¹ Lohne, Johs, “Hooke versus Newton”, Centaurus, vii (1960), 42.Google Scholar

² No one cares to score points at the expense of Professor Koyré, but I will cite his “La gravitation universelle de Kepler à Newton”, Archives internationales d'histoire des sciences, iv (1951), 638–653Google Scholar, as a typical expression of the assertion that Hooke first advanced the conception of universal gravitation.

³ Hooke, Robert, An Attempt for the Explication of the Phaenomena, Observable in an Experiment Published by the Honourable Robert Boyle, Esq; in the XXXV. Experiment of his Epistolical Discourse Touching the Aire (London, 1661)Google Scholar. A facsimile reproduction is published in Gunther, R. T., Early Science in Oxford, 14 vols. (Oxford, 1923–1945), x, 1–50.Google Scholar Virtually the entire pamphlet, with some additional material, was included in the Micrographia (London, 1665), 11–31.Google Scholar

⁴ Gunther, , Early Science in Oxford, x, 7–8.Google Scholar

⁵ Ibid., x, 41.

⁶ Micrographia, 15–16.Google Scholar Hooke continued to speculate on vibratory motions for the rest of his life. His theory of light is only the best known among his speculations.

⁷ Ibid., 15, 16.

⁸ Roberval's memoir on gravity, read to the Académie des Sciences on 7 08 1669Google Scholar, is printed in Huygens, Christiaan, Oeuvres complètes, 22 vols. (La Haye, 1888–1950), xix, 628.Google Scholar

⁹ Kepler, Johannes, Gesammelte Werke, 18 vols. ed. von Dyck, Walther and Caspar, Max (München, 1937–1963), iii, 25.Google Scholar

¹⁰ Hooke, , Lectiones CutlerianaeGoogle Scholar;, facsimile reproduction in Gunther, , Early Science in Oxford, viii, 27–28.Google Scholar

¹¹ From the variation of magnetic north, Hooke argued that the inner parts of the earth are not solid. The magnetic virtue “(which may be called one emanation of the Anima mundi, as gravity may be called another)” is diffused through every part of the earth, seeming all to be present both in the whole and in every part, and seeming “to be more spiritual, and to act more according to Magical and Mystical Laws than Light, Sound, or the like, it giving to every magnetical body, and every piece of it, though infinitely divided, the same properties it hath it self …”. Thus if the magnetic virtue varies, it follows that the internal parts of the earth must also vary and must therefore be fluid. Ibid., viii, 227.

¹² Instead of continuing around the central body, the comet in this state flies off on a tangent, and passes through the spheres of activity of multitudes of central bodies “in passing through which spheres,” tis not improbable that those parts which by their dissolution are made of a nature differing from the body in the center, are rather expelled from than attracted toward it …”. Hence the tail becomes more and more tenuous and spreads out farther and farther. The central core of the planet, which still retains the “gravitating principle”, is attracted by the sun and its path curves around it. The parts which are “changed into another state, and are very much rarified, and produce light, are of a clean contrary nature, and recede from the center of the Sun”—like smoke which has positive levity. Hooke appears both to say that the entire comet is repelled by the sun and to assert that the central body of it continues to be attracted. Ibid., viii, 228–230.

¹³ Ibid., viii, 230–231.

¹⁴ Hooke, Robert, The Posthumous Works of Robert Hooke, M.D., S.R.S. Geom. Prof. Gresh. & c., pub. Richard Waller (London, 1705), 176.Google Scholar

¹⁵ Ibid. 175. He continued by asserting that the two powers are only distinct effects produced by one and the same power; this power is implanted in every such great globular body in the world. Thus he approached once more the concept of a universal power, though not necessarily a universal gravitation.

¹⁶ Ibid. 182.

¹⁷ Ibid. 191.

¹⁸ Ibid. 546.

¹⁹ Ibid. 547.

²⁰ Hall, A. R., “Two Unpublished Lectures of Robert Hooke”, Isis, xlii (1951), 224–225.Google Scholar

²¹ Aubrey, and Hooke, to Anthony à Wood, 15 09 1689Google Scholar; The Correspondence of Isaac Newton, ed. Turnbull, H. W., 3 vols, continuing (Cambridge, 1959), iii, 40–42.Google Scholar

²² Birch, Thomas, The History of the Royal Society of London, 4 vols. (London, 1756–1757), ii, 91–92.Google Scholar In the demonstration Hooke made three simple errors which cancelled each other out and yielded the solution he wished. Obviously he had seized the answer intuitively, and the “demonstration” was only a façade thrown up hurriedly to justify it. With three errors it was not much justification. An imperfect approach to the conical pendulum as an illustration of orbital motion had been suggested a generation earlier by Jeremiah Horrocks (Horrocks to Crabtree, 25 July 1638, Jeremiae Horroccii Opera Posthuma, ed. Wallis, John (London, 1678), 312–314)Google Scholar. Since the Royal Society apparently had the edited copy by 1666, Hooke might have seen Horrocks's letter. If he did, Hooke's use of the conical pendulum, despite its imperfection, embodied a considerable improvement on Horrocks's use of it.

²³ Koyré, , “Gravitation universelle”, 649.Google Scholar

²⁴ Thus in a letter to Newton in 1680 he compared a body attracted by a force that is constant for all distances to a ball rolling in an inverted concave cone. Hooke, to Newton, , 6 01 1679/1680Google Scholar; Correspondence of Newton, ii, 309.Google Scholar

²⁵ Birch, , History, ii, 126Google Scholar. As it turns out, Hooke's proportion is a characteristic of the cycloid. In the cycloid defined by the equations x = r(θ+sin θ), y = r(1— cos θ), s = ∫2r cos ½ θdθ. Thus s varies as sin ½θ and s ² varies as (1—cos θ); that is to say, s ² varies asy. The relation is a necessary consequence of simple harmonic motion for which vmax² ∝ xmax²; but in the case of the pendulum, ½mvmax² = mgh.

²⁶ Ibid. ii, 337. Since Hooke's was not a small mind troubled by the hobgoblin of foolish consistency, it is not surprising that he sometimes supported the formula F ∝ v instead of F ∝ v ². In 1663 he read a paper before the Royal Society on thé “force of falling bodies” in which he asserted “that a body moved with twice the celerity acquires twice the strength, and is able to move a body as big again” (Ibid., i, 195–196.) Again, in De Potentia Restitutiva (1678) he stated that motion and body “always counterballance each other in all the effects, appearances, and operations of Nature, and therefore it is not impossible but that they may be one and the same; for a little body with great motion is equivalent to a great body with little motion as to all its sensible effects in Nature”. If the phrase is ambiguous, three pages later he asserted that in the case of vibrating particles motion is in reciprocal proportion to the size of a body (Gunther, , Early Science in Oxford, viii, 339, 342)Google Scholar. Nevertheless, F ∝ v ² was his usual formula.

²⁷ If I understand his meaning, Hooke was using a mechanism suggested by his spring-driven watches, substituting weights on lines for the spring that drove the balance wheel or fly.

²⁸ Birch, , History, ii, 338–339.Google Scholar

²⁹ Once again Hooke's imprecision suggests a shallowness of understanding. As Mersenne and others had shown, he said, if the volume of flow from a hole in unit time is to be doubled, the depth of the hole below the surface must be quadrupled. For the pressure of fluids increases in proportion to the depth, and since the forces necessary “to accelerate motions” must be in duplicate proportion to the accelerations, the depths must be in duplicate proportion to the velocities required. A page later he stated with somewhat better phraseology that the “force that makes that Fluid run” is always in the same proportion with the altitude of the fluid parts above the hole and consequently the motion is exactly according to the plain and obvious rules of mechanical motions (Gunther, Early Science in Oxford, viii, 182, 183–184).Google Scholar

³⁰ Ibid. viii, 186–187.

³¹ Ibid. viii, 184.

³² In our terms, (For simplicity I place the origin at A; Hooke placed it at C.)

³³ If I understand Hooke at this point, he has applied two conclusions from Galileo— v ² = 2as, s = ½at ² (in algebraic form). He combined the two to eliminate acceleration, neglecting the fact that the constants in the two ratios are different. Hence in a problem dealing with non-uniformly accelerated motion he ended up with a ratio equivalent to the formula for uniform motion, s = vt.

³⁴ Gunther, , Early Science in Oxford, viii, 349–350.Google Scholar

³⁵ The Diary of Robert Hooke, M.A., M.D., F.R.S., 1672–1680, ed. Robinson, Henry W. and Adams, Walter (London, 1935), 246Google Scholar. I owe both this citation from Hooke's diary and the following one to Lohne, , “Hooke versus Newton”, op. cit. (1), 14.Google Scholar

³⁶ Diary, 314.Google Scholar I assume that Hooke in haste wrote that velocity would be as the areas when he meant that the areas would be as the times. Even so the relation is incorrect unless a special meaning is attached to distance (i.e. the length of the perpendicular to the tangent).

³⁷ Hooke, to Newton, , 6 01 1679/1680Google Scholar; Correspondence of Newton, ii, 309.Google Scholar

³⁸ Posthumous Works, 93, 114, 178, 185.Google Scholar At the risk of appearing to harbour a grudge against Hooke, I feel obliged to call attention to one of his discussions of the intensity of light. Since the area of the base of a given cone increases as the square of the height, the same amount of motion has to be spread over a correspondingly larger area—hence the inverse square relation. But there is a second factor operating to decrease the power of light as well. In every imaginable equal part of the cone there is the same amount of matter; if it expands in breadth, it must decrease in thickness. Hence as distance from the apex (or source) increases, the thickness of the base decreases as its square. This decrease will give the “Proportions of the length of the Pulses or strokes of Light, at several distances from the Luminous Body, and consequently the Velocity of those Pulses”. In fact then the force or power of light decreases as the fourth power of the distance. Fortunately, however, the effect of light or the motion it causes varies in subduplicate proportion to the power of light and thus as the inverse square of the distance (Ibid., 114).

³⁹ In a recent article, “Newton's Early Thoughts on Planetary Motion: a Fresh Look”, British Journal for the History of Science, ii (1964–1965), 117–137Google Scholar, D. T. Whiteside called attention to exactly this aspect of the correspondence of Newton and Hooke in 1679–80, although he stated the case in rather different terms from those I have used.

⁴⁰ Newton, to Boyle, , 28 02 1678/1679Google Scholar; Correspondence of Newton, ii, 292.Google Scholar