¹ For a discussion of these explanations see especially Cajori, F., “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, pp. 127–188.Google Scholar

² Whiteside, D. T., “Newton's Early Thoughts on Planetary Motion”, British Journal for the History of Science, ii, No 6. (12 1964), 117–137.CrossRefGoogle Scholar

³ Whiteside also suggests (op. cit., n. 55) that another contributary cause was Newton's uncertainty up to 1679 over the correct principle of inertia to apply to the case of the motion of celestial bodies. He bases this on Newton's apparent implicit acceptance in his letter of 13 December 1679 to Hooke of Borelli's qualitative analysis of elliptical motion as resulting from an imbalance between a centrifugal force and a gravitational attraction. For Whiteside this appears to imply that both Borelli and Newton believed circular motion to be inertial (or force-free as Whiteside puts it), and this in spite of Newton's very explicit early formulations of the (rectilinear) principle of inertia in the Waste Book. This seems to me a most improbable deduction based on far too slender evidence. It would mean, for example, that Newton had failed to understand Descartes's formulation of the principle of inertia in Part II of his Principia Philosophiae, and had not progressed beyond the terrestrially centred notion of Galileo before 1679. But in fact there is much stronger evidence against Newton continuing to hold to a belief in circular inertia. In the early researches he approaches the problem of centrifugal force in two distinct ways, but in each case the central notion is that of Descartes. Namely that this force is a manifestation of the bodies instantaneous tendency to move always in a straight line along the tangent to its path. When we combine this with his very careful explicit formulation of the (true) principle of inertia in the Waste Book, the conclusion seems inescapable that Newton believed that centrifugal force (at least at the surface of the earth) was one outcome of Descartes's principle of inertia. This, of course, does not prove that he necessarily believed the same principle applied to celestial motion. I think myself that to believe otherwise would go against the whole tendency of Newton's thought as I find it in the early dynamical researches, namely, the view of dynamics as an abstract mathematical subject to be applied where needed in any situation, and why not then to celestial phenomena. However, apart from such personal and unprovable assumptions there is the additional hard fact that Newton used his formula for centrifugal force to derive an inverse square law for the motion of the planets via Kepler's third law. Since this law of centrifugal force was (as we have seen) itself based on the rectilinear principle of inertia one seems justified in assuming that he believed this principle was just as applicable to the motion of celestial bodies as “to the globe revolving within a sphere” referred to in the Portsmouth Draft Memorandum. I admit that there is in fact a contradiction between the rectilinear principle of inertia and centrifugal force, namely, that the force necessary to maintain circular as opposed to rectilinear motion is centripetal rather than centrifugal, and centrifugal force is itself non-existent. But I find no difficulty in assuming that Newton and Descartes were both quite genuinely deceived into a belief in the actual existence of centrifugal force (which continues after all to be shared by a large percentage of present-day scientists and engineers), and for which there is so much apparently good evidence, such as the tendency of people to be thrown about in buses, or for fly-wheels to disintegrate, or for smooth balls to move outward in rotating tubes (the example given by Descartes in Part III of his Principia Philosophiae). Likewise, I sympathize with Newton if he believed (like Borelli) that circular orbits could result from a balance of inward force and an outward centrifugal force. For me, then, the true revolution in Newton's thought in 1679 (or earlier) was not the transition from one principle of inertia to another—for I believe that he never deviated from the true principle of inertia from 1665 or so onwards—but the sudden realization that it was a centripetal force which alone was required to account for the deviation of a body away from its rectilinear inertial path. Newton's reference to over and under balancing between this centrifugal force and gravity in his letter of 13 December 1679, could then simply be an indication that he had not at that time got down to the hard task of formulating the problem of non-circular orbital motion in mathematical terms.

⁴ Relevant here are the findings of J. L. Russell in his paper “Kepler's Laws of Planetary Motion: 1609–1666” in a recent number of the present Journal (B.J.H.S., ii, No. 5 (06 1964), 1–24)Google Scholar. These findings seem to prove that Kepler's laws were recognized much more quickly and widely than has been supposed hitherto.

⁵ I have suggested elsewhere (Arch. Int. D'Hist. Sci., xiv (1960), 23–33Google Scholar; ibid., xvi (1962), 13–22) that the original of the Manuscript CUL Add. 3965. I may possibly represent Newton's first solution to the problem of Kepler Motion in 1679. Though I still hold to the position advanced in these papers, I would not regard it as in any sense certain. I take this opportunity, however, of replying to one item of evidence advanced against my argument by A. R. Hall in a note following the second of the papers referred to above, namely, that it was the opinion of D. T. Whiteside that the handwriting in the manuscript in question was consistent with the possibility of it having been written in 1689. An examination of the handwriting of Newton in his correspondence with Hooke in 1679 leads me to believe that the handwriting of the manuscript in question is also consistent with the view that it was written in 1679. The fact is that Newton's handwriting in the period 1684–87 (at any rate in the dynamical manuscripts) seems to have been curiously different from that in both the preceding and succeeding periods.

⁶ The surprising feature here is the perfectly general nature of the result. As Newton himself expressed it “I found now that whatsoever was the law of the forces … the areas described by a radius … would be proportional to the times in which they were described.” Notice, too, that the result proved by Newton in the Principia (and presumably also in 1679) corresponded to the converse of Kepler's second law. In the Principia (Prop. 2, Theor. 2) Newton proves that if the rate of description of area is constant about a given centre—as found by Kepler—then the force must be directed to this point. This was evidently the real dynamical significance of Kepler's second law to Newton in 1679. It implied the central nature of the force on the planet, and thus abolished all need for a pushing force of the kind considered by Kepler. Before this there was no way for either Hooke or Newton or anyone else to rule out the possibility of a transverse component. Once ruled out, however, the way was open for a consideration of the law of central force necessary to account for the actual elliptical orbits predicted by Kepler's first law.

⁷ I have drawn QR parallel to SP. Whiteside appears to attach (op. cit., n. 60) some special significance to the possibility of QR being in line with SQ in Newton's diagram in the tract de Motu. But in the text itself Newton firmly notes ab alio puncto QR agatur QR distantiae SP parallela.

⁸ It was this assumption, rather than the geometrical formula for an ellipse given in (4), which represented in company with Prop, I and the transition from centrifugal to centripetal force the real breakthrough by Newton in 1679. This breakthrough was dynamical rather than mathematical. Failure to grasp this makes it impossible for one to appreciate the true nature of Newton's achievement in 1679 (and in 1684 and in the Principia). There were many of Newton's contemporaries, such as Barrow, Wallis, Halley, to name only his compatriots, who would have been perfectly capable of deriving the mathematical result RQ. = QT²/L. But there seems to me no good reason to suppose that any of his contemporaries apart from Huygens was remotely capable of supplying the dynamical reasoning needed to solve the problem of Kepler Motion, while Huygens himself was probably debarred from achieving a solution by reason of his inability to accept action at a distance. Newton remains, therefore, not only the person who actually solved the problem of Kepler Motion (and thus consummated the revolution in science begun by Copernicus), but also the one person of his age who by reason of a combination of mathematical ability, dynamical insight, and absence of preconceived notions about the nature of things was capable of achieving such a solution.