.Google Scholar 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.Google Scholar

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, 1888–1950], vii. 314)Google Scholar, 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.Google Scholar

35 See Oeuvres de Huygens, op. cit. (34), xvi. 237–311.Google Scholar 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.Google Scholar

36 Hooke, R., An attempt to prove the motion of the earth from observations … (London, 1674)Google Scholar, included in his Lectiones Cutlerianae (London, 1679)Google Scholar, which is reprinted in Gunther, R. T., Early science in Oxford (Oxford, 1931), viii, see pp. 27–8.Google Scholar 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, 447Google Scholar, 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.Google Scholar 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.Google Scholar

38 Bacon, F., Sylva sylvarum: or a naturall historie in ten centuries … (2nd edn., London, 1628), pp. 11–12.Google Scholar

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.Google Scholar

40 Ibid., p. 211.

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

42 Wilkins, , op. cit. (39), pp. 210–20.Google Scholar 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.Google Scholar Note also ibid., pp. 125, 130, and Power, H., Experimental philosophy (London, 1664), p. 177.Google Scholar

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

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.Google Scholar For later references to Hooke's experiments, see Sprat, T., The history of the Royal Society of London (London, 1667), pp. 224, 227, 247Google Scholar; Waller, , op. cit. (10), pp. 182, 563Google Scholar (with hindsight Hooke could place the experiments in a much wider context). In De potentia restitutiva, in Gunther, , op. cit. (36), pp. 337–8Google Scholar, 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.Google Scholar

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

54 Ibid., ii. 65.

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

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

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), 263–88Google Scholar; 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 (1966–1967), 26.Google Scholar

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

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.Google Scholar

70 Note the edition of Sprat's History by Cope, J. I. and Jones, H. W. (London, 1966), pp. xiii–xivGoogle Scholar, and Purver, M., The Royal Society: concept and creation (London, 1967), pp. 9–15.Google Scholar 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.Google Scholar

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.Google Scholar Another useful article is Patterson, L. D., ‘Pendulums of Wren and Hooke’, Osiris, x (1952), 277–321.CrossRefGoogle Scholar

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

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

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, 395Google Scholar (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), 39–52.CrossRefGoogle Scholar

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

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

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

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. viiGoogle Scholar; Works of Boyle, op. cit. (13), i. 41Google Scholar; Birch 1756, op. cit. (13), iii. 464.Google Scholar

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

83 For Huygens on this, see Oeuvres, op. cit. (34), vi. 383, 386Google Scholar; xvi. 204; xxii. 573; Oldenburg correspondence, op. cit. (76), v. 126–7Google Scholar; for Moray, see ibid., ii. 561, 624; Oeuvres de Huygens, vi. 371Google Scholar; for Wallis, see Oldenburg correspondence, v. 193Google Scholar. 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, 386Google Scholar. 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. 335Google Scholar. Cf. ibid., ii. 315, 337; Oldenburg correspondence, op. cit. (76), v. 117–18, 134–5Google Scholar; Sprat, , op. cit. (51), p. 312Google Scholar. 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.Google Scholar

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), 867–8Google Scholar, and there is a full translation in Oldenburg correspondence, op. cit. (76), v. 320–1Google Scholar. The theory is discussed in Hall, , op. cit. (66), pp. 30–2Google Scholar, and in Westfall, 1971, op. cit. (i), pp. 203–6.Google Scholar

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 1668Google Scholar, in Oldenburg correspondence, op. cit. (76), v. 125Google Scholar. See also note 84, above.

87 Ibid., v. 320.

88 Ibid., v. 320.

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

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

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

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

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

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

95 Ibid., i. 511.

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

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

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

99 Birch, 1756, op. cit. (13), ii. 11Google Scholar, 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. 356Google Scholar, 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.Google Scholar

102 See Oldenburg correspondence, op. cit. (76), ii. 353–4Google Scholar; and cf. Horrox, J., Opera posthuma, ed. Wallis, J. (London, 1678), pp. 310–11, 321Google Scholar, and Hooke, , in Gunther, , op. cit. (36), pp. 251–2Google Scholar. 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.Google Scholar

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

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

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

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.Google Scholar

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

110 Birch, 1756, op. cit. (13), ii. 12Google Scholar. 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. 256–9Google Scholar. 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. 120Google Scholar. 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.Google Scholar

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

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

114 Ibid., p. 258.

115 All Souls Drawings, i. no. 3; published in Wren Society, xii (1935)Google Scholar, 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. 215Google Scholar. Hooke referred to Wren's method on two later occasions, see Waller, , op. cit. (10), p. 104Google Scholar; Philosophical collections, no. 4 (10 01 1681/1682), p. 108.Google Scholar

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.Google Scholar

119 Oeuvres de Huygens, op. cit. (34), v. 235–6Google Scholar. 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. 240Google Scholar, 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.Google Scholar

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

123 Ibid., v. 320.

124 Ibid., v. 322.

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

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

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

128 Hooke, to Wren, , 4 05 1665Google Scholar, in Wren, Jnr, op. cit. (12), p. 219Google Scholar; note Oldenburg correspondence, op. cit. (76), iii. 82–3, 84–5.Google Scholar We know that Hooke was using Wren's double-telescope while making these observations; see Gunther, , op. cit. (36), p. 77Google Scholar, and note also ibid., p. 54, and Waller, , op. cit. (10), pp. 498–503.Google Scholar

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

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)Google Scholar and later applied his theory to a comet which appeared in 1680; see Birch, 1756, op. cit. (13), iv. 67.Google Scholar

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

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

133 Birch, 1756, op. cit. (13), ii. 107Google Scholar: ‘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.)Google Scholar 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)Google Scholar, 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.Google Scholar 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. 219–20Google Scholar, 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.Google Scholar) 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.Google Scholar Wren had brought Petit's book back from France; see Oldcnburg correspondence, op. cit. (76), iii. 48.Google Scholar 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.Google Scholar 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.Google Scholar

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.Google Scholar Hooke dated his interest in the conical pendulum to 1665; see Gunther, , op. cit. (36), p. 105.Google Scholar

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

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

144 Birch, 1756, op. cit. (13), ii. 72.Google Scholar Compare Hooke's later ideas in his.‘Discourse on the nature of comets’ of 1682, in Waller, , op. cit. (10), pp. 177, 178Google Scholar, 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.Google Scholar

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

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

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

148 See ibid., p. 211; Westfall, 1967, op. cit. (1), p. 259Google Scholar; Lawrence, and Molland, , op. cit. (1), pp. 151–2.Google Scholar Huygens sent a copy of Horologium oscillatorium to Wren; see Oeuvres de Huygens, op. cit. (34), vii. 303, 321.Google Scholar 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.Google Scholar

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.Google Scholar

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

151 Ibid., ii. 309.