Abstract
Inflection—the encurvation of celestial motion—was a great novelty and a major step towards meeting Galileo’s challenge and establishing celestial mechanics. But it was not enough. For Hooke’s speculations to become a Programme, i.e., an outline for research, he had to suggest a cause for this encurvation. To complicate matters, the planetary trajectories are not only curved—they are cyclic. Unlike the effect on the light passing through them of the water in his microscope and the salt water in his tank, the gradual bending of the planetary motions results in continuous, repetitive orbits. Hooke’s hypothesis of the cause of celestial inflection had to allow for that as well.
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Notes
My references will be both the edition of published of De Potentia published independently by John Martin in 1678 and to the edition published in Gunther (vol. 8: C.L.) which is more available.
Reconstructions of the theory were offered by Hesse (“Hooke’s Vibration Theory”) and Patterson (“Pendulums of Wren and Hooke”).
Patterson (“Robert Hooke and the Conservation of Energy,” 151) thinks he does. The part authored by Hooke is titled “An Explication of Rarefaction” (178–182). C.f. Hesse, (“Hooke’s Vibration Theory,” 436–437); Clericuzio.
I will attend to this analogy in details later. C.f. Clericuzio, 74–75.
On January 23rd, 1675/6, Hooke first remarked in his Diary: “wrote a theory of springs.”
See Clericuzio for Hooke’s part in formulating Boyle’s Law and the `spring of air’ hypothesis.
Hooke’s acquaintance with it was probably via Galileo’s writing, in which he was clearly versed. One reason to believe that he has learned of O’resme’s diagram from Galileo is the fact that, like the latter, he treats the areas as sums of the ordinates (De Potentia,19; C.L.,351).
See Discorsi,Third Day, Theorem I, Propositions I and II and Corollary I; Figs. 47–49. For an earlier, somewhat different diagram see Dialogo,Second Day, Fig. 15.
C.f. Westfall (Force,206–208) and Pugliese, in Hunter and Schaffer, for other occasions in which Hooke makes use of this assumption. Pugliese remarks that this assumption is `an axiom of motion’ for Hooke, but does not elaborate on the particularities of Hooke’s notion of `powers’.
In the Introduction, I presented Hooke’s “General Rule of Mechanicks” as derived from interpretation of Galileo’s theorem. One may understand Hooke’s proof here as proceeding along the same lines; if (translating Galileo into “Mechanicks”) constant power along distance produces velocity proportional to the root of the distance, then power which varies as the distance (as, according to Hooke, is the case with displaced springs) produces velocity proportional to the distance.
Patterson’s is still the most extensive analysis of Of Spring.
“The distended rope, by the same endeavor to relax or unbend itself, will draw the horse as much towards the stone as it does the stone towards the horse” (Newton, Mathematical Principles,14. Henceforth: Principia). It is tempting to wonder whether Newton did not have Hooke in mind when he formulated his third law in the Principia. Otherwise, the rope illustration seems somewhat out of place.
The problem, as Peter Machamer has pointed out to me, is principal: parallel processes cannot measure each other.
White notes that the origins of the fusee mechanism are probably in military technology—a device for spanning heavy cross-bows called in typical medieval chivalry `the virgin’.
Another mechanism for this purpose is the stackfreed,which operates on similar principles but to a somewhat less satisfactory results, and was therefore less popular.
Cycloid is the curve described by a point on the circumference of a circle rolling on a plain (see Figure 14—top). A cycloidal pendulum can be visualized as a ball rolling up and down in a bowl whose cross-section is a cycloid. A cycloid, Huygens proved in his Horologium Oscilatorium,is it own “evolute” (see Figure 14—bottom). Therefore the pendulum can be made to describe a cycloid by two cycloidal `cheeks’ limiting the motion of its chord (see Figure 13).
Cf. ‘Espinasse, 1956, 62 ff.
This text survived as Trinity College Ms. 0.11a.115, without the diagrams referred to in the text, and was transcribed by Wright (102–118), who also beautifully reconstructed the devices described. The 1675 dating is hindered by the absence of any reference to Huygens’ all-important Horologium Oscilatorium of 1673.
Hooke, A Manuscript Concerning Huygens’ HoroloRium Oscilatorium. British Museum MSS, Sloane 1039, folio 129. Transcribed by Robertson (167–173). Henceforth: Sloane.
Most notably the clock given by Charles II to his mistress Countess of Castelmaine—cf. Symonds, 21.
A prize of £20,000 was finally offered by the British Government in 1714, and won by John Harrison in 1761 (but was only half-paid in 1765). Cf Gould.
Writing the Longitude Timekeeper,however, Hooke is not yet familiar with Huygens’ proof of isochrony, which was published only in the Horologium Oscilatorium of 1673. If he learned about the proof before amending the text, he did not add anything to indicate that (see Section 4.1).
Huygens did try to develop methods of suspending pendulum clocks that would make them immune to “the heaving of the ship” (The Pendulum Clock,30–32). See Figure 15.
C.f. Patterson, “Pendulums of Wren and Hooke.”
Cited by Wright, “Robert Hooke’s Longitude Timekeeper,”66–67.
This is Oxford English Dictionary’s definition of `force’.
Cf Hesse, “Hooke’s Vibration Theory,” 437; Clericuzio, 73–74.
Concerning his musical interests see Gouk.
For a modern theory of tropes and the difference between metaphors, metonyms and synecdoches see Vickers. A more philosophical approach to these particular `master tropes’ is Burke’s Grammar of Motives.
The examples in my “Tropes and Topics” are terms like gravity, levity, proper places and natural form, the never-questioned relations between which structured texts in the tradition of Aristotelian cosmology. I show there how Galileo, carefully observing these relations, is able to introduce radical changes into the (`tropic’) meaning of these terms without rendering his text unintelligible.
In “Tropes and Topics” I explored Galileo’s use of terms like `natural motion’ and `proper places’ in discussing falling bodies after depriving these terms of their traditional Aristotelian (tropic) meaning.
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Gal, O. (2002). Power. In: Meanest Foundations and Nobler Superstructures. Boston Studies in the Philosophy of Science, vol 229. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2223-0_3
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