Before the Principia : The Maturing of Newton's Thoughts on Dynamical Astronomy,1664–1684

A composite of two papers, one read at the Department of History of Science, Yale University, on 14 March 1969, the other at the Cambridge summer meeting of the British Society for History of Science on 8 July 1969. Much of the technical detail here lightly touched upon is discussed more fully in my “Newton's Early Thoughts on Planetary Motion: A Fresh Look”, British journal for the history of science, ii (1964), 117–37; see also my essay review of J. W. Herivel's Background to Newton's “Principia” (“Newtonian Dynamics”, History of science, v (1966), 104–17) for certain complements.

The following extract from a superseded, cancelled partial draft (ULC. Add. 3968.41,85^r) of the letter as sent was first published, in H. R. Luard's inferior transcription, in A catalogue of the Portsmouth Collection of books and papers written by or belonging to Sir Isaac Newton (Cambridge, 1888), Preface, xviii, and was reprinted five years later as “the Portsmouth draft Memorandum” in W. W. Rouse Ball's An essay on Newton's “Principia” (London, 1893), 7. The present more accurate version was first presented in my “Newton's Marvellous Year: 1666 and all that” (Notes and records of the Royal Society of London, xxi (1966), 32–41), 32 with reference given to allied unpublished drafts in ULC. Add. 3968.27. In the light of the argument I develop it is interesting to observe that Newton first wrote “… I deduced that the centripeta[l] forces w^ch keep the Planets in their Orbs …” and then hastily cancelled the crucial qualifying adjective.

Cajori Florian , “Newton's Twenty Years' Delay in Announcing the Law of Gravitation” (in Sir Isaac Newton, 1727–1927: A bicentenary evaluation of his work (Baltimore, 1928), 127–88). Despite his rather tedious investigation of the value assumed by Newton for the earth's radius (which we now know he took to be 3,500 millia) and his loose conjectures regarding a whole series of Newtonian Moon tests for none of which is there any adequate evidence, Cajori's conclusion (page 186) that “the explanation of Newton's delay … was due to theoretical difficulties involved in the earth-moon test” is not wholly unacceptable: Certainly, I do not doubt that for a time in 1685 Newton was sorely troubled by doubts that “y^e duplicate proportion … did not reach accurately enough down so low [as y^e superficies of y^e earth]” (Newton to Halley, 20 June 1686, quoted from The correspondence of Isaac Newton, ii (Cambridge, 1960), 435).

Rigaud S. P. , Historical essay on the first publication of Sir Isaac Newton's “Principia” (Oxford, 1838); Edleston J. , Correspondence of Sir Isaac Newton and Professor Cotes … with notes, synoptic view of the philosopher's life, and a variety of details illustrative of his history (London, 1850); Ball W. W. Rouse , Essay (note (3)).

Catalogue (note (2)), xii–xv, xxiii–xxx.

“The Bi-centenary of Newton's Principia. Address by Dr [J. W. L.] Glaisher [19 April 1888]”, The Cambridge chronicle and University journal, Isle of Ely herald, and Huntingdonshire gazette, Friday, 20 April 1888, [7–8].

Gaps in Rouse Ball's publication of the Newton-Hooke letters (Essay (note (3)), 139–50) were filled by Jean Pelseneer and Alexandre Koyré, who in his “An Unpublished Letter of Robert Hooke to Isaac Newton”, Isis, xliii (1952), 312–37 [= Newtonian studies (London, 1965), 221–60] gave an excellent account of the whole correspondence and the insights it affords into the general development of Newton's ideas on planetary motion. For an already obsolescent summary of current literature on Newton's science see my “Expanding World of Newtonian Research”, History of science, i (1962), 16–29.

See the Pilgrim Trust's Library of Sir Isaac Newton: Presentation to Trinity College, Cambridge, 30 October 1943 (Cambridge, 1944), especially H. Zeitlinger's appended essay (pages 13–24) “Newton's Library and its Discovery”. The only ready guide to the volumes now in the Wren Library at Trinity (shelf-marked NQ) is the handwritten shelf catalogue, but this lists only main titles and is not completely accurate.

See my “Isaac Newton: Birth of a Mathematician”, Notes and records of the Royal Society of London, xix (1964), 53–62; and the general introductions to my edition of The mathematical papers of Isaac Newton (Cambridge, 1967–), especially i (1967), 3–15; ii (1968), ix–xv, 165–9, 280–91; iii (1969), xi–xviii, 3–9.

ULC. Add. 3996, 88^r–135^v; compare Westfall R. S. , “The Foundations of Newton's Philosophy of Nature”, British journal for the history of science, i (1962), 171–82. These “Questiones” contain (115^r–116^v) Newton's records of observations of the 1664/5 comet made on 9, 23, 24, 27, 28, 29, 30 December 1664 and 1, 2, 10, 23 January 1664/5.

See the section headed “Systema mundanum secundū Copernicum” (written about the winter of 1664/5) in the Newton notebook now in the Pierpont Morgan Library, New York.

I. B. Cohen has drawn attention to “the lack of positive evidence … that Newton had ever seen Galileo's Discorsi” in his “Newton's attribution of the first two laws of motion to Galileo” (Atti del simposio su “Galileo Galilei nella storia e nella filosofia della scienza” (Florence, 1967), xxiii–xlii), xl. While no annotation on Kepler's Astronomia nova made by Newton is known, he had, for example, ready access to the copy in the college library at Trinity (ibid., xxvii, note 21).

“Newton and Descartes”, Newtonian studies (note (7)), 53–114, especially 65. See also Cohen I. B. , “Newton and Recent Scholarship” (Isis, li (1960), 489–514), 507.

ULC. Add. 3996, 27^v–30^v: “Out of Streete”, especially 29^r: “y^e meane distances of y^e primary Planets from y^e Sunne are in sesquialter proportion to the periods of their revolutions in time”. The modified Boulliau upper-focus hypothesis for determining “y^e middle motion” of “y^e Planetary Ellipsis” is noted on f.30^r; see my “Newton's Early Thoughts” (note 1.), 123.

In my “Newton's Early Thoughts” (note (1)), 120. In fairness I ought to cite J. W. Herivel's attempted riposte (British journal for the history of science, ii (1965), 350–4), whose circumstantial conjectures I sought to disprove in my critique of his Background to Newton's “Principia” (see note 1).

“Kepler's Laws of Planetary Motion: 1609–66”, British journal for history of science, ii (1964), 1–24. I may note that his attribution (page 19) of Wren's trochoidal solution of Kepler's problem to Wallis is, as he now agrees, gainsaid by Wallis's remark to Collins on 22 February 1676/7 that “Keplers probleme you speake of; is solved (by y^e Cycloide) by D^r Wren, in what of his is subjoined to mine, De Cycloide” (Correspondence of Isaac Newton, ii, 196).

“Ipse [Keplerus] mira sagacitate viam Planetæ Ellipticam esse primus invenit, adeoque rationem veram determinandi motus cœlestes tradidit. Coniecturis autem Physicis minus tribuisse virum illum vellem”, Ismaeli Bullialdi astronomiæ Philolaicæ fundamenta clarius explicata, & asserta (Paris, 1657), 44–5.

Wallis John , Tractatus de cycloide (Oxford, 1659), 801: “Asseruit Keplerus, ex causis physicis, planetas ita ferri circa solem in Orbitâ Ellipticâ, ut velocitas planetæ sit ubique distantiæ ejusdem à Sole reciproce proportionalis; unde sequentem Hypothesin ingeniose commentus est. Secat scilicet aream Ellipseos Planetariæ lineis à Sole ductis in infinita Triangula Mixtilinea æqualia …: Per has autem portiones ponit Planetam æqualibus temporibus ferri”. As A. R. Hall has pointed out (“Wren's Problem”, Notes and records of the Royal Society of London, xx (1965), 140–4), Wren had already published an accurate précis of Kepler's areal law in appendix to his solution (in a rare 1658 broadsheet) of Jean de Montfert's problem as “Hypothesis Kepleriana … quæ per areas partium Ellipseos medio motui Planetarum analogas, Anomaliam coæquatam rimatur”. There is no reason to think that a copy of the broadsheet ever reached Newton.

“Some Considerations of Mr. Nic. Mercator, concerning the Geometrick and direct Method of Signior Cassini for finding the Apogees, Excentricities, and Anomalies of the Planets …” (Philosophical transactions, v (1670), 1168–75), 1174: “cum id Observationibus nequaquam congruere animadverteret Keplerus, mutavit sententiam quod Planeta ex foco superiore videtur æquabili motu incedere, & lineam veri motûs Planetæ æqualibus temporibus æquales areas Ellipticas verrere professus est”; Institutionum astronomicarum libri duo, de motu astrorum communi & proprio, secundum hypotheses Veterum & Recentiorum præcipuas (London, 1676), Caput XX: “De Hypothesi Kepleri”, 144: “Est autem prima inter ellipticas hypothesis Kepleri, qui existimat Solem in inferiore foco orbitæ ellipticæ cujusque Planteæ positum, volutione corporis sui circa axem proprium … rapere Planetas circumpositos virtute radiorum tanquam vecti quodam …; eâ quidem ratione ac lege, ut areæ, quas radius vector à Sole ad Planetam extensus verrit, crescant æqualiter æqualibus temporis momentis”. Mercator is a little too rigid in asserting that Kepler rejected all equant theories after he had come upon his area-law: In particular, he never discarded the hypothesis vicaria whose equant circle he well knew to be an accurate measure of time of orbit in the solar planets (and which, indeed, Mercator clipped onto the “true” focal ellipse in his own soi-disant “Hypothesis Astronomica Nova”).

ULC. Add. 4004, 1191^r; see my “Newton's Early Thoughts”, 122.

See note 14.

Trinity College, NQ.18.36; see my “Newton's Early Thoughts”, 124–6.

Newton to Halley, 27 July 1686 (Correspondence, ii, 447).

ULC. Add. 3963.1, 1^v; see my “Newton's Early Thoughts”, 127–8.

See note 10. The following citation concerning sunspots occurs on ULC. Add. 3996, 93^v.

See Cohen I. B. , “Quantum in se est: Newton's Concept of Inertia in Relation to Descartes and Lucretius” (Notes and records of the Royal Society of London, xix (1964), 131–55); also his “Quantum in se est: Newton, Kepler, Galileo, Descartes and Lucretius” in Proceedings of the American Catholic Philosophical Association (Washington, 1964), 36–46.

ULC. Add. 4004, 10^r–15^r/38^v/38^r, reproduced (except for the trivial omission of the two concluding corollaries on f. 38^v) as “Dynamical Writings in the Waste Book” in J. W. Herivel's Background to Newton's “Principia” (Oxford, 1966), 132–82.

ULC. Add. 3958.5, 87^r–88^r, first published (apart from the final paragraph) in Hall A. R. , “Newton and the Calculation of Central Forces” (Annals of science, xiii (1957), 62–71), 64–6; given in full in H. W. Turnbull's first volume of Newton's Correspondence (Cambridge, 1959), 297–303, and also in Herivel's Background (note 27), 192–5.

Pemberton Henry , A view of Sir Isaac Newton's philosophy (London, 1728), Preface; Memoirs of the life and writings of Mr. William Whiston. Containing memoirs of several of his friends also. Written by himself (London, 1749), 36–8; Conduitt John , “Memorandum relating to S^r Isaac Newton given me by M^r Abraham Demoivre in Nov^r 1727” (original in private possession; H. R. Luard's nineteenth-century transcript is now ULC. Add. 4007, 706^r–707^r). The relevant passages in the Pemberton and Whiston accounts are conveniently gathered in Ball's Rouse Essay (note 2), 8–11; sections of De Moivre's memorandum are quoted in notes 30. and 41. below.

In his Memoirs (note 29), 37, Whiston wrote that “Upon Sir Isaac's first Trial [of the Moon], when he took a Degree of a Great Circle on the Earth's Surface … to be 60 measured Miles only, according to the gross Measures then in Use, he was, in some Degree, disappointed, and the Power that restrained the Moon in her Orbit, appeared not to be quite the same that was to be expected, had it been the Power of Gravity alone, by which the Moon was there influenc'd. Upon this Disappointment, which made Sir Isaac suspect that this Power was partly that of Gravity, and partly that of Cartesius's Vortices, he threw aside the Paper of his Calculation, and went to other Studies”. Much to the same end, De Moivre affirmed that when Newton “fell a calculating what would be the effect of that supposition, … he found himself disappointed for a while [and] entertained a notion that the force of gravity there [at the moon's orbit] might be a mixture of that force which the Moon would have if it was carried along in a vortex”.

Following A. R. and M. B. Hall's running head in their reproduction of the manuscript (ULC. Add. 4003, untitled) in their Unpublished scientific papers of Isaac Newton (Cambridge, 1962), 90–121. The text itself opens “De Gravitatione et æquipondio fluidorum et solidorum in fluidis, scientiam duplici methodo tradere convenit…”.

Rosenfeld L. , “Newton and the Law of Gravitation” (Archive for history of exact sciences, ii (1965), 365–86), 380–2; Aiton E. J. , “Newton's Aether Hypothesis and the Inverse Square Law of Gravitation” (unpublished communication at the winter meeting of the British Society for History of Science at Imperial College, London on 3 January 1969).

Newton to Robert Boyle, 28 February 1678/9 (Correspondence ii, 289).

Koyré A. , La révolution astronomique: Copernic, Kepler, Borelli (Paris, 1961), 491–506, especially 496: “La solution borellienne est extrêmement simple …: Des forces constantes et égales, mais de sens contraire, produisent, généralement parlant, un état d'équilibre. Toutefois, lorsque l'équilibre se trouve rompu au profit de l'une de ces forces, il en résulte des variations périodiques….” Subsequently (page 499) he asserts more accurately that “Là … nous avons affaire à des forces opposées … dont le déséquilibre initial se perpétue et se reproduit éternellement en vertu de simples principes mécaniques”. J. W. Herivel in his Background (note 27.), 59 has sought to locate the Borellian “balance between a centripetal pull of the Earth, or the Sun, inwards, and a centrifugal force of the Moon, or the planets, outwards” as the avenue by which Newton was led to discard the Cartesian conatus recedendi a centro as merely the apparent effect, in a constrained circle orbit, of the real centripetal force of gravitation by which the circular planetary orbit is maintained in the heavens. But it seems to me that Newton was far more taken with the general case of elliptical motion, where (in the Borellian theory) vis centrifuga and inward gravity pull are quantitatively unequal—in which case there is no such easy identification of the two to be made conceptually.

Correspondence, ii, 361. In his letter Newton supposes a comet in its solar orbit “to be directed by y^e Sun's magnetism as well as attracted … & by the centrall attraction to have been made to fetch a compass about the sun …, the vis centrifuga at [perihelion] overpow'ring the attraction & forcing the Comet there notwithstanding the attraction, to begin to recede from y^e Sun”.

Acta eruditorum (February 1689), 82–96), especially 88–92. For an accurate interpretation of this widely misunderstood exposition of Leibniz's provocative essay into planetary dynamics see Aiton's E. J. articles, “The Celestial Mechanics of Leibniz”, “The Celestial Mechanics of Leibniz in the Light of Newtonian Criticism” and “The Celestial Mechanics of Leibniz: A New Interpretation” (Annals of science, xvi (1960), 65–82; xviii (1962), 31–41; xx (1964), 111–23).

See my “Newton's Early Thoughts”, 132, note 52; and compare my “Newtonian Dynamics” (note 1), 117, note 10. Newton's crude sketch has several interesting features not usually (compare Ball's Rouse Essay (note 2), 142, Turnbull's Correspondence, ii, 301 and Herivel's Background (note 27), 239) brought out in reproduction; see Lohne J. A. , “The Increasing Corruption of Newton's Diagrams” (History of Science, vi (1967), 69–89, especially 72–6).

Correspondence, ii, 307. The accompanying figure is there—much as in Herivel's Background (note 27), 243—misdrawn: Newton's sketch is reproduced in photocopy in Lohne J. A. , “Hooke versus Newton” (Centaurus, vii (1960), 6–52), 27.

See note 23. In this letter to Halley on 27 July 1686 Newton was careful to add that “yet am I not beholden to him for any light into y^t business but only for y^e diversion he gave me from my other studies to think on these things & for his dogmaticalnes in writing as if he had found y^e motion in y^e Ellipsis, w^ch inclined me to try it after I saw by what method it was to be done” (Correspondence, ii, 447).

These extracts are snipped from Hooke's letters to Newton of 9 December 1679 and 17 January 1679/80 (Correspondence, ii, 306, 313).

According to Conduitt (see note 29.) De Moivre affirmed in November 1727 that “In 1684 [Conduitt has added “May—Quære” in the margin of the manuscript at this point] D^r Halley made S^r I. a visit at Cambridge & there in a conversation the D^r asked him what he thought the curve would be that would be described by the Planets supposing the force of attraction towards the sun to be reciprocal to the square of their distance from it. S^r I. replied immediately that it would be an Ellipsis. The Doctor struck with joy & amazement asked him how he knew it. Why saith he I have calculated it. Whereupon D^r Halley asked him for his calculation without any further delay. S^r Isaac looked among his papers but could not find it, but he promised him to renew it, & then to send it him. S^r Isaac in order to make good his promise fell to work again, but he could not come to that conclusion w^ch he thought he had before examined with care. However he attempted a new way which tho^u longer than the first, brought him again to his former conclusion, then he examined carefully what might be the reason why the calculation he had undertaken before did not prove right, & he found that having an Ellipsis coursely with his own hand, he had drawn the two Axes of the Curve, instead of drawing two Diameters somewhat inclined to one another, whereby he might have fixed his imagination to any two conjugate diameters, which was requisite he should do. That being perceived, he made both his calculations agree together”. Clearly, having not only restored his first approach to his satisfaction but also contrived a variant solution, there would have been no pressure on Newton to search out his original computation, and it is never heard of again. I will not haggle over the query “May?” here interpolated by Conduitt but would insist that the only strictly contemporary reference to the date of Halley's first visit to Newton in 1684 is that in Halley's letter to Newton on 29 June 1686, where, having described his discourse with Wren and Hooke “one Wednesday” in January 1684 on the problem of planetary motion, he continued: “The August following when I did myself the honour to visit you, I then learnt the good news that you had brought this demonstration to perfection” (Correspondence, ii, 442).

As the second and third of sixteen lemmas on cometary motion he asserted (ULC. Add. 3965.14, 613^r): “Materiam cœlorum fluidam esse [et] circa centrum systematis cosmici secundum cursum Planetarum gyrare”. I owe this reference to Mr J. A. Ruffner.

See my essay “Huygens, Brouncker and Pardies on Cycloidal Motion” (The mathematical papers of Issac Newton, iii, 391–401).

Appended to “Patrick Mathers” [William Sanders], The great and new art of weighing vanity (Glasgow, 1672), and reproduced, with multiple misprints, in Babbage C. and Maseres F. , Scriptores optici (London, 1823), 372–6.

ULC. Add. 4002, revised as the “Opticæ Pars Prima/Altera” (ULC. Dd. 9.67, published posthumously as Lectiones opticæ, annis [1669, 1670] & [1671] in scholis publicis habitæ (London, 1729)); see The mathematical papers of Isaac Newton, iii, 468, note 37, and 549–50, note 1.