Abstract
Hooke believed that the curved course of a planet about the sun was the resultant of a combination of two straight-line motions. Where Hooke originally acquired the idea that a planet’s path is the combination of two motions is not clear. Newton once suggested in a letter to Halley (20 June 1686) that Hooke very well may have acquired it from Borelli. Newton’s suggestion, however, has been exploded by Angus Armitage and Alexander Koyré.1
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References
See A. Armitage, “Borell’s Hypothesis and the Rise of Celestial Mechanics,” Annals of Science, Vol. 6 (1948–1950), pp. 268–282 and A. Koyré, La Révolution Astronomique (Paris, 1961), pp. 461-520. Herivel (p. 59 n. 4) dismisses Borelli’s contributions to astronomy in one brief footnote.
See Armitage, art. cit., pp. 269–271 and Koyré, op. cit., p. 466.
See Armitage, art. cit., pp. 281–282 and Koyré, op. cit., p. 512 n. 27. If Hooke were to be accused of purloining from anyone, it might be Jeremiah Horrox or Horrocks (1619–1641), a minor English astronomer. In a letter to a friend (25 July 1638) Horrox used a circular pendulum to illustrate the motion of a planet around the sun. If maneuvered properly, the pendulum could be made to describe an ellipse. The sun, he claimed, was both driving the planets around and drawing them to itself as it rotated. Horrox thought that the two factors working against each other, plus the sun’s tendency to repulse more than it attracted, would produce an elliptical orbit. It would appear that Horrox did not possess the principle of inertia either. Horrox’s works were published in 1673 by John Wallis but in the interim between Horrox’s death and 1673 his manuscripts were widely dispersed throughout England. If Hooke did learn anything from Horrox, or anyone else for that matter, he did not mention it. See J. Horrox, Opera Posthuma (London, 1673), pp. 312ff.
See Gunther, Vol. 6, 5/23/1666. Huygens’ law of centrifugal force (F = mv2/r) was first published in 1673. It is possible that Huygens, hearing of Hooke’s reports, was stimulated to publish his basic notions at the end of his work on clocks.
P.W., pp. 196-197. As far as the ultimate cause of planetary motion is concerned, Hooke was convinced that one need go no further back than God. It was God who originally set up the motions of the planets by combining the component motions into closed elliptical paths. It is the duty of the philosopher of nature to discover what the Lord of nature has done. It appears, furthermore, that Hooke had no idea of the vast length of time the universe had been in existence. Hooke said, in a discourse he read on carriages, that he did not know who invented the wheel. As far as he could tell it was first mentioned in the Bible when Joseph asked to ride in Pharaoh’s chariot. He also wondered why the “Americans” did not know of the wheel before 1492 if all people originally came from the Garden of Eden. In any event, it was invented a long time ago when the world was young; perhaps thousands of years ago. It must also have been thousands of years ago, he thought, that God set the planets in their courses. See Gunther, Vol. 7, 2/25/1685.
Gunther, Vol. 6, 3/21/1666.
Gunther, Vol. 6, 12/31/1662.
See Gunther, Vol. 6, 12/14/1664.
See M., pp. 242-246.
Gunther, Vol. 6, 3/21/1666.
See Gunther, Vol. 6, 3/28/1666.
See Gunther, Vol. 7, 4/30/1674.
See Gunther, Vol. 6, 5/20/1663.
See M., p. 22.
See Gunther, Vol. 6, 3/9/1671.
See Gunther, Vol. 6, 3/30/1671.
See P.W., p. 175.
hoc. cit.
P.W., p. 176.
See P.W., p. 177.
See P.W., p. 178.
P.W., pp. 184-185.
See P.W., p. 185.
See P.W., pp. 192, 481-483.
More has reprinted with commentary this whole series of letters in his life of Newton.
See Gunther, Vol. 7, 1/22/1680. See also Hooke’s Diary for 16 January 1680 and his letter to Newton on 17 January 1680 for statements of his positive results indoors. For a study of the problem before Hooke see A. Koyré, “A Documentary History of Fall from Kepler to Newton,” Transactions of the American Philosophical Society, Vol. 45 (1955), part 4, pp. 329-395. For a study of the topic after Hooke see A. Armitage, “The Deviation of Falling Bodies,” Annals of Science, Vol. 5 (1947), pp. 342-351. The Curator’s predecessor with respect to the body’s path to the earth’s center was Borelli, while it was Newton who urged Hooke to provide experimental verification of the earth’s diurnal motion. According to Borelli, a body would fall in a curved path, moving to the east of the point from which dropped, on its way to the earth’s center. To understand what he had in mind one must imagine a long hollow tube extending from the earth’s center to its surface on the equator. This tube will of course rotate with the earth. Now imagine a uniformly accelerated stone descending in the tube. The stone has two motions: one down and one east. If exaggerated and graphed, the total path would look like the cross section of a snail’s shell. However, the actual deviation from perpendicular would be very small. Under ideal conditions in the twenty minutes it takes a stone to fall the 4,000 miles to the center, the earth would have moved a mere 330 miles (about five degrees of arc), thus inscribing a path so close to the perpendicular, especially when near the earth’s surface, as to be indistinguishable from it. On 15 June 1668, James Gregory, who had studied in Italy, reported upon the work of Borelli and others to the Royal Society. Hooke was familiar with most of what Borelli had to say. At a meeting of the Royal Society in 1680, Hooke mentioned that he had followed Borelli’s work with interest and was sorry to hear that he had died. See Gunther, Vol. 7, 8/9/1680. We might also mention that, theoretically, Hooke’s results were correct. However, practically speaking, he could never have gotten the results claimed. Given the latitude of London and the low heights from which he worked, the deviations from the perpendicular would be imperceptible. This indicates that he had not read Borelli very well. In fact, it is highly doubtful that Hooke was even acquainted with Borelli’s Risposta di Gio (Messina, 1668) in which Borelli showed that the deviation of a freely falling body from the perpendicular would be so small as to be insensible. Undoubtedly, Hooke, and those witnessing the experiment, did see the weight fall into the S. S. E. section of the pan of clay. But how can this be reconciled with the fact that we know from modern calculations and fine, precision instruments that such a thing could not have been observed? We can only call upon the crudity of their apparatus and the anxiousness of their mental state to see the results seen.
Concerning the close friendship between Hooke and Aubrey see M.’ Espinasse, Robert Hooke (London, 1956), ch. 6.
For the background to this letter see More, p. 353. Herivel does not mention it.
Hooke, in his Diary for 15 September, records laconically “letter for Mr. Wood about Newton.”
L. D. Patterson, “Hookes Gravitation Theory and Its Influence on Newton,” Isis, Vol. 40 (1949), pp. 327–328.
See ibid., pp. 328-341 for details. Hooke did say during the critical years 1684–1686 that he wanted to present the Society with a paper on celestial bodies but decided not to since Newton would shortly do so. Newton’s treatise was referred to as being “now in the press.” See P.W., pp. 173, 330.
See ibid., Vol. 41 (1950), pp. 32-45.
See W. Whiston, Memoirs of the Life of Mr. William Whiston by Himself (London, 1749), Vol. I, pp. 35–38.
As quoted by More, p. 290. See also Herivel, pp. 66-67.
See More, p. 291.
See Herivel, pp. 72-76.
See Herivel, pp. 192-198. Although it does not directly discuss the question of priority, an article by Florian Cajori should be mentioned here. Cajori maintains that the twenty year delay in publishing the inverse square law was not due to inaccurate calculations for the distance of one degree of latitude as is most commonly claimed, but was rather due to fears Newton had concerning the universality of the law, i.e., whether it could be applied to all bodies everywhere, even those very close to the earth. Implicitly, Cajori sides with those who accept Newton’s claims to have been aware of the law before Hooke. See his “Newton’s Twenty Years’ Delay in Announcing the Law of Gravitation,” Sir Isaac Newton 1727–1927 (ed. by the History of Science Society, Baltimore, 1928), pp. 127-188.
H. Butterfield, The Origins of Modern Science (New York, 1962), p. 167. The reader may be interested in knowing what it was that Hooke was apparently incapable of doing. By combining Huygens’ law for centripetal (or centrifugal) force with Hooke’s hunch on universal attraction Newton was able to come upon a formula which agreed with Kepler’s third law for planetary motion. This agreement between mathematical reasoning and observation was the proof to which Hooke was yet the stranger. (the time needed for a planet to complete its orbit as related to its distance from the sun) Therefore, the distance must be squared in the formula for universal gravitation
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© 1970 Martinus Nijhoff, The Hague, Netherlands
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Centore, F.F. (1970). The Mechanics of Celestial Local Motions. In: Robert Hooke’s Contributions to Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-9413-6_5
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