Abstract
The correspondence in 1680 and 1681 between John Flamsteed and Isaac Newton on Flamsteed’s theory of the comet of 1680 tells half the story. Related manuscripts reveal Newton was pursuing his own comprehensive line of inquiry based on principles that were the antithesis of Flamsteed’s procedures. Following generally accepted views in England, Newton’s work was marked by critical evaluation of data but marred by uncritical use of simple calculating techniques based on what might be termed Platonic archetypes of straightness. Flamsteed’s intervention provided useful data and allowed Newton to seek additional information. Although Newton supposedly briefly considered a solution that vaguely resembled his parabolic approximation of the path of the comet determined 5 years later, the evidence Newton provided (based on simple hypotheses) did not support such a highly curved path or one in which the sun apart from the solar vortex exerted influence. Newton’s work, including an alleged harmonic law of tails, was quietly abandoned in favor of other work. With new insight, Newton revived work on comets as fully gravitational objects immediately following Halley’s visit in 1684. This little known side of the episode provides a fresh opportunity to examine Newton’s sources and actual practice in developing a new line of inquiry. An appendix dating sections of Newton’s Waste Book entries on comets is included.
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Notes
According to Wallis, Wren issued the challenge in 1661 or 1662 (Horrox 1678, appendix, p. 1). The manuscript of Wallis’ derivation which I have not seen (Bodleian Library Oxford MS Don. D. 45, ff. 283v-280r (reversed) carries the title “Problema. Di Christophori Wren, mihi propositur, J. K. Joh. o. \(A^{\circ }\) 1665,” the first part of which translates, “Problem, proposed to me by Dr. Christopher Wren.” D. T. Whiteside conjectured long ago in a personal communication that the rest of the title probably refers to “Pridie kalendarum Junii Anno 1665” or “the day before the first day of June, 1665,” which might refer to the actual date of the Wren’s challenge but more likely to the date of the manuscript. Wallis’ derivation is in Horrox (1678, appendix, pp. 1–9). Wren’s solution is in Hooke (Horrox 1678, pp. 41–42, table 5, figure 19).
Cometæ in linea recta ... uniformiter progeredientis positionem cursus ex tribus observtionibus detemininare.
E Cometæ motu uniformi rectilineo per Cœlum trajicientis locus quatuor observatis, distantiam a terra, motusque determinationem, in Hypothesi Copernicanæa colligere.
De invention distantiæ Cometæ in Systemate Copernicæa.
Hooke (in London) managed without instruments to obtain reasonable fixes of the comet’s position on 2 days in November which were briefly discussed at the Royal Society (Birch 1756–1757, 4, pp. 57–58). Hooke’s observations from late December to early February gathered details of the comet’s physical appearances rather than its motion. Hooke presented this information in a lecture at the Royal Society in fall 1682 (Hooke 1705, pp. 150–159).
While conditions also prevented Flamsteed from making measurements in relation to reference stars, he judged the tail to be \(50^{\circ }\) long (Flamsteed 1995–2002, 1, p. 747).
Newton’s initial response of Burnet’s theory, now lost, was dated 24 December 1680. A relevant fragment concerning the vortex was subsequently quoted by Burnet (Newton 1959–1977, 2, p. 322).
Flamsteed (at Greenwich) did not see the comet in November but based on reports he predicted the return of the comet in the evening after passing the sun. When the tail appeared in early December 1680 Flamsteed launched a systematic series of observations continuing into early February. As fast as he could make them, Flamsteed sent hastily reduced observations to various correspondents. Flamsteed routed a letter to Newton because he had been impressed by the telescope Newton sent to the Royal Society and assumed Newton would be interested. A few months later Flamsteed referred to Newton as the learned Professor of Astronomy at Cambridge (Forbes 1975, p. 113). For other recipients see Flamsteed (1995–2002, 1, pp. 747–763, 780–784).
See Buchwald and Feingold (2013, pp 252–257) who also discuss the similar problems that Newton faced in the early 1700s when dealing with positions of the Colures in the constellations as described by Hipparchus.
According to Harrison (1978) Newton owned an edition of Uranometria published without the guide in 1655 and a separate Explicatio published in 1640. Acquisition dates are not known. The unified edition is available on the Internet at lindahall/bayer.
Buchwald and Feingold (2013, pp. 36–42) provide a detailed account of technical issues concerning Newton’s observation of the comet of 1664 but fail to note Newton’s use of a globe in this observation of the comet of 1665. Hall (1992, p. 91) notes that the duties of the Professor of Mathematics included instructing students in the use of globes and other mathematical instruments.
For Newton’s possible interest in astronomy around 1671 see CUL MS Add. 3985B, ff. 38r-40r, “Table of ye fixed Starrs for ye yeare 1671 of ye three first magnitudes.” The table is in Newton’s hand and includes about 225 first three magnitude stars, plus about fifty \(4\)th magnitude stars, one \(5\)th magnitude star and several “nebula.” The coordinates most likely are from Tycho’s catalog in Wing (1669) with \(60^{\prime }\) longitude added for precession. It has slight differences from Kepler (1627) which may not matter in this case. Corresponding equatorial coordinates are added. Newton’s descriptors are in English, freely translated in brief from Tycho’s Latin. Wing (1651) was not likely Newton’s source because it has many significant typographical errors and the English translations do not match Newton’s descriptions. The purpose is not known. Around the same time Newton admitted he would have paid more attention to a dull star-like object if it had displayed a tail (Philosophical Transactions #81, 1672, pp. 4017–4018). See also Buchwald and Feingold (2013, pp. 271–272) who discuss the discrepancy in the precession allowed for the year 1671 but think the document might have been written later.
Borealiorem in pede sinistro Pegasi and mediam in ventre Cassiopeiae.
Stella exiquam in latere sinisrtro persei juxto cingulum ubi desinebat.
Reproductions of individual images from Mercator’s globe are available at lib.harvard.edu. Gores for Blaeu’s globe are at the Bodleian Library, Oxford and for Plancius’ globe at BNF, Paris. I have seen only small scale reproductions of one half of Blaeu’s gores in Whitfield (1995, p. 84) and the full set of Plancius’ gores in Lachièze-Rey and Luminet (2001, p. 96). I have not seen images from Joseph Moxon’s celestial globes or those of his London rivals, but they undoubtedly displayed some variations in the depictions. A case in point is the celestial map by J. Moxon (Cosgrave 2001, p. 155) which included several images significantly different from those depicted by Mercator, Blaeu or Plancius and which also shows various points of agreement with Newton’s descriptions of Aries and Cassiopeia but disagreements with Newton’s descriptions in Perseus and Pisces. Cosgrave (2001) attributes the Moxon map to Joseph dated variously as 1654 (pp. 154–155) and 1674 (p. 196) but the dedication to John, the Archbishop of Canterbury on Cosgrove’s reproduction of the map indicates otherwise. John Tuttle was Archbishop from May 1691 to November 1694. Joseph Moxon died in February 1691. The map was printed by his son, James Moxon. In any case, the connection between the iconography of the globe and the map needs to be established.
An important exception to the use of Tycho’s coordinates occurred with Newton’s observation of December 29. Newton referred to a star in Andromeda, annulum in termino catenae (the ring at the end of the chain). Based on Newton’s determination of the arc-distance from Andromeda’s head, the star was not Tycho’s star in Andromeda with a similar name, Quae in extremo catenae annulo (the outermost ring of the chain), but rather Bayer omicron Andromeda, In Cathenae annulo, nonnullus tres in dextra manu antecedens (the star in the ring of the chain preceding the three stars in the right hand). The latter star was catalogued by Ptolemy (1998, p. 380) without mention of a chain. According to Whitfield (1995, pp. 68–69) images of Andromeda including the chain became commonplace following the Vienna Manuscript c. 1440, the earliest surviving star map of the northern hemisphere. Mercator used Ptolemy’s coordinates adjusted to 1551. Blaeu and Plancius, who usually adopted Tycho’s coordinates, used Ptolemy’s coordinates adjusted to 1601.
It is interesting to note that one of the scholars also used a small pocket perspective when viewing the November comet (Newton 1957–1977, 2, p. 344).
Dec 30 Hor 9 Cometa erat in linea ducta per australiorem duarum in pectore Pegasi ad medium in ventre Cassiopeiæ & distabat ab illa australiori 3/4 partibus distantiæ australioris illus a borealiori, jacens ab illa australiores utrusque
The sector would have permitted measurements of star altitudes from which the apparent time and equation of time could be calculated, if that was his method.
Newton did not list the coordinates and provided only the distance between each pair of dates. For example Newton indicated the distance between the comet on January 4, 8 pm and January 11, 10:30 pm was \(14^{\circ } 55^{\prime }\). My reductions using Newton’s parameters and Tycho’s co-ordinates plus \(68^{\prime }\) place the comet on January 4 at about ♈ \(6^{\circ } 51^{\prime }\), \(26^{\circ } 36^{\prime }\) N and on January 11 at ♈ \(22^{\circ } 52^{\prime }\), \(23^{\circ } 12^{\prime }\) 1/2 N . The distance between these positions calculated by the cosine rule is \(14^\circ 54^{\prime }\).
The Paris observations had a gap between January 13 and 23. The gap at Greenwich was between January 11 and 25. Newton obtained a partial view on January 13. The final round of correspondence with Burnet on the sacred theory of the earth was completed late in this period (Newton 1959–1977, 2, pp. 321–335).
For example, in what could be a tabulation error, the comet’s elongation from the sun on January 11, 10 pm is given as \(80.17^{\circ } (80^{\circ } 10^{\prime })\) whereas the sun’s longitude is given as ♒ \(2.7^{\circ } (2^\circ 42^{\prime })\) and the comet’s longitude as ♈ \(22.817^{\circ } 22^{\circ } 49^{\prime }\) for a difference of \(80.117^{\circ } (80^{\circ } 7^{\prime })\).
Newton commonly made calculations using ratios but sometimes used decimal equivalents.
Flamsteed had corrected for refraction but had made a mistake in the position of the planet Venus used for one of the reference points. The corrected value differed by almost 2\(^\circ \) longitude and 1\(^\circ \) latitude (Newton 1959–1977, 2, p. 353). Most importantly the revised position fitted its expected spot along Newton’s rectilinear path.
Newton may not have ventured beyond the analysis in the Snell/Rothmann (1619) and not yet realized how greatly the apparent position of the node can vary with different selections of data points, as in the case of 1680 (Forbes 1975, p. 28; Ruffner 2010, pp. 436–437).
Wren also found from Flamsteed’s observations of December and January that the comet was moving in accord with his hypothesis of uniform straight motion (Birch 1756–1757, 4, p. 67). At this point Wren believed there were two comets. Wren’s reaction to Flamsteed’s subsequent hypothesis of a single comet is not known.
The original report included a mangled statement that mixed equatorial and ecliptic coordinates which Newton converted to preferred ecliptic style for the Latin version in the Waste Book, f. 99r. Its entry in the margin near the appropriate date may indicate Newton temporarily misplaced the sheet or only belatedly decided to include the information after correcting the error.
An enhanced version of historical material selected fromCometographia is in CUL MS Add. 3965.11, ff. 172r-173v drafted in 1685 as a worksheet for De Motu Corporum Liber Secundus, CUL MS Add. 3990. Newton selected more than fifty major comets and accepted Hevelius’ date of 371 BC for ‘Aristotle’s’ comet. See Ruffner 2010, pp. 429–432.
Tycho, Kepler, Gassendi, Hevelius, and others noted deviations from strict anti-solarity. Published indications that the deviation was backwards from the line of motion however have not been found. Newton’s generalizations, here and elsewhere, may have been based on just a few examples in his own observations. Flamsteed’s analogy of smoke trailing from a moving ship was also consistent with Newton’s view.
Riccioli did not provide exact statements of great circle departures in these four examples. Tycho had touted the exquisite apparent great circle path of the comet of 1577 and the data provided by Riccioli (p.11) was clearly based on such a track. The only counterclaim noted by Riccioli (p. 52) was due to Claramontius in Antitycho (1621). Whether Newton accepted Claramontius or used some other source is not clear. Riccioli’s information for the comet of 1582 (p. 13) extracted from Kepler (1619, p. 126) indicated it was retrograde and became stationary at the end. Newton might have understood this evidence as indicating departure from a great circle track. Tycho’s data for 1585 provided by Riccioli (p. 14) revealed a slight decline from an initial great circle track as was also demonstrated by Rothmann (Snell 1619, p. 85). Riccioli (p. 10) credited Kepler (1619, pp. 114, 129) with information the comet of 1569 deflected from its line of motion and became stationary at the end but Kepler provided different information about the comet of 1659 on those pages. The information on deflection in fact pertained to the comet of 1596 which Riccioli properly cited as from Kepler (1619, p. 120). Newton evidently accepted Riccioli’s erroneous information about the comet 1569 without noting the discrepancy when selecting the comet of 1596 as an example indicating parallax due to the earth’s annual motion. The error was first noted by Pingré (1783–1784, 1, p. 510).
A small 80 was squeezed in above the capital letter that begins the category in the next line, possibly at a later time using a different quill. There was ample room for double entries if Newton wanted them. In 1680/1681 Newton may not have made any entry for 1680 because he intended to list only the prior comets, but we cannot be certain. See facsimile (Ruffner 2000, p. 261).
Having completely changed his mind, Newton drafted an enhanced version (CUL MS Add. 3965.11, f. 172r) in 1685 that lists 1531 as a single comet along with the notation 1680 \(=\) 1681. See facsimile (Ruffner 2010, p. 431).
The gap in Newton’s observations from February 11 to 24 was largely due to bad weather or the obscuring effect of the full moon. Observations at Paris Observatory had a similar gap between February 12 and 27.
The maximum differences resulting from these correction factors would have amounted to about \(5^{\prime }\) or \(6^{\prime }\).
This data is the first entry of the section in the Waste Book devoted to comets. As explained in the appendix, the entry was probably one of Newton’s last additions after earlier notes on comets ran out of space and reverted to a blank folio at the beginning of the section.
The stars were omicron and zeta Perseus. Coordinates were readily available in Tycho’s tables used by Newton for other work at the time. Fresh measurements from Flamsteed in 1684 established the distance at the beginning of 1681 as \(2^{\circ } 6^{\prime } 46^{\prime \prime }\). Tycho’s coordinates would have yielded 2\(^{\circ } 10^{\circ } 28^{\prime \prime }\). Newton’s result is a mystery unless it was one of his many computational errors.
A list of corrected values using different terminology is found in CUL MS Add. 3965.14, f. 552. The data for March 7 is deleted and also omitted from the first edition of the Principia but restored later.
Flamsteed or a copyist carelessly mixed old and new style dates. The same mistake was sent to Richard Towneley on February 7, 1680/1681 (Flamsteed 1995–2002, 1, p. 756.) The data sent to John Caswell on February 4 had correct dates, ibid., 1, p. 753 In the Principia the correct place is Avignon as indicated by Cassini (1681).
Cassini’s book (1681) evidently did not arrive in England until May 1681 although there were two impressions under different titles. Hooke gave a review at the Royal Society meeting of June 8 (Birch 1756–1757, 4, p. 90).
Later, in an unsent draft of April, Newton pointed out that Flamsteed’s explanation required the speed of the comet to increase continuously. By that time, Flamsteed had recognized the problem which he solved by assuming the comet had attained its highest possible speed during ingress which weakened with increased distance from the sun (Forbes 1975, p. 115).
Knox returned to England in September 1680. Wren recommended the publication of Knox’s memoir. Hooke’s preface was dated August 1, 1681. When the December comet appeared Knox must have told friends of resemblances between it and what he had seen in 1666 and a report somehow reached Newton. Comets were a hot philosophical topic.
It is doubtful Newton understood at this point the effort required to get these observations into usable form.
This material is inserted from the opposite end of the map and table of unknown stars cited in note 38. What Newton meant by Flamsteed’s astrolabe is unclear to me.
Cauda desinebat accurate ad exiguas duas stellas in medio Sagittae. A stellis duabus in pede Antinoi, a cubito sinistrae Antonoi ab ancone alae sinistrae axis caudae equidistabat et distantia illa erat tertia pars distantiae cubiti illius Antonoi a stella in termino caudae Serpentis. This description presents many problems of interpretation that may depend on the particular pictorial guide used by Newton. The terminus at the stars in the middle stars of Sagitta may be a misstatement for two small stars above the middle of Sagittae since Flamsteed indicated that the tail extended a little beyond the middle. Moreover, Newton’s coordinates are roughly consistent with certain largely un-cataloged “unformed” stars above the middle of Sagitta, particularly as depicted on Bayer’s map, or as he might have identified himself. After further revisions, Newton indicated the end of the tail although not well defined extended above the middle of Sagittae to at least ♒ 4\(^{\circ }\) with north latitude of about 42 1/2 or 43 (CUL MS Add. 4004, f. 99r). Few constellations showed more differences of artistic depiction than the intertwined combination of Aquila and Antinous. The brightest star in the foot of Antinous (\(\lambda \) Aql) was surrounded by several smaller stars which were portrayed variously in the foot or just outside. Tycho catalogued one star in the foot and one just outside. Bayer presents a better option with two small stars just above \(\lambda \) Aql in the foot. The overlapping nature of the two constellations in Bayer’s depiction, however, would lead to both the knee of Antinous and the bend in the wing of Aquila being identified as \(\delta \) Aql. Newton’s only unambiguous designation is the star in the end of the serpent’s tail (\(\theta \) Ser).
\({\ldots }\) debent esse in progression seu gemet[ri]ca seu arithmetrica aut alia quavis regulari.
Si in globo ducatur circulus maximus qui secet ecliplipiticam [sic] in ♐ 20 gr in angulo 54 gr transiens per stellam \(\alpha \) in ala septentionali Sagittae, dein per stellam \(\theta \) quartae magnitudinis in orientali brachio Cassiopeiae, denique per stellam \(\iota \) in tergo Persei aut punctum 1/4 gradus australis.
CUL Add MS 4004, f. 98v. Newton copied a few remaining details from Flamsteed’s letter of February 12 onto a blank sheet of Flamsteed’s March 7 letter. The full letter vanished as having nothing else of interest to him.
Halley indicated in a letter to Flamsteed from Paris dated January 22, 1680/1681 that the nearest hypothesis for the second comet was that it moved nearly in a line that crossed the ecliptic a great distance beyond the sun at an angle of about 13\(^{\circ }\) and passed over the sun in the direction of 25\(^{\circ }\) ♊ Halley found the line would have been straight only if the speed was allowed to change (Newton 1959–1977, 2, p. 339).
In 1685 the coordinates for March 9 proved to be ♊ \(0^{\circ } 43^{\prime } 2^{\prime \prime }, 11^{\circ } 44^{\prime }~3/5\) N.
Newton’s notes from various observers indicated: December 10, a small tail (Newton 1959–1977, 2, p. 315); December 11, the tail was broader than the moon (ibid., 2, 352); December 15, the tail was broader than the moon (ibid., 2, p. 315); Dec 16, 2\(^{\circ }\) wide (CUL MS 4004, f. 99r); December 17, the tail was broader than 2\(^{\circ }\) (ibid.); December 21, 2\(^{\circ }\) wide (ibid.); December 23, the tail was wider than before (ibid.); December 28, the tail was wider than before (ibid., f. 99v); December 30 the tail was 1? \(36^{\prime }\) wide near the head widening to 4\(^{\circ }\) at the end (ibid.); on January 4 the tail was \(1^{\circ } 15^{\prime }\) wide near the head widening to 3\(^{\circ }\) 1/2 at the end (ibid., f. \(100\)r). Newton’s Waste Book entry for December 12 does not include width.
Newton (1959–1977, 2, pp. 362, 367) originally wrote 3/5 and changed it to 1/5, an obvious slip for 1/2.
Calculations using available observations for December 12 and 21 available to Newton would have placed the node in ♐ \(21^{\circ } 43^{\prime }\). Flamsteed’s calculations using slightly different data placed the node in ♐ \(21^{\circ } 46^{\prime } 2/3\). Flamsteed found the values varied with different pairs of observations (Forbes 1975, pp. 28, 109).
Newton indexed the initial page of Wing’s solar tables which were based on London time on the flyleaf of his copy of Wing (1669) preserved in the Trinity College Library NQ. 18.36. He converted the times of observation to London time using an erroneous time difference between Gedani (Gedansk) and London of \(36^{\prime }\). Wing (1669, tables, p. 69) listed the difference between Dantzig (using the alternative name) and London as 1 h \(14^{\prime }\) or 1 h \(16^{\prime }\). Philosophical Transactions #129 (1676, p. 724) lists the difference between Dantzig and Greenwich as 1 h 14\(^{\prime }\) 45\(^{\prime \prime }\), also found in an annotation on a flyleaf of Newton’s copy of Mercator (1676), Trinity NQ. 10.152. Perhaps Newton confused Gedani with another place but I have not found one with a time difference of \(36^{\prime }\).
Newton 1959–1977, 2, p. 373. See Newton (1967–1981), 6, p. 329. The Todd letter concerns money owed to Newton’s half sister Mary Pilkington from their mother’s estate and possibly dates from about the middle of 1680 with the blank side retrieved later for the calculations.
Contrast this approach with observations at elaborate fully staffed observatories headed by expert astronomers such as Tycho, Cassini, Flamsteed, Hevelius, and others who made repeated measurements.
The process would have involved adjusting observations for time differences and hourly rates of change and comparing them among themselves. This comparison probably included averages where several values were involved with some sort of smoothing of the results.
I ignore the unused subject headings left by the previous owner of the notebook.
Flamsteed’s tables were used to calculate solar places corresponding to Ponthio’s observations. These calculations are found on a sheet with early drafts of definitions for the original book I of the Principia. (CUL MS Add. 3965.5, f. 22v.
The original set of data from Paris in the Waste Book at folio 98v was received by letter and differs slightly from listings in Cassini (1681, p. 86, either imprint). Limited space allowed Newton to add only three additional observations from Cassini’s much longer table.
The first known reference to Ponthio’s observations was deleted from the manuscript of the original book two of the Principia CUL MS Add. 3990, f. 41r. The details attributed to Ango and Montenaro may have derived from Cassini (1681).
References
Unpublished Newton manuscripts in Cambridge University Library (CUL) with estimated dates.
MS Add. 3958.1, ff. 9–13 (1667).
MS Add. 3965.5, f. 22v (Jan 1684/5).
MS Add. 3965.11, f. 153r (Jan 1680/1); ff. 154r–155v (Mar 1680/1); ff. 172r–173v (1685); ff. 175r–176v (1685).
MS Add. 3965.14, f. 554r (1684–85); f. 554v (February 1680/1?); f. 598 (Jan–Mar 1680/1); ff. 613r–614v (Mar 1680/1, 1685?); ff. 615r–616v (Feb-Mar 1680/1 with additions possibly as late as the 1720s.).
MS Add. 3990 (1685).
MS Add. 4004, ff., 97r, 98r–105r, largely Mar-Apr 1680/1 with additions in 1682, 1684 and 1685.
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Acknowledgments
Invaluable access and assistance was provided by various libraries: Cambridge University Library, British Library, Harvard University Houghton Library, Adler Observatory Library, Dibner Library, University of Michigan Library, and latterly the resources of the internet. I am grateful to Alan Shapiro for helpful suggestions about revision.
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As to ye Hypoth. of Monsieur Mallemont, though it should not be true yet if it were to answer to ye Phænomena it would be very valuable by reason of its simplicity. Newton to Hooke (28 November 1679).
Appendix: Dating the Waste Book entries
Appendix: Dating the Waste Book entries
Newton’s Waste Book has data entries for the comets of 1680 and 1682 (CUL Add 4004, ff. 97r-105r).Footnote 61 Incomplete entries for the micrometer readings based on an erroneous distance between two key reference stars are found at folio 97r. This entry probably dates from fall 1684 and was at issue in December 1684 when Newton sought corrections from Flamsteed. The first entries most likely were made around the end of March 1680/1681 starting at folio 98v, leaving several blank pages after the previous subject section. The November observations by Hill, Cellio, and Gallet (with correct dates) extracted from Flamsteed’s letter of March 7 (received March 26) were listed first. Also listed was the scholar’s observation as corrected in March. These data were followed by coordinates for the “subsequent” comet made at Paris and the “same” comet made at Greenwich beginning in December. On close examination the Greenwich data proves to be the version sent in February 1680/1681, with the addition of solar positions received in March. The longitude for January 10 was originally a now barely discernible ♈ \(20^{\circ } 49^{\prime }~1/2\) which according to Newton’s April letter he preferred over ♈ \(20^{\circ } 42^{\prime }\) listed in the revised set sent in March. Later Newton altered this position to ♈ \(20^{\circ } 41^{\prime }~1/2\), more nearly in accord with the March version. The discrepancies between the Paris and Greenwich observations noted in the Waste Book tabulation were cited in Newton’s April letter.
The facing folio 99r continuing to folio 101r provided corresponding information about the tail for the “prior” and “posterior” comets from all four of Flamsteed’s letters, Flamsteed’s “astrolabe,” Newton’s observations, with a marginal entry for observations from Scotland. This marginal entry continued with a partial listing of observations from Hamburg with the rest of the Hamburg information incorporated in chronological sequence of the main text. Descriptions provided by Cassini (1681) and Ponthio (1681) from Gallet and other Jesuit observers in France and Spain were not included. Those sources began to be used in 1685. Another indication of an original date of March 1680/1681 was the use of Tycho’s coordinates for a certain star with \(68^{\prime }\) added for precession. Newton had become generally dissatisfied by the time of his April correspondence by all available star catalogues and in 1685 was pressing Flamsteed for more accurate coordinates. The compilation of tail data culminated in folios 101r/v with a discussion about a law of tails. This material was essentially work in progress in late March 1680/1681 with variations found in other manuscripts and Newton’s drafts and letter of April 1681. Nothing was heard of the law of tails later.
The law of tails was followed in folio 101v with no obvious break or variation in handwriting by “what Halley told me” about his observation of December 8, 1680, information Newton wished for in April 1681. A close examination of the entry for December 8, 1680 in folio 99r reveals certain details from what Halley told him have been squeezed in with information that had come from Flamsteed in February 1680/1681. Again with no obvious break or variation in handwriting the text in folio 101v ended with an unrelated and incomplete note (in English) about Jean Richer’s pendulum experiments at Cayenne (5\(^{\circ }\) N latitude) in French Guiana. It is reasonable to suppose that the information attributed to Halley and Richer was an insertion following a meeting in fall 1684 when both comets and gravitation were in the forefront of Newton’s thoughts.
Rounding out the data for the posterior comet, folio 102r provided information about the appearance of the head gleaned from Flamsteed’s letters, arguably entered in March 1680/1681. Folio 102v is blank.
Newton’s entries on Folios 103r-104v consisted of notes from Hooke’s Cometa and related material from Hevelius that led directly to Newton’s attempted rectilinear calculations for the comet of 1664 in CUL MS Add. 3965.11, ff. 154r-155v. While the use of Wing’s solar tables in the calculations suggest a date in 1680/1681, Newton might have used them for a while in 1684/5 before shifting to Flamsteed’s solar theory.Footnote 62 Overall, the selections and omissions from Cometa and sequel mirrored concerns of Newton in 1680/1681. A different version of some of this material on the comet of 1664 was added to the crazy quilt document (CUL MS Add. 3965.14, f. 616r).
Newton followed on folio 105r with his observations of 1682 that were probably entered contemporaneously. A brief mathematical entry at folio 107r may have been in place by 1684 to block continuation of comet data. This arrangement would explain why the incomplete listing of micrometer corrections that likely date from fall 1684 reverted to blank space on folio 97r left at the beginning of the section.
Cassini (1681) was not available in England until about May 1681. As work revived in early 1685, Flamsteed urged Newton to consult it. Newton probably did not get around to it until late summer 1685 at which time he noted discrepancies with other reports and requested clarification from Flamsteed (Newton 1959–1977, 2, pp. 419–421). Newton squeezed additional observations from the book in the earlier table at folio 98v of Paris observations received via Flamsteed.Footnote 63 Continuing, folio 98r which had been blank, Newton included coordinates for the November comet from Ponthio, Pierre Ango, Geminiano Montenaro, and ended with observations from Hevelius (1685).Footnote 64
The comet notes in the Waste Book almost certainly date in late March or early April with entries in 1682, 1684, and 1685 as noted.
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Ruffner, J.A. The snare of simplicity: the Newton–Flamsteed correspondence revisited. Arch. Hist. Exact Sci. 67, 415–455 (2013). https://doi.org/10.1007/s00407-013-0116-2
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DOI: https://doi.org/10.1007/s00407-013-0116-2